Explicit Chiral Symmetry Breaking Research Articles

Rare kaon decays on the lattice

We show that long-distance contributions to the rare decays K→πνν¯ and K→πℓ+ℓ− can be computed using lattice QCD. The proposed approach requires well established methods, successfully applied in the calculations of electromagnetic and semileptonic form factors. The extra power divergences, related to the use of weak four-fermion operators, can be eliminated using only the symmetries of the lattice action without ambiguities or complicated non-perturbative subtractions. We demonstrate that this is true even when a lattice action with explicit chiral symmetry breaking is employed. Our study opens the possibility of reducing the present uncertainty in the theoretical predictions for these decays.

Analysis ofUA(1)symmetry breaking and restoration effects on the scalar-pseudoscalarmeson spectrum

We explore patterns of effective restoration of the chiral ${\mathrm{U}}_{A}(1)$ symmetry using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction, and assuming that the coefficient of the anomaly term is temperature and density dependent. The special case of explicit breaking of chiral symmetry without ${\mathrm{U}}_{A}(1)$ anomaly is also considered, since this scenario can provide additional information allowing to understand the interplay between the ${\mathrm{U}}_{A}(1)$ anomaly and (spontaneous) chiral symmetry-breaking effects. The pseudoscalar and scalar sectors are analyzed in detail bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on the issue under discussion. In the region of temperatures (densities) studied, we do not observe signs indicating a full restoration of $\mathrm{U}(3)\ensuremath{\bigotimes}\mathrm{U}(3)$ symmetry as, for instance, the degeneracy of both ${a}_{0}$ and ${f}_{0}$ mesons with the pion. As we work in a real world scenario (${m}_{u}={m}_{d}\ensuremath{\ll}{m}_{s}$), we only observe the return to symmetries of the classical QCD Lagrangian in the nonstrange sector.

QCD, Symmetry Breaking and the Random Lattice

According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eigenvalues from simulations of quenched QCD on random lattices in four dimensions, focusing on chiral symmetry breaking.

Domain-Wall Fermions at Strong Coupling

The DWF formulation becomes increasingly problematic at gauge couplings for which $a^{-1}<2$ GeV, where the roughness of the gauge field leads to increased explicit chiral symmetry breaking ($\mres$). This problem becomes especially severe for sufficiently strong coupling where the underlying 4-dimensional Wilson theory is in the Aoki phase. We review our attempts to find a suitable modification of the gauge and/or the fermion action which would allow the DWF method to work reliably at stronger coupling.

Effective restoration of theUA(1)symmetry with temperature and density

We investigate the full $\mathrm{U}(3)\ensuremath{\bigotimes}\mathrm{U}(3)$ chiral symmetry restoration, at finite temperature and density, on the basis of a quark model which incorporates the most relevant properties of QCD in this context: explicit and spontaneous breaking of chiral symmetry and axial ${U}_{A}(1)$ symmetry breaking. A specific lattice-inspired behavior of the topological susceptibility, combined with the convergence of chiral partners, signals the onset of an effective chiral symmetry restoration. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full $\mathrm{U}(3)\ensuremath{\bigotimes}\mathrm{U}(3)$ chiral symmetry can occur. This conclusion is valid in the context of both finite temperature and density.

Chirally improving Wilson fermions II. Four-quark operators

In this paper we discuss how the peculiar properties of twisted lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the $\Delta S=1,2$ effective weak Hamiltonian and at the same time have a positive determinant for non-degenerate quarks as well as full O($a$) improvement in on-shell quantities with no need of improving the lattice action and the operators.

Chemical equilibration in relativistic heavy ion collisions

In the hadronic sector of relativistic heavy ion physics, the ρ ⇆ 2 π reaction is the strongest one, strong enough to equilibrate the ρ with the pions throughout the region from chemical freezeout to thermal freezeout when free-particle interactions (with no medium-dependent effects) are employed. Above the chiral restoration temperature, only ρ's and π's are present, in that the chirally restored A 1 is equivalent to the ρ and the mesons have an SU(4) symmetry, with no dependence on isospin and negligible dependence on spin. In the same sense the σ and π are “equivalent” scalars. Thus the chirally restored ρ ⇆ 2 π exhaust the interspecies transitions. We evaluate this reaction at T c and find it to be much larger than below T c , certainly strong enough to equilibrate the chirally restored mesons just above T c . When emitted just below T c the mesons remain in the T c + ε freezeout distribution, at least in the chiral limit because of the Harada–Yamawaki “vector manifestation” that requires that mesonic coupling constants go to zero (in the chiral limit) as T goes to T c from below. Our estimates in the chiral limit give deviations in some particle ratios from the standard scenario (of equilibrium in the hadronic sector just below T c ) of about double those indicated experimentally. This may be due to the neglect of explicit chiral symmetry breaking in our estimates. We also show that the instanton molecules present above T c are the giant multipole vibrations found by Asakawa, Hatsuda and Nakahara and of Wetzorke et al. in lattice gauge calculations. Thus, the matter formed by RHIC can equivalently be called: chirally restored mesons, instanton molecules, or giant collective vibrations. It is a strongly interacting liquid.

Light hadron spectroscopy in two-flavor QCD with small sea quark masses

We extend the study of the light hadron spectrum and the quark mass in two-flavor QCD to smaller sea quark mass, corresponding to $m_{PS}/m_{V}=0.60$--0.35. Numerical simulations are carried out using the RG-improved gauge action and the meanfield-improved clover quark action at $\beta=1.8$ ($a = 0.2$ fm from $\rho$ meson mass). We observe that the light hadron spectrum for small sea quark mass does not follow the expectation from chiral extrapolations with quadratic functions made from the region of $m_{PS}/m_{V}=0.80$--0.55. Whereas fits with either polynomial or continuum chiral perturbation theory (ChPT) fails, the Wilson ChPT (WChPT) that includes $a^2$ effects associated with explicit chiral symmetry breaking successfully fits the whole data: In particular, WChPT correctly predicts the light quark mass spectrum from simulations for medium heavy quark mass, such as $m_{PS}/m_V \simgt 0.5$. Reanalyzing the previous data %at $m_{PS}/m_{V}=0.80$--0.55 with the use of WChPT, we find the mean up and down quark mass being smaller than the previous result from quadratic chiral extrapolation by approximately 10%, $m_{ud}^{\bar{\rm MS}}(\mu=2 {GeV}) = 3.11(17)$ [MeV] in the continuum limit.

LargeNcand chiral dynamics

We study the dependence on the number of colors of the leading $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude computed from the simple sum of the current algebra and vector meson terms is crossing symmetric and unitary at leading order in a truncated and regularized ${1/N}_{c}$ expansion. The critical number of colors turns out to be ${N}_{c}=6$ and is insensitive to the explicit breaking of chiral symmetry. Below this critical value, an additional state is needed to enforce the unitarity bound; it is a broad one, most likely of a ``four quark'' nature.

Chiral perturbation theory with Wilson-type fermions including a2 effects

Abstract We derive the quark mass dependence of m π 2 , m AWI and fπ , using the chiral perturbation theory which includes the a 2 effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the N f = 2 degenerate quarks. By fitting the mass dependence of m π 2 and m AWI , obtained by the CP-PACS collaboration for N f = 2 full QCD simulations, it is shown that the data are consistently described by the derived formulae.

Chiral perturbation theory with Wilson-type fermions includinga2effects:Nf=2degenerate case

We derive the quark mass dependence of ${m}_{\ensuremath{\pi}}^{2},$ ${m}_{\mathrm{AWI}},$ and ${f}_{\ensuremath{\pi}},$ using chiral perturbation theory, which includes the ${a}^{2}$ effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the ${N}_{f}=2$ degenerate quarks. The distinct features of the results are (1) the additive renormalization for the mass parameter ${m}_{q}$ in the Lagrangian, (2) $O(a)$ corrections to the chiral log ${(m}_{q}\mathrm{log}{m}_{q})$ term, (3) the existence of a more singular term $\mathrm{log}{m}_{q}$ generated by ${a}^{2}$ contributions, and (4) the existence of both ${m}_{q}\mathrm{log}{m}_{q}$ and $\mathrm{log}{m}_{q}$ terms in the quark mass from the axial Ward-Takahashi identity ${m}_{\mathrm{AWI}}.$ By fitting the mass dependence of ${m}_{\ensuremath{\pi}}^{2}$ and ${m}_{\mathrm{AWI}},$ obtained by the CP-PACS Collaboration for ${N}_{f}=2$ full QCD simulations, we find that the data are consistently described by the derived formulas. Resumming the most singular terms $\mathrm{log}{m}_{q},$ we also derive modified formulas, which show a better control over the next-to-leading order correction.

The quark–meson model and the phase diagram of two-flavour QCD

We study the qualitative features of the QCD phase diagram in the context of the linear quark–meson model with two flavours, using the exact renormalization group. We identify the universality classes of the second-order phase transitions and calculate critical exponents. In the absence of explicit chiral-symmetry breaking through the current quark masses, we discuss in detail the tricritical point and demonstrate that it is linked to the Gaussian fixed point. In its vicinity we study the universal crossover between the Gaussian and O(4) fixed points, and the weak first-order phase transitions. In the presence of explicit chiral-symmetry breaking, we study in detail the critical endpoint of the line of first-order phase transitions. We demonstrate the decoupling of pion fluctuations and identify the Ising universality class as the relevant one for the second-order phase transition.

Finite Temperature Spectral Function of the σ Meson from Large N Expansion

The spectral function of the scalar-isoscalar channel of the O(N) symmetric linear $\sigma$ model is studied in the broken symmetry phase. The investigation is based on the leading order evaluation of the self-energy in the limit of large number of Goldstone bosons. We describe its temperature dependent variation in the whole low temperature phase. This variation closely reflects the trajectory of the scalar-isoscalar quasiparticle pole. In the model with no explicit chiral symmetry breaking we have studied near the critical point also the corresponding dynamical exponent.

Meson Effects on the Chiral Condensate at Finite Density**The project supported in part by China Postdoctoral Science Foundation, the National Natural Science Foundation of China under Grant Nos. 10105005, 10135030, and 19925519, and the Major State Basic Research Development Program under Contract No. G2000077407

Meson corrections on the chiral condensate up to next-to-leading order in a expansion at finite density are investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiral phase transition is still of the first order while the properties near the critical density for chiral phase transition are found to change significantly.

Nonperturbative renormalization of domain wall fermions: Quark bilinears

We find the renormalisation coefficients of the quark field and the flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent in the fifth dimension of 16. We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalisation factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero-modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalisation scale dependence.

Unquenching the topological susceptibility with an overlap action

We estimate the quark-mass dependence of the topological susceptibility with dynamical overlap and clover fermions. Unquenching effects on the susceptibility turn out to be well approximated by a reweighting of a quenched ensemble with a low-eigenmode truncation of the fermionic determinant. We find that it is most likely due to the explicit chiral symmetry breaking of the fermion action that present day dynamical simulations do not show the expected suppression of the topological susceptibility.

Renormalization group flow in large N

We calculate renormalization group flow equations for the linear sigma-model in large N_c approximation. The flow equations decouple and can be solved analytically. The solution is equal to a self consistent solution of the NJL model in the same approximation, which shows that flow equations are a promising method to extend the calculation to higher order in 1/N_c. Including explicit chiral symmetry breaking, the large N_c approximation describes physics reasonably well. We further compare the analytic solution to the usually used polynomial truncation and find consistency.

Linear Model in the Gaussian Functional Approximation

We apply a self-consistent relativistic mean-field variational “Gaussian functional” (or Hartree) approximation to the linear σ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or “gap” and the Bethe-Salpeter equations. We check and confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone theorem and the (partial) axial current conservation [CAC], both in and away from the chiral limit. With explicit chiral symmetry breaking, we confirm the Dashen relation for the pion mass and partial CAC. We solve numerically the gap and Bethe-Salpeter equations, discuss the solutions’ properties and the particle content of the theory.

Non-perturbative renormalization in lattice field theory

A review the strategies which have been developped in recent years to solve the non-perturbative renormalization problem in lattice field theories. Although the techniques are general, the focus will be on applications to lattice QCD. I discuss the momentum subtraction and finite volume schemes, and their application to scale dependent renormalizations. The problem of finite renormalizations is illustrated with the example of explicit chiral symmetry breaking, and I give a short status report concerning Symanzik's improvement programme to O( a).

Effective chiral meson Lagrangian for the extended Nambu–Jona-Lasinio model

We present a derivation of the low-energy effective meson Lagrangian of the extended Nambu--Jona-Lasinio (ENJL) model. The case with a linear realization of broken $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ chiral symmetry is considered. There are two crucial points why this revision is needed. First, it is the explicit chiral symmetry breaking effect. On the basis of symmetry arguments we show that relevant contributions related with the current quark mass terms are absent from the effective Lagrangians derived so far in the literature. Secondly we suggest a chiral covariant way to avoid the nondiagonal terms responsible for the pseudoscalar--axial-vector mixing from the effective meson Lagrangian. In the framework of the linear approach this diagonalization has not been done correctly. We discuss as well the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)/SU(2)$ coset space parametrization for the revised Lagrangian (nonlinear ansatz). Our Lagrangian differs in an essential way from those that have been derived until now on the basis of both linear and nonlinear realizations of chiral symmetry.