The effect of quark coalescence on conical signals

We explore the effect of hadronization by partonic coalescence on a “conical” signal at the partonic level. We show that, by transferring partons from a lower to a higher pT , coalescence makes the conical signal stronger and hence less susceptible to thermal smearing, provided the signal is integrated over a large momentum bin and effects such as non-collinearity and a finite Wigner function width are taken into account. We explore the role of this effect in baryon/meson scaling and calculate the effect of resonances decays on such a conical signal. An experimental observation that has aroused quite a lot of recent theoretical interest in the heavy ion community is the detection, in hard-soft particle correlations, of a pattern commonly associated with “conical flow”, [1, 2]. For two-particle hard-soft correlations, it was found that the soft away-side bump, once the flow contribution has been subtracted, exhibits a two peak structure. Such a correlation could, in principle, arise if the energy-momentum deposited by the jet is thermalized and released into sound waves. As was known from the last century, such waves produce a characteristic conical interference pattern, whose angle is related to the speed of sound [3]. Finding such a pattern in heavy ion collisions [4, 5] would confirm the general consensus that the matter created in heavy ion collisions behaves like a “perfect fluid” [6, 7, 8, 9] (though the signal has been observed at energies where flow observables are well below the perfect fluid limit [10]) and provide a way to link two-particle correlations directly to the equation of state. Unfortunately, while the conclusive detection of Mach cones would provide evidence for the perfect fluid behavior, the opposite is not the case. Many hypothetical situations exist where, while the fluid is perfect, the Mach cone will not be observed at the end of its evolution. As shown in [11, 12, 13, 14, 15, 16], two factors strongly go against a conical correlation even in a perfect fluid: Firstly, The thermal broadening in a Cooper-Frye type freeze-out [17], which, to first order in pT U/T (where pT is the transverse momentum of the produced parton, U is the flow component magnitude and T is the temperature) just gives a phenomenologically uninteresting “broad away-side peak”. Hence, to see a cone, one would either have to be in the non-linearized hydrodynamic regime (where what is being seen is not a “true” Mach cone [12, 13, 14, 15, 16]), or at high pT (where the effect of non-thermalized partons can not anymore be neglected). The second factor is the formation of a “diffusion wake” if the parton deposits momentum as well as energy in the medium. The wake contributes to the broad away-side peak. The fact that Mach cones are not an inevitable consequence of the “hydrodynamics+CooperFrye” paradigm, together with their experimental detection, suggests that a hadronization mechanism different from Cooper-Frye freeze-out might have a role in creating the conical signal. Preprint submitted to Nuclear Physics A September 23, 2009 That possibility is, in fact, hinted at by the momentum range where Mach cone signals are seen [2]: At the moment, the consensus is that up to a momentum of 1-1.5 GeV hydrodynamics with a Cooper-Frye freeze-out provides a good description of soft data. At higher momentum, nonequilibrium effects such as quark coalescence [18, 19, 20, 21] may appear. [2] shows that the away-side trigger required for a robust “conical” signal goes well into the coalescence regime, and in fact the away-side signal changes very little between the hydrodynamic and the coalescence regimes. (Note that, if coalescence happens by kinetic energy and not momentum, coalescence can fit elliptic flow (v2) data until a negligible transverse momentum [22]). Thus, one naturally expects that coalescence might play a big role in the generation of conical-like signals, and it is worth investigating what this role might be. This is the purpose of the current work. It is immediately clear that the effect of the simplest collinear coalescence model (the one associated with the v2(pT ) = nv2(p q T/n) scaling of mesons and baryons [18]) is to amplify an already existing conical signal (by a factor of 2 for mesons and 3 for baryons) rather than create one (Fig. 1 (a)). Generally it can be shown that coalescence can enhance locally the angular correlation and from a quark distribution without a double peak structure it can generate two peaks. On the other hand if the quark distribution is exponential (as is the case for a locally thermalized system freezing via Cooper-Frye) in the entire pT range, the weakening of the signal at low pT is balanced with the enhancement due to the shift to the higher hadronic pT (Fig 1(a)), so the hadron distribution from coalescence and Cooper-Frye become very similar. This scaling is broken in non-collinear coalescence (expected from energy-momentum conservation when quark masses are non-negligible, eg in constituent quark coalescence), where the angular distribution has the potential to change (Fig. 1 (b)) . This effect is amplified if one assumes a local, but not δ−function Wigner function [19], so nearby, but not perfectly overlapping quarks (ie, quarks emitted from cells flowing in slightly different directions) can coalesce. For the subsequent calculations, we have used the coalescence Montecarlo, incorporating these features, developed in [21]. The parameters (constituent quark masses, Wigner function etc.) are tuned to reproduce baryon/meson and v2 data [21]. It should be underlined that the effects described here depend on such a “realistic” coalescence model. If coalescence is perfectly collinear, the distributions of the locally thermalized partons, are locally much closer to exponentials, at the weakness of the signal at lower pT exactly cancels out the sharpening of the signal by coalescence. The quark distribution function we used exhibits a generic “conical flow” in a static