- Email: [email protected]
Energy loss of quarks in deconfined matter at RHIC: photon-tagged jets, single electron and dilepton spectra from open charm
Nuclear
ELSEVIER
Physm
A715 (2003)
705cm708~ www.elsevier.com/locate/npe
Energy loss of quarks in deconfined matter at RHIC: photon-tagged single electron and dilepton spectra from open charm K. Gallmri&r”*.
B. KBmpferat
aForsclnlngszerltrllm bITP Kiev.
jets,
and O.P. Pavlcnkob
Rossendorf.
PF 510119.
01314 Dresden,
Germany
Tikraine
We report a first attempt, (i) to derive const,raint,s on t,he energy loss of charm quarks in a deconfined medium from the recent PHENIX singlr-electron transverse momentum spectra and (ii) t,o estimate the rosult,ing suppression of dileptons from correlated semilept,onic decays of open charmed mesons. The momentum imbalance of photon-t,aggcd light-quark jet,s is also considered.
1. INTRODUCTION Induced gluon radiation of a fast) quark propagating through a deconfined medium of quarks and gluons causes an energy loss which should considerably modify various observables in relat,ivist,ic heavy-ion collisions as compared to pp collisions. In such a wa? the properties of t,he deconfined medium (part,on composition and space-time dependent densities etc.) can be probed. The QCD based theory of the energy loss has been elaborated by various groups (cf. [l-4] and further references t,herein). As pointed out, in [s] the modified t,ransverse momcntjum spcctjrum of final hadrons at, midrapidity appears as a convolution of the energy loss distribution and the primary spectrum. To enable a comparison wit,h earlier work [6,7], me employ here a simplified version by using a Monte Carlo averaging over traversed pat,h lengths and by shifting the transverse momentum of a quark with energy E and mean free, path X before hadronizing by the mean energy loss according to [2] 0 : L < X or in hadron
AE = -$<
4GP &@JzL
matter
2 : LL,
(1)
where L is the traversed path inside the deconfined medium, L, = ,/m, and i encodes t,he t,ransport propcrt,ies of t,he medium. Remarkable is the apparent, independence of the initial st,atr. i.e. the energy loss depeuds on the temperature TJ at, which the quark leaves the medium. As we show below. however. due t,o lift t,imc and geometrical size> effects. a sensitivit,? OII t,he initial conditions oc(‘urs. *present, tspeaker
address: Institut at QM2002
fiir
0375-9474/03/$ see front matter doi:10.1016/S0375-9474(02)01471-9
Theoretische
0 2003 Elsevier
Physik,
Science
IJniwrsit%t
B.V.
Giessen.
All rights
Germane
reserved.
706c
K. Gallmcister
2. SINGLE
et ~1. /Nucleus
ELECTRONS
FROM
Physics
A715
OPEN
(2003)
CHARM
7OS-708~
DECAYS
Using the PYTHIA version 6.206 with charm quark ulass parameter m, = 1.5 GeV, intrinsic parton transverse 111011i~1iturn distribut,ion m = 2.5 GeV.’ default, Q scale and I< factor K: = 3.7 one gets the charm cross section 0:” = A04 pb at \/sNN = 130 GeV. \Vith t,he hytxid fragmentation scheme (Peterson fragmentation function with E = 0.06) and the electron/positron decay channels of charmed hadrons within PYTHIA the resulting inclusive transverse momentum spectrum agrees fairly well (x$.~,~, = 0.27 (0.39)) with the PHENIS data [8] 11.h cn using the appropriate t,hickness functions TA,~ = 6.2 (22.6) rrlb~’ for minimum bias (cent,ral) collisions: see Figure 1. IO2
w'> a, u go-'
e-
10'
-.**
min bias (x100) central
,
a' 1 o-* F p3
T10' > al loo c2 >r 10-l -0 a' 1o-2 R $.d
zw4 u a' 1o-5
g10m4 75 a' 1o-5
l
loo
-~ 5 1o-6 0
2
1 pT
3
PW
Figure 1. Comparison of our PYTHI.4 result,s with the PHENI,X data [8] (st,atistical and syst,cmatical errors are quadratically added).
-i5
1o-6
0
2
1 pT
3
WV1
Figure 2. Comparison of various energy loss strengths C = 0, 0.2, 0.3, 1.0, 2.0 (from top to bottom) with PHENIX data [8] of central collisions.
To see which space is left for an energy loss we use the above described schmc with B,jorkcn symmetries (transverse radius R,A = 7 fm; no transverse expansion, full chemical equilibrium, initial time 7c = 0.2 fm/c) and initial temperature T, = 550 MeV. The final tcmpcrature Tf depends on the creation point ard propagation direction of the charm quarks; the minimum of Tf is given by the chiral transition t,emperature of 170 MeV. lbTe pararneterize different energy loss strengths by <. Thr, results of our Llonte Carlo harupling are exhibited in Figure 2. Xn optimunl description of the data is accomplished by < = 0.2 0.5. as quantified tq yi,,,f, = 0.32. .0.31. It, t,urns out, however; t,hat larger energy losses are also compatit)lc with data (e.g.. ,yiO-s- = 0.43 (0.76) for < = 1.0 (2.0)). as no energy loss does ( y%,,,f = 0.39 for C = 0). Insofar, the present data do not constrain significantly the energy loss of charm quarks. Our neglect of the dead cone effect [4] and the use of the mean energy loss inst,ead of the proper dist,ribution [5] overestimates the theoretical energy loss. \Ve arc aware that it would be better to compare pp data with central =I=1 data hecause the minimum bias data might be c~ontaminatrd 1)~ energy lossrs.
K. Gallmeister
3. DILEPTON
ct al. /Nuclear
Physics
A 715 (2003)
705c-708~
IOIC
SUPPRESSION
As pointed out in [9] and quant,ificd in [6,10], energy loss effects can suppress the dileptons from charm decays. This is a pot)c:ntially import,ant, effect since these charm cont,ribut,ions compete with the Drell-Yan yield [l l] and hide t,he interesting thermal contribution. Given the above parameterization of the modifications of inclusive single electrons by energy losses of charm quarks, we proceed to estimate the possible suppression of dileptons from correlated semi-leptonic decays of open charm mesons. Our predictions are displayed in Figure 3 for various values of the strength parameter <. Indeed. the dilepton spectra arp quite srnsitivcl t,o energy losses. however, assuming a small loss. as suggrstpd by the above analysis. the corresponding suppression is small. This implies that, wit,hout, subtracting the charm component, in dilepton spectra, an identification and quantificat,ion of the thermal yield will hardly hc possible. Otherwise. as shown in [12] the thermal dilepton contribution allows a vcxry concise c:harac,t,c~rizat,iori of the highly excited strongly interacting rnat,ter. Therefore. it would be very useful t,o get experimental dilepton spectra with id(mtifiird charm contribution.
lo-'
1 1.5
2
2.5
3
3.5
4 4.5
5
5.5
6
1
1.5
M [GeV]
2
2.5
3
3.5
4
Figure 3. Predicted dilepton spectra frorn open charm mesons for various ram&ers of the energy loss within t,hr PHENIX acceptance. T.4.4 = 31/mb. GeV. Left, (right) panel: single-lept,on p’;‘” = 0.5 (1.0) GeV/c. 4. MOMENTUM
IMBALANCE
4.5
5
5.5
6
M [GeV]
OF PHOTON-TAGGED
strengt,h pafi = 200
JETS
Following the suggestion in [13] one can try to extract information on energy losses from phot,on-tagged jets. After the hard reaction y + q + y + q the outgoing phot,on does not suffer any noticeable modification by the ambient medium. Therefore, t,he momentum imbalance p: - (&) ma. y serve as a sensible quantity to characterize the energy loss of the outgoing quark 4 which can be identified in a jet, by selecting a sufficiently narrow cone [7]. Within the above described scheme t,he resulting momentum imbalance is depicted in Figure 4. Clearly seen is the dependence on the initial condition which essentially comes from lifcl time effects. For T, = 550 nlc\’ thtl‘two-regime behavior from Eq. (1) is evidenced. For more details consult [7].
K. Gallnzei.~ter
708c
et al. /Nuclear
T,=55OMeV
Physics
1
.._._. _-..-s ..,.. -..-.-
i-
., ,
T,=45OMeV
/ .. :
A715
(2003)
705c-708~
Figure 4. I\lonirnt~um imbalancc~ of photon-tagged jet,s at, midrapidity for two initial t,emperatures. < = 2 in the encrgy loss sche~nc according t,o Ey. (1) is used (solid curves). The tlot,tctl curves are for a COIlStilIlt energy loss clE/d.x = -1 Gc\./fm.
5. SUMMARY The receruly published [8] inclusive single-clect,ron spectra from open charm decays in Au + Au collisions at fi = I30 GeV seem to point, to a small energy loss. More quantitative conclusions can be drawn after the release of the data of Au + Au collisions at & = 200 GeV which have bett,er statistics and centrality selection [14]; also the pp d&a taken at the same energy will be very helpful for such an analysis. Photon-tagged jet,s are considered very useful t,o accomplish t,he goal of jet tomography of deconfined matter. Discussions with R. Averbeck, ‘I’. .4kiba, and B. Cole are gratefully acknowledged. REFERENCES 1. 2. 3. 1. .5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
hf. Gyulassy, P. Levai. I. Vitev, Phys. Rev. D 66 (2002) 014005. R. Baier, D. Schiff, B.G. Zakharov, Ami. Rev. iYuc1. Part. Sci. 50 (2000) 37; R. Baier; Yu.L. Dokshitzer, AH. Mueller, D. Schiff, Phys. Rev. C 58 (1998) 1706. C.-A. \Viedemann, n’ucl. Phys. B 588 (2000) 303, B 582 (2000) 409. K1.L. Dokshitzrr. D.E. Kharzeev, Phys. Lett. B 519 (2601) 199. R. Baier. Yu.L. Dokshitzer, A.H. Mueller, D. Schiff, JHEP 0109 (2001) 033. K. Gallmeister, B. KCmpfer, O.P. Pavlrnko, Phys. Rev. C 57 (1998) 3276. K. Gallmeister, B. Kampfer. OP. Pavlcnko. Phys. Rev. C 66 (2002) 014908. Ii. .4dcox et al. (PHENX Collaboration), Phys. Rev. Lctt,. 88 (2002) 192303. E.1’. Shurpak. Phys. Rev. C 52 (1997) 961. Z. Lin. R. Vogt, X.-N. Wang, Phys. Rev. C 57 (1998) 899. S. Gavin, L. McGaughey, P.V. Ruuskanen, R. \yogt, Phys. Rev. C 54 (1996) 2606. K. Gallmrister, B. Kampfer, O.P. Pavlenko: C. Gale, Nucl. Phys. .4 688 (2001) 939. X.-N. 1Vang; Z. Huang, I. Sarcevic. Phys. Rev. Lett. 77 (1996) 231. R. A\verbcck and J. Nagle (PHENIS Collaboration), contributions in this volume.
ELSEVIER
Physm
A715 (2003)
705cm708~ www.elsevier.com/locate/npe
Energy loss of quarks in deconfined matter at RHIC: photon-tagged single electron and dilepton spectra from open charm K. Gallmri&r”*.
B. KBmpferat
aForsclnlngszerltrllm bITP Kiev.
jets,
and O.P. Pavlcnkob
Rossendorf.
PF 510119.
01314 Dresden,
Germany
Tikraine
We report a first attempt, (i) to derive const,raint,s on t,he energy loss of charm quarks in a deconfined medium from the recent PHENIX singlr-electron transverse momentum spectra and (ii) t,o estimate the rosult,ing suppression of dileptons from correlated semilept,onic decays of open charmed mesons. The momentum imbalance of photon-t,aggcd light-quark jet,s is also considered.
1. INTRODUCTION Induced gluon radiation of a fast) quark propagating through a deconfined medium of quarks and gluons causes an energy loss which should considerably modify various observables in relat,ivist,ic heavy-ion collisions as compared to pp collisions. In such a wa? the properties of t,he deconfined medium (part,on composition and space-time dependent densities etc.) can be probed. The QCD based theory of the energy loss has been elaborated by various groups (cf. [l-4] and further references t,herein). As pointed out, in [s] the modified t,ransverse momcntjum spcctjrum of final hadrons at, midrapidity appears as a convolution of the energy loss distribution and the primary spectrum. To enable a comparison wit,h earlier work [6,7], me employ here a simplified version by using a Monte Carlo averaging over traversed pat,h lengths and by shifting the transverse momentum of a quark with energy E and mean free, path X before hadronizing by the mean energy loss according to [2] 0 : L < X or in hadron
AE = -$<
4GP &@JzL
matter
2 : L
(1)
where L is the traversed path inside the deconfined medium, L, = ,/m, and i encodes t,he t,ransport propcrt,ies of t,he medium. Remarkable is the apparent, independence of the initial st,atr. i.e. the energy loss depeuds on the temperature TJ at, which the quark leaves the medium. As we show below. however. due t,o lift t,imc and geometrical size> effects. a sensitivit,? OII t,he initial conditions oc(‘urs. *present, tspeaker
address: Institut at QM2002
fiir
0375-9474/03/$ see front matter doi:10.1016/S0375-9474(02)01471-9
Theoretische
0 2003 Elsevier
Physik,
Science
IJniwrsit%t
B.V.
Giessen.
All rights
Germane
reserved.
706c
K. Gallmcister
2. SINGLE
et ~1. /Nucleus
ELECTRONS
FROM
Physics
A715
OPEN
(2003)
CHARM
7OS-708~
DECAYS
Using the PYTHIA version 6.206 with charm quark ulass parameter m, = 1.5 GeV, intrinsic parton transverse 111011i~1iturn distribut,ion m = 2.5 GeV.’ default, Q scale and I< factor K: = 3.7 one gets the charm cross section 0:” = A04 pb at \/sNN = 130 GeV. \Vith t,he hytxid fragmentation scheme (Peterson fragmentation function with E = 0.06) and the electron/positron decay channels of charmed hadrons within PYTHIA the resulting inclusive transverse momentum spectrum agrees fairly well (x$.~,~, = 0.27 (0.39)) with the PHENIS data [8] 11.h cn using the appropriate t,hickness functions TA,~ = 6.2 (22.6) rrlb~’ for minimum bias (cent,ral) collisions: see Figure 1. IO2
w'> a, u go-'
e-
10'
-.**
min bias (x100) central
,
a' 1 o-* F p3
T10' > al loo c2 >r 10-l -0 a' 1o-2 R $.d
zw4 u a' 1o-5
g10m4 75 a' 1o-5
l
loo
-~ 5 1o-6 0
2
1 pT
3
PW
Figure 1. Comparison of our PYTHI.4 result,s with the PHENI,X data [8] (st,atistical and syst,cmatical errors are quadratically added).
-i5
1o-6
0
2
1 pT
3
WV1
Figure 2. Comparison of various energy loss strengths C = 0, 0.2, 0.3, 1.0, 2.0 (from top to bottom) with PHENIX data [8] of central collisions.
To see which space is left for an energy loss we use the above described schmc with B,jorkcn symmetries (transverse radius R,A = 7 fm; no transverse expansion, full chemical equilibrium, initial time 7c = 0.2 fm/c) and initial temperature T, = 550 MeV. The final tcmpcrature Tf depends on the creation point ard propagation direction of the charm quarks; the minimum of Tf is given by the chiral transition t,emperature of 170 MeV. lbTe pararneterize different energy loss strengths by <. Thr, results of our Llonte Carlo harupling are exhibited in Figure 2. Xn optimunl description of the data is accomplished by < = 0.2 0.5. as quantified tq yi,,,f, = 0.32. .0.31. It, t,urns out, however; t,hat larger energy losses are also compatit)lc with data (e.g.. ,yiO-s- = 0.43 (0.76) for < = 1.0 (2.0)). as no energy loss does ( y%,,,f = 0.39 for C = 0). Insofar, the present data do not constrain significantly the energy loss of charm quarks. Our neglect of the dead cone effect [4] and the use of the mean energy loss inst,ead of the proper dist,ribution [5] overestimates the theoretical energy loss. \Ve arc aware that it would be better to compare pp data with central =I=1 data hecause the minimum bias data might be c~ontaminatrd 1)~ energy lossrs.
K. Gallmeister
3. DILEPTON
ct al. /Nuclear
Physics
A 715 (2003)
705c-708~
IOIC
SUPPRESSION
As pointed out in [9] and quant,ificd in [6,10], energy loss effects can suppress the dileptons from charm decays. This is a pot)c:ntially import,ant, effect since these charm cont,ribut,ions compete with the Drell-Yan yield [l l] and hide t,he interesting thermal contribution. Given the above parameterization of the modifications of inclusive single electrons by energy losses of charm quarks, we proceed to estimate the possible suppression of dileptons from correlated semi-leptonic decays of open charm mesons. Our predictions are displayed in Figure 3 for various values of the strength parameter <. Indeed. the dilepton spectra arp quite srnsitivcl t,o energy losses. however, assuming a small loss. as suggrstpd by the above analysis. the corresponding suppression is small. This implies that, wit,hout, subtracting the charm component, in dilepton spectra, an identification and quantificat,ion of the thermal yield will hardly hc possible. Otherwise. as shown in [12] the thermal dilepton contribution allows a vcxry concise c:harac,t,c~rizat,iori of the highly excited strongly interacting rnat,ter. Therefore. it would be very useful t,o get experimental dilepton spectra with id(mtifiird charm contribution.
lo-'
1 1.5
2
2.5
3
3.5
4 4.5
5
5.5
6
1
1.5
M [GeV]
2
2.5
3
3.5
4
Figure 3. Predicted dilepton spectra frorn open charm mesons for various ram&ers of the energy loss within t,hr PHENIX acceptance. T.4.4 = 31/mb. GeV. Left, (right) panel: single-lept,on p’;‘” = 0.5 (1.0) GeV/c. 4. MOMENTUM
IMBALANCE
4.5
5
5.5
6
M [GeV]
OF PHOTON-TAGGED
strengt,h pafi = 200
JETS
Following the suggestion in [13] one can try to extract information on energy losses from phot,on-tagged jets. After the hard reaction y + q + y + q the outgoing phot,on does not suffer any noticeable modification by the ambient medium. Therefore, t,he momentum imbalance p: - (&) ma. y serve as a sensible quantity to characterize the energy loss of the outgoing quark 4 which can be identified in a jet, by selecting a sufficiently narrow cone [7]. Within the above described scheme t,he resulting momentum imbalance is depicted in Figure 4. Clearly seen is the dependence on the initial condition which essentially comes from lifcl time effects. For T, = 550 nlc\’ thtl‘two-regime behavior from Eq. (1) is evidenced. For more details consult [7].
K. Gallnzei.~ter
708c
et al. /Nuclear
T,=55OMeV
Physics
1
.._._. _-..-s ..,.. -..-.-
i-
., ,
T,=45OMeV
/ .. :
A715
(2003)
705c-708~
Figure 4. I\lonirnt~um imbalancc~ of photon-tagged jet,s at, midrapidity for two initial t,emperatures. < = 2 in the encrgy loss sche~nc according t,o Ey. (1) is used (solid curves). The tlot,tctl curves are for a COIlStilIlt energy loss clE/d.x = -1 Gc\./fm.
5. SUMMARY The receruly published [8] inclusive single-clect,ron spectra from open charm decays in Au + Au collisions at fi = I30 GeV seem to point, to a small energy loss. More quantitative conclusions can be drawn after the release of the data of Au + Au collisions at & = 200 GeV which have bett,er statistics and centrality selection [14]; also the pp d&a taken at the same energy will be very helpful for such an analysis. Photon-tagged jet,s are considered very useful t,o accomplish t,he goal of jet tomography of deconfined matter. Discussions with R. Averbeck, ‘I’. .4kiba, and B. Cole are gratefully acknowledged. REFERENCES 1. 2. 3. 1. .5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
hf. Gyulassy, P. Levai. I. Vitev, Phys. Rev. D 66 (2002) 014005. R. Baier, D. Schiff, B.G. Zakharov, Ami. Rev. iYuc1. Part. Sci. 50 (2000) 37; R. Baier; Yu.L. Dokshitzer, AH. Mueller, D. Schiff, Phys. Rev. C 58 (1998) 1706. C.-A. \Viedemann, n’ucl. Phys. B 588 (2000) 303, B 582 (2000) 409. K1.L. Dokshitzrr. D.E. Kharzeev, Phys. Lett. B 519 (2601) 199. R. Baier. Yu.L. Dokshitzer, A.H. Mueller, D. Schiff, JHEP 0109 (2001) 033. K. Gallmeister, B. KCmpfer, O.P. Pavlrnko, Phys. Rev. C 57 (1998) 3276. K. Gallmeister, B. Kampfer. OP. Pavlcnko. Phys. Rev. C 66 (2002) 014908. Ii. .4dcox et al. (PHENX Collaboration), Phys. Rev. Lctt,. 88 (2002) 192303. E.1’. Shurpak. Phys. Rev. C 52 (1997) 961. Z. Lin. R. Vogt, X.-N. Wang, Phys. Rev. C 57 (1998) 899. S. Gavin, L. McGaughey, P.V. Ruuskanen, R. \yogt, Phys. Rev. C 54 (1996) 2606. K. Gallmrister, B. Kampfer, O.P. Pavlenko: C. Gale, Nucl. Phys. .4 688 (2001) 939. X.-N. 1Vang; Z. Huang, I. Sarcevic. Phys. Rev. Lett. 77 (1996) 231. R. A\verbcck and J. Nagle (PHENIS Collaboration), contributions in this volume.