Marlene Nahrgang, Marcus Bleicher
We give a general overview about the approaches to study the phase diagram of QCD. Thereafter, we examine the evolution of a fireball in a chiral fluid dynamic model including nonequilibrium effects.
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N* masses in the spin-1/2 and spin-3/2 sectors are computed using two non-perturbative methods: lattice QCD and QCD sum rules. States with both positive and negative parity are isolated via parity projection methods. The basic pattern of the mass splittings is consistent with experiments. The mass splitting within the same parity pair is directly linked to the chiral symmetry breaking QCD.
I show an updated QCD phase diagram with recent developments from chiral effective theories and phenomenological models. Expected signals of a QCD critical point accessible in heavy-ion collisions are also discussed. In particular, non-monotonic behavior of fluctuations associated with conserved charges is focused on.
Standard QCD sum-rule analyses of the nucleon mass give results that are inconsistent with chiral perturbation theory due to an overly simple continuum ansatz on the phenomenological side of the sum rule. We show that a careful treatment of the continuum, including $π$-$N$ states and other states with virtual pions, resolves the inconsistency associated with chiral logs.
Nonperturbative Wilson coefficients associated with the leading chiral-symmetry-breaking operators in the operator product expansion of the pseudoscalar QCD correlation function are derived. Implementation of the new, instanton-induced operators enables the corresponding spectral sum rule to reproduce the small pion mass scale, thereby reconciling it with Goldstone's theorem. The same operators suppress the contributions of pionic resonances. Several predictions and structural insights from the new sum rule are discussed.
A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global symmetries of QCD and permits a $1/N_c$ expansion. The model dependence of the chiral coefficients is tested for several forms of the quark-quark interaction by varying the form of the running coupling, $α(q^2)$, in the infrared region. The pattern in the coefficients that arises at tree level is consistent with large $N_c$ QCD, and is related to the model trun…
We derive the chiral effective Lagrangian for heavy-light mesons in the heavy quark limit from QCD under proper approximations. The low energy constants in the effective Lagrangian are expressed in terms of the light quark self-energy. With typical forms of the running coupling constant of QCD and the quark self-energy obtained from Dyson-Schwinger equations as well as lattice QCD, we estimate the low energy constants in the model and the strong decay widths. A comparison with data and some discussions of the numerical results are presented.
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in th…
We investigate the influence of the isospin asymmetry on the phase structure of quark matter near the chiral critical point systematically using a generalized version of Ginzburg-Landau approach. The effect has proven to be so profound that it brings about not only a shift of the critical point but also a rich variety of phases in its neighborhood. In particular, there shows up a phase with spatially varying charged pion condensate which we name the "solitonic pion condensate" in addition to the "chiral defect lattice" where the chiral condensate is partially destructed by periodic placements …
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.
Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c \approx 8 \pm 1$, in agreement with the state-of-the-art direct lattice analy…
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 …
We discuss a minimal holographic model for the description of heavy-light and light mesons with chiral symmetry, defined in a slab of AdS space. The model consists of a pair of chiral Yang-Mills and tachyon fields with specific boundary conditions that break spontaneously chiral symmetry in the infrared. The heavy-light spectrum and decay constants are evaluated explicitly. In the heavy mass limit the model exhibits both heavy-quark and chiral symmetry and allows for the explicit derivation of the one-pion axial couplings to the heavy-light mesons.
We report on our progress in the calculation of nuclear ground-state properties using effective Lagrangians whose construction is constrained by QCD scales and chiral symmetry. Good evidence is found that QCD and chiral symmetry apply to finite nuclei.
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…
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.
We study a chiral relativistic theory of nuclear matter aimed at the desciption of both the binding and saturation properties and the QCD properties, quark condensate and QCD susceptibilities. For this purpose the nucleon scalar response of the quark-meson coupling model is introduced in the linear sigma model. The consequences for the nuclear and the QCD scalar susceptibilities are discussed.
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…
A survey is given of the evolution from Yukawa's early work, via the understanding of the pion as a Nambu-Goldstone boson of spontaneously broken chiral symmetry in QCD, to modern developments in the theory of the nucleus based on the chiral effective field theory representing QCD in its low-energy limit.
QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. This allows for the identification of such QCD condensates which drive the non-degeneracy of chiral partners in lowest order of the strong coupling alpha_s and which therefore may serve as "order parameters" for chiral restoration (or elements thereof).
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.
In the article "On chiral symmetry restoration at finite density in large-$N_c$ QCD" by Adhikari, Cohen, Ayyagari and Strother [Phys. Rev. C 83, 065201 (2011)] the description of dense nuclear matter by means of Skyrmions in hyperspherical unit cells is severely criticized. We point out that this criticism is based on invalid assumptions and therefore unwarranted.
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…
We present a novel description of nuclear many-body systems, both for nuclear matter and finite nuclei, emphasizing the connection with the condensate structure of the QCD ground state and spontaneous chiral symmetry breaking. Lorentz scalar and vector mean-fields are introduced in accordance with QCD sum rules. Nuclear binding arises from pionic fluctuations, using in-medium chiral perturbation theory up to three-loop order. Ground state properties of $^{16}$O and $^{40}$Ca are calculated. The built-in QCD constraints reduce the number of input parameters significantly in comparison with pure…
In QCD matter under an external magnetic field, the chiral magnetic effect (CME) leads to the collective gapless mode called the chiral magnetic wave (CMW). Since dynamic universality class generally depends on low-energy gapless modes, it is nontrivial whether the CME and the resulting CMW change that of the second-order chiral phase transition in QCD. To address this question, we study the critical dynamics near the chiral phase transition in massless two-flavor QCD under an external magnetic field. By performing the dynamic renormalization-group analysis within the epsilon expansion, we fin…
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…
In certain circumstances, chiral (parity-violating) medium can be described hydrodynamically as a chiral fluid with microscopic quantum anomalies. Possible examples of such systems include strongly coupled quark-gluon plasma, liquid helium 3He-A, neutron stars and the Early Universe. We study first-order hydrodynamics of a chiral fluid on a vortex background and in an external magnetic field. We show that there are two previously undiscovered modes describing heat waves propagating along the vortex and magnetic field. We call them the Thermal Chiral Vortical Wave and Thermal Chiral Magnetic Wa…
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.
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…
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.
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.
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