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Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in $\tau$-decay analyses. Using an $SU(3)_L\otimes SU(3)_R$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio $\varepsilon'/\varepsilon$, using the measured hadronic spectral functions in $\tau$ decay. Second, we fit our $SU(3)$ dynamical parameters to the most recent lattice data on $K\to\pi\pi$ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the $\Delta I = \frac{1}{2}$ enhancement, confirming old suggestions about its underlying dynamical origin., Comment: 46 pages, 7 figures. Published version

Physical review / D 102(9), 094510 (1-21) (2020). doi:10.1103/PhysRevD.102.094510, We study the dependence of the electric conductivity on chemical potential in finite-density SU(2) gauge theory with Nf=2 flavors of rooted staggered sea quarks, in combination with Wilson-Dirac and domain-wall valence quarks. The pion mass is reasonably small with mπ/mρ≈0.4. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient c(T) of the expansion of conductivity σ(T,μ)=σ(T,0)(1+c(T)(μ/T)2+O(μ4)) in powers of μ, which has rather weak temperature dependence and takes its maximal value c(T)≈0.10±0.07 around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows toward the diquark condensation phase and also becomes closer to the free-quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for SU(2) gauge theory the ratio of crossover temperature to pion mass Tc/mπ≈0.4 at μ=0 is significantly smaller than in real QCD., Published by Inst., Melville, NY

Physical review / D D 101(7), 074509 (2020). doi:10.1103/PhysRevD.101.074509, Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths., Published by Inst.302363, Melville, NY

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter densiy $n_0$ the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise to the long-standing quenched $g_A$ in nuclear Gamow-Teller transitions at $\sim n_0$ and to the pseudo-conformal sound velocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$. These properties are confronted with the recent observations in superallowed Gamow-Teller transitions and in astrophysical observations., The title is changed. Most part is rewritten

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with {\it ab-initio} lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential., Comment: 51 pages, 29 figures

The aim of this work is to shed light on some lesser known aspects of Polyakov-loop--extended chiral models (namely the Polyakov-loop extended Nambu--Jona-Lasinio and Quark-Meson models), especially on the correlation of the quark sector with the Polyakov loop. We show that the ordering of chiral and Polyakov-loop transitions and their difference in temperature as seen in lattice QCD calculations could be realized with a critical scale of the Polyakov-loop potential that is larger than the one in pure gauge theory. The comparison of the results for the Polyakov-loop susceptibility obtained using the self-consistent medium-dependent quark mass with those obtained while keeping these masses at a fixed value allows to disentangle chiral-symmetry restoration and center-symmetry breaking effects. Furthermore, a confined chirally restored phase is identified by a plateau in the quark contribution to thermodynamics and by sigma and pion spectral functions that coincide but have a small width. We also discuss that, for some large chemical potential values, the explicit center-symmetry breaking is so strong that statistical deconfinement is realized at infinitely small temperatures. Both the missing sensitivity of the Polyakov loop to the quark mass, except at close to the chiral transition, and the Polyakov loop being zero at zero temperature at all chemical potentials, can be interpreted as indications of a missing mechanism which accounts for the quark back-reaction on the Polyakov loop., Comment: 18 pages, 13 figures, version published in Phys. Rev. D

The process at the heart of neutrinoless double-$\ensuremath{\beta}$ decay, $nn\ensuremath{\rightarrow}pp\phantom{\rule{0.16em}{0ex}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading-order corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-$\ensuremath{\beta}$ decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-$\ensuremath{\beta}$ decay for $^{6}\mathrm{He}$ and $^{12}\mathrm{Be}$. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

Within the framework of chiral effective field theory we discuss the leading contributions to the neutrinoless double-beta decay transition operator induced by light Majorana neutrinos. Based on renormalization arguments in both dimensional regularization with minimal subtraction and a coordinate-space cutoff scheme, we show the need to introduce a leading-order short-range operator, missing in all current calculations. We discuss strategies to determine the finite part of the short-range coupling by matching to lattice QCD or by relating it via chiral symmetry to isospin-breaking observables in the two-nucleon sector. Finally, we speculate on the impact of this new contribution on nuclear matrix elements of relevance to experiment., 6 pages, 3 figures

Following Golterman and Shamir, we develop scale-chiral perturbation theory in the large $N_c$ and large $N_f$ Veneziano limit that incorporates both light-quark baryons and hidden local symmetric bosons and derive a leading-order scale symmetry Lagrangian applicable in nuclear physics. Some applications in the medium-free space and baryonic matter are discussed., 8 pages

The Quark-Meson-Coupling model, which self-consistently relates the dynamics of the internal quark structure of a hadron to the relativistic mean fields arising in nuclear matter, provides a natural explanation to many open questions in low energy nuclear physics, including the origin of many-body nuclear forces and their saturation, the spin-orbit interaction and properties of hadronic matter at a wide range of densities up to those occurring in the cores of neutron stars. Here we focus on four aspects of the model (i) a full comprehensive survey of the theory, including the latest developments, (ii) extensive application of the model to ground state properties of finite nuclei and hypernuclei, with a discussion of similarities and differences between the QMC and Skyrme energy density functionals, (iii) equilibrium conditions and composition of hadronic matter in cold and warm neutron stars and their comparison with the outcome of relativistic mean-field theories and, (iv) tests of the fundamental idea that hadron structure changes in-medium., Comment: 84 pages, 11 figures, in print in Progress in Particle and Nuclear Physics

We calculate the scalar and tensor charges of the nucleon in 2+1-flavor lattice QCD, for which the systematics of the renormalization of the disconnected diagram is well controlled. Numerical simulations are performed at a single lattice spacing a = 0.11 fm. We simulate four pion masses, which cover a range of $m_\pi \sim$ 290 - 540 MeV, and a single strange quark mass close to its physical value. The statistical accuracy is improved by employing the so-called low-mode averaging technique and the truncated solver method. We study up, down, and strange quark contributions to the nucleon charges by calculating disconnected diagrams using the all-to-all quark propagator. Chiral symmetry is exactly preserved by using the overlap quark action to avoid operator mixing among different flavors, which complicates the renormalization of scalar and tensor matrix elements and leads to possibly large contamination to the small strange quark contributions. We also study the nucleon axial charge with contribution from the disconnected diagram. Our results are in reasonable agreement with experiments and previous lattice studies., Comment: 39 pages, 17 figures

35th International Symposium on Lattice Field Theory, Lattice 2017, Granada, Spain, 18 Jun 2017 - 24 Jun 2017; The European physical journal / Web of Conferences 175, 08017 (2018). doi:10.1051/epjconf/201817508017, We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions to implement the required chiral symmetry. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa model and show results for a first numerical study in the pure $O(4)$ scalar sector of the theory., Published by EDP Sciences, Les Ulis

I describe the long-standing search for a "smoking-gun" signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown's last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ($\rho$,$\omega$) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau-Migdal fixed point interaction $G_0^\prime$, the nuclear tensor forces and Brown-Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, "run the show and make all forces equal.", Comment: To appear in G.E. Brown Memorial Volume

Study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of the Standard Model (SM), where both electroweak and chiral symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken Electroweak symmetry represent the topological insulators of different types. We discuss in details the topological invariants in both symmetric and broken phases and establish their relation to the stability of vacuum., 14 pages, no figures, submitted to New Journal of Physics

Chiral symmetry, first entering in nuclear physics in the 1970's for which Gerry Brown played a seminal role, has led to a stunningly successful framework for describing strongly-correlated nuclear dynamics both in finite and infinite systems. We review how the early germinal idea, conceived with the soft-pion theorems in the pre-QCD era, has evolved into a highly predictive theoretical framework for nuclear physics, aptly assessed by Steven Weinberg: "it (chiral effective field theory) allows one to show in a fairly convincing way that what they (nuclear physicists) have been doing all along... is the correct first step in a consistent approximation scheme." Our review recounts both how the theory presently fares in confronting Nature and how one can understand its extremely intricate workings in terms of the multifaceted aspects of chiral symmetry, namely, chiral perturbation theory, skyrmions, Landau Fermi-liquid theory, the Cheshire cat phenomenon, and hidden local and mended symmetries., 108 pages, 50 figures, submitted to Physics Reports special volume dedicated to Gerry Brown