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Electromagnetic Signals and Backgrounds

arXiv:hep-ph/9308319v1 23 Aug 19931HLRZ 53/93Electromagnetic Signals and Backgroundsin Heavy-Ion CollisionsSourendu GuptaHLRZ, c/o KFA J¨ulich, D-52425 J¨ulich, GermanyAspects of the dilepton spectrum in heavy-ion collisions are discussed, with special em-phasis on using lattice computations to guide the phenomenology of finite temperaturehadronic matter. The background rates for continuum dileptons expected in forthcomingexperiments are summarised.

Properly augmented by data from ongoing measurements atHERA, these rates will serve as a calibrating background for QGP searches. Recent resultson the temperature dependence of the hadronic spectrum obtained in lattice computa-tions below the deconfinement transition are summarised.

Light vector meson masses arestrongly temperature dependent. Accurate measurements of a resolved ρ-peak in dimuonspectra in present experiments are thus of fundamental importance.Invited talk at the Quark Matter ’93 Conference, Borl¨ange, Sweden, June 1993

2Electromagnetic Signals and Backgrounds in Heavy-Ion CollisionsSourendu Gupta aaHLRZ, c/o KFA J¨ulich, D-5170 J¨ulich, GermanyAspects of the dilepton spectrum in heavy-ion collisions are discussed, with special em-phasis on using lattice computations to guide the phenomenology of finite temperaturehadronic matter. The background rates for continuum dileptons expected in forthcomingexperiments are summarised.

Properly augmented by data from ongoing measurements atHERA, these rates will serve as a calibrating background for QGP searches. Recent resultson the temperature dependence of the hadronic spectrum obtained in lattice computa-tions below the deconfinement transition are summarised.

Light vector meson masses arestrongly temperature dependent. Accurate measurements of a resolved ρ-peak in dimuonspectra in present experiments are thus of fundamental importance.1.

IntroductionElectromagnetic probes of the quark gluon plasma have been surveyed extensively inthe last few years. I will not repeat the material covered by these excellent reviews [1].Since there has not been much development in the theory of photon signals since the lastQuark Matter meeting, therefore, in the rest of this talk I will concentrate on dileptonsignals and backgrounds.Recall that mass spectra for opposite sign dileptons form a continuum with conspicuousresonances sitting over it.

The cross section is very closely related to a theorist’s favouritequantity— the spectral density of a vector correlation function. All observed resonancescorrespond to flavour singlet vector mesons.

With sufficient mass resolution in the spectrathe fate of each such meson can be seen in the dense and, possibly, thermalised hot matterformed as a result of heavy ion collisions. The ease with which individual resonances canbe isolated and studied by well-designed experiments makes the dilepton signal a toolwhich is neglected only by the most foolhardy physicist.

The continuum itself may beinteresting for various reasons, many of which have been reviewed before.I shall spend most of my allotted pages on scenarios which are built for matter in, ornot far from, thermal equilibrium. The main reason for this emphasis is the ease withwhich theorists can do these computations; but, as reported in this meeting [2,3], there aremodel computations now which indicate a fairly short thermalisation times in heavy-ioncollisions.

Nevertheless, it is necessary to keep in mind that the dense systems formedmay spend a significant fraction of their lifetimes trying to come to a state of equilibrium.If they succeed, they will be doing much better than most people.Uptil now very little work has been done with non-equilibrium scenarios. It should bementioned that Shuryak’s two-step thermalisation model [4] is an attempt at construct-ing a toy model of non-equilibrium phenomena.

Other such attempts are hydrodynamicalshock waves and burning walls [5], swiss-cheese instabilities [6], etc. All these dynamical

3modes can be married to standard dilepton production processes, thereby yielding pos-sible signals of non-equlibrium phenomena. All these modes yield continuum dileptons.However it is known that non-equilibrium dynamics can give rise to narrow peaks in spec-tral densities which have no relation to the equilibrium energy levels of the system [7].This feature seems so generic that one wonders whether such a peak may not be seen inheavy-ion collisions.

The moral I want to draw is that experiments should keep watchfor phenomena which theories cannot yet deal with. Non-equilibrium statistical physicsis a growing new branch of fundamental physics and heavy-ion experiments can makeimportant contributions here.To turn to concrete physics, I shall divide my talk into two major parts.

The first willbe concerned with continuum dileptons in various mass regions; the second with a fewselected resonances. These are discussed in the next two sections.

I shall emphasise theutility of lattice computations to guide phenomenology. The point is that the lattice isa non-perturbative tool to compute matrix elements in QCD which are usually obtainedin models or perturbation theory.

Such work started a year ago [8] and is being pursuedfurther [9].2. The ContinuumContinuum dileptons may be useful as a probe for thermal matter.

All computations ofthe thermal signal to date have been performed in high temperature perturbation theory.Lattice computations give clear evidence for non-perturbative phenomena at temperaturesclose to Tc. It would, therefore, be interesting to obtain non-perturbative lattice estimatesfor the relevant QCD matrix elements at high temperature.

This is now being done; theresults will be available in the near future.I shall speak of the high mass (M>∼5 GeV), low mass (M<∼1 GeV) and the intermediatemass region. Rougly speaking, the intermediate mass region is bounded by the ρ and J/ψresonances.

I shall also speak of the region with M>∼10 GeV as the very-high mass region.This is the region beyond the Υ resonances.2.1. Low mass continuumIn hadron-hadron collisions, the low-mass continuum seems to be understood in termsof several processes— Dalitz pairs, bremsstrahlung from pions etc.

There have been quan-titative attempts to extend this picture to heavy-ion collisions [10]. The low-mass dileptonspectrum may be strongly dependent on properties of thermalised hadronic matter, spe-cially if the thermalisation time turns out to be close to this year’s favourite number— afraction of a fermi.

A first attempt at such estimates now exists [11]. Such computationsneed, quite crucially, input on hadronic masses, widths and interaction strengths at finitetemperatures.

These can be obtained in lattice computations, and I shall summarise arecent computation [9] in the next section.2.2. High mass continuumEven if thermalisation times are short, the high mass continuum cross section consists ofpre-equilibrium processes.

The very high mass region is expected to consist essentially ofDrell-Yan pairs at both the LHC and RHIC energies. At LHC, in the mass range betweenthe Υ and J/ψ, there could be substantial contribution from open bottom production.

4This has yet to be estimated.A state-of-the-art computation of rates for LHC and RHIC was presented in the AachenWorkshop in 1990 [12]. These were based on exponentiated O(αS) cross sections computedin perturbative QCD [13].

Needless to say, these cross sections agree extremely well withdata obtained in the range of energies 19.4 ≤√S ≤640 GeV [14]. There have beentwo advances since the last estimates were made.

One is theoretical— the full O(α2S)Drell-Yan cross section has now been computed [15]. In the high mass region these do notaffect the old estimates.

The second advance is experimental— measurements of structurefunctions in the range x ≤10−3 have now been performed [16]. These have possible effecton estimates of cross sections at LHC energies; and must be taken into account once thedata from HERA has been analysed.The main kinematic features of the Drell-Yan cross section are the following.

Withincreasing√S, the rapidity distribution of Drell-Yan pairs develops a plateau. At RHICenergies this is 3 units wide; at LHC energies the width increases to about 5 units.

Withincreasing√S, at fixed M, the increase in the pT-integrated cross section comes from thegrowth of the perturbative tail in the pT-distribution. A consequence of this is a roughlylinear growth of ⟨p2T⟩with S which occurs for√S>∼50–100 GeV.

Detailed predictions aregiven in [12].It should be remembered that there are no mass scales involved in the QCD predictionsapart from ΛQCD. Thus absolute normalisations of cross sections, ⟨p2T⟩, etc, and theirdependence on√S are predictions.

Approximate Monte-Carlo schemes [2], on the otherhand, contain various mass parameters in momentum cutoffs. Thus absolute normalisa-tions and other such dimensional quantities are fitted at each√S seperately.

As a resultof this, it is necessary that these Monte Carlo generators be compared with a properDrell-Yan estimate and data at all relevant values of√S.2.3. Intermediate mass continuumThe intermediate region of the dilepton continuum comes from a complex mixture ofsources.

This is probably the most poorly understood part of the continuum spectrum. Itis also the most important region for the continuum thermal dilepton signal.

If the initialtemperature is around 250 MeV, then it turns out that the thermal signal vanishes belowthe extrapolated Drell-Yan cross section at M ≈2–2.5 GeV. If the initial temperatureturns out to be about 1 GeV, then this signal may be visible above the same backgroundeven for M ≈5 GeV [17].The extrapolation of Drell-Yan cross sections into this region suffers from two mainambiguities.

The strongest source of uncertainty is in the parton luminosities at smallx. At LHC, the range of masses of interest corresponds to x ≈5 × 10−4.

New physicsmay come into play in this region of kinematics. Structure function measurements nowbeing done at HERA will be crucial for a better understanding of this region.

A seconduncertainty is in the importance of higher order resummed perturbative corrections. Thenew results mentioned above show that these are under control.

I estimate an uncertaintyof a factor of three when extrapolating Drell-Yan results to the intermediate mass rangeat RHIC and LHC energies. The thermal signal turns out to have a much steeper slopethan the Drell-Yan continuum.

Hence this large uncertainty still yields a small error (lessthan 0.5 GeV) in the cutoffmass below which the thermal signal dominates over this

5background.It should be remembered that the Drell-Yan process is only one of the many backgroundsin the dilepton channel in the intermediate mass region. At the higher end of this regiondecays of heavy-flavour quarks give rise to a large dilepton rate.

Such a contribution hadbeen pointed out by Shor long back. A minijet computation [19] for the processA + B →jets →c(b) →leptons,(1)shows that one should expect a large number of single leptons per event.

These combineinto a large dilepton background. This is relatively innocuous, since the rate for unlikesign is the same as for like sign pairs, and thus can be subtracted.

A detailed MonteCarlo study is reportedly in progress [20]. More problematic is the background from thecascade decay of bottom into strange with unlike sign pairs.

This background also needsto be computed.At the lower end of the intermediate mass range the situation is even more complicated.The processes which contribute in heavy-ion collisions have probably not been completelyenumerated yet. NA36 has some new data which they will discuss in this meeting [21].2.4.

The deconfined phaseThe continuum dimuon cross section in the deconfined phase is the signal for whichthe processes discussed in the previous subsections are the background. It is customaryto compute this cross section in high-temperature perturbation theory.

The lattice canfurnish cross checks on this procedure.In recent years several studies of lattice QCD [22,8] have furnished evidence that thehigh temperature phase really consists of deconfined quarks. Thus the primary conditionfor perturbation theory seems to be validated— the degrees of freedom are correctlyidentified.However, there are indications that these quarks, under certain circumstances, havefairly strong self-interactions.

A study [8] has clarified this situation. For mass scalesbelow the Debye screening mass, one could write an effective theory for the quarks in theformSeff =Zd4x"ψ(γµ∂µ + m)ψ +XΓgΓψΓψ2 + · · ·#,(2)where Γ denotes a direct product of spin and flavour matrices, and the sum is over thewhole set of such products.

The ellipsis denote neglected terms of higher mass dimension.From lattice measurements it has been found [8] that, although the effective couplings gin the scalar and pseudo-scalar channels are large, those in the vector and pseudo-vectorchannels are rather small already at temperatures close to Tc. Thus, this observationimplies that perturbative computations of dilepton and photon production rates maybe reliable quite close to the phase transition temperature.

A similiar computation inunquenched QCD is now in progress.For T < 1.2Tc, however, perturbation theory does break down. This is reflected in thegrowth of all the effective couplings as one approaches Tc from above.

It may be possibleto use lattice measurements to obtain the matrix element relevant to photon or dileptoncross sections. Such studies are planned.

63. The ResonancesHeavy-quark resonances have been the subject of concerted study for the last five years.The situation is slowly being clarified; there is new and exciting data this year from theNA38 collaboration [23].

Lighter resonances have been studied in models for many yearsnow. There is exciting news on these from recent lattice computations.3.1.

CharmoniumBased on lattice studies of the static inter-quark potential, heavy-quarkonia have beensuggested as a signal for screening. Screening sets in at the QCD phase transition andthe screening length decreases with increasing T. Consequently, different resonances aresuppressed to different extent under the same physical circumstances.

This year’s resultfrom NA38 [23] shows a strong ET-dependence to the relative suppression between the ψ′and the J/ψ. The data is compatible with estimates given in [24] as well as in [25].Figure 1.The temperature dependence of⟨ψψ⟩, for quenched simulations with Nτ = 4(filled circles) and 8 (squares) and from a 4-flavour simulation with Nτ = 8 (open cir-cles).Figure 2.The temperature dependenceof fπ.Data for T = 0 (open circles)and at finite temperatures (filled circles)T ≈0.75Tc (β = 5.9) and T ≈0.9Tc(β = 5.95).3.2.

The ρ mesonTwo recent studies of quenched lattice QCD have concentrated on hadronic propertiesfor 0 < T < Tc. One of these [8] was done on Nτ = 4 lattices on very large spatial volumes,extending to (8/T)3, at 0.5Tc.

Work now in progress [9] extends these computations toNτ = 8 on spatial volumes of (4/T)3 at 0.75Tc and 0.88Tc. In both these studies the valuesof the quark condensate, ⟨ψψ⟩, pion decay constant, fπ, and the pion and ρ masses havebeen studied.

The temperature dependence of these quantities is obtained by comparisonwith T = 0 measurements at the same lattice spacing.It is known that the quark condensate goes to zero with a discontinuity at Tc in both thequenched [8,9] and 4-flavour [26] theories. In Figure 1 we show the measured temperaturedependence of ⟨ψψ⟩(T)/⟨ψψ⟩(0) (the T = 0 values are taken from [27]).

Two featuresbear comment. First, note that the discontinuity at Tc is similiar in the two cases.

Second,⟨ψψ⟩seems to be relatively temperature independent up to T ≈0.9Tc.

7A non-vanishing quark condensate implies a vanishing pion mass in the chiral limit.The physical pion mass is obtained from the relationm2π = Aπmq. (3)Here mq is the quark mass.

Measurements of Aπ on the lattice, thus give information onthe temperature dependence of the pion mass. Our measurements reveal no change in Aπcompared to the values at T = 0 for temperatures up to 0.9Tc (see Figure 3a).

Consequentto these two facts, the pion decay constant, fπ, shows no change with temperature uptoT = 0.9Tc. This is explicitly shown in Figure 2, using the data of [9] and the T = 0 dataof [28].

In Figures 1 and 2, mass ratios have been used in order to remove most latticeeffects.Figure 3. The dependence of (a) m2π and (b) mρ on mq at T ≈0.9Tc (circles) comparedto data at T = 0 (squares) at the same lattice spacing (β = 5.95).The value of mρ, on the other hand, seems to be quite strongly dependent on the tem-perature.

Measurements show that there is very little shift in the vector meson masses ata temperature of 0.75Tc. Within the errors of measurement, in fact, no shift is discernible.However, at 0.9Tc there is a large temperature dependent shift, visible in Figure 3b.

It isinteresting that a large shift in the mass of the ρ meson occurs already at a temperaturewhere the chiral sector of the theory sees no temperature effect.It should be noted that most phenomenological models of the hadron spectrum and itstemperature dependence emphasise chiral aspects of the theory. Thus the temperaturedependence of the quark condensate is one of the primary objects of study.

The vacuum ofQCD, however, is characterised by many different condensates, some invisible to the chiralsector of the theory. In most phenomenological models, the temperature dependence of,say, the gluon condensate is a secondary quantity, often neglected.

One interpretationof this lattice data is that some of these other condensates have strong temperaturedependence. This would imply a dynamical role for the glue sector which is stronger thanis usually assumed.

Efforts to extract the temperature dependence of at least a few ofthese other condensates are now underway. If the influence of the glue sector is indeedso strong, then the use of an universal chiral theory at finite-temperatures to obtaininformation on vector and pseudo-vector mesons may not be justified.

8The variation of the vector meson mass with the quark mass mq is shown in Figure 3bat a temperature T ≈0.9Tc. For comparison the corresponding data for T = 0 at thesame lattice spacing, β = 5.95 [29], is also shown.

It is seen that the magnitude of thethermal shift is dependent on mq. Thus, the maximum effect is seen for the ρ meson,somewhat less for the ω and φ, and virtually none (at this temperature, at least) for anyheavier meson.

Of course, an accurate determination of the mass shift of a state heavierthan the inverse lattice spacing is difficult.It is interesting to speculate what the effect of differential shifts in the masses of the ρ,ω and φ mesons would be on an experiment like NA38 which cannot resolve these seperatepeaks. An obvious effect would be to broaden this peak.

Further phenomenology mightbe interesting.Figure 4. Local masses for the (a) pseudoscalar and (b) vector mesons at T ≈0.9Tc(β = 5.95) for mq = 0.05 (filled circles), 0.025 (squares) and 0.01 (open circles).

Theestimates and errors are obtained by jack-knife. The lines are explained in the text.We conclude this section with some technical remarks.

The masses reported here wereextracted by global fits to vector and pseudoscalar correlation functions constructed fromlocal sources. The well-known oscillatory behaviour in the vector channel was suppressedby the usual stratagem of defining a correlation function on even sitesG(2z) = 12[G(2z −1) + 2G(2z) + G(2z + 1)].

(4)Local masses were extracted assuming that this correlation function can be described byone mass, i.e., by a single hyperbolic cosine. The global fits were made to a two-massfunctional form by minimising a χ2 functional which took into account the covarianceof the measurements at different seperations.

An useful cross check is to use the fittedfunction to then extract ‘local masses’ to compare with the direct measurement. Such acomparison then checks the validity of the global fits.

Example are given in Figure 4.Acknowledgements: I would like to thank K. Eskola, R. Gavai, S. Gavin, A. Irb¨ack,F. Karsch, B. Petersson, V. Ruuskanen, H. Satz, K. Sridhar and R. Vogt for the discussionsand/or collaborations, the results of which are reflected in this talk.

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