Conference Presentations by Angel Nicola
We have performed a thermal analysis of the light scalar susceptibilities in the context of SU(3)... more We have performed a thermal analysis of the light scalar susceptibilities in the context of SU(3)-Chiral Perturbation Theory to one loop taking into account the QCD source of isospin breaking (IB), i.e corrections coming from m u = m d . We find that the value of the connected scalar susceptibility in the infrared regime and below the critical temperature is entirely dominated by the π 0 − η mixing, which leads to model-independent O(ε 0 ) corrections, where ε ∼ m d − m u , in the combination χ uu − χ ud of flavour breaking susceptibilities.
We present preliminary results on a study about the thermal variation of the charged and neutral ... more We present preliminary results on a study about the thermal variation of the charged and neutral pion masses to one loop, analyzing their electromagnetic difference, in the context of Chiral Perturbation Theory with two flavours, as well as using a light resonance model. We find that the pion mass difference increases for, at least, low and intermediate temperatures, unlike the chiral limit decreasing result. The axial-vector mixing arising from chiral restoration smooths the Debye-screening temperature increase. Taking into account further corrections due to axial and vector resonances, dominated by a 1 and ρ particles respectively, does not change significantly the ChPT prediction.
Papers by Angel Nicola
We analyze quark condensates and chiral (scalar) susceptibilities including isospin-breaking effe... more We analyze quark condensates and chiral (scalar) susceptibilities including isospin-breaking effects at finite temperature T. These include m u Þ m d contributions as well as electromagnetic (e Þ 0) corrections, both treated in a consistent chiral Lagrangian framework to leading order in SUð2Þ and SUð3Þ chiral perturbation theory, so that our predictions are model-independent. The chiral restoration temperature extracted from h "
We describe scalar-pseudoscalar partner degeneration at the QCD chiral transition in terms of the... more We describe scalar-pseudoscalar partner degeneration at the QCD chiral transition in terms of the dominant low-energy physical states for the light quark sector. First, we obtain within model-independent one-loop chiral perturbation theory that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low T. Next, we show that this chiral-restoring behavior for P is compatible with recent lattice results for screening masses and gives rise to degeneration between the scalar and pseudoscalar susceptibilities ð S ; P Þ around the transition point, consistently with an Oð4Þ-like current restoration pattern. This scenario is clearly confirmed by lattice data when we compare S ðTÞ with the quark condensate, expected to scale as P ðTÞ. Finally, we show that saturating S with the =f 0 ð500Þ broad resonance observed in pion scattering and including its finite temperature dependence, allows us to describe the peak structure of S ðTÞ in lattice data and the associated critical temperature. This is carried out within a unitarized chiral perturbation theory scheme which generates the resonant state dynamically and is also consistent with partner degeneration.
We investigate the charged-neutral difference in the pion self-energy at finite temperature T . W... more We investigate the charged-neutral difference in the pion self-energy at finite temperature T . Within Chiral Perturbation Theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T = 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to O(T 2 ) ∼ O(M 2 π ). Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being O(T 2 M 2 π /M 2 R ) with MR the involved resonance masses.
We analyze the isospin-breaking corrections to quark condensates within oneloop SU(2) and SU(3) c... more We analyze the isospin-breaking corrections to quark condensates within oneloop SU(2) and SU(3) chiral perturbation theory including m u � = m d as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the m u � = m d ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.
We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3... more We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3) chiral perturbation theory including mu ≠ md as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the mu ≠ md ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.
International Journal of Modern Physics E, 2007
We present recent results on a systematic method to calculate transport coefficients for a meson ... more We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory. Our method is based on the study of Feynman diagrams with a power counting which takes into account collisions in the plasma by means of a non-zero particle width. In this way, we obtain results compatible with analysis of Kinetic Theory with just the leading order diagram. We show the behavior with temperature of electrical and thermal conductivities and shear and bulk viscosities, and we discuss the fundamental role played by unitarity. We obtain that bulk viscosity is negligible against shear viscosity near the chiral phase transition. Relations between the different transport coefficients and bounds on them based on different theoretical approximations are also discussed. We also comment on some applications to heavy-ion collisions. * [email protected] † [email protected]
We consider the O(N + 1)/O(N ) Non-Linear Sigma Model for large N as an effective theory for low-... more We consider the O(N + 1)/O(N ) Non-Linear Sigma Model for large N as an effective theory for low-energy QCD at finite temperature T , in the chiral limit. At T = 0 this formulation provides a good description of scattering data in the scalar channel and generates dynamically the f0(500) pole, the pole position lying within experimental determinations. Previous T = 0 results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite T and show that it satisfies exactly thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the T = 0 result and we show that one can define a proper renormalization scheme with T = 0 counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behaviour of the f0(500) pole at finite T , which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f0(500) state, in a second-order transition scenario and in accordance with lattice and theoretical analysis. as a derivative and mass expansion L = L p 2 + L p 4 + . . . , where p denotes generically a meson energy scale compared to the chiral scale Λ χ ∼ 1 GeV. The lowest order Lagrangian L p 2 is the Non-linear Sigma Model (NLSM). The use of energy expansions in chiral effective theories is also justified at finite temperature to describe Heavy Ion Physics. Pions are actually the most copiously produced particles after a Heavy Ion Collision and most of their properties from hadronization to thermal freeze-out can be reasonably described within the temperature range where these theories are applicable. Thus, the chiral restoring behaviour in terms of the quark condensate is qualitatively obtained within ChPT . Moreover, the introduction of realistic pion interactions by demanding unitarity through the Inverse Amplitude Method (IAM) [21] extended at finite T 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 . This approach also provides a novel understanding of the role of the σ/f 0 (500) broad resonant state in chiral symmetry restoration, without having to deal with the typical LSM drawbacks. Thus, the unitarized ππ scattering amplitude within ChPT at finite temperature develops a I = J = 0 thermal pole at
Nuclear Physics A
ABSTRACT
Physical review D: Particles and fields
ABSTRACT
We review our recent work on Chiral Lagrangians out of thermal equilibrium, which are introduced ... more We review our recent work on Chiral Lagrangians out of thermal equilibrium, which are introduced to analyse the pion gas formed after a Relativistic Heavy Ion Collision. Chiral Perturbation Theory is extended by letting fπ be time dependent and allows to describe explosive production of pions in parametric resonance. This mechanism could be relevant if hadronization occurs at the chiral phase transition.
The two dimensional (1+1) sine-Gordon model finds many applications in condensed matter physics. ... more The two dimensional (1+1) sine-Gordon model finds many applications in condensed matter physics. These in turn provide an experimental means for the study of topological defects, some of which may have had a huge impact on the early universe. As a first step in trying to exploit this analogy and also others which exist with low-energy QCD, we study bosonisation in the massive Thirring and sine-Gordon models at finite temperature T and nonzero fermion chemical potential µ. Both canonical operator and path integral approaches are used to prove the equality of the partition functions of the two models at T > 0 and µ = 0, as was recently shown. This enables the relationship between thermal normal ordering and path-integral renormalisation to be specified. Furthermore, we prove that thermal averages of zero-charge operators can be identified as long as one uses the usual T = 0 identification between coupling constants. Analysis of the point-split regularised fermion current then leads to the thermal equivalence between sine-Gordon kinks and Thirring fermions. At µ = 0 and T > 0, we show, in perturbation theory around the massless Thirring model, that the bosonised theory is the sine-Gordon model plus an additional topological term which accounts for the existence of net fermion charge excitations (the fermions or the kinks) in the thermal bath. This result generalises that recently obtained for the massless case, and it is the two-dimensional version of the low-energy QCD chiral Lagrangian at finite baryon density. * Proceedings of the talk based on [1] and given by D.
Quark Confinement and the Hadron Spectrum V - Proceedings of the 5th International Conference, 2003
We show the results for the scattering poles associated to the ρ, f 0 , a 0 , K * , σ and κ reson... more We show the results for the scattering poles associated to the ρ, f 0 , a 0 , K * , σ and κ resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.
Nuclear Physics B, 2003
The conductivity of a finite temperature 1+1 dimensional fermion gas described by the massive Thi... more The conductivity of a finite temperature 1+1 dimensional fermion gas described by the massive Thirring model is shown to be related to the retarded propagator of the dual boson sine-Gordon model. Duality provides a natural resummation which resolves infra-red problems, and the boson propagator can be related to the fermion gas at non-zero temperature and chemical potential or density. In addition, at high temperatures, we can apply a dimensional reduction technique to find resummed closed expressions for the boson self-energy and relate them to the fermion conductivity. Particular attention is paid to the discussion of analytic continuation. The resummation implicit in duality provides a powerful alternative to the standard diagrammatic evaluation of transport coefficients at finite temperature. *
Nuclear Physics B, 1999
We study bosonisation in the massive Thirring and sine-Gordon models at finite temperature T and ... more We study bosonisation in the massive Thirring and sine-Gordon models at finite temperature T and nonzero fermion chemical potential µ. For that purpose we use both canonical operator and path integral approaches, paying particular attention to the issues of thermal normal ordering and renormalisation. At T > 0 and µ = 0, the massive Thirring model bosonises to the sine-Gordon model with the same T = 0 identification between coupling constants. We prove that not only the partition functions of the two models coincide, as was recently shown, but also that thermal averages of zero-charge operators can be identified. In particular, analysis of the point-split regularised fermion current then leads to the thermal equivalence between sine-Gordon kinks and Thirring fermions. At µ = 0, T > 0 and working in perturbation theory about the massless Thirring model, we show that the bosonised theory is the sine-Gordon model plus an additional topological term which accounts for the existence of net fermion charge excitations (the fermions or the kinks) in the thermal bath. This result generalises one recently obtained for the massless case, and it is the two-dimensional version of the low-energy QCD chiral Lagrangian at finite baryon density. *
We review recent results on properties of the meson gas relevant for Heavy Ion Collision and Nucl... more We review recent results on properties of the meson gas relevant for Heavy Ion Collision and Nuclear Matter experiments, within the framework of chiral lagrangians. In particular, we describe the temperature and density evolution of the σ and ρ poles and its connection with chiral symmetry restoration, as well as the chemical nonequilibrated phase and transport coefficients.
Physical Review D, 2006
The electrical conductivity of a pion gas at low temperatures is studied in the framework of Line... more The electrical conductivity of a pion gas at low temperatures is studied in the framework of Linear Response and Chiral Perturbation Theory. The standard ChPT power counting has to be modified to include pion propagator lines with a nonzero thermal width in order to properly account for collision effects typical of Kinetic Theory. With this modification, we discuss the relevant chiral power counting to be used in the calculation of transport coefficients. The leading order contribution is found and we show that the dominant higher order ladder diagrams can be treated as perturbative corrections at low temperatures. We find that the DC conductivity σ(T ) is a decreasing function of T , behaving for very low T as σ(T ) ∼ e 2 mπ mπ/T , consistently with nonrelativistic Kinetic Theory. When unitarization effects are included, σ(T ) increases slowly as T approaches the chiral phase transition. We compare with related works and discuss some physical consequences, especially in the context of the low-energy hadronic photon spectrum in Relativistic Heavy Ion Collisions.
Physical Review D, 2014
We investigate the charged-neutral difference in the pion self-energy at finite temperature T . W... more We investigate the charged-neutral difference in the pion self-energy at finite temperature T . Within Chiral Perturbation Theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T = 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to O(T 2 ) ∼ O(M 2 π ). Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being O(T 2 M 2 π /M 2 R ) with MR the involved resonance masses.
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Conference Presentations by Angel Nicola
Papers by Angel Nicola