Axial-vector Currents Research Articles

Uncertainties in constraining low-energy constants from 3H $ \beta$β decay

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from $^3$H $\beta$ decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling $c_D$ of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the $^3$H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such $^3$H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the $c_D$ coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to $^3$H $\beta$ decay underestimate the uncertainty in $c_D$. We explore a range of $c_D$ values that is compatible within cutoff variation with the experimental $^3$H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter.

Generalized fermion symmetry, its currents algebra, and Ward-Takahashi identities

We introduce a new local symmetry into the fermion sector of a gauge invariant Lagrangian which may or may not contain a scalar or spontaneous symmetry breaking. The Standard Model in the unitary gauge and QCD are particular cases where this symmetry may apply. We determine the associated vector and axial vector currents and their conservation laws. We show that a single current conservation law may lead to multiple Ward-Takahashi identities. Our results can potentially have important consequences for effective models of low-energy QCD and hadron structure. As an specific example, we discuss the construction of tetraquark states within a generalized linear sigma model and show that this new symmetry probes the tetraquarks in a manner that is consistent with the large $N_c$ limit of QCD.

Axial U(1) current in Grabowska and Kaplan’s formulation

Recently, Grabowska and Kaplan suggested a non-perturbative formulation of a chiral gauge theory, which consists of the conventional domain-wall fermion and a gauge field that evolves by the gradient flow from one domain wall to the other. In this paper, we discuss the U(1) axial-vector current in 4 dimensions using this formulation. We introduce two sets of domain-wall fermions belonging to complex conjugate representations so that the effective theory is a 4-dimensional vector-like gauge theory. Then, as a natural definition of the axial-vector current, we consider a current that generates the simultaneous phase transformations for the massless modes in 4 dimensions. However, this current is exactly conserved and does not reproduce the correct anomaly. In order to investigate this point precisely, we consider the mechanism of the conservation. We find that this current includes not only the axial current on the domain wall but also a contribution from the bulk, which is non-local in the sense of 4-dimensional fields. Therefore, the local current is obtained by subtracting the bulk contribution from it.

η−η′ mixing and the derivative of the topological susceptibility at zero momentum transfer

The couplings of the isosinglet axial-vector currents to the Eta and Eta' mesons are evaluated in a stable, model independent way by use of polynomial kernels in dispersion integrals. The corrections to the Gell-Mann-Oakes-Renner relation in the isoscalar channel are deduced. The derivative of the topological susceptibility at the origin is calculated taking into account instantons and instanton screening.

Nonperturbative determination of improvement coefficients using coordinate space correlators in Nf=2+1 lattice QCD

We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\beta=3.4,3.46,3.55$ and $\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.

Heavy-quark Form Factors at Two Loops in Perturbative QCD

We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.

Two-Point Correlators of Fermionic Currents in External Magnetic Field

We study the two-point correlation functions under an influence of the constant homogeneous magnetic field. In addition to the correlators of scalar, pseudoscalar, vector and axial-vector fermionic currents, we calculate the non-diagonal one including the tensor and pseudoscalar currents. The tensor current is a fermionic part of the Pauli Lagrangian relevant for the electromagnetic interaction of fermions through the anomalous magnetic moment. Its contribution to the photon polarization operator is briefly discussed.

Small flow-time representation of fermion bilinear operators

Fermion bilinear operators of mass dimension 3, such as the axial-vector and vector currents, the pseudo-scalar and scalar densities, whose normalizations are fixed by Ward–Takahashi (WT) relations, are related to small flow-time behavior of composite operators of fermion fields evolved by Lüscher’s flow equation. The representations can be useful in lattice numerical simulations, as recently demonstrated by the WHOT QCD collaboration for the chiral condensation of the [Formula: see text] quantum chromodynamics (QCD) at finite temperature.

Anomalous magnetohydrodynamics in the extreme relativistic domain

The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo-Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost invariant and with vanishing four-acceleration, the corresponding evolution equations are explicitly integrated so that the various physical regimes can be directly verified.

Aspects of QCD current algebra on a null plane

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial–vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial–vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler–Weisberger, Gerasimov–Drell–Hearn, Cabibbo–Radicati and Fubini–Furlan–Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.

Λb→Λℓ+ℓ−form factors, differential branching fraction, and angular observables from lattice QCD with relativisticbquarks

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.

Universal formula for the flavor non-singlet axial-vector current from the gradient flow

By employing the gradient/Wilson flow, we derive a universal formula that expresses a correctly normalized flavor non-singlet axial-vector current of quarks. The formula is universal in the sense that it holds independently of regularization and especially holds with lattice regularization. It is also confirmed that, in the lowest non-trivial order of perturbation theory, the triangle diagram containing the formula and two flavor non-singlet vector currents possesses non-local structure that is compatible with the triangle anomaly.

B -meson decay constants from 2+1 -flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the B-meson decay constants f_B, f_Bs, and their ratio in unquenched lattice QCD using domain-wall light quarks and relativistic b-quarks. We use gauge-field ensembles generated by the RBC and UKQCD collaborations using the domain-wall fermion action and Iwasaki gauge action with three flavors of light dynamical quarks. We analyze data at two lattice spacings of a ~ 0.11, 0.086 fm with unitary pion masses as light as M_pi ~ 290 MeV; this enables us to control the extrapolation to the physical light-quark masses and continuum. For the b-quarks we use the anisotropic clover action with the relativistic heavy-quark interpretation, such that discretization errors from the heavy-quark action are of the same size as from the light-quark sector. We renormalize the lattice heavy-light axial-vector current using a mostly nonperturbative method in which we compute the bulk of the matching factor nonperturbatively, with a small correction, that is close to unity, in lattice perturbation theory. We also improve the lattice heavy-light current through O(alpha_s a). We extrapolate our results to the physical light-quark masses and continuum using SU(2) heavy-meson chiral perturbation theory, and provide a complete systematic error budget. We obtain f_B0 = 199.5(12.6) MeV, f_B+ = 195.6(14.9) MeV, f_Bs = 235.4(12.2) MeV, f_Bs/f_B0 = 1.197(50), and f_Bs/f_B+ = 1.223(71), where the errors are statistical and total systematic added in quadrature. These results are in good agreement with other published results and provide an important independent cross check of other three-flavor determinations of $B$-meson decay constants using staggered light quarks.

Three-body decay of B0→D¯*(2007) 0π+π−

We investigate the [Formula: see text] decay using Dalitz plot analysis. There are two tree diagrams for this decay mode in the factorization approach: the transition matrix element is factorized into a B0 → π+π− form factor multiplied by [Formula: see text] decay constant; and a [Formula: see text] form factor multiplied by a π+ decay constant. In this research we evaluate the matrix elements of the vector and axial vector currents between the B0 and [Formula: see text] meson states by using the B*+ pole. The contributions of intermediate resonances, such as f0(980), f0(1370), f0(1500) and ρ(770), ρ(1450), ρ(1700), have been taken into account. According to the QCD factorization approach and using Dalitz plot analysis, we calculate the branching ratio of [Formula: see text] decay and obtain 3.81 ± 1.31 × 10−4 and 7.49 ± 2.71 × 10−4 at the μ = mb and 2mb scales, respectively, whereas the experimental result is (6.20 ± 2.20) × 10−4.

QCD NLO corrections to inclusiveBc*production inZ0decays

We calculate the next-to-leading order(NLO) quantum chromodynamics(QCD) corrections to the inclusive process of $Z_0 \rightarrow B^*_c+\bar{c}+b$ under the non-relativistic QCD(NRQCD) factorization scheme. Technical details about contributions from vector and axial-vector currents in dimensional regularization scheme are discussed. Numerical calculation shows that the NLO correction enhances the leading-order decay width by about 50%, and the dependence on renormalization scale $\mu$ is reduced. The uncertainties induced by quark masses and the renormalization scale $\mu$ are also analyzed.

Spectroscopy of heavy baryons with heavy-quark symmetry breaking: Transition relations at next-to-leading order

Transition decay widths by one-pion emissions for excited heavy baryons with a single heavy (charm and bottom) quark are investigated by following the heavy-quark symmetry and its breaking effects at $\mathcal{O}(1/M)$ for a heavy-baryon mass $M$. Based on heavy-baryon effective theory, interaction Lagrangians for the heavy baryons with an axial-vector current induced by a pion are constructed. We show that the transition decay widths in several channels are related up to $\mathcal{O}(1/M)$. The results will be useful in the experimental study of excited heavy baryons.

Nonperturbative renormalization of overlap quark bilinears on2+1-flavor domain wall fermion configurations

We present renormalization constants of overlap quark bilinear operators on $2+1$-flavor domain wall fermion configurations. This setup is being used by the $\ensuremath{\chi}\mathrm{QCD}$ Collaboration in calculations of physical quantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity. The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOM scheme. Results in the $\overline{\mathrm{MS}}$ scheme are also given. The step scaling function of quark masses in the RI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three sea quarks, each on two lattices with sizes ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ at spacings $a=(1.73\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$ and $(2.28\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$, respectively.

Chiral two-body currents and neutrinoless double-βdecay in the quasiparticle random-phase approximation

We test the effects of an approximate treatment of two-body contributions to the axial-vector current on the quasiparticle random-phase approximation (QRPA) matrix elements for neutrinoless double-beta decay in a range of isotopes. The form and strength of the two-body terms come from chiral effective-field theory. The two-body currents typically reduce the matrix elements by about 20%, not as much as in shell-model calculations. One reason for the difference is that standard practice in the QRPA is to adjust the strength of the isoscalar pairing interaction to reproduce two-neutrino double-beta decay lifetimes. Another may be the larger QRPA single-particle space. Whatever the reasons, the effects on neutrinoless decay are significantly less than those on two-neutrino decay, both in the shell model and the QRPA.

Full pseudoscalar mesonic chiral Lagrangian atp6order under the unitary group

We construct the full p6 order chiral Lagrangians for the unitary group and special unitary groups, including nf-, three- and two-flavor cases, all bilinear currents (scalar, pseudoscalar, vector, axial-vector and tensor currents) and theta parameter. The number of independent operators are 1391, 1326 and 969 for each of the flavor unitary groups. From these results, we find one extra linear relation among the traditional p4 order low-energy constants under the U(3) group, and some more linear relations with tensor sources for the p6 order low-energy constants in the special unitary groups. We develop a scheme to obtain the relations for the dependent operators in terms of independent operators.

Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules

Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken , the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the U(1) and SU(N c) models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical O(α 4) and $ O\left( {\alpha_s^2} \right) $ conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed.