Effects of ρ-meson width on pion distributions in heavy-ion collisions

Abstract

The influence of the finite width of ρ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find that the proper treatment of resonances which accounts for their production dynamics encoded in data for partial wave scattering amplitudes can substantially modify spectra of daughter particles originating in their two body decays. In particular, it results in an enhancement of the low-pT pions from the decays of ρ mesons which improves the quantitative description of the pion spectra in heavy ion collisions obtained by the ALICE collaboration at the LHC energy. Recent measurements of the transverse momentum, p T -distributions of identified particles produced in √ s N N = 2.76 TeV Pb+Pb collisions at CERN Large Hadron Collider (LHC) [1] revealed an excess of lowmomentum (p T < ∼ 0.3 GeV) pions over the conventional fluid-dynamical calculations [1-3].It is well known that pions originating from decays of resonances have a steeper p T -distribution than the thermal pions [4], and that they provide a dominant contribution to the spectrum at low transverse momentum. Thus, resonance decays require a particular attention when modeling spectra of particles originating from an expanding thermal fireball.In fluid-dynamical calculations, the interacting hadrons are usually described by the hadron resonance gas (HRG), where the system is modeled as a gas of free hadrons with resonances considered as particles with vanishing widths.This approximation yields reasonable description of the bulk properties of the hadronic medium [5][6][7][8]. The HRG model also provides a very satisfactory description of particle yields measured in heavy ion collisions [9][10][11][12][13][14][15][16][17], as well as the hadronic equation of state and some fluctuation observables obtained in lattice QCD (LQCD) [18][19][20][21][22]. However, as we show in this letter, when p T -differential observables are involved, a more refined approach may be necessary.To properly address the dynamics of hadrons, the effect of resonance width must be included. A conventional way is to impose a Breit-Wigner distribution on the resonance mass. Unfortunately, this approach proves to be too crude in many circumstances. For example, for a broad resonance like the σ meson [23], or the (yet-to-beconfirmed) κ meson [24], the Breit-Wigner approach can give misleading results on the resonance contribution to the thermodynamics.We thus take a more fundamental approach to evaluate the properties of interacting hadrons based on the S-matrix formulation of Dashen, Ma and Bernstein [25]. For elastic scatterings, the interaction part of the partition function reduces to the Beth-Uhlenbeck form for the second virial coefficient, expressed in terms of the scattering phase shifts [26]. In the context of heavy-ion physics, this approach has been applied to evaluate the contribution of πN [5,7,27], ππ [5,23], and πK interactions [5,24] ...

Thermodynamics of the strange baryon system from a coupled-channels analysis and missing states

“…Instead, the current approach suggests multiple mechanisms are at work in the thermodynamic quantities: threshold effects, repulsive channels, coupled-channel effects, and the effect of averaging over many channels. A momentum-differential observable such as the momentum spectrum [49,50] would allow one to differentiate between different models of the effective spectral functions.…”

Finite resonance widths influence the thermal-model description of hadron yields

“…The results should rather be viewed as an illustration of the sensitivity of the thermal model description with respect to the modeling of resonance widths. In that regard it can also be interesting to consider other approaches, such as the ones based on the K-matrix formalism [45,46] or empirical phase shifts [44,47]. Analysis within the latter formalism does show indications for a reduced proton yield [48], similar to the eBW scheme.…”

Pseudorapidity distribution and decorrelation of anisotropic flow within the open-computing-language implementation CLVisc hydrodynamics

“…The hydrodynamic simulations always underestimate low p T pions as compared to the experimental data at LHC. This problem is not solved up to date, but may be partially explained by the missing finite widths of resonances [117]…”