Olaf Kaczmarek, Frithjof Karsch, Anirban Lahiri, Lukas Mazur, Christian Schmidt
备注：
Prepared for the proceeding of NIC Symposium 2020 held at Jülich, Germany. Based on arXiv:1903.04801. Link to the proceeding contributions : http://hdl.handle.net/2128/24435
发表信息：
NIC Series volume 50, page 193 (2020); ISBN : 978-3-95806-443-0
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 find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV. We also present some preliminary calculations on interplay of effective $U_A(1)$ restoration and chiral phase transition towards chiral limit.
As an extension of $QCD$, consider a theory with ``$2+1$'' flavors, where the current quark masses are held in a fixed ratio as the overall scale of the quark masses is varied. At nonzero temperature and baryon density it is expected that in the chiral limit the chiral phase transition is of first order. Increasing the quark mass from zero, the chiral transition becomes more weakly first order, and can end in a chiral critical point. We show that the only massless field at the chiral critical point is a sigma meson, with the universality class that of the Ising model. Present day lattice simul…
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.
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.
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.
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 …
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…
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…
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…
It has been found very recently on the lattice that at high temperature at vanishing chemical potential QCD is increasingly SU(2)_CS and SU(2N_F) symmetric. We demonstrate that the chemical potential term in the QCD Lagrangian has precisely the same symmetry. Consequently the QCD matter beyond the chiral restoration line on the T - μplane is at least approximately SU(2)_CS and SU(2N_F) symmetric.
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.
We study physics at temperatures just above the QCD phase transition (Tc) using chiral (overlap) Fermions in the quenched approximation of lattice QCD. Exact zero modes of the overlap Dirac operator are localized and their frequency of occurrence drops with temperature. This is closely related to axial U(1) symmetry, which remains broken up to 2Tc. After subtracting the effects of these zero modes, chiral symmetry is restored, as indicated by the behavior of the chiral condensate. The pseudoscalar and vector screening masses are close to ideal gas values.
Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of 1) a static monopole-antimonopole pair and 2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo ca…
In this paper we discuss the combined effects on nuclear matter properties of the quark confinement mechanism in nucleon and of the chiral effective potential resulting from the spontaneous breaking of the chiral symmetry in nuclear matter. Based on the Nambu-Jona-Lasinio predictions, it is shown that the chiral potential acquires a specific scalar field cubic dependence, which contributes to the three-body interaction. We also discuss the constraints induced by Lattice-QCD on the model parameters governing the saturation properties. We introduce the term "QCD-connected parameters" for these q…
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.
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.
Out of the many exciting results obtained with the lattice approach to QCD under extreme conditions, I discuss a few selected items related to chiral symmetry: the chiral condensate as an approximate order parameter, meson screening masses, and masses of baryons and mesons, including D(s) mesons, when approaching the crossover from the hadronic side.
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.
The quenched approximation for QCD is, at present and in the foreseeable future, unavoidable in lattice calculations with realistic choices of the lattice spacing, volume and quark masses. In these lectures, I review the analytic study of the effects of quenching based on chiral perturbation theory. Quenched chiral perturbation theory leads to quantitative insight into the difference between quenched and unquenched QCD, and reveals clearly diseases which plague quenched QCD. A short review of the ideas underlying chiral perturbation theory is included.
Violation of scale symmetry, scale anomaly, being a radical concept in quantum field theory, is of importance to comprehend the vacuum structure of QCD, and should potentially contribute to the chiral phase transition in thermal QCD, as well as the chiral and U(1) axial symmetry. Though it should be essential, direct evidence of scale anomalies has never been observed in the chiral phase transition. We propose a methodology to detect a scale anomaly in the chiral phase transition, which is an electromagnetically induced scale anomaly: apply a weak magnetic field background onto two-flavor mass…
If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a metal-insulator transition or a percolation transition in d$\leq 4$. Our results are accessible to current lattice QCD simulations.
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 report on recent work about the study of quark mass dependence of nucleon magnetic moments and axial-vector coupling constant. We examine the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD data obtained at relative large pion masses down to the physical values.
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…
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…
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.
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.
Chiral chemical potential does not cause the sign problem in the Monte Carlo simulation of lattice QCD. Using the chiral chemical potential, we study the chiral magnetic effect in two-flavor full QCD. We show that a strong external magnetic field induces an electric current in a chirally imbalanced QCD matter. The qualitative feature of the induced current is consistent with an analytical prediction.
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.
The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly attributable to QCD-induced dynamics. We observe a transition in the qualitative behavior of this absolute X-distribution of low-lying eigenmodes which, we propose, defines a chiral polarization scale of the QCD vacuum.
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.
A chiral invariant effective action for lattice QCD is proposed. Its connection to the multifermion model is established. A possibility of using this action for computer simulations is discussed.
The QCD phase transition is studied on 32^3x8 quenched lattices. One expects from simple arguments that the quenched chiral condensate should diverge as the chiral limit is approached. Previous studies have not been able to observe this behavior, perhaps due to relatively large lattice spacings used. The topic is revisited here on N_t=8 lattices, where the physical spacing is approximately 2(Gev^-1).
In our work we extend the ideas of the derivation of the chiral effective theory from the lattice QCD [1] to the case of the random lattice regularization of QCD. Such procedure allows in principle to find contribution of any order into the chiral effective lagrangian. It is shown that an infinite subseries of the chiral perturbation can be summed up into tne Born-Infeld term and the logarithmic correction to them.
Scaling behavior is analyzed for the two-flavor QCD lattice gauge theory chiral transition. Leading scaling behavior and correction to leading scaling from lattice spacing effects are examined for the quark condensate. Scaling predictions under the assumption of quark mass dominance are tested for the longitudinal correlation length. Second order scaling behavior is consistent with present data.
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…
One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods, one has to perform expensive lattice simulations at multiple bare quark masses, and employ some modeled function to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quark…
Continuum reduction in large N QCD enables one to extract physical quantities in the $N\to\infty$ limit of QCD by working in small physics volumes. The computation of chiral condensate is an example of such a calculation.
Chiral symmetry breaking is calculated as a function of cooling in quenched lattice QCD. A non-zero signal is found for the chiral condensate beyond one hundred cooling steps, suggesting that there is chiral symmetry breaking associated with instantons. Quantitatively, the chiral condensate in cooled gauge field configurations is small compared to the value without cooling.
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.
Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.
