We investigate chiral symmetry breaking and strong CP violation effects in the phase diagram of strongly interacting matter. We demonstrate the effect of strong CP violating terms on the phase structure at finite temperature and densities in a 3-flavor Nambu-Jona-Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term. This is investigated using an explicit structure for the ground state in terms of quark-antiquark condensates for both in the scalar and the pseudoscalar channels. CP restoring transition with temperature at zero baryon density is found to be a second order transition at $θ= π$ while the same at finite chemical potential and small temperature turns out to be a first order transition. Within the model, the tri-critical point turns out to be $(T_c,μ_c)\simeq(273,94)$ MeV at $θ= π$ for such a transition.
In a constituent quark model at nonzero temperature, the amplitude for $π^0 \rightarrow 2 γ$ vanishes in a chirally symmetric phase, while that for $π^0 σ\rightarrow 2 γ$ does not.
By applying chiral-perturbation-theory methods to the QCD sector of the Lorentz-violating Standard-Model Extension, we investigate Lorentz violation in the strong interactions. In particular, we consider the CPT-even pure-gluon operator of the minimal Standard-Model Extension. We construct the lowest-order chiral effective Lagrangian for three as well as two light quark flavors. We develop the power-counting rules and construct the heavy-baryon chiral-perturbation-theory Lagrangian, which we use to calculate Lorentz-violating contributions to the nucleon self energy. Using the constructed effe…
Chiral restoration phase transition in hot and/or dense hadronic matter is discussed in terms of the BR scaling based on chiral symmetry and scale anomaly of QCD. The precise connection between the scalar field that figures in the trace anomaly and the sigma field that figures in the linear $σ$ model is established. It is suggested that in hot and/or dense medium, the nonlinear $σ$ model linearizes with the help of a dilaton to a linear $σ$ model with medium-renormalized constants. The relevance of Georgi's vector symmetry and/or Weinberg's ``mended symmetry" in chiral restoration is pointed o…
We study the thermodynamics of the Nambu--Jona-Lasinio model with Polyakov loops, where spontaneous chiral symmetry breaking and confinement are taken into account. We focus on the phase structure of the model and explore the susceptibilities associated with corresponding order parameters under the mean-field approximation.
We show that local parity violation due to chirality imbalance in relativistic nuclear collisions can be revealed by measuring the projection of the polarization vector onto the momentum, i.e. the helicity, of final state baryons. The proposed method does not require a coupling to the electromagnetic field, like in the Chiral Magnetic Effect. By using linear response theory, we show that, in the presence of a chiral imbalance, the spin 1/2 baryons and anti-baryons receive an additional contribution to the polarization along their momentum and proportional to the axial chemical potential. The a…
A new mechanism of photon emission in the quark-gluon plasma is proposed. Photon dispersion relation in the presence of the $CP$-odd topological regions generated by the chiral anomaly acquires an imaginary mass. It allows photon radiation through the decay $q\to qγ$ and annihilation $q\bar q\to γ$ processes closely related to the chiral Cherenkov radiation. Unlike previous proposals this mechanism does not require an external magnetic field. The differential photon emission rate per unit volume is computed and shown to be comparable to the rate of photon emission in conventional processes.
I consider parity violation of the chiral symmetry broken vacuum. It is shown that the parity of the true vacuum in the chiral symmetry breaking model is violated. I propose new mechanism of massive neutrino, which the neutrinos have mass in terms of the chiral symmetry breaking. In this mechanism, it may give us new understanding why almost neutrinos have left chirality. Further, NJL model is proposed as alternative phenomenological model of neutrinos.
We investigate chiral symmetry breaking and strong CP violation effects on the phase diagram of strongly interacting matter in presence of a constant magnetic field. The effect of magnetic field and strong CP violating term on the phase structure at finite temperature and density is studied within a three flavor Nambu-Jona-Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term. This is investigated using an explicit variational ansatz for ground state with quark anti-quark pairs leading to condensates both in scalar and pseudoscalar channels. Magnetic field enhances…
The photon self-energy from chirally imbalanced quark matter is evaluated at finite temperature and density using the real time formulation of thermal field theory. The analytic structure is explored in detail exposing the cut structure which corresponds to a variety of physical scattering and decay processes in the medium and their thresholds. The mass of the quarks in the chiral symmetry broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio model. It is found that, in presence of finite chiral chemical potential, the chiral condensate tends to get stronger at low tempera…
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bou…
In a recent paper (arXive:hep-ph/0406125) entitled {\em Parity violation in hot QCD: why it can happen, and how to look for it}, D. Kharzeev argues for the possibility of P- and/or CP- violation effects in heavy-ion collisions, the effects that can manifest themselves via asymmetry in $π^{\pm}$ production with respect to the direction of the system angular momentum. Here we present an experimental observable that can be used to detect and measure the effects.
We examine the isospin violation in the timelike pion form factor near threshold at next-to-leading order in the chiral expansion using the techniques of Chiral Perturbation Theory. This next-to-leading order contribution contains the first nonvanishing isospin violation. This isospin violation is found to be very small near threshold. In particular, the isospin violation at threshold is found to be of order 10^-4, which should be compared with the few percent level seen in the vector meson resonance region.
We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD and discuss the properties of hadronic matter at high density and temperature. As the "dilaton limit" is taken, which drives a system from nuclear matter density to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that as the dilaton limit is approached, the omega-nucleon interaction gets strongly suppressed at high density. This is shown to be a f…
Chiral thermodynamics of charmed mesons is formulated at finite temperature within a $2+1+1$-flavored effective Lagrangian incorporating heavy quark symmetry. The charmed-meson mean fields act as an extra source which breaks the chiral symmetry explicitly. This leads to effective interactions between the light and heavy-light mesons, which intrinsically depend on temperature. Effective masses of the scalar and pseudoscalar charmed-mesons tend to approach each other as increasing temperature, so that the splitting between the chiral partners is reduced. These chiral splittings are shown to be l…
I explain, as simply and pedagogically as I can, recent arguments that the high-temperature baryon number violation rate depends on the electroweak coupling as $Γ= # α_\w^5 T^4$ (up to higher order corrections). This is in contrast to the form $Γ= # α_\w^4 T^4$ that has historically been assumed in discussions of electroweak baryogenesis. I will give a general analysis of the time scale for non-perturbative gauge field fluctuations in hot non-Abelian plasmas.
The arguments for the possibility of violation of P and CP symmetries of strong interactions at finite temperature are presented. A new way of observing these effects in heavy ion collisions is proposed -- it is shown that parity violation should manifest itself in the asymmetry between positive and negative pions with respect to the reaction plane. Basing on topological considerations, we derive a {\it lower} bound on the magnitude of the expected asymmetry, which may appear within the reach of the current and/or future heavy ion experiments.
We explore the phase structure of a chiral model of constituent quarks and gluons implementing scale symmetry breaking at finite temperature and chemical potential. In this model the chiral dynamics is intimately linked to the trace anomaly saturated by a dilaton field. The thermodynamics is governed by two condensates, thermal expectation values of sigma and dilaton fields, which are the order parameters responsible for the phase transitions associated with the chiral and scale symmetries. Within the mean field approximation, we find that increasing temperature a system experiences a chiral p…
We suggest that for QCD in the limit of a large number of colors, N, the axial U(1) symmetry of massless quarks is effectively restored at the deconfining=chiral phase transition. If the deconfining transition is of second order, then the chiral transition is weakly first order. In this case, metastable states in which parity is spontaneously broken appear at temperatures below the phase transition. The production of these metastable states would have dramatic signatures, including enhanced production of eta and eta' mesons, which can decay through parity violating decay processes such as eta …
The recent discoveries by the BaBar and CLEO II collaborations on the splitting between $D_s$ and ${\tilde D}_s$ which exhibited surprises in the structure of heavy-light-quark systems are connected -- via the Harada-Yamawaki "vector manifestation" of hidden local symmetry -- to chiral symmetry restoration expected to take place at some critical temperature $T_c$ in heavy-ion collisions or at some critical density $n_c$ in the deep interior of compact stars, the main theme of this symposium. This unexpected connection exemplifies the diversity of astro-hadronic phenomena discussed in this meet…
We review recent progress in the theoretical description of the violation of discrete space-time symmetries in hadronic and nuclear systems. We focus on parity-violating and time-reversal-conserving interactions which are induced by the Standard Model weak interaction, and on parity- and time-reversal-violating interactions which can be caused by a nonzero QCD theta term or by beyond-the-Standard Model physics. We discuss the origins of such interactions and review the development of the chiral effective field theory extension that includes discrete symmetry violations. We discuss the construc…
We present here the computation of electrical and thermal conductivity by solving the Boltzmann transport equation in relaxation time approximation. We use the $q$-generalized Boltzmann distribution function to incorporate the effects of non-extensivity. The behaviour of these quantities with changing temperature and baryochemical potential has been studied as the system slowly moves towards thermodynamic equilibrium. We have estimated the Lorenz number at NICA, FAIR and the top RHIC energies and studied as a function of temperature, baryochemical potential and the non-extensive parameter, $q$…
The emergence and importance of hidden local symmetry in the structure of hadrons under extreme conditions is discussed. The topics covered are the potentially important role played by an infinite tower of vector mesons encoded in holographic dual QCD (or AdS/QCD) in chiral dynamics of mesons and baryons, in the vector dominance and its violation in EW response functions and the presence of the vector manifestation fixed point and its influence on the properties of hadrons in hot temperature (i.e., in relativistic heavy ion collisions) and in dense matter (i.e., in compact stars). Also discuss…
It is possible that isospin violating dynamical effects are amplified due to coherence if a disoriented chiral condensate (or other source of a coherent pion state) is formed in a heavy ion collison. It is shown explicitly that altering the isospin of the coherent state by order of one unit can change the number of $π^0$'s in the condensate by some finite fraction of the total number. A possible signature of such amplified isospin violating effects is that the ratio of neutral to total low $p_T$ pions averaged over many events may differ markedly from 1/3. Such a signal would not be washed out…
The photoproduction rate of pentaquark $Θ^+$ is calculated in a hot and dense medium. At high temperature and density, due to the restoration of chiral symmetry, photoproduction energy threshold is increased. Above the thresold the production cross section is strongly enhanced.
We study the $ηN$ interactions in the hot and dense isospin asymmetric nuclear matter using two different approaches. In the first approach, the in-medium mass and optical potential of $η$-meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry breaking term and range terms in the $ηN$ interaction Lagrangian density. In the second scenario, the conjunction of chiral perturbation theory and chiral SU(3) model is employed. In this case, the next-to-leading order $ηN$ interactions are evaluated from the chiral perturbation theory (ChPT), and the in-medium…
The space of static finite-energy configurations of the electroweak theory admits a ${\bf Z}_{2}$ topological structure. Odd-parity configurations with odd pure-gauge behavior at spatial infinity (S sphaleron, W-Z strings, multisphalerons) mediate rapid $B+L$ violation in the Early Universe. Configurations with even pure-gauge behavior (S$^{*}$ sphalerons, W-Z strings, multisphalerons) are trivial and topologically equivalent to the vacuum.
LHCb has recently reported more than $2σ$ deviation from the Standard Model prediction in the observable $R_{J/ψ}$. We study this anomaly in the framework of a vector leptoquark along with other lepton flavor universality violating measurements which include $R_{K^{(*)}}$, and $R_{D^{(*)}}$. We show that a chiral vector leptoquark can explain all the aforementioned anomalies consistently while also respecting other experimental constraints.
A complete analysis of isospin breaking in $K\to 2π$ amplitudes, including both strong and electromagnetic corrections at next-to-leading order in chiral perturbation theory, has been achieved recently. We discuss the implication of these effects, together with the previously known chiral loop corrections, on the direct CP-violating ratio epsilon'/epsilon.
We investigate the time evolution of a system of quarks interacting with sigma and pion fields starting from an initial configuration consisting of a tube of hot quark plasma undergoing a boost-invariant longitudinal expansion. We work within the framework of the linear sigma model using classical transport equations for the quarks coupled to the mean-field equations for the meson fields. In certain cases we find strong amplifications of any initial pion fields. For large-radius tubes, starting from quark densities that are very close to critical, we find that a disoriented chiral condensate c…
Motivated by the phenomenological scenario of the chiral magnetic effect that can be possibly found in high-energy heavy ion collisions, we study the role of very intense magnetic fields and strong CP violation in the phase structure of strong interactions and, more specifically, their influence on the nature of the chiral transition. Direct implications for the dynamics of phase conversion and its time scales are briefly discussed. Our results can also be relevant in the case of the early universe.
We present recent results from lattice simulations of 2+1 flavors of improved staggered fermions at zero baryon number density near the high temperature crossover. Included are new results from simulations of asqtad fermions at Nt = 12 and a nearly physical Goldstone pion mass and from simulations of HISQ fermions at Nt = 6 and 8. We focus on observables sensitive to chiral symmetry and confinement. A companion HotQCD talk discusses the effects of staggered-fermion taste-symmetry breaking on thermodynamic quantities.
A review of the recent results obtained in the Nambu -- Jona-Lasinio model is given. In particular, the effect of screening of meson fields at finite temperature or density is analyzed and the formulation of a chirally invariant transport theory for quark matter is presented.
We summarize main mechanisms to realize the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, at the critical temperature in hot QCD within the framework of the model based on the hidden local symmetry. Then, we show a recent analysis on the direct photon-pi-pi coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: The VM predicts that the VD is largely violated at the critical temperature.
Non-Abelian gauge theories "live" in a space-time with non-trivial topology that can be characterized by an odd-dimensional Chern-Simons form. In QCD, Chern-Simons form is induced by the chiral anomaly and the presence of topological solutions; it opens a possibility for the breaking of P and CP invariances in strong interactions ("the strong CP problem"). While there is apparently no global P and CP violation in QCD, here I argue that topological fluctuations in hot quark-gluon matter can become directly observable in the presence of a very intense external magnetic field by inducing local P-…
If any violation of Lorentz symmetry exists in the hadron sector, its ultimate origins must lie at the quark level. We continue the analysis of how the theories at these two levels are connected, using chiral perturbation theory. Considering a two-flavor quark theory, with dimension-4 operators that break Lorentz symmetry, we derive a low-energy theory of pions and nucleons that is invariant under local chiral transformations and includes the coupling to external fields. The pure meson and baryon sectors, as well as the couplings between them and the couplings to external electromagnetic and w…
The time-evolution of the magnetic field in hot homogeneous nuclear matter has two qualitatively different stages separated by the sphaleron transition time $τ_c$. At early times the axial chemical potential and the corresponding chiral conductivity $σ_χ$ are slow functions of time. The soft chiral modes $k<σ_χ$ of the magnetic field grow exponentially with time, which is known as the chiral instability. At later times $σ_χ$ fluctuates due to the sphaleron transitions and can be regarded as a random process. It is argued that the average magnetic field is exponentially damped at later times. T…
We discuss various aspects of parity, CP, and time reversal invariances in QCD. In particular, we focus attention on the previously proposed possibility that these experimentally established symmetries of strong interactions may be broken at finite temperature and/or density. This would have dramatic signatures in relativistic heavy ion collisions; we describe some of the most promising signals.
The kinetics of chiral transitions in hot and dense quark matter is studied via a microscopic framework (Nambu-Jona-Lasinio model) and a phenomenological model (Ginzburg-Landau free energy). We focus on the far-from-equilibrium ordering dynamics subsequent to a quench from the massless quark phase to the massive quark phase. The morphology of the ordering system is characterized by the scaling of the order-parameter correlation function. The domain growth process obeys the Allen-Cahn growth law, $L(t)\sim t^{1/2}$. We also study the growth of bubble of the stable massive phase in a background …
We study the effects of CP violation on the nature of the chiral transition within the linear sigma model with two flavors of quarks. The finite-temperature effective potential containing contributions from nontrivial values for the parameter $θ$ is computed to one loop order and their minima structure is analyzed. Motivated by the possibility of observing the formation of CP-odd domains in high-energy heavy ion collisions, we also investigate the behavior of the effective potential in the presence of a strong magnetic background. We find that the nature of the chiral transition is influenced …
The important role played by chiral symmetry and axial anomaly in QCD in nuclear physics is reviewed. Some recent topics on possible chiral restoration in hot and/or dense matter are picked up. We also discuss so called {\em effective} restoration of chiral anomaly hot and/or dense matter, as may be seen in a character change of $η'$ meson.
We calculate the quark self-energy at one-loop level at high temperature, taking into account contributions from both the (chromo)electric scale $gT$ and the (chromo)magnetic scale $g^2T$. While reproducing standard massive excitations due to the electric scale, we uncover a novel massless excitation ascribable to the magnetic scale. The residue of this massless excitation is nonpositive at all temperatures, which consequently gives rise to positivity violation in the quark spectral functions. This demonstrates the profound impact of confinement effects on thermal quark collective excitations,…
It is expected that in a hot QCD system, a local parity-odd domain can be produced due to nonzero chirality, which is induced from the difference of winding numbers carried by the gluon topological configuration (QCD sphaleron). This local domain is called the chiral-imbalance medium characterized by nonzero chiral chemical potential, which can be interpreted as the time variation of the strong CP phase. We find that the chiral chemical potential generates the parity breaking term in the electromagnetic form factor of charged pions. Heavy ion collision experiments could observe the phenomenolo…
We review our recent work on thermal meson properties within the Chiral Perturbation Theory framework. We will focus on the pion electromagnetic form factor, stressing its importance for Relativistic Heavy Ion Collisions. We obtain model-independent predictions (based only on chiral symmetry) such as the temperature dependence of the pion electromagnetic charge radius. Imposing unitarity allows to describe the thermal effects of resonances such as the $ρ$ meson.
We show that the presence of a magnetic monopole in position space gives rise to a violation of the fermion number conservation in chiral matter. Using the chiral kinetic theory, we derive a model-independent expression of such a violation in nonequilibrium many-body systems of chiral fermions. In local thermal equilibrium at finite temperature and chemical potential, in particular, this violation is proportional to the chemical potential with a topologically quantized coefficient. These consequences are due to the interplay between the Dirac monopole in position space and the Berry monopole i…
In the chiral symmetric phase, the polarized instanton--anti-instanton molecule pairing induces a nontrivial repulsive interaction in the iso-scalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration phase, there is a first order phase transition for the spontaneous generation of local CP violation and chiral imbalance. Furthermore, it is found that external magnetic fields will lower the critical temperature for the local CP-odd phase transition and catalyze the chiral imbalance, which destroys the chiral condensate with pairing quarks betw…
Using chiral symmetry we investigate the leading SU(3) violation in light-cone distribution functions phi_M(x) of the pion, kaon, and eta. It is shown that terms non-analytic in the quark masses do not affect the shape, and only appear in the decay constants. Predictive power is retained including the leading analytic m_q operators. With the symmetry violating corrections we derive useful model independent relations between phi_pi, phi_eta, and phi_K. Using the soft-collinear effective theory we discuss how factorization generates the subleading chiral coefficients.
Models of extended gauge mediation, in which large A-terms arise through direct messenger-MSSM superpotential couplings, are well-motivated by the discovery of the 125 GeV Higgs. However, since these models are not necessarily MFV, the flavor constraints could be stringent. In this paper, we perform the first detailed and quantitative study of the flavor violation in these models. To facilitate our study, we introduce a new tool called FormFlavor for computing precision flavor observables in the general MSSM. We validate FormFlavor and our qualitative understanding of the flavor violation in t…
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.
In this article we present the complete resummation of the leading chirally-enhanced corrections stemming from gluino-squark, chargino-sfermion and neutralino-sfermion loops in the MSSM with non-minimal sources of flavor-violation. We compute the finite renormalization of fermion masses and the CKM matrix induced by chirality-flipping self-energies. In the decoupling limit Msusy>>v, which is an excellent approximation to the full theory, we give analytic results for the effective gaugino(higgsino)-fermion-sfermion and the Higgs-fermion-fermion vertices. Using these vertices as effective Feynma…
The effects of the CP violating $θ$ term in the QCD Lagrangian upon low energy hadronic phenomenology are reconsidered. Strong CP violating interactions among Goldstone bosons and octet baryons are incorporated into an effective chiral Lagrangian framework. The $θ$ term's impact upon the decays $η\toππ$ and $π^0\toγγ$ is then investigated but found to be extremely small. A refined model independent estimate of nonanalytic contributions to the neutron electric dipole moment is also determined using velocity dependent Baryon Chiral Perturbation Theory. We obtain the approximate upper bound $|θ| …
Strong interaction $Λπ$ phase shifts relevant for the weak nonleptonic decay $Ξ\rightarrow Λπ$ are calculated using baryon chiral perturbation theory. We find in leading order that the S-wave phase shift vanishes and the $J={1 \over 2}$ P-wave phase shift is $-1.7 ^{\rm o} $. The small phase shifts imply that CP violation in this decay will be difficult to observe. Our results follow from chiral $SU(2)_L\times SU(2)_R$ symmetry.
The conventional derivation of neutrino oscillation treats neutrino mass eigenstate as plane wave with an overall evolution phase. Nevertheless, due to the intrinsic parity-violating nature of weak interactions, only the left-chiral neutrino can be produced as initial condition. On the other hand, the neutrino mass term connects the left-chiral component to the right-chiral one and unavoidably leads to generation of the later through oscillation. This chiral oscillation has significant consequences on the detection of the cosmological relic neutrinos. The event rate is reduced by a factor of 2…
Indirect CP violation is analyzed in the framework of the electroweak gauge theory of J=0 mesons proposed in ref.[1], in which they transform like composite fermion-antifermion operators by the chiral U(N)left x U(N)right group and by the SU(2)left x U(1) gauge group of the Glashow-Salam-Weinberg model. It is shown that, in this model where, in particular, mass terms can be introduced for the mesons themselves, and unlike what happens in the standard model for fermions: - electroweak mass eigenstates can differ from CP eigenstates even in the case of two generations; - the existence of a compl…
Bodeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) are logarithmically enhanced over previous estimates and take place at a rate per unit volume of order $α^5 T^4 \ln(1/α)$ for small coupling. We give a simple physical interpretation of Bodeker's qualitative and quantitative results in terms of Lenz's Law -- the fact that conducting media resist changes in the magnetic field -- and earlier authors' calculations of the color conductivity of such plasmas. In the proc…
