Broken symmetries and dilepton production from gluon fusion in a quark gluon plasma

Broken symmetries and dilepton production from gluon fusion in a quark gluon plasma A. Majumder, 1 A. Bourque, 2 and C. Gale 2 Nuclear Science Division, Lawrence Berkeley National Laboratory 1 Cyclotron road, Berkeley, CA 94720 Physics Department, McGill University 3600 University Street, Montreal, QC, Canada H3A 2T8 (Dated: November 13, 2003) arXiv:hep-ph/0311178 v1 13 Nov 2003 The observational consequences of certain broken symmetries in a thermalised quark gluon plasma are elucidated. The signature under study is the spectrum of dileptons radiating from the plasma, through gluon fusion. Being a pure medium effect, this channel is non-vanishing only in plasmas with spontaneously broken charge conjugation invariance. The emission rates are also sensitive to rotational invariance through the constraints imposed by Yang’s theorem. This theorem is inter- preted in the medium via the destructive interference between various multiple scattering diagrams obtained in the spectator picture. Rates from the fusion process are presented in comparison with those from the Born term. PACS numbers: 12.38.Mh, 11.10.Wx, 25.75.Dw I. INTRODUCTION Experiments are now underway at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory to study nuclear collisions at very high energies. The aim is to create energy densities high enough for the production of a state of essentially deconfined quarks and gluons: the quark gluon plasma (QGP). The QGP is rather short lived and soon hadronizes into a plethora of mesons and baryons. Hence, the existence of such a state in the history of a given collision must likely be surmised through a variety of indirect probes. One of the most promising signatures has been that of the electromagnetic probes: the spectrum of lepton pairs and real photons emanating from a given collision. These particles once produced interact only electromagnetically with the plasma. As a result they escape the plasma with almost no further rescattering and convey information from all time sectors of the collision. In this article, the focus will be on the spectrum of dileptons radiating from a heavy-ion collision. The primary motivation for measuring such a spectrum is the hope that the formation of a QGP in the history of a collision will produce a qualitative or quantitative difference in the observed rates. The measured quantity is the number of dileptons, usually binned according to their invariant mass. It is assumed that this may be estimated by the following factorized form, dN e + e − dM d 4 R t f x + (t) z + (t) z − (t) y + (t) y − (t) dt x − (t) d 3 x d 3 q M d 4 R e + e − 0 (q , q, T (t, x), µ(t, x)). q 0 d 4 q e + e − where, is the number of lepton pairs produced per unit space time, per unit four-momentum, from the unit d 4 q cell at (x, t) in a plasma in local equilibrium (local equilibrium is assumed here). Ostensibly, this depends on the four-momentum of the virtual photon (q 0 , q), the temperature (T ), and the relevant chemical potential (µ). The temperature and relevant chemical potential are, in general, local properties for an expanding plasma and vary from point to point in the plasma as indicated. Finally, the rates from each space time cell have to be integrated over the entire space time evolution of the plasma; where, the spatial limits of the expanding plasma are represented by the variables x − (t), x + (t), y − (t), y + (t), z − (t), z + (t). Many calculations of the dilepton radiation in the deconfined sector have concentrated on the Born term q q → e + e − d 4 R e + e − to estimate the differential rate d 4 q [1, 2]. In those, the focus has usually been more on the effect of the space time evolution of the plasma on the final spectrum. Higher order rates have also become recently available [3]. All these rates essentially consist of vacuum processes that have been generalized to include medium effects of incoming medium particles along with Pauli blocking (Bose enhancement) for outgoing fermions (bosons). They also include thermally generated widths and masses for the propagating particles. However, these rates have non-zero vacuum counterparts. Contrary to these are the pure medium reactions, i.e. processes whose vacuum counterparts are identically zero. Such processes arise as a result of the medium breaking various symmetries which are manifest in the vacuum [14]. The motivation behind exploring such processes is the possibility of observing a spectrum (emanating from these) which