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Dilepton Production at SIS EnergiesDLS Puzzle Part II: The ∆ Crisis
Janus Weil
in collab. with U. Mosel, H. van Hees, K. Gallmeister, ...
Transport MeetingFIAS, 07.02.2013
J. Weil Dilepton Production at SIS Energies
Outline
1 motivation:in-medium physics, “DLS puzzle”
2 the GiBUU transport model
3 dileptons from elementary reactions:pp, dp, pNb (at 1-4 GeV)
[arXiv:1203.3557, EPJ A48 (2012) 111]
4 dileptons from heavy-ion collisions:CC, ArKCl, AuAu[arXiv:1211.3761]
5 conclusions
J. Weil Dilepton Production at SIS Energies
Motivation: Hadrons in Medium
how do vector mesons behave inside ahadronic medium?
Brown/Rho, Hatsuda/Lee:mass shift (restoration of chiral sym.)m∗V (ρ)/mV ≈ 1− α(ρ/ρ0) ,α ≈ 0.16± 0.06collisional broadening (LDA):Γcoll = ρ < vrelσVN >
QCD sum rules (Leupold, NPA 628, 1998)
coupling to resonances can introduceadditional structures in the spectralfunction (Post, 2003)
but: do we even know what the ρmeson looks like in vacuum?
J. Weil Dilepton Production at SIS Energies
ρ-baryon coupling
coupling of ρ meson to baryon resonances known to be crucialfor in-medium self-energies at SPS energies (Hees/Rapp)
dominant source of collisional broadening
should be even more important at low energies
this coupling can even play a role in the vacuum: ρproduction through baryons at low energies
J. Weil Dilepton Production at SIS Energies
The DLS Puzzle(s)
mid-90s: no one can fully explaindilepton data measured by DLS infew-GeV regime
data wrong? models incomplete?
today: DLS data fully confirmedby new HADES data (betteracceptance/resolution/statistics)
there are still two (theory) puzzles:
1 how to explain the elementary(N+N) dilepton spectra?
2 are there additional ’in-medium’effects in A+A?
UrQMD, Ernst et al., PRC 58 (1998)
HSD, Bratkovskaya et al., PLB 445 (1999)
J. Weil Dilepton Production at SIS Energies
Starting points for a solution
1 early observation (Winckelmann et al, PRC 51, 1995):“The ρ mass spectrum is strongly distorted due to phasespace effects, populating dominantly dilepton masses below770 MeV.” (already in pp, due to production via baryonresonances. Unfortunately mostly ignored in later works!)
2 later claim (Bratkovskaya et al, NPA 807, 2008):“We find that the DLS puzzle [...] may be solved whenincorporating a stronger bremsstrahlung contribution in linewith recent OBE calculations.” (and: a stronger ∆contribution)
J. Weil Dilepton Production at SIS Energies
Teaser: C + C @ 2 GeV
10-5
10-4
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
mb
/Ge
V]
dilepton mass mee [GeV]
C + C @ 2.0 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.πN Brems.D13(1520)S31(1620)
ππ
both HSD and GiBUU describe the data quite well
but: with a rather different cocktail composition!
∆ channel is very strong in HSD, but almost negligible inGiBUU
⇒ the “∆ crisis”!
J. Weil Dilepton Production at SIS Energies
The GiBUU Transport Model
BUU-type hadronic transport modelunified framework for various types of reactions(γA, eA, νA, pA, πA, AA) and observablesBUU equ.: space-time evolution of phase space density(∂t + (∇~pHi )∇~r − (∇~rHi )∇~p
)fi (~r , t, ~p) = Icoll [fi , fj , ...]
Hamiltonian Hi :hadronic mean fields, Coulomb, “off-shell potential”
collision term Icoll :decays and scattering processes (2- and 3-body)low energy: resonance model, high energy: string fragment.
O. Buss et al., Phys. Rep. 512 (2012),http://gibuu.physik.uni-giessen.de
J. Weil Dilepton Production at SIS Energies
Modeling collisions in the few-GeV regime
baryon-baryon collisions at low energies:resonance models vs. string fragmentation
HADES energy range is clearly in the resonance regime!
we need one consistent model for the whole energy range!
J. Weil Dilepton Production at SIS Energies
Resonance Model
assumption: inel. NN cross section is dominated byproduction and decay of baryonic resonances
NN → NR,∆R (R : ∆, 7 N∗ and 6 ∆∗ states)based on Teis RM [Z. Phys. A 356, 1997] with several extensions
all π, η and ρ mesons produced via R decays (ω, φ: non-res.)
good descr. of total NN cross sections up to√s ≈ 3.5GeV
0
5
10
15
20
25
30
35
40
2 2.5 3 3.5 4
σin
el [
mb]
sqrt(s) [GeV]
pp → X
HADES
2 2.5 3 3.5 4 0
5
10
15
20
25
30
35
40
sqrt(s) [GeV]
np → X
datainel.N∆
NN*N∆*∆∆
∆N*∆∆*
NNπω/φ
BYK
J. Weil Dilepton Production at SIS Energies
Resonance Production
NN → N∆: OBE model [Dmitriev et al, NPA 459 (1986)]
other resonances produced via phase-space approach(constant matrix elements):
σNN→NR =CIpi s
|MNR |2
16π
∫dµAR(µ)pF (µ)
σNN→∆R =CIpi s
|M∆R |2
16π
∫dµ1dµ2A∆(µ1)AR(µ2)pF (µ1, µ2)
lately: introduced angular distributions dσ/dt = b/ta, a ≈ 1(→ A. Dybczak)
J. Weil Dilepton Production at SIS Energies
∆ production cross section
only exclusive ∆+ production constrained by data
resonance models (UrQMD/GiBUU) agree roughly oninclusive production
but: inclusive cross section much larger in HSD/FRITIOF
string models do not obey isospin relations!
10-1
100
101
2 2.5 3 3.5 4 4.5 5 5.5
σpp [m
b]
sqrt(s) [GeV]
pp → ∆+X production
∆+X (Res)
∆+p (Res)
∆+X (Py)
∆+p (Py)
∆+X (Fr)
∆+p (Fr)
HSD inclHSD excl
UrQMD inclUrQMD excl
∆+p data
2 2.5 3 3.5 4 4.5 5 5.5
sqrt(s) [GeV]
pp → ∆++
X production
∆++
X (Res)∆
++n (Res)
∆++
X (Py)∆
++n (Py)
∆++
X (Fr)∆
++n (Fr)
2 2.5 3 3.5 4 4.5 5 5.5-0.5
0
0.5
1
1.5
2
2.5
3
3.5
sqrt(s) [GeV]
isospin ratio ∆++
/∆+
incl. (Res)excl. (Res)
incl. (Py)excl. (Py)incl. (Fr)
excl. (Fr)
lesson: don’t trust string fragmentation models at low energies!J. Weil Dilepton Production at SIS Energies
Hadronic decays
all resonance parameters, decays modes and width parametriz.taken from: Manley/Saleski, Phys. Rev. D 45 (1992)Manley: PWA including πN → πN and πN → 2πN dataimportant point: consistency! (coupled-channel constraints)
ΓR→ab(m) = Γ0R→ab
ρab(m)
ρab(M0)
ρab(m) =
∫dp2adp
2bAa(p2a)Ab(p2b)
pabm
B2Lab(pabR)F2ab(m)
J. Weil Dilepton Production at SIS Energies
Dilepton decays
V → e+e− (with V = ρ, ω, φ) via strict VMD: Γ(µ) ∝ µ−3
P → γe+e− (with P = π0, η, η′) [Landsberg, Phys.Rep.128, 1985]:
dΓ
dµ=
4α
3π
ΓP→γγµ
(1− µ
2
m2P
)3|FP(µ)|2,
ω → π0e+e− [Landsberg]:
dΓ
dµ=
2α
3π
Γω→π0γµ
[(1 +
µ2
µ2ω −m2π
)2− 4µ
2ωµ
2
(µ2ω −m2π)2
]3/2|Fω(µ)|2
∆→ Ne+e− [Krivoruchenko, Phys.Rev.D65, 2002]:
dΓ
dµ=
2α
3πµ
α
16
(m∆ + mN)2
m3∆m2N
√(m∆ + mN)2 − µ2
[(m∆ −mN)2 − µ2
]3/2|F∆(µ)|2
important: form factors well restricted for π0, η and ω,but completely unknown for ∆!
we use Delta FF model of Ramalho/Pena [Phys.Rev.D85, 2012]
J. Weil Dilepton Production at SIS Energies
Dilepton decays of baryonic resonances
how to treat R → Ne+e−?option 1: do Dalitz decay (as for ∆), with proper form factor!(fixed at photon point, ’extrapolate’ to q2 > 0)
option 2: do two-step decay R → ρN → e+e−N(using ’hadronic’ info from PWA)
consequence: dilepton contributions from all N∗ and ∆∗
resonances, which have a ρ coupling
and: we get an ’implicit’ form factor from decay kinematics
J. Weil Dilepton Production at SIS Energies
Bremsstrahlung
soft-photon approximation[Gale/Kapusta, PRC40, 1989]:
dσpn→pne+e−
dMdEdΩ=
α2
6π3q
ME2σ̄(s)
R2(s2)
R2(s),
σ̄(s) =s − (m1 + m2)2
2m21σpnel (s) ,
R2(s) =√
1− (m1 + m2)2/s ,
s2 = s + M2 − 2E
√s ,
used for NN, πN
NN: pn only (destr. interference in pp not treated)
OBE: Kaptari-Kämpfer [NPA764, 2006],Shyam-Mosel [PRC82, 2010]
J. Weil Dilepton Production at SIS Energies
Results: elementary reactions
if we want to investigate in-medium effects, we better makesure we understand the dilepton signal from elementary NNcollisions (“in the vacuum”)
this is not a trivial task and represents the most importantprerequisite for understanding the heavy-ion collisions
HADES has measured:p+p at Ekin = 1.25, 2.2 and 3.5 GeVd+p at Ekin = 1.25 GeV
all simulation results filtered through HADES acceptance filter
opening angle cut: θee > 9◦
lepton momentum cut: pmine < pe < pmaxe
J. Weil Dilepton Production at SIS Energies
p+p at 3.5 GeV
using resonance model
important: ρ production viabaryonic resonances
R → ρN → e+e−Nlow-mass part enhanced bylight resonances (and 1/m3
factor from dilepton decaywidth)
same effect seen in UrQMD
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
J. Weil Dilepton Production at SIS Energies
p+p at 3.5 GeV: resonance contributions
ρ channel is given by a mix ofseveral resonance contributions
shape depends on the mass of theresonance (phase space of decay)
contributions of single resonancesnot well constrained, but goodagreement in total
cross check from πN mass spectraneeded
the same ρNR coupling thatdominates in-medium self-energy isresponsible for a ’modified’ ρalready in pp collisions!
10-3
10-2
10-1
100
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
ρ → e+e
-
D13(1520)S11(1535)S11(1650)F15(1680)P13(1720)
all Res.S31(1620)D33(1700)F35(1905)
0
200
400
600
800
1000
1200
1400
1600
1800
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
dσ
/dm
[µ
b/G
eV
]
m [GeV]
ρ totalD13(1520)S11(1535)S11(1650)F15(1680)P13(1720)S31(1620)D33(1700)F35(1905)
Pythia
J. Weil Dilepton Production at SIS Energies
p+p at 3.5 GeV: comparison to HSD
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
0 0.2 0.4 0.6 0.8 1
transverse momentum pT [GeV]
0 0.2 0.4 0.6 0.8 1
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2
dσ
/dy [
µb]
m < 150 MeV
0 0.5 1 1.5 2
rapidity y
150 MeV < m < 470 MeV
0 0.5 1 1.5 2
470 MeV < m < 700 MeV
0 0.5 1 1.5 2
10-4
10-3
10-2
10-1
100
dσ
/dy [
µb]
700 MeV < m
HSD fails to describe pT data due to large ∆ and Bremsstr. contr.!J. Weil Dilepton Production at SIS Energies
other elementary collisions
10-3
10-2
10-1
100
101
0 0.1 0.2 0.3 0.4 0.5
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
p + p at 1.25 GeV
dataGiBUU total
π0 → e
+e
-γ
∆ → Ne+e
-
ρ → e+e
-
D13(1520)
10-3
10-2
10-1
100
101
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
p + p at 2.2 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)P13(1720)
10-4
10-3
10-2
10-1
100
101
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
d + p at 1.25 GeV
dataGiBUU total
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.ρ → e
+e
-
D13(1520)S11(1535)
p+p at 1.25 and 2.2 GeV rather well described
d+p misses factor 2-10
reason not completely clear, OBE models might help
isopsin effects not completely understood?
J. Weil Dilepton Production at SIS Energies
In-medium effects in p+A and A+A
constrained by NN spectra:
basic cocktail composition (in ’vacuum’)
particle production from NN
form factors (limited)
ρ spectral distribution in vacuum (non-trivial!)
additional effects:
secondary collisions:
mB → X : meson absorption, secondary production (πN → R)mm→ X : most importantly ππ → ρ
modifications of spectral functions:
collisional broadening: Γtot = Γdec + Γcollmass shifts? m∗ = m · (1− ρ/ρ0)may be important for: ρ meson, baryonic resonances
J. Weil Dilepton Production at SIS Energies
Off-Shell Transport
off-shell EOM for test particles[Cassing/Juchem (NPA 665, 2000), Leupold (NPA 672, 2000)]:
~̇ri =1
1− Ci1
2Ei
[2~pi +
∂
∂~piRe(Σi ) + χi
∂Γi∂~pi
],
~̇pi = −1
1− Ci1
2Ei
[∂
∂~riRe(Σi ) + χi
∂Γi∂~ri
],
Ci =1
2Ei
[∂
∂EiRe(Σi ) + χi
∂Γi∂Ei
],
χi =m2i −M2
Γi,
dχidt
= 0
needed to incorporate density-dependent self energies Σi ,widths Γi ∼ Im(Σi ) and spectral functionsbut: neglecting momentum dependence
J. Weil Dilepton Production at SIS Energies
p + 93Nb at 3.5 GeV
after [email protected] is fixed: goodoverall agreement in p+Nb
moderate mediummodifications (of VMspectral functions)
10-1
100
101
102
103
0 0.2 0.4 0.6 0.8 1 1.2
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)S31(1620)F35(1905)
10-1
100
0.6 0.7 0.8
dσ
/dm
ee [
µb/G
eV
]
datavacCB
CB+shiftshift
0.6 0.7 0.8
dilepton mass mee [GeV]
ρ
0.6 0.7 0.8
ω
J. Weil Dilepton Production at SIS Energies
12C + 12C at 1.0 and 2.0 GeV
10-5
10-4
10-3
10-2
10-1
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dσ
/dm
ee [
mb
/Ge
V]
dilepton mass mee [GeV]
C + C @ 1.0 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.πN Brems.D13(1520)S31(1620)
ππ
10-5
10-4
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1d
σ/d
me
e [m
b/G
eV
]dilepton mass mee [GeV]
C + C @ 2.0 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.πN Brems.D13(1520)S31(1620)
ππ
C+C is a light system, can be described roughly by asuperposition of NN collisions
2 GeV data well described by GiBUU
some discrepancies at 1 GeV (↔ “deuteron problem”?)J. Weil Dilepton Production at SIS Energies
40Ar + 39K 35Cl at 1.76 GeV
10-5
10-4
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
mb
/Ge
V]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.πN Brems.D13(1520)S31(1620)
ππ
]2 [MeV/ceeM
0 0.2 0.4 0.6
)ee
/dM
NN
)/(d
Nee
/dM
AA
) (d
N0
πAA
/N0
πNN
(N 0
1
2
3
4
5
6
7
8
(b)Ar+KCl 1.76A GeVC+C 1A GeV
C+C 2A GeV
Ar+KCl seems to show some excess over NN/CC (∼ factor 3)GiBUU with vacuum SF: discrepancy is smaller than factor 3⇒ we get some enhancement over ’reference cocktail’,but: still room for in-medium effects
J. Weil Dilepton Production at SIS Energies
Conclusions
1 large ∆ and Bremsstrahlung contributions (as claimed byHSD) do not provide a proper solution of the DLS puzzle:they are in conflict with HADES data (pT )!
2 alternative approach: significant yield from N∗ and ∆∗
resonances coupling to the ρ meson provides betterdescription of the data
3 independent analysis with a third model (UrQMD!) would behelpful to settle the discrepancy between GiBUU and HSD(aka “the ∆ crisis”)→ requires readjustments of UrQMD resonance model
4 more work on in-medium modifications needed
J. Weil Dilepton Production at SIS Energies