We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $μ_π$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $μ_π\neq 0$ generalization of Luscher and Gell-Mann-Oakes-Renner type relations. We pay special attention to the comparison with the conventional kinetic theory approach in the dilute regime, which allows for a check of consistency of our approach. Several phenomenological applications are discussed, concerning chiral symmetry restoration, freeze-out conditions and Bose-Einstein pion condensation.
We extend chiral perturbation theory to study a meson gas out of thermal equilibrium. Assuming that the system is initially in equilibrium below the critical temperature and working within the Schwinger-Keldysh contour technique, we define consistently the time-dependent pion decay functions, the counterparts of the pion decay constants, and calculate them up to next to leading order. The link with curved space-time QFT allows to establish nonequilibrium renormalisation. The short-time behaviour and the applicability to a heavy-ion collision plasma are also discussed in this work.
We apply the formalism of Chiral Perturbation Theory out of thermal equilibrium to describe explosive production of pions via the parametric resonance mechanism. To lowest order the lagrangian is that of the Nonlinear Sigma Model where the pion decay constant becomes a time-dependent function. This model alows for a consistent nonequilibrium formulation within the framework of the closed time path method, where one-loop effects can be systematically accounted for and renormalized. We work in the narrow resonance regime where there is only one resonant band. The present approach is limited to r…
We develop a kinetic equation approach to nonequilibrium pion and sigma meson production in a time-dependent, chiral symmetry breaking field (inertial mechanism). We investigate the question to what extent the low-momentum pion enhancement observed in heavy-ion collisions at CERN - LHC can be addressed within this formalism. In a first step, we consider the inertial mechanism for nonequilibrium production of $σ-$mesons and their simultaneous decay into pion pairs for two cases of $σ$ mass evolution. The resulting pion distribution shows a strong low-momentum enhancement which can be approximat…
In a homogeneous pionic gas system, chemical nonequilibrium process is considered to understand its effect in the expansion processes that are realized immediately after heavy ion collisions. The chemical relaxation time is calculated by incorporating the $π+π\leftrightarrow π+π+π+π$ reaction, which is given in the second order of perturbation in the $σ$ model. The $π+π\leftrightarrow π+π+π+π$ reaction is assumed to be less frequent than the $π+π\leftrightarrow π+π$ scattering that is expected to establish the local equilibrium, and hydrodynamical equation is solved for various initial conditi…
We discuss how the nonequilibrium process of pion production within the Zubarev approach of the nonequilibrium statistical operator leads to a theoretical foundation for the appearance of a nonequilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC.
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 $\fpi$ 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.
We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The \emph{static} limit of critical phenomena is shown to be described by a Ginzburg-Landau effective action including \emph{spatial} gradients. Hence \emph{static} critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. \emph{Dynam…
We explore the extension of chiral perturbation theory out of thermal equilibrium. The pion decay constant becomes then a time-dependent function and we work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to renormalise the model. We discuss the applicability of our approach within a relativistic heavy-ion collision environment.
We consider bosonisation of the low-energy QCD based on integrating the anomaly of the extended chiral (E$χ$) transformation which depends both on pseudoscalar meson and scalar diquark fields as parameters. The relationship between extended chiral and usual chiral anomalies and related anomalous actions is studied. The effective action for the extended chiral field $\U$ depending on complete set of anomalous generators of the E$χ$-transformation is given. The terms of this effective action relevant to interaction of pions and $\bar 3_c$ scalar diquarks are written down explicitly.
The nonequilibrium dynamics of the chiral phase transition expected during the expansion of the quark-qluon plasma produced in a high energy hadron or heavy ion collision is studied in the O(4) linear sigma model to leading order in a large $N$ expansion. Starting from an approximate equilibrium configuration at an initial proper time $τ$ in the disordered phase we study the transition to the ordered broken symmetry phase as the system expands and cools. We give results for the proper time evolution of the effective pion mass, the order parameter $<σ>$ as well as for the pion two point correla…
Nonequilibrium Phenomenology of Identified Particle Spectra in Heavy-Ion Collisions at LHC Energies
Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Center for Advanced Systems Understanding (CASUS)（高级系统理解中心）；Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗斯多夫亥姆霍兹中心）；Institut für Kernphysik, Goethe Universität Frankfurt am Main（法兰克福歌德大学核物理研究所）；Institute of Physics, University of Rostock（罗斯托克大学物理研究所）
We discuss two-pion correlations as a possible experimental probe into disoriented chiral condensates. In particular, we point out that the iso-singlet squeezed states of the BCS type have peculiar two-particle correlations in the back-to-back and the identical momentum configurations which should be detectable experimentally. We motivate the examination of the squeezed state by showing that such state naturally appears in a final stage of nonequilibrium phase transitions via the parametric resonance mechanism proposed by Mrówczyński and Müller.
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via…
The effective theory of an open boson or fermion system is studied, which evolves out of equilibrium with time-dependent Hamiltonian $\hat{H}(t)$. A measure of nonequilibrium temperature for the open system evolving from an equilibrium is proposed as the time-averaged energy expectation value $T(t) = T_i(\bar{< \hat{H} (t) >_Ψ}/ \bar{< \hat{I} (t) >_Ψ})$, where $\hat{I} (t)$, the action operator, satisfies the quantum Liouville-von Neumann equation and determines the true density operator. It recovers the result for the adiabatic (quasi-equilibrium) and nonadiabatic (out of equilibrium) evolut…
Charged-pion decay offers many opportunities to study Lorentz violation. Using an effective field theory approach, we study Lorentz violation in the lepton, W-boson, and quark sectors and derive the differential pion-decay rate, including muon polarization. Using coordinate redefinitions we are able to relate the first-generation quark sector, in which no bounds were previously reported, to the lepton and W-boson sector. This facilitates a tractable calculation, enabling us to place bounds on the level of $10^{-4}$ on first-generation quark parameters. Our expression for the pion-decay rate ca…
In this work we reveal that the inside-outside dynamic model for the production of fermion-antifermion pair (or quark-antiquark in QCD), is an out of equilibrium process. Properties of a complex system as the self-similarity and the critical point of a continuous phase transition in equilibrium appear. In this work we show that this is accomplished imposing a type of mapping process through a self-composition operator on a QED_2 bosons (or pions) field.
We discuss the production of photon-pion and pion pairs with a large invariant mass at collider energies. We present a study based on a perturbative QCD calculation at full next-to-leading order accuracy, implemented in the computer programme DIPHOX. We give estimations for various observables, which concern the reducible background to the Higgs boson search in the channel H --> gamma gamma, in the mass range 80-140 GeV at the LHC. We critically discuss the reliability of these estimates due to our imperfect knowledge of fragmentation functions at high z and a subtle interplay between higher o…
The implications of the hidden, spontaneously broken symmetry for the properties of the sound waves of a solid are analyzed. Although the discussion does not go beyond standard wisdom, it presents some of the known results from a different perspective. In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.
We consider right handed neutrino emission from charged and neutral pion condensate matter likely to be present in the supernova core associated with SN 1987 A. This is used to constrain the strength of right handed interaction and we get excluded range of values for the right handed $W$ boson and extra neutral $Z'$ boson masses. For vanishing $W_L-W_R$ mixing we obtain $ (1.3-1.8)\,M_{W_L} \,\approx \leq\,M_{W_R} \, \leq\approx 100\, M_{W_L} \, {\rm and}\, (1.3-1.8)\,M_{W_L}\, \approx \leq \, M_{N'}\,\leq\approx \,225 \,M_{W_L}$
Based on the 2PI quantum effective action of the linear sigma model with constituent quarks, we develop a transport approach to study systems out of equilibrium. In particular, we focus on the chiral phase transition as well as the critical point, where nonequilibrium effects near the phase transition give rise to critical behavior such as the fluctuation of the baryon number density. Predictions for long-range correlations and fluctuations of observables in our model could be used to study fundamental properties of the QCD phase transition. In the previous version of our transport model the c…
The behaviour of pseudoscalar mesons within the SU(3)PNJL-like models is considered for finite T and $μ_B$. We compare the pole approximation (Breit-Wigner) with the Beth-Uhlenbeck approach. We evaluate the $K/π$ ratios along the phase transition line in the T-$μ_B$ plane with constant and $T/μ_B$-dependent pion and strange quark chemical potentials. Using the model, we can show that the splitting of kaon and anti-kaon masses appears as a result of introduction of density and this explains the difference in the $K^+/π^+$ ratio and $K^-/π^-$ ratio at low $\sqrt{s_{NN}}$ and their tendency to th…
A model has been proposed in which neutral scalar particles chi, of mass 1-10 MeV, annihilate through the exchange of a light vector boson U, of mass 10-100 MeV, to produce the 511 keV line observed emanating from the center of the galaxy. The chi interacts weakly with normal matter and is a viable dark matter candidate. If the U-boson couples to quarks as well as to electrons, it could enhance the branching ratio for the rare decay pi0 -> e+e-. A recent measurement by the KTeV Collaboration lies three standard deviations above a prediction by Dorokhov and Ivanov, and we relate this excess to …
The two-pion correlation function can be defined as a ratio of either the measured momentum distributions or the normalized momentum space probabilities. We show that the first alternative avoids certain ambiguities since then the normalization of the two-pion correlator contains important information on the multiplicity distribution of the event ensemble which is lost in the second alternative. We illustrate this explicitly for specific classes of event ensembles.
Chiral symmetry breaking in QCD leads to the emergence of pions as Goldstone bosons. Their existence in turn affects the Green functions of the theory. Here we study the effect of pion corrections on the light quark's Green function in Feynman gauge using the framework of Gribov's approach to the Dyson-Schwinger equation.
We investigate the structure of constituent quarks and study implications for quark distribution functions of hadrons. Constituent quarks are constructed by dressing bare quarks with Goldstone bosons using the chiral quark model. We calculate resulting corrections to the twist-2 structure functions $f_1(x)$, $g_1(x)$ and $h_1(x)$. The Goldstone boson fluctuations produce a flavor asymmetry of the quark distribution in the nucleon in agreement with experimental data. They also generate significant depolarization effects which reduce the fraction of the nucleon spin carried by quarks. Correction…
We construct from first principles a perturbative framework for studying nonequilibrium quantum-field systems that include gauge bosons. The system of our concern is quasiuniform system near equilibrium or nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. No further approximation is introduced. We construct a gauge-boson propagator, with which a well-defined perturbative framework is formulated. In the course of construction of the framework, we obtain the generalized Boltzmann equation (GBE) that describes the evoluti…
Instead of the fermion-fermion scattering which identifies the BCS-BEC crossover in cold atom systems, boson-boson scattering is measurable and characterizes the BCS-BEC crossover at quark level. We study $π$-$π$ scattering in a pion superfluid described by the Nambu--Jona-Lasinio model. We found that the scattering amplitude drops down monotonically with decreasing isospin density and finally vanishes at the boundary of the phase transition. This indicates a BCS-BEC crossover in the pion superfluid.
Multiparticle boson states, proposed recently for 'independently' emitted pions in heavy ion collisions, are reconsidered in standard second quantized formalism and shown to emerge from a simplistic chaotic current dynamics. Compact equations relate the density operator, the generating functional of multiparticle counts, and the correlator of the external current to each other. 'Bose-Einstein-condensation' is related to the external pulse. A quantum master equation is advocated for future Monte-Carlo simulations.
We discuss a consistent treatment of the light-front gauge-boson and meson wave functions in the analyses of the generalized parton distributions(GPDs) and the scattering amplitudes in deeply virtual Compton scattering(DVCS) for the pion. The continuity of the GPDs at the crossover, where the longitudinal momentum fraction of the probed quark is same with the skewedness parameter, and the finiteness of the DVCS amplitude are ensured if the same light-front radial wave function as that of the meson bound state wave function is used for the gauge boson bound state arising from the pair-creation(…
We study chiral symmetry restoration by analyzing thermal properties of QCD's (pseudo-)Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In the chiral limit, the pion and its partner sigma degenerate at the critical temperature $T_c$. At $T \gtrsim T_c$, it is found that the pion rapidly dissociates, which sign…
We show that there exist two types of universal phenomena for three-boson systems with isospin degrees of freedom. In the isospin symmetric limit, there is only one universal three-boson bound state with the total isospin one, whose binding energy is proportional to that of the two-boson bound state. With large isospin symmetry breaking, the standard Efimov states of three identical bosons appear at low energies. Both phenomena can be realized by three pions with the pion mass appropriately tuned in lattice QCD simulations, or by spin-one bosons in cold atom experiments. Implication to the in-…
We calculate the volume dependence of the ground-state energy of n identical bosons with short-range repulsive interactions in a periodic spatial volume of side L, up to and including terms of order 1/L^6. With this result, Lattice QCD calculations of the ground-state energies of three or more pions will allow for a systematic extraction of the three-pion interaction at this order in the volume expansion.
We construct exact solutions of BPS pion domain walls in the four-dimensional $\mathcal{N}=1$ supersymmetric SU(N) chiral Lagrangian with pion masses introduced via linear and quadratic superpotentials. The model admits N discrete vacua in the center of SU(N) for the linear superpotential. In addition to the latter, new vacua appear for the quadratic superpotential. We find that the domain wall solutions of pions (Nambu-Goldstone bosons) that interpolate between a pair of (pion) vacua preserve half of supersymmetry. Contrary to our expectations, we have not been able to find domain walls invol…
We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $σ$ oscillations, which may be appropriate for the late …
The preliminary results of PIBETA experiment strongly suggest the presence of non V-A anomalous interactions in the radiative pion decay. Without a guiding idea about the nature of these new interactions it is very difficult to interpret and fit experimental data. We assume that they arise as a result of the exchange of new intermediate chiral bosons which interact anomalously with matter. Their mixing with W-bosons leads effectively to a small anomalous weak moment for W. Based on these assumptions, we show that the most general form of the radiative pion decay rate can be parametrized by thr…
The one solitary boson exchange potential (OSBEP) is used to evaluate observables of NN elastic scattering below pion threshold. In this approach, we use a nonlinear model of self-interacting mesons as a substitution for the commonly used phenomenological form factors. NN data support an empirical scaling law between the pion and other meson fields, which suggests a link to QCD and significantly reduces the number of parameters in the boson exchange potential. The analysis of np and pp observables distinguishes the model by its fit and few adjustable parameters. An outlook to apply OSBEP in pi…
The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.
Production of single neutrinos as well as neutrino-antineutrino pairs by photons interacting with pseudo Nambu-Goldstone bosons is studied within the Standard Model. The corresponding cross sections are found analytically. The energy loss due to neutrino emission in a thermal plasma of photons and pions is calculated. It is shown that the obtained neutrino emissivity may be significantly enhanced in hot and dense matter due to in-medium modification of the pion decay constant. Phenomenological consequences for ultrarelativistic heavy-ion collisions and astrophysics are discussed.
Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, s…
We argue that the $125 GeV$ "Higgs" particle is unlikely to arise as a fermion- antifermion composite if the underlying dynamics is a vectorial gauge theory. The reason is that the lightest scalar in such theories is heavier than the lightest pseudo-scalar with the mass difference being fixed by the scale of the theory. LHC searches suggest that the scale of any new physics, including that of a putative new theory dynamically generating the 125 GeV "Higgs" particle, is relatively high $\sim{(1/2TeV-1TeV)}$. Also the LHC analysis suggests that it is {\it scalar} namely $J^P = 0^+$ rather than p…
At finite temperature, the Nambu-Goldstone bosons of a spontaneously broken chiral symmetry travel at a velocity $v < 1$. This effect first appears at order $\sim T^4$ in an expansion about low temperature, and can be related to the appearence of two distinct pion decay constants in a thermal bath. We discuss some consequences on the thermodynamics of a gas of massless pions.
We investigate how the CP quantum numbers of a neutral Higgs boson or spin-zero resonance, produced at the CERN Large Hadron Collider, can be determined in its tau-pair decay mode. We use a method developed in an earlier paper based on the distributions of two angles and apply it to the major 1-prong tau decays. We show for the resulting dilepton, lepton-pion, and two-pion final states that appropriate selection cuts significantly enhance the discriminating power of these observables. From our analysis we conclude that, provided a Higgs boson will be found at the LHC, it appears feasible to co…
In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the effic…
The off--shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu--Jona-Lasinio model with a gauge--invariant proper--time cutoff. The slope of the pion form factor with respect to the pion 4--momentum is found to be equal to the on--shell pion charge radius in the chiral limit. The off--shell slope of the $K^0$ form factor is zero, that of the $K^\pm$ about 15\% smaller than that of the pion. We compare our results with those of a recent calculation in chiral perturbation theory.
Dynamical chiral symmetry breaking (DCSB) is one of the keystones of low-energy hadronic phenomena. Dyson-Schwinger equations provide a model-independent quark-level understanding and correlate that with the behaviour of the pion's Bethe-Salpeter amplitude. This amplitude is a core element in the calculation of pion observables and combined with the dressed-quark Schwinger function required by DCSB it yields a valence-quark distribution function for the pion that behaves as (1-x)^2 for x~1, in accordance with perturbative analyses. This behaviour can be verified at contemporary experimental fa…
Magnetic field effect on pion superfluid phase transition is investigated in frame of a Pauli-Villars regularized NJL model. Instead of directly dealing with charged pion condensate, we apply the Goldstone's theorem (massless Goldstone boson $π^+$) to determine the onset of pion superfluid phase, and obtain the phase diagram in magnetic field, temperature, isospin and baryon chemical potential space. At weak magnetic field, it is analytically proved that the critical isospin chemical potential of pion superfluid phase transition is equal to the mass of $π^+$ meson in magnetic field. The pion s…
A succinct review of the QCD gap equation and dynamical chiral symmetry breaking; their connection with Bethe-Salpeter equations and resolving the dichotomous nature of the pion; the calculation of the pion's valence-quark distribution; and first results for the pi-exchange contribution to the gamma N -> omega N cross-section, which is important in the search for missing nucleon resonances.
We derive expression for the large b_perp asymptotic of the 3D parton distributions q(x,b_perp) in the pion. The asymptotic depends exclusively on the mass scales F_pi and m_pi. Therefore it provides us with a nice example of a strict non-perturbative result for the partonic structure of Nambu-Goldstone bosons in QCD. Analyzing the x-dependent pion transverse radius we reveal a new phenomenon of "chiral inflation"-- in the parametrically wide region of Bjorken x (m_pi^2/(4 pi F_pi)^2 << x << 1) the pion radius grows exponentially fast with the rapidity eta=ln(1/x). We show that the partons in …
In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the effic…
The conceptual issues of low-energy baryon physics are discussed. In particular, a comparison between the naive one gluon exchange model for the interaction between constituent quarks in hadrons and the Goldstone boson exchange picture is made. The "defects" of the Goldstone boson exchange model for baryons, indicated by Isgur are examined in detail. {\it All} of the purported ``defects'' are shown to lack a valid basis.
Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature $T$ and baryochemical potential $μ_B$. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the $T-μ_B$ plane as a proxy for the chemical freezeout line, whereby the variable $x=T/μ_B$ is introduced that corres…
The possibility of pion--pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans--Rashid transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two--particle propagator. In bose systems there exists a second, lower critical temperature, associated with the appearance of the single--particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usua…
In a Poincare'-covariant vector-boson-exchange theory, the pion possesses components of pseudovector origin, which materially influence its observable properties. For a range of such quantities, we explore the consequences of a momentum-independent interaction, regularised in a symmetry-preserving manner. The contact interaction, whilst capable of describing pion static properties, produces a form factor whose: evolution for Q^2>0.17GeV^2 disagrees markedly with experiment; and asymptotic power-law behaviour conflicts strongly with perturbative-QCD.
