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Charles GaleMcGill
Intermediate-mass lepton pairsIntermediate-mass lepton pairsin relativistic heavy-ion collisionsin relativistic heavy-ion collisions
Charles GaleCharles GaleMcGillMcGill
Charles GaleMcGill
• The physics of (very) hot and dense matter is best explored in the laboratory with relativistic nuclear collisions
• Photons and dileptons are penetrating probes
Introduction and Outline
0.2
0.007s
em
• New physics: collective, many-body effects• Quark-gluon plasma• In-medium modifications
– Modified spectral densities– Chiral symmetry restoration– Mixing effects– Pion dispersion relation
Charles GaleMcGill
Outline, cont’nd
• Experiments (IM): DLS, Helios, NA-38, -50, -60 CERES,WA98, HADES, PHENIX
• Electromagnetic radiation as a tool for hadronic tomography:– Low mass dileptons– Intermediate mass dileptons– Low pT photons– High pT photons– High pT intermediate mass
dileptons
SPS
RHICLHC
Sangyong Jeon’s talk
Charles GaleMcGill
Why? Investigation of the QCD phase diagram
S. B. Ruster et al., PRD 72, 034004 (2005)
F. Karsch, E. Laermann, hep-lat/0305025
Charles GaleMcGill
How? The information carried by EM probes
3
3 3
1Im ( )
(2 ) 1Rd R g
kd k e
Emission rates:
[photons]
6 2
3 3 6 4
2 1 1Im ( )
(2 ) 1Rd R e
E E L kd p d p k e
[dileptons]
•The electromagnetic spectra will be direct probes of the in-medium photon self-energy•They are hard probes:
•EM signals as probes for hadronic tomography
EM 3%s
McLerran, Toimela (85), Weldon (90), Gale, Kapusta (91)
Charles GaleMcGill
The current-current correlatorA model for the hadronic electromagnetic current: VMD
2 2 2e e eJ m m m
g g g
The current-field identity(J. J. Sakurai)
Im Im ImVMD
TT TJ J D Spectral density
The photon/dilepton signal can tell us about the in-medium
spectral densities of vector mesons. Rates need to be integrated
over the space-time history, with some dynamical model
3 3( , ) Im ( , )RdR
E E C p p k Td p d p
D
2 2 2 2 2 2( , )
L TP P k kk T
k m F k m G m k
D
Charles GaleMcGill
What is expected (dileptons)• Low masses receive
significant contribution from radiative decays
• High masses dominated by DY
• Intermediate mass region interesting from QGP perspective, (Shuryak (78), Shor (89))
• Photons: similar story, but featureless spectra
• Experiments: DLS, Helios, TAPS, NA38, -50, WA98, CERES, PHENIX, HADES, NA60
DD
Charles GaleMcGill
Vector Meson Spectral Densities: A Sample Calculation I
Ralf Rapp and Charles Gale, Phys. Rev. C 60, 024003 (1999)
Charles GaleMcGill
The interaction is constrained by basic hadronic phenomenology
Chiral, Massive Yang-Mills:O. Kaymakcalan, S. Rajeev, J. Schechter, PRD 30, 594 (1984)
2 † 2 †
2 L0
1 1Tr Tr M U + U
8 81
Tr Tr2non-minimal terms
L L R R L R R
F D UD U F
F F F F m A A A A
L
Parameters and form factors are constrained by hadronic phenomenology:•Masses & strong decay widths•Electromagnetic decay widths•Other hadronic observables:
• e.g. 1 /a D S
Charles GaleMcGill
Low Masses:Vector Meson Spectral Densities:Hot Meson Gas
The spectral density is flattened
and broadened. Even more with
baryons.
Rapp, Gale (PRC, 99)
Charles GaleMcGill
NA60 Comparison of data to RW, BR and NA60 Comparison of data to RW, BR and Vacuum Vacuum
pT dependence
Sanja DamjanovicQuark Matter 05 (andthis meeting)
New!
New!
Charles GaleMcGill
Two approaches:H. Van Hess, R. Rapp, nucl-th/0603084
T. Renk, J. Ruppert, hep-ph/0603110See J. Ruppert’s talk this aft.
Many-body (in-medium) effects are observed!
Charles GaleMcGill
The intermediate mass sector: some background
• Direct connection to Hard Probes
• Off-shell effects are potentially important for effective hadronic interactions Gao & Gale, PRC 57, 254 (1998)
DD_
DY
NA50Pb-Pb 158 GeV
central collisions
charm DY
A. Shor, PLB 233, 231 (1989)
Charles GaleMcGill
On the dangers of extrapolations…• (a) B. A. Li, Phys.
Rev D 52, 5165 (1995).
• (b) Gomm, Kaymakcalan, Schechter, Phys. Rev. D 30, 2345 (1984).
• (c) Janssen, Holinde, Speth, Phys. Rev. C 49, 2763 (1994).
• (d) Ko, Rudaz, Phys. Rev. D 50, 6867 (1994).
• (e) Xiong, Shuryak, Brown, Phys. Rev. D 46, 3798 (1992).
Gao & Gale, PRC 57, 254 (1998)
But, a lot of data exists!...
Charles GaleMcGill
e+ e- Data: A Wealth of Information
• OLYA
• CMD
• DM-1(2)
• ARGUS
• M3N
•
Charles GaleMcGill
2 2
12
4( / ) ( ) ( ) ( )
2 2em VdR
MT K M T M M MdM
I. Kvasnikova, C. Gale, and D. K. Srivastava, PRC 65, 064903 (2002)
Z. Huang, PL B361, 131 (1995)
Charles GaleMcGill
A larger comparison
• Agreement across theoretical
models
• Those channels are mostly absent from the spectral densities used in comparisons with CERES and the new NA60 data.
Charles GaleMcGill
Li and Gale, PRC (1998)
Intermediate mass data
A. L. S. Angelis et al. (Helios 3), Eur. Phys. J. (1998)
R. Rapp & E. Shuryak, PLB (2000)
Charles GaleMcGill
NA50 Data (cont’nd)
I. Kvasnikova, C. Gale, and
D. K. Srivastava, PRC 2002
•In agreement with multiplicity dependence•Includes detector acceptance & efficiency
(O. Drapier, NA50)
Charles GaleMcGill
NA60 IMR analysis: weighted offset fits (A. David’s talk)
or
Fix Charm contribution to “world average” value
Fix Charm contribution to NA50 p-A expected value
Fit always requires ~2 times more Prompts
1
Extract prompts by fixing Open Charm contribution
Charles GaleMcGill
Low and Intermediate masses: partial summary
• Thermal sources shine in the LMR and IMR. No great sensitivity to the QGP. Intermediate-mass excess is not charm enhancement!
• The new data is precise enough to consider a differentiation of space-time models
• DY? At low M, medium-enhanced multiple parton scatterings might be large (Qiu, Zhang (02), Fries, Schaefer, Stein, Mueller (00). pA measurement.)
2 21 ( )NNAB
AB
ddAB R Q
dQ dQ
Charles GaleMcGill
A recent analysis: (van Hees & Rapp, hep-ph/0603084)
•Sensitive to the space-time modeling:•Still sensitive to the low-mass spectral densities
(4 )R e
Analyses should be redone with those
Charles GaleMcGill
Homework
• Unite (standardize?) space-time modeling [nD hydro, fireballs, transport approaches…].
• The power of the data is fully realized if a general-purpose acceptance filter exists. (On the way!...)
• Chiral symmetry? Still not obvious… An independent access to a1 spectral density is missing. More work on the theory side too. (Urban, Buballa, Hochsch. & Wambach, PRL, 88, 042002 (2002))
Charles GaleMcGill
Charles GaleMcGill
hadrons
q
q
hadrons
leadingparticle
leading particle
Jet-quenching
hadrons
q
q
hadrons
leadingparticle suppressed
leading particle suppressed
Source of energy loss: medium-induced gluonBremsstrahlung (+ elastic scattering?)
Charles GaleMcGill
Quenching = Jet-Plasma interaction. Does this have an EM signature?
qg q
The plasma mediates a jet-photon conversion
Fries, Mueller & Srivastava, PRL 90, 132301 (2003)
Charles GaleMcGill
Photon sources• Hard direct photons
• Fragmentation
• Thermal photons from hot medium
• Jet-photon conversion
• Jet in-medium bremsstrahlung
Charles GaleMcGill
Dilepton sources• Drell-Yan dileptons
• Thermal dileptons
• Jet-virtual photon conversion
Charles GaleMcGill
Energy loss in the jet-photon conversion? Jet bremsstrahlung?
Use the approach of Arnold, Moore, and Yaffe
JHEP 12, 009 (2001); JHEP 11, 057 (2001)
• Incorporates LPM
• Complete leading order in S
• Inclusive treatment of collinear enhancement, photon and gluon
emission
Can be expressed in terms of the solution to a linear integral equation
Charles GaleMcGill
E loss/gain: some systematics
( , )qqg k p k
( ) ( , ) ( , )( ) ( )
( , )2 ( )
q qq qg qg
q qk
gqq
g
dP p d p k k d p kP p k P p
dt dk dt dk dt
d p k kP p k
dk dt
( ) ( , ) ( , )( ) ( )
( , )( ) (2 )
q gg qg gg
q gk
g gqq gg
g
dP p d p k p d p k kP p k P p k
dt dk dt dk dt
d p k dP p k p
dk dt dk dt
•Includes E gain•Evolves the whole distribution function
S. Jeon’s talk
Charles GaleMcGill
Jet characteristics:
Charles GaleMcGill
Time-evolution of quark distribution
The entiredistribution isevolved by the collision Kernel(s)of the FP equation
Turbide, Gale, Jeon, and Moore (2004)
Charles GaleMcGill
Jet-plasma dileptons?• Same basic idea as photons, details are slightly
different:– High pT cut helps with background subtraction
• Go beyond LO, do a HTL analysis4
4 4 2
Im
12 1
R
E
d R
d p M e
2 32
3( ) 3 Tr ( ) ( )
(2 )f
Df n
e d qp e T S q S q p
e
0 0
( )2 ( ) 2 ( )D
q qS q
D q D q
0( )D q iq q A B
Charles GaleMcGill
The thermal “baseline” calculation agrees with that of M. Thoma, C. T. Traxler, Phys. Rev. D 56, 198 (1997)
Im
Charles GaleMcGill
Dileptons from jet-thermal interactions•Jet-thermal as large as DY/heavy quark decay (RHIC)•Jet-thermal still as large as DY. S/B could improve with harder pT cut.•At RHIC, there is a contribution to the IM region•In-medium jet bremsstrahlung will also add to the signal•No heavy quark energy loss•Signal as large as it is for photons
Turbide, Gale, Srivastava, Fries, PRC (2006)
Charles GaleMcGill
But: other signature of jet-photon conversion?
• Jet-plasma photons will come out of the
hadron-blind region. “Optical” v2 < 0
1 2 cos2 n
nT T T T
dN dNv n
p dp d p dp
Turbide, Gale, Fries (PRL 06)
Charles GaleMcGill
Photons from primordial interactions and fragmenting jetsAll photons (NN, frag, jet-photon conv., bremss., Th.)
0 + - - +
Charles GaleMcGill
• v2 from “Isolated photon cut” is negative• Photons associated with a “crowded photon cut” show v2 with changing sign• Same game can be played with dileptons (in progress)• See talk by U. Heinz
Similar story for the LHC
Charles GaleMcGill
Jet-plasma interactions: measurable EM signatures! These are fairly robust with respect to changing temperature & dynamics
• RHIC & LHC:– Jet-plasma interactions: dilepton channel: signal
competes with Drell-Yan (NLO)
Towards a consistent treatment of jets & EM radiation
Intermediate-mass dileptons•New data will put further stringent tests on models, both rates & space-time modeling
Conclusions, part I
Charles GaleMcGill
Conclusions, part II
• Low and mass dileptons: NA60 data can distinguish between models. In-medium effects!
• RHIC/LHC: There are measurable electromagnetic signatures of jet-plasma interaction: those constitute complementary observables to signal the existence of conditions suitable for jet-quenching
• Photon v2: a revealing probe • EM radiation and hard probes: the start of a
beautiful friendship…• EM radiation: change of paradigm
Charles GaleMcGill
• Interested in the techniques discussed here?
• Want to know more?
Found where fine books are sold(July 2006)
Charles GaleMcGill
Charles GaleMcGill
• Chatterjee, Frodermann, Heinz, Srivastava, nucl-th/0511079
Charles GaleMcGill
Jet-plasma photons:
• S. Jeon’s talk
Charles GaleMcGill
New (preliminary) PHENIX Data
Charles GaleMcGill
Charles GaleMcGill
Vector Meson Spectral Densities, II(adding baryons)
R. Rapp & J.Wambach, 1999
Charles GaleMcGill
Soft photons @ RHIC:
• There is a window
Turbide, Rapp & Gale PRC (2004)
Charles GaleMcGill
Same spectral densities:Low mass dileptons and real photons
S. Turbide, R. Rapp, and C. Gale, PRC (2004)
Charles GaleMcGill
• Same spectral densities as low mass dileptons• Same dynamical model; same boundary conditions• Cronin contribution estimated from pA data (E629, NA3)• QGP: small
Turbide, Rapp & GalePRC 2004