Thermalρandσmesons from chiral symmetry and unitarity

Abstract

We study the temperature evolution of the ρ and σ mass and width, using a unitary chiral approach. The one-loop ππ scattering amplitude in Chiral Perturbation Theory at T = 0 is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the ρ and σ widths. The masses decrease slightly for high T , while the ρππ coupling increases. The ρ behavior seems to be favored by experimental results. In the σ case, it signals chiral symmetry restoration.PACS numbers: 11.10. Wx, 12.39.Fe, 11.30.Rd, One of the outstanding phenomena related to heavy ion collisions is the flatness of the dilepton spectrum near the mass of the ρ meson, which is so clearly visible in many processes involving hadrons and electromagnetic probes. This flatness has been observed by the HELIOS and CERES collaborations [1,2] and has been the subject of widespread discussion. Dileptons and photons provide neat signals of the early stages of the quark-gluon plasma and its subsequent evolution into a hadron gas [3]. In fact, the most credible explanation of the absence of a prominent hill in the dilepton spectrum is a change in the mass and width of the ρ due to its interactions with the hot hadron gas [4,5,6,7]. Since the baryons, with a large forward momentum, have almost escaped the central collision region, this gas is composed mainly of pions. Our aim is to study the thermal evolution of the ρ mass M ρ and width Γ ρ , from the first principles of chiral symmetry and unitarity in ππ scattering.What happens to the ρ in extreme conditions is a hadronic physics problem, involving non perturbative physics and hence difficult to be treated. Prior to this work, a copious number of models and estimations have appeared. In most of them Γ ρ increases with temperature, simply as a consequence of stimulated emission in the pion thermal bath or, equivalently, because the effective phase space increases [8,9]. This behavior is often interpreted as a deconfining effect, or hadron "melting". As for the mass, Vector Meson Dominance (VMD) implies that M ρ changes very little at low temperatures [8,10,11]. As T approaches the critical temperature, earlier works claimed that M ρ increases [8,11,12] but the analysis of experimental dilepton data seems to favor a decreasing behavior [5,7]. Let us remark that in all these works, the ρ is introduced as an explicit degree of freedom and often a dilute pion gas is assumed, so that the thermal effects appear, to leading order, only through the pion distribution function and not through the interaction details. Other approaches include the NJL model [13], where M ρ and Γ ρ slightly decrease (but there is an spurious quark threshold near M ρ ) as well as qq wavefunction analysis in the π channel yielding a decreasing width [14].In this work we will use a thermal treatment of the effective degrees of freedom, the pions in the aftermath of the collision at moderate temperatures. The guiding fundamental principles will be just chiral symmetry and unitarity. We will build on a previous work ...

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

“…This condition holds perturbatively in ChPT [22], and the unitarized amplitude is constructed by requiring thermal unitarity to all orders, based on the physical collision processes occurring in the thermal bath [23,28]. However, it is important to emphasize that thermal unitarity for the full amplitude was not formally proven in those works; in fact, that will be one of the relevant issues discussed in the present work.…”

“…Thus, the chiral restoring behavior in terms of the quark condensate is qualitatively obtained within ChPT [19,20]. Moreover, the introduction of realistic pion interactions by demanding unitarity through the inverse amplitude method (IAM) [21] extended at finite T [22,23] improves ChPT, providing a more accurate description of several effects of interest in a heavy ion environment, such as thermal resonances, transport coefficients and electromagnetic corrections [24,25]. This approach also provides a novel understanding of the role of the σ=f 0 ð500Þ broad resonant state in chiral symmetry restoration, without having to deal with the typical LSM drawbacks.…”

Electromagnetic fields and transport coefficients in a hot pion gas

“…Estimating the deconfinement temperature as (4π/3) r 2 3/2 T d n π (T d ) = 1 with n π the pion density, gives T d ≃ 200 MeV, about 65 MeV lower than using the same estimate with r 2 T =0 [7]. In order to account for the ρ-resonance contribution, we have used unitarized thermal form factors F and partial waves t IJ [5,8] satisfying unitarity in the center of mass frame:…”

Rho meson properties from combining QCD-based models

“…At finite temperature the thermally excited pions change the properties of the ρ-meson. In the framework of the IAM this has been addressed in [52]. However, in addition the underlying quark structure might change at finite temperature.…”