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Hadron Spectroscopy at COMPASSand Related Experiments
Boris Grubefor the COMPASS Collaboration
Physik-Department E18Technische Universität München,
Garching, Germany
International Workshop on Hadron Structure and SpectroscopyErlangen, 23. July 2013
E
1 8
COMPASS
Outline
1 IntroductionQCD and constituent quark modelBeyond the constituent quark model
2 Hadron spectroscopySearch for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
3 Conclusions and Outlook
2 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Outline
1 IntroductionQCD and constituent quark modelBeyond the constituent quark model
2 Hadron spectroscopySearch for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
3 Conclusions and Outlook
3 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
QCD: The Theory of Strong InteractionQuantum chromodynamics describes interaction of quark and gluon fields
Non-abelian gauge theory: gluons carry charge and self-interactRunning coupling constant αs(Q)
Asymptotic freedom
αs small at short distances (high-energies)Quarks and gluons relevant degrees of freedomLagrangian calculable by series expansion in αs
Confinement of quarks and gluons into hadrons
αs large at distances O(1 fm)
Relevant d.o.f.: color-neutral hadronsSeries in αs does not converge=⇒ non-perturbative regime
Origin of confinement and connection to chiralsymmetry breaking still not understoodExplanation for 98 % of mass of visible matter in theuniverseStudy of hadron spectra provides more insight
PDG 2012
4 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
QCD: The Theory of Strong InteractionQuantum chromodynamics describes interaction of quark and gluon fields
Non-abelian gauge theory: gluons carry charge and self-interactRunning coupling constant αs(Q)
Asymptotic freedom
αs small at short distances (high-energies)Quarks and gluons relevant degrees of freedomLagrangian calculable by series expansion in αs
Confinement of quarks and gluons into hadrons
αs large at distances O(1 fm)
Relevant d.o.f.: color-neutral hadronsSeries in αs does not converge=⇒ non-perturbative regime
Origin of confinement and connection to chiralsymmetry breaking still not understoodExplanation for 98 % of mass of visible matter in theuniverseStudy of hadron spectra provides more insight
PDG 2012
4 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
QCD: The Theory of Strong InteractionQuantum chromodynamics describes interaction of quark and gluon fields
Non-abelian gauge theory: gluons carry charge and self-interactRunning coupling constant αs(Q)
Asymptotic freedom
αs small at short distances (high-energies)Quarks and gluons relevant degrees of freedomLagrangian calculable by series expansion in αs
Confinement of quarks and gluons into hadrons
αs large at distances O(1 fm)
Relevant d.o.f.: color-neutral hadronsSeries in αs does not converge=⇒ non-perturbative regime
Origin of confinement and connection to chiralsymmetry breaking still not understoodExplanation for 98 % of mass of visible matter in theuniverseStudy of hadron spectra provides more insight
PDG 2012
4 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Constituent Quark Model (CQM)
Goes back over 40 years to Gell-Mann and Zweig“Constituent” quarks: quasi-particles with additional effectivemass due to interaction with gluon field
E.g. for light-quark mesons mu = md = 310 MeV/c2,ms = 485 MeV/c2 Gasiorowicz et al., AJP 49 (1981) 954
Caveat: no connection to QCD
Mesons in CQM
Color-singlet |qq′〉 states, grouped into SU(N)flavor multiplets
Meson masses are sum of constituent quark masses
Together with hyperfine (spin-spin) interaction, meson spectrumis roughly described
5 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Constituent Quark Model (CQM)
Goes back over 40 years to Gell-Mann and Zweig“Constituent” quarks: quasi-particles with additional effectivemass due to interaction with gluon field
E.g. for light-quark mesons mu = md = 310 MeV/c2,ms = 485 MeV/c2 Gasiorowicz et al., AJP 49 (1981) 954
Caveat: no connection to QCD
Mesons in CQM
Color-singlet |qq′〉 states, grouped into SU(N)flavor multiplets
Meson masses are sum of constituent quark masses
Together with hyperfine (spin-spin) interaction, meson spectrumis roughly described
5 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Spin-parity rules for bound qq system
Quark spins couple to total intrinsic spinS = 0 (singlet) or 1 (triplet)
Relative orbital angular Momentum~Land total spin ~S couple tomeson spin~J = ~L + ~S
Parity P = (−1)L+1
Charge conjugation C = (−1)L+S
Forbidden JPC: 0−−, 0+−, 1−+, 2+−, 3−+, . . .Extension to charged mesons via G parity: G = C (−1)I
I isospin of mesonConvention: assign JPC quantum numbers of neutral partner inisospin multiplet
6 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Spin-parity rules for bound qq system
Quark spins couple to total intrinsic spinS = 0 (singlet) or 1 (triplet)
Relative orbital angular Momentum~Land total spin ~S couple tomeson spin~J = ~L + ~S
Parity P = (−1)L+1
Charge conjugation C = (−1)L+S
Forbidden JPC: 0−−, 0+−, 1−+, 2+−, 3−+, . . .Extension to charged mesons via G parity: G = C (−1)I
I isospin of mesonConvention: assign JPC quantum numbers of neutral partner inisospin multiplet
6 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Spin-parity rules for bound qq system
Quark spins couple to total intrinsic spinS = 0 (singlet) or 1 (triplet)
Relative orbital angular Momentum~Land total spin ~S couple tomeson spin~J = ~L + ~S
Parity P = (−1)L+1
Charge conjugation C = (−1)L+S
Forbidden JPC: 0−−, 0+−, 1−+, 2+−, 3−+, . . .Extension to charged mesons via G parity: G = C (−1)I
I isospin of mesonConvention: assign JPC quantum numbers of neutral partner inisospin multiplet
6 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Light-quark meson spectrum
a2(1320)
K2*(1430)
f2(1270)
f2'(1525)
a1(1260)
K1af1(1285)
f1(1420)
a0(1450)
K0*(1430)
f0(1370)
f0(1710)
b1(1235)
K1bh1(1170)
h1(1380)
p(1300)K(1460)h(1295)h(1440)
r(1450)
K*(1410)w(1420)f(1680)
pKhh'
r(770)
K*(892)w(782)f(1020)
L
n=n+L-1
10 2
3S1=1--1S0=0
-+
3P2=2++
1P1=1++
1P1=1+-3P0=0
++
n
n2S+1
LJ
= JPC
0
1
1 1
1 1
13
3S =1--1S0=0-+
2 2 1
L
Amsler et al., Phys. Rept. 389 (2004) 61
7 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Light-quark meson spectrum (cont.)
a2(1320)
K2*(1430)
f2(1270)
f2'(1525)
a1(1260)
K1af1(1285)
f1(1420)
a0(1450)
K0*(1430)
f0(1370)
f0(1710)
b1(1235)
K1bh1(1170)
h1(1380)
a2(1700)
K2*(1980)
f2(2010)
f2(1950)
a1(1640)
p(1300)K(1460)h(1295)h(1440)
r(1450)
K*(1410)w(1420)f(1680)
p(1800)
pKhh'
r(770)
K*(892)w(782)f(1020)
r3(1690)
K*3(1780)
w3(1670)f3(1850)
K2(1820)
p2(1670)
K2(1770)
h2(1645)h2(1870)
r(1700)
K*(1680)w(1650)
L
n=n+L-1
10 2
3S1=1--1S0=0
-+
3P2=2++
1P1=1++
1P1=1+-3P0=0
++
1D2=2-+ 3D1=1
--
3D2=2--3D3=3
--
n2S+1
LJ
= JPC
K(1830)
h(1760)
0
1
2
1 1
1 1
13 1 1
1 13P2=2++
2P1=1++
23
3S =1--1S0=0-+
2 2 1
3S =1--1S0=0-+
3 3 1
L
n
Amsler et al., Phys. Rept. 389 (2004) 61
“Light meson frontier”:
Many missing and disputedstates in mass regionm ≈ 2 GeV/c2
Identification of higherexcitations becomesexceedingly difficult
Wider states + higher statedensityMore overlap and mixing
8 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Mesons in the Constituent Quark Model
Light-quark meson spectrum (cont.)
a2(1320)
K2*(1430)
f2(1270)
f2'(1525)
a1(1260)
K1af1(1285)
f1(1420)
a0(1450)
K0*(1430)
f0(1370)
f0(1710)
b1(1235)
K1bh1(1170)
h1(1380)
a2(1700)
K2*(1980)
f2(2010)
f2(1950)
a1(1640)
p(1300)K(1460)h(1295)h(1440)
r(1450)
K*(1410)w(1420)f(1680)
p(1800)
pKhh'
r(770)
K*(892)w(782)f(1020)
r3(1690)
K*3(1780)
w3(1670)f3(1850)
K2(1820)
p2(1670)
K2(1770)
h2(1645)h2(1870)
r(1700)
K*(1680)w(1650)
L
n=n+L-1
10 2
3S1=1--1S0=0
-+
3P2=2++
1P1=1++
1P1=1+-3P0=0
++
1D2=2-+ 3D1=1
--
3D2=2--3D3=3
--
n2S+1
LJ
= JPC
K(1830)
h(1760)
0
1
2
1 1
1 1
13 1 1
1 13P2=2++
2P1=1++
23
3S =1--1S0=0-+
2 2 1
3S =1--1S0=0-+
3 3 1
L
n
Amsler et al., Phys. Rept. 389 (2004) 61
“Light meson frontier”:
Many missing and disputedstates in mass regionm ≈ 2 GeV/c2
Identification of higherexcitations becomesexceedingly difficult
Wider states + higher statedensityMore overlap and mixing
8 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD: Gluonic d.o.f. should manifest themselves in hadron spectra
Hybrids |qqg〉Resonances with excited glue
Definition of “excited glue” model dependent
Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+
Mass 1.3 to 2.2 GeV/c2
Experimental candidates π1(1400, 1600, 2000) controversial
Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++
Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2
Experimental candidate f0(1500); glueball interpretation disputed
9 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD: Gluonic d.o.f. should manifest themselves in hadron spectra
Hybrids |qqg〉Resonances with excited glue
Definition of “excited glue” model dependent
Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+
Mass 1.3 to 2.2 GeV/c2
Experimental candidates π1(1400, 1600, 2000) controversial
Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++
Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2
Experimental candidate f0(1500); glueball interpretation disputed
9 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD: Gluonic d.o.f. should manifest themselves in hadron spectra
Hybrids |qqg〉Resonances with excited glue
Definition of “excited glue” model dependent
Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+
Mass 1.3 to 2.2 GeV/c2
Experimental candidates π1(1400, 1600, 2000) controversial
Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++
Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2
Experimental candidate f0(1500); glueball interpretation disputed
9 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD: Gluonic d.o.f. should manifest themselves in hadron spectra
Hybrids |qqg〉Resonances with excited glue
Definition of “excited glue” model dependent
Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+
Mass 1.3 to 2.2 GeV/c2
Experimental candidates π1(1400, 1600, 2000) controversial
Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++
Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2
Experimental candidate f0(1500); glueball interpretation disputed
9 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD: Gluonic d.o.f. should manifest themselves in hadron spectra
Hybrids |qqg〉Resonances with excited glue
Definition of “excited glue” model dependent
Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+
Mass 1.3 to 2.2 GeV/c2
Experimental candidates π1(1400, 1600, 2000) controversial
Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++
Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2
Experimental candidate f0(1500); glueball interpretation disputed
9 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD in the confinement regime: αs = O(1)QCD Lagrangian not calculable using perturbation theory
General ab-initio method: Lattice Gauge Theory
Simulation of QCD Lagrangian on finite discreet space-time latticeusing Monte Carlo techniques (computationally very expensive)Challenge: extrapolation to physical point
Heavier u and d quarks than in reality=⇒ extrapolation to physical quark masses
Extrapolation to infinite volumeExtrapolation to zero lattice spacing
Rotational symmetry broken due to cubic lattice
Tremendous progress in past yearsFiner lattices =⇒ spin-identified spectraLarger operator bases =⇒ extraction of many excited statesAccess to gluonic content of calculated states
10 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD in the confinement regime: αs = O(1)QCD Lagrangian not calculable using perturbation theory
General ab-initio method: Lattice Gauge Theory
Simulation of QCD Lagrangian on finite discreet space-time latticeusing Monte Carlo techniques (computationally very expensive)Challenge: extrapolation to physical point
Heavier u and d quarks than in reality=⇒ extrapolation to physical quark masses
Extrapolation to infinite volumeExtrapolation to zero lattice spacing
Rotational symmetry broken due to cubic lattice
Tremendous progress in past yearsFiner lattices =⇒ spin-identified spectraLarger operator bases =⇒ extraction of many excited statesAccess to gluonic content of calculated states
10 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD in the confinement regime: αs = O(1)QCD Lagrangian not calculable using perturbation theory
General ab-initio method: Lattice Gauge Theory
Simulation of QCD Lagrangian on finite discreet space-time latticeusing Monte Carlo techniques (computationally very expensive)Challenge: extrapolation to physical point
Heavier u and d quarks than in reality=⇒ extrapolation to physical quark masses
Extrapolation to infinite volumeExtrapolation to zero lattice spacing
Rotational symmetry broken due to cubic lattice
Tremendous progress in past yearsFiner lattices =⇒ spin-identified spectraLarger operator bases =⇒ extraction of many excited statesAccess to gluonic content of calculated states
10 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
QCD in the confinement regime: αs = O(1)QCD Lagrangian not calculable using perturbation theory
General ab-initio method: Lattice Gauge Theory
Simulation of QCD Lagrangian on finite discreet space-time latticeusing Monte Carlo techniques (computationally very expensive)Challenge: extrapolation to physical point
Heavier u and d quarks than in reality=⇒ extrapolation to physical quark masses
Extrapolation to infinite volumeExtrapolation to zero lattice spacing
Rotational symmetry broken due to cubic lattice
Tremendous progress in past yearsFiner lattices =⇒ spin-identified spectraLarger operator bases =⇒ extraction of many excited statesAccess to gluonic content of calculated states
10 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Light-Meson Spectrum in Lattice QCDState-of-the-art light-meson spectrum Dudek, PR D84 (2011) 074023
Resonance widths and decay modes still very difficult11 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
Finding states beyond the CQM is difficult
Physical mesons = linear superpositions of allallowed basis states: |qq〉, |qqg〉, |gg〉, |q2q2〉, . . .
Amplitudes determined by QCD interactions
Resonance classification in quarkonia, hybrids,glueballs, tetraquarks, etc. assumes dominanceof one basis state
In general “configuration mixing”Disentanglement of contributions difficult
Special case: “exotic” mesons
Have quantum numbers forbidden for |qq〉Discovery =⇒ unambiguous proof for meson states beyond CQM
Especially attractive:“spin-exotic” states with JPC = 0−−, 0+−, 1−+, 2+−, 3−+, . . .
12 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
Finding states beyond the CQM is difficult
Physical mesons = linear superpositions of allallowed basis states: |qq〉, |qqg〉, |gg〉, |q2q2〉, . . .
Amplitudes determined by QCD interactions
Resonance classification in quarkonia, hybrids,glueballs, tetraquarks, etc. assumes dominanceof one basis state
In general “configuration mixing”Disentanglement of contributions difficult
Special case: “exotic” mesons
Have quantum numbers forbidden for |qq〉Discovery =⇒ unambiguous proof for meson states beyond CQM
Especially attractive:“spin-exotic” states with JPC = 0−−, 0+−, 1−+, 2+−, 3−+, . . .
12 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
QCD and constituent quark modelBeyond the constituent quark model
Beyond the Constituent Quark Model
Finding states beyond the CQM is difficult
Physical mesons = linear superpositions of allallowed basis states: |qq〉, |qqg〉, |gg〉, |q2q2〉, . . .
Amplitudes determined by QCD interactions
Resonance classification in quarkonia, hybrids,glueballs, tetraquarks, etc. assumes dominanceof one basis state
In general “configuration mixing”Disentanglement of contributions difficult
Special case: “exotic” mesons
Have quantum numbers forbidden for |qq〉Discovery =⇒ unambiguous proof for meson states beyond CQM
Especially attractive:“spin-exotic” states with JPC = 0−−, 0+−, 1−+, 2+−, 3−+, . . .
12 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Outline
1 IntroductionQCD and constituent quark modelBeyond the constituent quark model
2 Hadron spectroscopySearch for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
3 Conclusions and Outlook
13 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Production of Hadrons in Diffractive DissociationBNL E852, VES, COMPASS
P
π´beam
Target Recoil
X´π´beam
Target Recoil
π´beam
Target Recoil
π´beam
Target Recoil
π´π+
π´
Soft scattering of beam hadron off nuclear target (remains intact)Beam particle is excited into intermediate state XX decays into n-body final state
High√
s, low t′: Pomeron exchange dominantRich spectrum: large number of overlapping and interfering XGoal: use kinematic distribution of final-state particles to
Disentangle all resonances XDetermine their mass, width, and quantum numbers
Method: partial-wave analysis (PWA)
14 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Production of Hadrons in Diffractive DissociationBNL E852, VES, COMPASS
P
π´beam
Target Recoil
X´π´beam
Target Recoil
π´beam
Target Recoil
π´beam
Target Recoil
π´π+
π´
Soft scattering of beam hadron off nuclear target (remains intact)Beam particle is excited into intermediate state XX decays into n-body final state
High√
s, low t′: Pomeron exchange dominantRich spectrum: large number of overlapping and interfering XGoal: use kinematic distribution of final-state particles to
Disentangle all resonances XDetermine their mass, width, and quantum numbers
Method: partial-wave analysis (PWA)
14 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Production of Hadrons in Diffractive DissociationBNL E852, VES, COMPASS
P
π´beam
Target Recoil
X´π´beam
Target Recoil
π´beam
Target Recoil
π´beam
Target Recoil
π´π+
π´
Soft scattering of beam hadron off nuclear target (remains intact)Beam particle is excited into intermediate state XX decays into n-body final state
High√
s, low t′: Pomeron exchange dominantRich spectrum: large number of overlapping and interfering XGoal: use kinematic distribution of final-state particles to
Disentangle all resonances XDetermine their mass, width, and quantum numbers
Method: partial-wave analysis (PWA)
14 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Diffractive Dissociation of π− into π−π+π− Final StateBNL E852, VES, COMPASS
π´beam
Target Recoil
X´[JPCMǫ]
Isobar
π´beam
Target Recoil
π´beam
Target Recoil
π´beam
Target
P
Recoil
[L]
Bachelorπ´
π+
π´
π´beam
Target
P
Recoil
[L]
Bachelorπ´
π+
π´
Isobar model: X− decay is chain of successive two-body decays
“Wave”: unique combination of isobar and quantum numbersFull wave specification (in reflectivity basis): JPC Mε[isobar]L
Fit model: σ(mX , τ) = σ0
∣∣∣∑waves Twave(mX) Awave(mX , τ)∣∣∣2
Calculable decay amplitudes Awave(mX , τ)
Transition amplitudes Twave(mX) determined frommulti-dimensional fit to final-state kinematic distributions taking intoaccount interference effects
15 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Diffractive Dissociation of π− into π−π+π− Final StateBNL E852, VES, COMPASS
π´beam
Target Recoil
X´[JPCMǫ]
Isobar
π´beam
Target Recoil
π´beam
Target Recoil
π´beam
Target
P
Recoil
[L]
Bachelorπ´
π+
π´
π´beam
Target
P
Recoil
[L]
Bachelorπ´
π+
π´
Isobar model: X− decay is chain of successive two-body decays
“Wave”: unique combination of isobar and quantum numbersFull wave specification (in reflectivity basis): JPC Mε[isobar]L
Fit model: σ(mX , τ) = σ0
∣∣∣∑waves Twave(mX) Awave(mX , τ)∣∣∣2
Calculable decay amplitudes Awave(mX , τ)
Transition amplitudes Twave(mX) determined frommulti-dimensional fit to final-state kinematic distributions taking intoaccount interference effects
15 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslowCOMPASS
π´beam
ptarget pslow
X´[JPCMǫ]
Isobar
π´beam
ptarget pslow
π´beam
ptarget pslow
π´beam
ptarget
P
pslow
[L]
Bachelorπ´
π+
π´
π´beam
ptarget
P
pslow
[L]
Bachelorπ´
π+
π´
190 GeV/c negative hadron beam: 97 % π−, 2 % K−, 1 % p
Liquid hydrogen target
Recoil proton pslow measured by RPD
Kinematic range 0.1 < t′ < 1.0 (GeV/c)2
16 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
World’s largest diffractive 3π data set: ≈50 M exclusive events
Challenging analysisNeeds precise understanding of apparatusModel deficiencies become visible
π−π+π− invariant mass distribution Dalitz plot for π2(1670) region
17 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
World’s largest diffractive 3π data set: ≈50 M exclusive events
Challenging analysisNeeds precise understanding of apparatusModel deficiencies become visible
π−π+π− invariant mass distribution
Dalitz plot for π2(1670) region
17 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
World’s largest diffractive 3π data set: ≈50 M exclusive events
Challenging analysisNeeds precise understanding of apparatusModel deficiencies become visible
π−π+π− invariant mass distribution Dalitz plot for π2(1670) region
17 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
π−π+π− invariant mass spectrum
1++ 0+ [ρπ]S: a1(1260)
2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)
18 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
π−π+π− invariant mass spectrum 1++ 0+ [ρπ]S: a1(1260)
2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)
18 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
π−π+π− invariant mass spectrum 1++ 0+ [ρπ]S: a1(1260)
2−+ 0+ [ f2π]S: π2(1670)
2++ 1+ [ρπ]D: a2(1320)
18 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
π−π+π− invariant mass spectrum 1++ 0+ [ρπ]S: a1(1260)
2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)
18 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
π−π+π− invariant mass spectrum 1++ 0+ [ρπ]S: a1(1260)
2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)
18 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Data described by model consisting of 52 waves+ incoherent isotropic backgroundIsobars:
(ππ)S−wavef0(980)ρ(770)f2(1270)f0(1500)ρ3(1690)
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
Spin-exotic 1−+ 1+ [ρπ]P
1−+ 1+ [ρπ]P− 1++ 0+ [ρπ]S
1++ 0+ [ρπ]S: a1(1260)
Structure around 1.1 GeV/c2
unstable w.r.t. fit modelEnhancement around1.6 GeV/c2
Phase motion w.r.t. to tail ofa1(1260)Phase locked w.r.t. π2(1670)Ongoing analysis
19 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
Spin-exotic 1−+ 1+ [ρπ]P 1−+ 1+ [ρπ]P− 1++ 0+ [ρπ]S
1++ 0+ [ρπ]S: a1(1260) Structure around 1.1 GeV/c2
unstable w.r.t. fit modelEnhancement around1.6 GeV/c2
Phase motion w.r.t. to tail ofa1(1260)Phase locked w.r.t. π2(1670)Ongoing analysis
19 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslow
Spin-exotic 1−+ 1+ [ρπ]P 1−+ 1+ [ρπ]P− 2−+ 0+ [ f2π]S
2−+ 0+ [ f2π]S: π2(1670) Structure around 1.1 GeV/c2
unstable w.r.t. fit modelEnhancement around1.6 GeV/c2
Phase motion w.r.t. to tail ofa1(1260)Phase locked w.r.t. π2(1670)Ongoing analysis
19 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with BNL E852 and VES
COMPASS
190 GeV/c π beamp target50 · 106 events0.1 < t′ < 1.0 (GeV/c)2
Rank-2 fit with 53 waves
BNL E852 PR D73 (2006) 072001
18 GeV/c π beam2.6 · 106 events0.1 < t′ < 0.5 (GeV/c)2
Rank-1 fit with 21/36 waves
20 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with BNL E852 and VES
COMPASS
190 GeV/c π beamp target50 · 106 events0.1 < t′ < 1.0 (GeV/c)2
Rank-2 fit with 53 waves
BNL E852 PR D73 (2006) 072001
18 GeV/c π beam2.6 · 106 events0.1 < t′ < 0.5 (GeV/c)2
Rank-1 fit with 21/36 waves
20 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with BNL E852 and VES
COMPASS
190 GeV/c π beamp target50 · 106 events0.1 < t′ < 1.0 (GeV/c)2
Rank-2 fit with 53 waves
BNL E852 PR D73 (2006) 072001
18 GeV/c π beam2.6 · 106 events0.1 < t′ < 0.5 (GeV/c)2
Rank-1 fit with 21/36 waves
20 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with BNL E852 and VES
COMPASS
190 GeV/c π beamp target50 · 106 events0.1 < t′ < 1.0 (GeV/c)2
Rank-2 fit with 53 waves
VES NP A675 (2000) 155
36.6 GeV/c π beamBe target9 · 106 events“Infinite”-rank fit with 44waves
20 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− Pb → π−π+π− Pb at low t′COMPASS
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
π−π+π− production in Primakoff reaction
Very small momentum transfer: t′ < 0.001 (GeV/c)2
Photoproduction in Coulomb field of heavy target nucleus (Pb)For M = 1 waves diffractive contribution kinematicallysuppressedNo intensity in 1.6 GeV/c2 region in spin-exotic 1−+ wave
21 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− Pb → π−π+π− Pb at low t′COMPASS
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
π−π+π− production in Primakoff reaction
Very small momentum transfer: t′ < 0.001 (GeV/c)2
Photoproduction in Coulomb field of heavy target nucleus (Pb)For M = 1 waves diffractive contribution kinematicallysuppressedNo intensity in 1.6 GeV/c2 region in spin-exotic 1−+ wave
21 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Photoproduction of Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with CLAS g12
COMPASS Primakoff
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
CLAS g12 C. Bookwalter, arXiv:1108.6112
π
γbeam
p n
X+γbeam
p n
γbeam
p n
γbeam
p n
π+
π´π+
Tagged photon beam3.6 < Eγ < 5.5 GeVp target502 000 events
22 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Photoproduction of Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with CLAS g12
COMPASS Primakoff
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
CLAS g12 C. Bookwalter, arXiv:1108.6112
π
γbeam
p n
X+γbeam
p n
γbeam
p n
γbeam
p n
π+
π´π+
Tagged photon beam3.6 < Eγ < 5.5 GeVp target502 000 events
22 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Photoproduction of Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with CLAS g12
COMPASS Primakoff
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
CLAS g12 C. Bookwalter, arXiv:1108.6112
1000 1200 1400 1600 1800 2000M(π+π+π−) (GeV/c2)
0
50
100
150
200
250
300
Acc
epte
dev
ents
per2
0M
eV/c
2
1−+1εP-wave [Y=ρ(770)] total intensity
1−+1+
1−+1−
Tagged photon beam3.6 < Eγ < 5.5 GeVp target502 000 events
22 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslowSummary
Understanding of spin-exotic 1−+ wave is work in progress
COMPASS: intensity in ρπ and η′π channelsSimilar to BNL E852 and VESResonance interpretation still unclearAs CLAS: no signal in photoproduction
Spin-exotic 1−+ also claimed in channelsf1(1285)π (E852, VES)b1(1235)π (E852, VES, Crystal Barrel)COMPASS will analyze these channels as well
Significant contributions fromnon-resonant Deck-like processes
Inclusion into fit model
Exploit t′-dependence ofpartial-wave amplitudes
PWA in narrow mπ−π+π−
and t′ bins
π´beam Isobarπ´beam
P
π´beam
Target Recoil
π´beam π´
π+
Target Recoil
π´
Improvements of wave set and isobar parameterization
23 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslowSummary
Understanding of spin-exotic 1−+ wave is work in progress
COMPASS: intensity in ρπ and η′π channelsSimilar to BNL E852 and VESResonance interpretation still unclearAs CLAS: no signal in photoproduction
Spin-exotic 1−+ also claimed in channelsf1(1285)π (E852, VES)b1(1235)π (E852, VES, Crystal Barrel)COMPASS will analyze these channels as well
Significant contributions fromnon-resonant Deck-like processes
Inclusion into fit model
Exploit t′-dependence ofpartial-wave amplitudes
PWA in narrow mπ−π+π−
and t′ bins
π´beam Isobarπ´beam
P
π´beam
Target Recoil
π´beam π´
π+
Target Recoil
π´
Improvements of wave set and isobar parameterization
23 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of π− p→ π−π+π− pslowSummary
Understanding of spin-exotic 1−+ wave is work in progress
COMPASS: intensity in ρπ and η′π channelsSimilar to BNL E852 and VESResonance interpretation still unclearAs CLAS: no signal in photoproduction
Spin-exotic 1−+ also claimed in channelsf1(1285)π (E852, VES)b1(1235)π (E852, VES, Crystal Barrel)COMPASS will analyze these channels as well
Significant contributions fromnon-resonant Deck-like processes
Inclusion into fit model
Exploit t′-dependence ofpartial-wave amplitudes
PWA in narrow mπ−π+π−
and t′ bins
π´beam Isobarπ´beam
P
π´beam
Target Recoil
π´beam π´
π+
Target Recoil
π´
Improvements of wave set and isobar parameterization
23 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Central ProductionCOMPASS, CERN Omega (WA76, WA91, WA102)
pbeam pfast
ptarget pslow
X0
pbeam pfast
ptarget pslow
pbeam pfast
ptarget pslow
[JǫM]
pbeam
P
pfast
ptarget
P
pslow
pbeam
P
pfast
ptarget
P
pslow
π+ π0 K+ K0S η
π´ π0 K´ K0S η
Search for glueball candidates
Glueballs: mesonic states with no valence quarksLattice QCD simulations predict lightest glueballs to be scalars
Glueball would appear as supernumerous stateStrong mixing with conventional scalar mesons expectedDifficult to disentangle
Pomeron-Pomeron fusion well-suited to search for glueballsIsoscalar mesons produced at central rapiditiesScalar mesons dominant in this channelGluon-rich environment
24 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
K+K− Central Productionpbeam pfast
ptarget pslow
X0
pbeam pfast
ptarget pslow
pbeam pfast
ptarget pslow
[JǫM]
pbeam
P
pfast
ptarget
P
pslow
pbeam
P
pfast
ptarget
P
pslow
K+
K´
Suppression of diffractive background by cut p(pfast) > 140 GeV/c
pfastK− invariant mass Rapidity in CM frame
25 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
K+K− Central Productionpbeam pfast
ptarget pslow
X0
pbeam pfast
ptarget pslow
pbeam pfast
ptarget pslow
[JǫM]
pbeam
P
pfast
ptarget
P
pslow
pbeam
P
pfast
ptarget
P
pslow
K+
K´
Suppression of diffractive background by cut p(pfast) > 140 GeV/c
pfastK− invariant mass K+K− invariant mass
25 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Fit of K+K− Mass Dependence
Fit model:Relativistic Breit-Wignerresonances
S−0 : f0(1370), f0(1500),f0(1710)
D−0 : f2(1270), f2′(1525)
Exponentially dampedcoherent background terms
26 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Fit of K+K− Mass DependenceComparison with WA102
COMPASS WA102 PL B453 (1999) 305
450 GeV/c p beamFit of wave intensities only
27 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Fit of K+K− Mass DependenceComparison with WA102
COMPASS WA102 PL B453 (1999) 305
450 GeV/c p beamFit of wave intensities only
27 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
PWA of p p→ pfast K+K− pslow
Summary
Clean K+K− central-production samplePWA result similar to WA102Mass dependence can be described by model with three S−0 andtwo D−0 Breit-Wigner resonances
Extracted Breit-Wigner parameters mostly comparable to PDGvalues
Surprisingly strong signal for f0(1370)f0(1370) resonance required by observed phase motion
Work in progress
Simplistic fit modelAngular information of the two proton scattering planes not takeninto accountMass dependence parametrized by sum of relativistic Breit-Wigners
Goal: combined analysis including K0SK0
S, π+π−, π0π0, and ηη
28 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy
Search for
“Missing” states
Gluonic excitations (hybrids)
Worldwide experimental program
ELSA, JLab, MAMI, J-PARCExcitation of baryon resonances using low-energy pion andphoton beams
E.g. γ + N → N + π, ππ, πππ, η, πη, πω, ηη, . . .
“Complete experiment”Polarized beam and target + measurement of recoil polarization8 carefully selected double/single-spin observablesWell-defined quantum numbers of initial and final stateUnambiguous determination of scattering amplitude
29 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy
Search for
“Missing” states
Gluonic excitations (hybrids)
Worldwide experimental program
ELSA, JLab, MAMI, J-PARCExcitation of baryon resonances using low-energy pion andphoton beams
E.g. γ + N → N + π, ππ, πππ, η, πη, πω, ηη, . . .
“Complete experiment”Polarized beam and target + measurement of recoil polarization8 carefully selected double/single-spin observablesWell-defined quantum numbers of initial and final stateUnambiguous determination of scattering amplitude
29 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
P
pbeam
ptarget pslow
X+pbeam
ptarget pslow
pbeam
ptarget pslow
pbeam
ptarget pslow
ph1...hn
Large data set with 190 GeV/c positive hadron beam on liquidhydrogen target in kinematic range 0.1 < t′ < 1.0 (GeV/c)2
Diffractive dissociation of beam p into various final states:pπ0, pη, pη′, pω
pπ+π−, pπ0π0, pK+K−, pK0SK0
S, pηη
. . .
Unpolarized beam and target; recoil polarization not measuredJP quantum numbers of initial state not fixedQuantization axis = beam direction (Gottfried-Jackson frame)JP Mε of intermediate state X deducible from kinematic distributionof final-state particles
30 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
P
pbeam
ptarget pslow
X+pbeam
ptarget pslow
pbeam
ptarget pslow
pbeam
ptarget pslow
ph1...hn
Large data set with 190 GeV/c positive hadron beam on liquidhydrogen target in kinematic range 0.1 < t′ < 1.0 (GeV/c)2
Diffractive dissociation of beam p into various final states:pπ0, pη, pη′, pω
pπ+π−, pπ0π0, pK+K−, pK0SK0
S, pηη
. . .
Unpolarized beam and target; recoil polarization not measuredJP quantum numbers of initial state not fixedQuantization axis = beam direction (Gottfried-Jackson frame)JP Mε of intermediate state X deducible from kinematic distributionof final-state particles
30 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
P
pbeam
ptarget pslow
X+pbeam
ptarget pslow
pbeam
ptarget pslow
pbeam
ptarget pslow
ph1...hn
Large data set with 190 GeV/c positive hadron beam on liquidhydrogen target in kinematic range 0.1 < t′ < 1.0 (GeV/c)2
Diffractive dissociation of beam p into various final states:pπ0, pη, pη′, pω
pπ+π−, pπ0π0, pK+K−, pK0SK0
S, pηη
. . .
Unpolarized beam and target; recoil polarization not measuredJP quantum numbers of initial state not fixedQuantization axis = beam direction (Gottfried-Jackson frame)JP Mε of intermediate state X deducible from kinematic distributionof final-state particles
30 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
pp→ pπ0 pslowpπ0 invariant mass
cos θGJ of π0 vs. mpπ0 φTY of π0 vs. mpπ0
31 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
pp→ pπ0 pslowpπ0 invariant mass
cos θGJ of π0 vs. mpπ0 φTY of π0 vs. mpπ0
31 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
pp→ pπ+π− pslowpπ+π− invariant mass pπ+ subsystem
pπ− subsystem π+π− subsystem
32 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
pp→ pπ+π− pslowpπ+π− invariant mass pπ+ subsystem
pπ− subsystem π+π− subsystem
32 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
Summary
Large data sets from p diffractionpπ0: 8.8 · 106 eventspη: 440 000 eventspπ+π−: more than 50 · 106 events. . .
Interesting structures visible in kinematic distributions
Pp data complementary to γp and πp dataWill start with PWA of two-body final states
Acceptance correction in preparationImplementation of PWA model started
Three-body final states require more work on PWA model
33 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
Summary
Large data sets from p diffractionpπ0: 8.8 · 106 eventspη: 440 000 eventspπ+π−: more than 50 · 106 events. . .
Interesting structures visible in kinematic distributions
Pp data complementary to γp and πp dataWill start with PWA of two-body final states
Acceptance correction in preparationImplementation of PWA model started
Three-body final states require more work on PWA model
33 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
Baryon Spectroscopy in Proton Diffraction
Summary
Large data sets from p diffractionpπ0: 8.8 · 106 eventspη: 440 000 eventspπ+π−: more than 50 · 106 events. . .
Interesting structures visible in kinematic distributions
Pp data complementary to γp and πp dataWill start with PWA of two-body final states
Acceptance correction in preparationImplementation of PWA model started
Three-body final states require more work on PWA model
33 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Outline
1 IntroductionQCD and constituent quark modelBeyond the constituent quark model
2 Hadron spectroscopySearch for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction
3 Conclusions and Outlook
34 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Conclusions and OutlookCOMPASS has acquired large data sets for many reactions
Diffractive dissociation of p, π−, and K− on various targetsCentral production with p and π− beams on proton targetπ−γ and K−γ Primakoff reactions on heavy targets
Main focus: search for mesonic states beyond the CQM
Huge diffractive π−π+π− data set: precision spectroscopy oflight-quark isovector sectorSpin-exotic JPC = 1−+ signals observed in π− diffraction
π−η and π−η′ channelsπ−π+π− and π−π0π0 final statesResonance interpretation still unclear
Study of scalar mesons in central production of ππ, KK, and ηηFurther analyses
π− diffraction into π−ηη, π−π+π−π+π−, (ππKK)−, . . .K− diffraction into K−π+π−
Radiative couplings of a2(1320) and π2(1670)
35 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Conclusions and OutlookCOMPASS has acquired large data sets for many reactions
Diffractive dissociation of p, π−, and K− on various targetsCentral production with p and π− beams on proton targetπ−γ and K−γ Primakoff reactions on heavy targets
Main focus: search for mesonic states beyond the CQM
Huge diffractive π−π+π− data set: precision spectroscopy oflight-quark isovector sectorSpin-exotic JPC = 1−+ signals observed in π− diffraction
π−η and π−η′ channelsπ−π+π− and π−π0π0 final statesResonance interpretation still unclear
Study of scalar mesons in central production of ππ, KK, and ηηFurther analyses
π− diffraction into π−ηη, π−π+π−π+π−, (ππKK)−, . . .K− diffraction into K−π+π−
Radiative couplings of a2(1320) and π2(1670)
35 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Conclusions and OutlookCOMPASS has acquired large data sets for many reactions
Diffractive dissociation of p, π−, and K− on various targetsCentral production with p and π− beams on proton targetπ−γ and K−γ Primakoff reactions on heavy targets
Main focus: search for mesonic states beyond the CQM
Huge diffractive π−π+π− data set: precision spectroscopy oflight-quark isovector sectorSpin-exotic JPC = 1−+ signals observed in π− diffraction
π−η and π−η′ channelsπ−π+π− and π−π0π0 final statesResonance interpretation still unclear
Study of scalar mesons in central production of ππ, KK, and ηηFurther analyses
π− diffraction into π−ηη, π−π+π−π+π−, (ππKK)−, . . .K− diffraction into K−π+π−
Radiative couplings of a2(1320) and π2(1670)
35 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Conclusions and OutlookCOMPASS has acquired large data sets for many reactions
Diffractive dissociation of p, π−, and K− on various targetsCentral production with p and π− beams on proton targetπ−γ and K−γ Primakoff reactions on heavy targets
Main focus: search for mesonic states beyond the CQM
Huge diffractive π−π+π− data set: precision spectroscopy oflight-quark isovector sectorSpin-exotic JPC = 1−+ signals observed in π− diffraction
π−η and π−η′ channelsπ−π+π− and π−π0π0 final statesResonance interpretation still unclear
Study of scalar mesons in central production of ππ, KK, and ηηFurther analyses
π− diffraction into π−ηη, π−π+π−π+π−, (ππKK)−, . . .K− diffraction into K−π+π−
Radiative couplings of a2(1320) and π2(1670)
35 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
IntroductionHadron spectroscopy
Conclusions and Outlook
Conclusions and Outlook
Running and upcoming experiments
VES
BESIII
Belle II
GlueX, CLAS12
PANDA
. . .
36 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Outline
4 Backup slides IIntroductionSearch for spin-exotic mesons in π− diffraction
π−π+π− final stateη′π− final state
PWA of π−η and π−η′ from final statesPWA of π−π+π−π+π− decay channel
5 Backup Slides IISearch for scalar glueballs in central production
PWA of π+π− system
37 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
The COMPASS Experiment at the CERN SPSExperimental Setup NIM A 577, 455 (2007)
38 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Fixed-target experiment
Two-stage spectrometer
Large acceptance over widekinematic range
Electromagnetic and hadroniccalorimeters
Beam and final-state particle ID(CEDARs, RICH)
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
The COMPASS Experiment at the CERN SPSExperimental Setup NIM A 577, 455 (2007)
38 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Fixed-target experiment
Two-stage spectrometer
Large acceptance over widekinematic range
Electromagnetic and hadroniccalorimeters
Beam and final-state particle ID(CEDARs, RICH)
Hadron spectroscopy 2008-09, 2012
190 GeV/c secondary hadron beamsh− beam: 97 % π−, 2 % K−, 1 % ph+ beam: 75 % p, 24 % π+, 1 % K+
Various targets: `H2, Ni, Pb, W> 1 PByte of data per year
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Meson Production in Diffractive Dissociation
Reaction similar to diffraction of light by black disk
Relevant kinematic variable is squared four-momentum transfert = (pbeam − pX)
2 < 0; more practical t′ ≡ |t| − |t|min > 0“Intermediate-t′” region: diffraction pattern of Pb nucleus“High-t′” region: scattering on individual nucleons in nucleus
t′ ∈ [0, 0.1] (GeV/c)2
39 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Meson Production in Diffractive Dissociation
Reaction similar to diffraction of light by black disk
Relevant kinematic variable is squared four-momentum transfert = (pbeam − pX)
2 < 0; more practical t′ ≡ |t| − |t|min > 0“Intermediate-t′” region: diffraction pattern of Pb nucleus“High-t′” region: scattering on individual nucleons in nucleus
t′ ∈ [0, 0.1] (GeV/c)2
39 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Meson Production in Diffractive Dissociation
Reaction similar to diffraction of light by black disk
Relevant kinematic variable is squared four-momentum transfert = (pbeam − pX)
2 < 0; more practical t′ ≡ |t| − |t|min > 0“Intermediate-t′” region: diffraction pattern of Pb nucleus“High-t′” region: scattering on individual nucleons in nucleus
t′ ∈ [0, 0.1] (GeV/c)2 t′ ∈ [0.1, 1] (GeV/c)2
39 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Gottfried-Jackson Coordinate System
p
p
p
p
p
p
z
a
xL
z L
GJ
y
c
b,
GJ
xGJ
d
a,
GJF
LAByL
,
d
40 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Canonical vs. Helicity Coordinate System
41 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Partial-Wave Analysis Formalism
Cross section parameterization in mass-independent PWA
σ(τ; mX) = σ0 ∑ε=±1
Nr
∑r=1
∣∣∣∣∣waves
∑i
Trεi (mX) Aε
i (τ)
∣∣∣∣∣2
ε, i: quantum numbers of partial wave (JPC Mε[isobar]L)Trε
i : complex production amplitudes; fit parametersAε
i : complex decay amplitudesτ: phase space coordinates
Spin-density matrix
ρεij =
Nr
∑r=1
Trεi Trε
j∗ σ(τ; mX) = σ0 ∑
ε=±1
waves
∑i,j
ρεij(mX) Aε
i (τ) Aε∗j (τ)
Diagonal elements ρii: intensitiesOff-diagonal elements ρii, i 6= j: interference terms
42 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Partial-Wave Analysis Formalism
Two-body decay amplitude in helicity formalism
Decay X(w, J, λ)→ 1(J1, λ1) [L, S] 2(J2, λ2)
AhelX =
√2L + 1 ∑
λ1,λ2
(J1 λ1 J2−λ2|S δ) (L 0 S δ|J δ)
D J∗λδ(θ, φ, 0) FL(q)∆(w) A1 A2
δ = λ1 − λ2D J∗
λδ(θ, φ, 0) — Wigner D-function describes rotational propertiesof helicity statesθ, φ — polar angles of decay daughter 1 in X rest frame (GJ orhelicity frame)FL(q) — Blatt-Weisskopf barrier factor∆(w) — amplitude that describes resonance shape of XA1,2 — decay amplitudes of (unstable) daughter particles 1 and 2
43 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Partial-Wave Analysis Formalism
Two-body decay amplitude in canonical formalism
Decay X(w, J, M)→ 1(J1, M1) [L, S] 2(J2, M2)
AcanX =
√2J + 1 ∑
M1,M2
(J1 M1 J2 M2|S MS) ∑ML
(L ML S MS|J M)√4π
2L + 1YL
ML(θ, φ) FL(q)∆(w) A1 A2
YLML
(θ, φ) — Spherical harmonic describes rotational property of|L ML〉 stateθ, φ — polar angles of decay daughter 1 in X rest frame (reachedby simple boost, no rotations)FL(q) — Blatt-Weisskopf barrier factor∆(w) — amplitude that describes resonance shape of XA1,2 — decay amplitudes of (unstable) daughter particles 1 and 2
44 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Partial-Wave Analysis Formalism
Extended maximum-likelihood method
Likelihood L to observe N events distributed according toσ(τ; mX) and acceptance Acc(τ; mX)
L =
[NN
N!e−N
]︸ ︷︷ ︸
Poisson likelihood
N
∏i=1
σ(τi; mX)Acc(τi)∫dΦn(τ) σ(τ; mX)Acc(τ; mX)
︸ ︷︷ ︸
Likelihood of event n
with N ∝∫
dΦn(τ) σ(τ; mX)Acc(τ; mX)
L ∝
[NN
N!e−N
][1
NN
N
∏i=1
σ(τi; mX)
]
L ∝ e−∫
dΦn(τ) σ(τ;mX)Acc(τ;mX)N
∏i=1
σ(τi; mX)
45 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
Partial-Wave Analysis Formalism
Extended maximum-likelihood method (cont.)
Insert parameterization of cross section for σ(τi; mX)
L ∝ e−∫
dΦn(τ) σ(τ;mX)Acc(τ;mX)N
∏i=1
Nr
∑r=1
∣∣∣∣∣ ∑waves
Trwave(mX) Awave(τi; mX)
∣∣∣∣∣2
Make expression less unwieldy by taking logarithm
lnL =N
∑i=1
ln
Nr
∑r=1
∣∣∣∣∣ ∑waves
Trwave(mX) Awave(τi; mX)
∣∣∣∣∣2
−∫
dΦn(τ) σ(τ; mX)Acc(τ; mX)︸ ︷︷ ︸Normalization integral
Normalization integral estimated using phase space Monte Carlo
46 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π−π+π− pslow
2++ 2+ [ρπ]D: a2(1320)
4++ 1+ [ f2π]F: a4(2040)
0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)
47 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π−π+π− pslow
2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)
0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)
47 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π−π+π− pslow
2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)
0−+ 0+ [ f0(980)π]S: π(1800)
4++ 1+ [ρπ]G: a4(2040)
47 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π−π+π− pslow
2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)
0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)
47 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
π−π+π− Final StateAcceptance (p Target)
π−π+π− mass
)2 System (GeV/c+π -π -πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
acce
ptan
ce
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
π+π− mass
)2 Subsystem (GeV/c+π -πMass of 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
acce
ptan
ce0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
48 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
π−π+π− Final StateAcceptance (p Target)
Gottfried-Jackson frame: cos θGJ
GJθcos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
acce
ptan
ce
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
Gottfried-Jackson frame: ϕTY
TYφ
-150 -100 -50 0 50 100 150
acce
ptan
ce
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
Helicity frame: cos θHF
HFθcos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
acce
ptan
ce
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
Helicity frame: ϕHF
HFφ
-150 -100 -50 0 50 100 150
acce
ptan
ce
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1COMPASS 2008
p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV
preliminary
49 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π− Pb at low t′ (Pilot Run)
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
π−π+π− production in Primakoff reaction
Very small momentum transfer: t′ < 0.001 (GeV/c)2
Photoproduction in Coulomb field of heavy target nucleus (Pb)For M = 1 waves diffractive contribution kinematicallysuppressedNo intensity in 1.6 GeV/c2 region in spin-exotic 1−+ wave
Consistent with CLAS result
50 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π− Pb at low t′ (Pilot Run)
γ˚
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´
π−π+π− production in Primakoff reaction
Very small momentum transfer: t′ < 0.001 (GeV/c)2
Photoproduction in Coulomb field of heavy target nucleus (Pb)For M = 1 waves diffractive contribution kinematicallysuppressedNo intensity in 1.6 GeV/c2 region in spin-exotic 1−+ wave
Consistent with CLAS result
50 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Selection of exclusive events with 3 charged tracks + 2 photons
Kinematic range 0.1 < t′ < 1.0 (GeV/c)2
η reconstructed from η → π+π−π0
η′ reconstructed via π+π−η decay with η → γγ
γγ invariant mass distribution
51 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Selection of exclusive events with 3 charged tracks + 2 photons
Kinematic range 0.1 < t′ < 1.0 (GeV/c)2
η reconstructed from η → π+π−π0
η′ reconstructed via π+π−η decay with η → γγ
γγ invariant mass distribution π+π−η invariant mass distribution
51 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslowπ−η invariant mass distribution
π−η: dominant a2(1320)
π−η′: dominant broad structure around 1.7 GeV/c2 and a2(1320)close to thresholdBulk of data described by 3 partial waves
1−+ 1+, 2++ 1+, and 4++ 1+
52 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslowπ−η invariant mass distribution π−η′ invariant mass distribution
π−η: dominant a2(1320)
π−η′: dominant broad structure around 1.7 GeV/c2 and a2(1320)close to thresholdBulk of data described by 3 partial waves
1−+ 1+, 2++ 1+, and 4++ 1+
52 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslowa2(1320) in 2++ 1+ Partial Wave
π−η final state π−η′ final state
η-η′ mixing together with OZI rule
Partial-wave amplitudes for spin J related by mixing angle φ,phase space, and barrier factors (q = breakup momentum)
Tπη′J (m)
TπηJ (m)
= tan φ
[qπη′(m)
qπη(m)
]J+1/2
53 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslowa2(1320) in 2++ 1+ Partial Wave
π−η final state π−η′ final state
η-η′ mixing together with OZI rule
Partial-wave amplitudes for spin J related by mixing angle φ,phase space, and barrier factors (q = breakup momentum)
Tπη′J (m)
TπηJ (m)
= tan φ
[qπη′(m)
qπη(m)
]J+1/2
53 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslowa2(1320) in 2++ 1+ Partial Wave
π−η final state π−η′ final state
π−η scaled, π−η′
53 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
2++ 1+
4++ 1+
Phase: 4++ 1+− 2++ 1+
Very similar even-spin waves
Expected for nn resonances(OZI rule)
Similar physical content alsoin non-resonant high-massregion
54 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
2++ 1+ 4++ 1+
Phase: 4++ 1+− 2++ 1+
Very similar even-spin waves
Expected for nn resonances(OZI rule)
Similar physical content alsoin non-resonant high-massregion
54 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
2++ 1+ Spin-exotic 1−+ 1+
Phase: 2++ 1+− 1−+ 1+Completely differentintensity of 1−+ wave
Suppression in πη channelpredicted for intermediate|qqg〉 state
Different phase motion in1.6 GeV/c2 region
55 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Summary
Found significant intensity in spin-exotic 1−+ wave in πη and πη′
2++ and 4++ waves very similar in both channels
1−+ wave enhanced in πη′
First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds
a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance
Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region
Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Summary
Found significant intensity in spin-exotic 1−+ wave in πη and πη′
2++ and 4++ waves very similar in both channels
1−+ wave enhanced in πη′
First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds
a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance
Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region
Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Summary
Found significant intensity in spin-exotic 1−+ wave in πη and πη′
2++ and 4++ waves very similar in both channels
1−+ wave enhanced in πη′
First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds
a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance
Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region
Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Summary
Found significant intensity in spin-exotic 1−+ wave in πη and πη′
2++ and 4++ waves very similar in both channels
1−+ wave enhanced in πη′
First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds
a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance
Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region
Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Non-resonant contributions
P
P
π´beam π´
fast
ptarget pslow
ηa2
P
π´beam
η
ptarget pslow
π´
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− p→ π− η pslow and π− η′ pslow
Summary
Found significant intensity in spin-exotic 1−+ wave in πη and πη′
2++ and 4++ waves very similar in both channels
1−+ wave enhanced in πη′
First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds
a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance
Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region
Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
η′π− Final Statecos θGJ vs. η′π− Invariant Mass
57 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
P
π´beam
Pb Pb
X´π´beam
Pb Pb
π´beam
Pb Pb
π´beam
Pb Pb
π´π+
π´π+
π´
First mass-dependent PWA of this reaction
Light-meson frontier: access to mesonic states in 2 GeV/c2 regionLittle information from previous experiments
Data from pilot run
Pb targetRecoil not measuredKinematic range t′ < 5 · 10−3 (GeV/c)2
58 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
Fit model
Complicated isobar structureLarge number of possible wavesData exhibit no dominant waves
Exploration of model space using evolutionary algorithm basedon goodness-of-fit criterion
284 waves testedAlso provides estimate for systematic uncertainty from fit model
Best model: 31 waves + incoherent isotropic backgroundIsobars
(2π)0 isobars: (ππ)S−wave, ρ(770)(3π)± isobars: a1(1260), a2(1320)(4π)0 isobars: f2(1270), f1(1285), f0(1370, 1500), and ρ′(1450, 1700)
Only few information available for (4π)0 isobars
59 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
60 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
61 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
Proof of Principle: First mass-dependent five-body PWA
Spin-density sub-matrix of 10 waves described using 7 resonances+ background termsRather simplistic fit model
Parameterization by sum of relativistic constant-width Breit-WignersMixing and coupled-channel effects neglectedMulti-peripheral processes (Deck-effect) not taken into account
Good description of data
Work in progress
Much more data on tapeProton target, kinematic range 0.1 < t′ < 1 (GeV/c)2
Improvement of fit modelsAnalysis of (4π)0 subsystem
62 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states
PWA of π− Pb → π−π+π−π+π− Pb
Proof of Principle: First mass-dependent five-body PWA
Spin-density sub-matrix of 10 waves described using 7 resonances+ background termsRather simplistic fit model
Parameterization by sum of relativistic constant-width Breit-WignersMixing and coupled-channel effects neglectedMulti-peripheral processes (Deck-effect) not taken into account
Good description of data
Work in progress
Much more data on tapeProton target, kinematic range 0.1 < t′ < 1 (GeV/c)2
Improvement of fit modelsAnalysis of (4π)0 subsystem
62 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Search for scalar glueballs in central production
PWA of p p→ pfast π+π− pslowpbeam pfast
ptarget pslow
X0
pbeam pfast
ptarget pslow
pbeam pfast
ptarget pslow
[JǫM]
pbeam
P
pfast
ptarget
P
pslow
pbeam
P
pfast
ptarget
P
pslow
π+
π´
Suppression of diffractive background with m(pfastπ±) > 1.5 GeV/c2
pfastπ+ invariant mass pfastπ
− invariant mass
63 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Search for scalar glueballs in central production
PWA of p p→ pfast π+π− pslow
pbeam pfast
ptarget pslow
X0
pbeam pfast
ptarget pslow
pbeam pfast
ptarget pslow
[JǫM]
pbeam
P
pfast
ptarget
P
pslow
pbeam
P
pfast
ptarget
P
pslow
π+
π´
Selected central events
xF distribution π+π− invariant mass
64 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Search for scalar glueballs in central production
PWA of p p→ pfast π+π− pslow
65 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Search for scalar glueballs in central production
PWA of p p→ pfast π+π− pslow
Work in progress
Analysis similar to WA102 experimentComparable results
Simplistic fit modelAngular information of the two proton scattering planes not takeninto account
8 different mathematically ambiguous solutionsAdditional constraints needed to select physical solution
Next steps
Fit of mass dependence
Analysis of K+K− final state
Data for K0SK0
S, π0π0, and ηη final states on tape
66 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS
Backup slides IBackup Slides II
Search for scalar glueballs in central production
PWA of p p→ pfast π+π− pslow
Work in progress
Analysis similar to WA102 experimentComparable results
Simplistic fit modelAngular information of the two proton scattering planes not takeninto account
8 different mathematically ambiguous solutionsAdditional constraints needed to select physical solution
Next steps
Fit of mass dependence
Analysis of K+K− final state
Data for K0SK0
S, π0π0, and ηη final states on tape
66 Boris Grube, TU München Hadron Spectroscopy at and related experiments
COMPASS