We study the scaling behavior of the two-flavor chiral phase transition using an effective quark-meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes.In particular, we find large scaling deviations for physical pion masses and significant finite volume effects for pion masses that are used in current lattice simulations.
Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k…
We discuss chiral and deconfinement aspects of the finite temperature transition in QCD using improved staggered actions. We study different quantities related to chiral and deconfinement transition and discuss their cutoff dependence. Contrary to some earlier lattice results we find that the chiral and deconfinement transition are not closely interconnected.
The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an $8^3\times 4$ lattice near the chiral transition point. It is shown that the chiral condensate which is the order parameter of chiral symmetry satisfies remarkably a scaling relation with the exponents of the three dimensional O(4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit.
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T-chi and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at T-chi is shown to be supported by finite temperature lattice calculations.
The superfluid transition of liquid Helium shares an interesting phenomenon with the chiral limit of QCD: the specific heat is finite at the critical point, but has a cusp. From this follows an interesting mixture of universal and non-universal features at the critical point. Through the CP symmetry of chiral QCD, this has implications for the fourth order baryon number susceptibility and susceptibilities of higher orders. Investigations of such a scaling will show us whether O(4) scaling is an accurate description of baryon-free QCD when the pion mass is realistic.
These lectures describe the use of effective field theories to extrapolate results from the parameter region where numerical simulations of lattice QCD are possible to the physical parameters (physical quark masses, infinite volume, vanishing lattice spacing, etc.). After a brief introduction and overview, I discuss three topics: 1) Chiral perturbation theory in the continuum; 2) The inclusion of discretization effects into chiral perturbation theory, focusing on the application to Wilson and twisted-mass lattice fermions; 3) Extending chiral perturbation theory to describe partially quenched …
We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for SU(3) gauge theory with quenched Kogut-Susskind quarks on the $10^4$ lattice are shown.
I present a selection of recent lattice data by major collaborations for the pseudo-Goldstone boson masses in full ($N_f=2$) QCD, where the valence quarks are chosen exactly degenerate with the sea quarks. At least the more chiral points should be consistent with Chiral Perturbation Theory for the latter to be useful in extrapolating to physical masses. Perspectives to reliably determine NLO Gasser-Leutwyler coefficients are discussed.
We calculate chiral susceptibilities in (2+1)-flavour QCD for different masses of the light quarks using the functional renormalisation group (fRG) approach to first-principles QCD. We follow the evolution of the chiral susceptibilities with decreasing masses as obtained from both the light-quark and the reduced quark condensate. The latter compares very well with recent results from the HotQCD collaboration for pion masses $m_π\gtrsim 100\,\text{MeV}$. For smaller pion masses, the fRG and lattice results are still consistent. In particular, the estimates for the chiral critical temperature ar…
It has been a big challenge for lattice QCD to simulate dynamical quarks near the chiral limit. Theoretically, it is well-known that the naive chiral symmetry cannot be realized on the lattice (the Nielsen-Ninomiya theorem). Also practically, the computational cost rapidly grows as the quark mass is reduced. The JLQCD collaboration started a project to perform simulations with exact but modified chiral symmetry using the the overlap-Dirac operator and the topology conserving action. The latter is helpful to reduce the numerical cost of the dynamical quarks. Our simulation of two-flavor QCD has…
We extend a technique for the chiral extrapolation of hadron masses calculated with dynamical fermions to those generated by quenched simulations. The method ensures the correct leading and next-to-leading non-analytic behaviour for either QCD or quenched QCD in the chiral limit, as well as the correct large quark mass behaviour. We find that the primary difference between quenched and dynamical baryon masses can be described by the meson loops which give rise to the different leading and next-to-leading non-analytic behaviour.
We discuss universal scaling properties of (2+1)-flavor QCD in the vicinity of the chiral phase transition at vanishing as well as non-vanishing light quark chemical potential (mu_l). We provide evidence for O(N) scaling of the chiral order parameter in (2+1)-flavor QCD and show that the scaling analysis of its derivative with respect to the light quark chemical potential provides a unique approach to the determination of the curvature of the chiral phase transition line in the vicinity of mu_l/T=0.
We calculate the kaon semileptonic form factors in lattice QCD with three flavors of dynamical overlap quarks. Gauge ensembles are generated at pion masses as low as 290 MeV and at a strange quark mass near its physical value. We precisely calculate relevant meson correlators using the all-to-all quark propagator. Twisted boundary conditions and the reweighting technique are employed to vary the momentum transfer and the strange quark mass. We discuss the chiral behavior of the form factors by comparing with chiral perturbation theory and experiments.
I review some aspects of the interplay between anomalies and chiral symmetry. The quantum anomaly that breaks the U(1) axial symmetry of massless QCD leaves behind a flavor-singlet discrete chiral invariance. When the mass is turned on this residual symmetry has a close connection with the strong CP violating parameter theta. One result is that a first order transition is usually expected when the strong CP violating angle passes through pi. This symmetry can be understood either in terms of effective chiral Lagrangians or in terms of the underlying quark fields.
We study the lattice QCD $Λ_c N$ phase shifts for the $^3S_1-{}^3D_1$ coupled channel using both the leading order covariant chiral effective theory and the next-to-leading order non-relativistic chiral effective field theory. We show that although it is possible to describe simultaneously the $^3S_1$ and $^3D_1$ phase shifts and the inelasticity $η_1$, the fitted energy range is pretty small, only up to $E_\mathrm{c.m.}=5$ MeV. This raises concerns regarding the consistency between leading/next-to-leading order chiral effective field theory and the lattice QCD simulations.
We present a study of the QCD interactions which do not conserve the chirality of quarks. These non-perturbative forces are responsible for the violation of the U_A(1) charge conservation and for the breaking of chiral symmetry. From a systematic analysis we argue that the leading dynamical sources chirality flips are the interactions mediated by topological vacuum field fluctuations. We study in detail the contribution of instantons and derive a simple model-independent semi-classical prediction. This result can be used to check on the lattice if instantons are the dynamical mechanism respons…
We perform a first lattice QCD simulation including two-flavor dynamical fermion with a chiral chemical potential. Because the chiral chemical potential gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD matter by the Monte Carlo simulation. By applying an external magnetic field to this system, we obtain a finite induced current along the magnetic field, which corresponds to the chiral magnetic effect. The obtained induced current is proportional to the magnetic field and to the chiral chemical potential, which is consistent with an analytical prediction.
We compute the QCD phase diagram in the plane of the chiral chemical potential and temperature using the linear sigma model coupled to quarks and to the Polyakov loop. The chiral chemical potential accounts for effects of imbalanced chirality due to QCD sphaleron transitions which may emerge in heavy-ion collisions. We found three effects caused by the chiral chemical potential: the imbalanced chirality (i) tightens the link between deconfinement and chiral phase transitions; (ii) lowers the common critical temperature; (iii) strengthens the order of the phase transition by converting the cros…
Relatively low crossover temperature suggests that chiral symmetry restoration in QCD may well be described within the low-energy effective theory. The shape of the pseudocritical line in the T-mu plane is estimated within this assumption. No critical endpoint is found for physical values of quark masses.
Using the recently proposed generalization to an arbitrary number of colors of the strong coupling approach to lattice gauge theories\cite{Grignani:2003uv}, we compute the chiral condensate of massless QCD in the 't Hooft limit.
Several recent papers -using effective QCD chiral Lagrangians- reproduced results obtained with the general QCD parameterization (GP). These include the baryon 8+10 mass formula, the octet magnetic moments and the coincidental nature of the "perfect" -3/2 ratio between the magnetic moments of p and n. Although we anticipated that the GP covers the case of chiral treatments, the above results explicitly exemplify this fact. Also we show by the GP that -in any model or theory (chiral or non chiral) reproducing the results of exact QCD- the Franklin (Coleman Glashow) sum rule for the octet magnet…
We discuss spontaneous chiral symmetry breaking and quark bilinear condensate in large $N_c$ QCD. It has been known that the existence of $η'$ meson is implied in large $N_c$ QCD as pointed out by Witten and Veneziano. First, we show that the existence of $η'$ and Ward-Takahashi identities imply the existence of the Nambu-Goldstone bosons from chiral symmetry breaking $SU(N_f)_L \times SU(N_f)_R \to SU(N_f)_V$. Second, we show that a QCD inequality implies a nonzero lower bound on the quark bilinear condensate.
We use the recently proposed directed-path algorithm to study the chiral limit of strongly coupled lattice QCD with staggered quarks at finite temperatures. The new algorithm allows us to compute the chiral susceptibility and the pion decay constant accurately on large lattices for massless quarks. In the low temperature phase we find clear evidence for the singularities predicted by chiral perturbation theory. We also show convincingly that the chiral phase transition is of second order and belongs to the O(2) universality class.
I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum limit, and of the topological susceptibility.
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature $T_χ$ and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behavior of Polyakov loop susceptibilities at $T_χ$ is shown to be supported by finite temperature lattice calculations.
We study the polarized structure functions in QCD. We show that $g_T$ which probes helicity flip interactions in hadrons on the light-front indeed measures the QCD dynamics of chiral symmetry breaking. The relation between chiral symmetry breaking and the observed $g_2$ data is explored.
We analyze the chiral phase transition with the help of the QCD gap equation. Various models for the effective interaction in rainbow truncation are contrasted with regard to the resulting chiral transition temperatures. In particular, we investigate possible systematic relations of the details of the effective interaction and the value of T_c. In addition, we quantify changes to the transition temperature beyond the rainbow truncation.
Chiral symmetry is an essential concept in understanding QCD at low energy. We treat the chiral condensate, which measures the spontaneous breaking of chiral symmetry, as a free parameter to investigate the effect of partially restored chiral symmetry on the physical quantities in the frame work of an AdS/QCD model. We observe an interesting scaling behavior among the nucleon mass, pion decay constant and chiral condensate. We propose a phenomenological way to introduce the temperature dependence of a physical quantity in the AdS/QCD model with the thermal AdS metric.
These are the proceedings of the workshop on ``Lattice QCD, Chiral Perturbation Theory and Hadron Phenomenology'' held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas from October 2 to 6, 2006. The workshop concentrated on bringing together researchers working in lattice QCD and chiral perturbation theory with the aim of improving our understanding how hadron properties can be calculated and analyzed from first principles. Included are a short contribution per talk.
The breaking of chiral symmetry in holographic light-front QCD is encoded in its longitudinal dynamics with its chiral limit protected by the superconformal algebraic structure which governs its transverse dynamics. The scale in the longitudinal light-front Hamiltonian determines the confinement strength in this direction: It is also responsible for most of the light meson ground state mass consistent with the Gell-Mann-Oakes-Renner constraint. Longitudinal confinement and the breaking of chiral symmetry are found to be different manifestations of the same underlying dynamics as found in 't Ho…
Chiral Symmetry Breaking (CSB) is derived in QCD starting from the QCD Lagrangian and using Field Correlators Method (FCM). The kernel in the resulting equations responsible for CSB is directly connected to confinement, and therefore both phenomena occur and vanish together as supported by lattice data. Chiral Lagrangian and quark-meson Lagrangian are derived with explicit coefficients and compared to standard expressions. Spectrum of Nambu-Goldstone mesons and their radial excitations is calculated in good agreement with experiment.
I review aspects of chiral dynamics pertinent to the structure of baryons and few-nucleon systems, such as chiral extrapolations for the nucleon and the delta mass, double pion photoproduction off protons, single neutral pion electroproduction off the deuteron, pion photoproduction in the delta region, the quark mass dependence of the nuclear forces and the possibility of an infrared limit cycle in QCD.
In this paper we study the properties of QCD at nonzero chiral density $ρ_5$, which is introduced through chiral chemical potential $μ_5$. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that $ρ_5$ is generated at nonzero $μ_5$ and in the chiral limit observe $ρ_5 \sim Λ_{QCD}^2 μ_5$. We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility $χ_{\mbox{\footnotesize top}}$ and string tension $σ$ for various values of $μ_5$. We observed that both s…
The definition of chiral transformations in light-front field theory is very different from the conventional form in equal-time formalism. We study the consistency of chiral transformations and chiral symmetry in light-front QCD and derive a complete new light-front axial-vector current for QCD. The breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new axial-vector current does not contain the pion pole part so that the associate chiral charge smoothly describes pion transitions for various hadronic proce…
In this paper we describe qualitatively some aspects of the holographic QCD. Inspired by a successfull 4D description, we try to separate the Confinement and the Chiral Symmetry Breaking dynamics. We also discuss the realization of the baryons as skyrmions in Soft Wall Holographic QCD, and the issue of the Vector Meson Dominance.
Hyperon-nucleon interactions serve as basic inputs to studies of hypernuclear physics and dense (neutron) stars. Unfortunately, a precise understanding of these important quantities have lagged far behind that of the nucleon-nucleon interaction due to lack of high precision experimental data. Historically, hyperon-nucleon interactions are either formulated in quark models or meson exchange models. In recent years, lattice QCD simulations and chiral effective field theory approaches start to offer new insights from first principles. In the present work, we contrast the state of art lattice QCD …
In the framework of Coulomb Gauge QCD we explore dynamical breaking of chiral symmetry and screening of the confinement potential at finite density. The screened potential is applied in study of charmonium dissociation.
The T-odd quark distrbutions are shown to vanish in the chiral sigma model in contrast to the opposite widespread opinion. This failure of the chiral sigma model is a feature of the model itself and has nothing to do with the recent progress in the clarification of the status of the T-odd distributions in QCD.
We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct …
In addition to temperature and baryon chemical potential there are other parameters that matter in the real quark matter. One of them is isospin asymmetry which does exist in nature, for example, in the compact stars and in heavy ion collisions. The chiral imbalance, the difference between left- and right-handed quarks, is another phenomenon that could occur in quark matter. We have shown that lattice QCD results support the existence of the approximate duality in real QCD. The rise of pseudo-critical temperature with increase of chiral chemical potential $μ_{5}$ (the much debated effect recen…
We derive the axial Ward identity for lattice QCD with domain-wall fermions, and from which we obtain a formula for the residual mass (45)-(46), that can be used to measure the chiral symmetry breaking due to the finite extension Ns in the fifth dimension. Furthermore, we obtain an upper bound for the residual mass in lattice QCD with the optimal domain-wall fermion.
We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim m_π\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. After thermodynamic, continuum and chiral extrapolations we fi…
We study confinement and chiral symmetry breaking phase transitions for QCD and supersymmetric QCD. The method is based on some justified assumption regarding the behavior of the Green function relevant for the potential between two charges or a gap equation. We determine the number of flavors at which the transitions to confinement and chiral symmetry breaking take place. We find that whereas for chiral symmetry breaking the results are in perfect agreement with those in the literature for confinement the situation is more complex.
I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime described by random matrix theory, diffusive regime described by chiral perturbation theory and the crossover between these two domains.
The chiral magnetic effect (CME) is an exact statement that connects via the axial anomaly the electric current in a system consisting of interacting fermions and gauge field with chirality imbalance that is put into a strong external magnetic field. Experimental search of the magnetically induced current in QCD in heavy ion collisions above a pseudocritical temperature hints, though not yet conclusive, that the induced current is either small or vanishing. This would imply that the chirality imbalance in QCD above $T_c$ that could be generated via topological fluctuations is at most very smal…
I report on recent work done in collaboration with M. Knecht on patterns of spontaneous chiral symmetry breaking in the large-Nc limit of QCD-like theories, and with S. Peris and M. Perrottet concerning the question of matching long and short distances in large-Nc QCD.
We present the renormalized Taylor expansion of the chiral condensate with chemical potential. The relation with the Taylor coefficients of meson susceptibilities and the quark mass dependence of the quark number susceptibilities are obtained through chiral Ward identities and Maxwell relations. The continuum limit is obtained in quenched and two flavour QCD. In Nf=2 QCD, the quadratic response coefficients (QRCs) of the chiral condensate to chemical potential indicate that pion fluctuations decrease at finite chemical potential toward the critical end point. We discuss how these observables c…
We investigate the interplay between chiral symmetry restoration and deconfinement both in two color QCD and adjoint QCD. In ordinary QCD we show how the behavior of the Polyakov loop near chiral phase transition is induced by the chiral order parameter, while in adjoint two color QCD one has two truly independent phase transitions. Introducing a finite baryochemical potential we find that adjoint QCD exhibits tetracritical behavior.
By matching the world of hadrons to that of some effective chiral quark theory, we determine the induced condensates for QCD sum rules in the presence of an external pion field. The observed values of the strong and weak $πNN$ coupling constants are understood.
We analyze the chiral symmetry breaking of QCD in the Coulomb gauge. Using flow equations, we derive the renormalized gap equation and the Bethe-Salpeter equation and show that they are finite in both UV and IR regions. No additional UV renormalization is required in the chiral limit. We take into account the hyperfine interaction as well as chiral symmetry breaking and obtain the $π-ρ$ mass splitting caused by the instantaneous and dynamical interactions.
Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fi…
