Characterizing quark gluon plasma by dilepton interferometry
aa r X i v : . [ nu c l - t h ] J a n Characterizing quark gluon plasma bydilepton interferometry
Payal Mohanty, Jan-e Alam and Bedangadas Mohanty
Variable Energy Cyclotron Centre, 1/AF, Bidhan Nagar, Kolkata - 700064,INDIA
Abstract
The Hanbury-Brown-Twiss (HBT) radii have been calculated from the two particlecorrelation functions with virtual photons produced in the collisions of two nucleiat ultra-relativistic energies. We show that the variation of the HBT radii with theinvariant mass of the virtual photon can be used to characterize and distinguishthe hadronic as well as the partonic phase that might have produced initially in thecollisions. It has been illustrated that the non-monotonic variation of the HBT radiiwith invariant mass provides an access to the development of collective flow in thesystem.
Key words:
Heavy ion collision, quark gluon plasma, photons, dileptons.
PACS:
The aim of the nuclear collisions at ultra-relativistic energies is to create and study- a state of matter, where quarks and gluons are dislocated from individual hadronsand make an excursion over a nuclear volume - such a phase of matter is called quarkgluon plasma (QGP). Several probes - both electromagnetic (EM) and hadronic havebeen proposed for the diagnostics of QGP. The electromagnetically interacting probes(real and virtual photons) has the advantage over the hadronic probes because oftheir nature of interaction. The EM probes has mean free path much larger than thesize of the system as a consequence they leave the system without re-scattering andhence can transmit the source information very efficiently [1]. However, photons andlepton pairs can be produced from both the partonic as well as hadronic phases [2].As a consequence the disentanglement of the contribution for the QGP still remainsa big challenge.In case of EM probes- dilepton has the advantage over the real photons. The photonswith low transverse momentum ( k T ) from the hadronic phase may receive largetransverse kick due to radial flow and consequently appear as high k T photons.These photons can mingle with the the contributions from the high temperature QGP Preprint submitted to Elsevier Science 20 November 2018 hase, making the detection of photons from QGP difficult. However, for dileptonsthere are two kinematic variables available - the k T and the invariant mass ( M ).While the k T spectra of dilepton is affected by the flow, the k T integrated M spectraremains unchanged. This suggests that a careful selection of k T and M windows willbe very useful to characterize the QGP and the hadronic phases.The interferometry of the dilepton pairs actually reflect correlation between twovirtual photons, the analysis then concentrates on computing the Bose-Einstein cor-relation (BEC) function for two virtual photons which can be defined as, C ( ~k , ~k ) = 1 + [ R d x ω ( x, K ) cos(∆ α )] + [ R d x ω ( x, K ) sin(∆ α )] P ( ~k ) P ( ~k ) (1)where k i is momentum of the individual photon, K = ( k + k ) /
2, ∆ α = α − α , α i = τ M iT cosh( y i − η ) − rk iT cos( θ − ψ i ), M iT = q k iT + M is the transverse massand ω ( x, K ) is the source function related to the thermal emission rate of the virtualphotons per unit four volume (see [3,4] for details).For the space time evolution of the system relativistic hydrodynamical model withcylindrical symmetry [5] and boost invariance along the longitudinal direction [6]has been used. For a system undergoing isentropic expansion, the initial tempera-ture ( T i ) and proper thermalization time ( τ i ) of the system may be constrained bythe measured hadronic multiplicity, dN/dy ∼ T i τ i . Here we have taken T i = 290MeV and τ i = 0 . T ch =170 MeV) and kinetic ( T fo =120 MeV) freeze-out temperatures are fixed by theparticle ratios and the slope of the k T spectra of hadrons [8]. With all these ingre-dients the correlation function C has been evaluated for different invariant masswindows ( h M i = ( M + M ) / q side and q out [3] which are related to transverse momentum of individual pair. Oncethe correlation function for the (time like) virtual photon is calculated, the sourcedimensions can be obtained by parameterizing it with the empirical (Gaussian) form: C = 1 + λ − R i q i ) . (2)where the subscript i stand for out and side . In Eq. 2 λ represents the degree ofchaoticity of the source. Deviation of λ from 1 will indicate the presence of non-chaotic sources.The R s ide , radius corresponding to q side is closely related to the transverse size ofthe system and considerably affected by the collectivity and the R o ut , radius corre-sponding to q out measures both the transverse size and duration of particle emission[9,10]. The R s ide shows non-monotonic dependence on h M i (Fig. 1a). It can be shownthat R side ∼ / (1 + E c ollective /E t hermal ). With the transverse expansion the radial size2
We are grateful to Tetsufumi Hirano for providing us the hadronicchemical potentials. We thank Nu Xu for very useful discussions. J A and P Msupported by DAE-BRNS project Sanction No. 2005/21/5-BRNS/2455 and B Msupported by DAE-BRNS project Sanction No. 2010/21/15-BRNS/2026.
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