Axial-vector Form Factors Research Articles

Axial-vector transition form factors of the baryon octet to the baryon decuplet with flavor SU(3) symmetry breaking

We investigate the axial-vector transition form factors of the baryon octet to the baryon decuplet within the framework of the chiral quark-soliton model, with the effects of flavor SU(3) symmetry breaking included. We consider the rotational $1/{N}_{c}$ corrections and regard the strange current quark mass as a perturbation. We compare the present results for the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}N$ axial-vector transition with those from other models and lattice QCD. We also compute all possible axial-vector transitions from the baryon decuplet to the octet with the strangeness changed, i.e., $|\mathrm{\ensuremath{\Delta}}S|=1$. We obtain the value of the essential form factor ${C}_{5}^{A}$ for the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}N$ axial-vector transition at the zero momentum transfer (${Q}^{2}=0$). Furthermore, the present results are in good agreement with those fitted with the T2K data. We extract the value of the axial-vector mass ${M}_{A}$ compared to the data.

Nucleon axial-vector and pseudoscalar form factors and PCAC relations

We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_A$ and $G_P$, and unify them with the pseudoscalar form factor $G_5$ or, equivalently, the pion-nucleon form factor $G_{\pi NN}$. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_A=G_A(0)=1.25(3)$ and a mass-scale $M_A = 1.23(3) m_N$, where $m_N$ is the nucleon mass, can accurately describe the pointwise behaviour of $G_A$. Concerning $G_P$, we obtain the pseudoscalar charge $g_p^\ast = 8.80(23)$, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{\pi NN}/m_N =14.02(33)/{\rm GeV}$ is consistent with recent precision determinations.

ρ meson generalized parton distributions in the Nambu–Jona-Lasinio model

In this paper, both the unpolarized and the polarized $\rho$ meson generalized parton distributions are investigated in the framework of the Nambu--Jona-Lasinio model using proper time regularization scheme. The symmetry properties of $\rho$ meson generalized parton distributions are checked. The three independent distribution functions in deep inelastic scattering, $F_1(x)$, $b_1(x)$ and $g_1(x)$, and the Sachs-like charge, magnetic, and quadruple form factors $G_C(t)$, $G_M(t)$ and $G_Q(t)$, which are the first Mellin moments of unpolarized generalized parton distributions are obtained. In addition, the $u$ quark axial vector form factors $\tilde{F}_1^u(t)$ and $\tilde{F}_2^u(t)$ related to the axial currents from the polarized generalized parton distributions are studied. The impact parameter dependent parton distribution functions, which are the two-dimensional Fourier transform of generalized parton distributions are studied, too. The obtained $\rho$ meson generalized parton distributions satisfy the required properties well.

Hyperon production in quasielastic ν¯τ−nucleon scattering

The theoretical results for the total cross sections and polarization components of the $\tau^{+}$ lepton produced in the charged current induced $|\Delta S| = 1$ quasielastic $\bar\nu_\tau - N$ scattering leading to hyperons ($\Lambda, \Sigma$) have been presented assuming T invariance. The theoretical uncertainties arising due to the use of different vector, axial vector and pseudoscalar form factors as well as the effect of SU(3) symmetry breaking have been studied. We have also presented, for the first time, a comparison of the total cross sections for the production of $e,\mu,\tau$ leptons to facilitate the implications of lepton flavor universality~(LFU) in the $|\Delta S| = 1$ quasielastic reactions induced by the antineutrinos of all flavors i.e., $\nu_{l};~l=e,\mu,\tau$.

Axial-Vector Form Factor of Nucleons in the AdS/QCD Models

Axial-Vector Form Factor of Nucleons in the AdS/QCD Models

Precision nucleon charges and form factors using ( 2+1 )-flavor lattice QCD

We present a high statistics study of the isovector nucleon charges and form factors using seven ensembles of $2+1$-flavor Wilson-clover fermions. The axial vector and pseudoscalar form factors obtained on each of these ensembles satisfy the partially conserved axial current relation between them once the lowest energy $N\ensuremath{\pi}$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $N\ensuremath{\pi}\ensuremath{\pi}$ excited state contributes to the correlation functions with the insertion of the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parametrization of the experimental electric and magnetic data. Our final estimates for the isovector charges are ${g}_{A}^{u\ensuremath{-}d}=1.32(6)(5{)}_{\mathrm{sys}}$, ${g}_{S}^{u\ensuremath{-}d}=1.06(9)(6{)}_{\mathrm{sys}}$, and ${g}_{T}^{u\ensuremath{-}d}=0.97(3)(2{)}_{\mathrm{sys}}$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, ${⟨{r}_{A}^{2}⟩}^{u\ensuremath{-}d}=0.428(53)(30{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; (ii) the induced pseudoscalar charge, ${g}_{P}^{*}=7.9(7)(9{)}_{\mathrm{sys}}$; (iii) the pion-nucleon coupling, ${g}_{\ensuremath{\pi}\mathrm{NN}}=12.4(1.2)$; (iv) the electric charge radius squared, ${⟨{r}_{E}^{2}⟩}^{u\ensuremath{-}d}=0.85(12)(19{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; (v) the magnetic charge radius squared, ${⟨{r}_{M}^{2}⟩}^{u\ensuremath{-}d}=\phantom{\rule{0ex}{0ex}}0.71(19)(23{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; and (vi) the magnetic moment, ${\ensuremath{\mu}}^{u\ensuremath{-}d}=4.15(22)(10{)}_{\mathrm{sys}}$. All our results are consistent with phenomenological/experimental values but with larger errors. Last, we present a Pad\'e parametrization of the axial, electric, and magnetic form factors over the range $0.04<{Q}^{2}<1\text{ }\text{ }{\mathrm{GeV}}^{2}$ for phenomenological studies.

Axial-vector form factors of the baryon octet and chiral symmetry

We consider the axial-vector form factors of the baryon octet in flavor-SU(3) chiral perturbation theory. The baryon octet and decuplet and the pseudoscalar-meson octet are included as explicit degrees of freedom. We explore the use of on-shell meson and baryon masses in the one-loop contributions to the axial-vector form factors and focus on a consistent treatment in terms of chiral power counting. The convergence properties of such an approach are scrutinized. We discuss the potential for comparison to upcoming QCD lattice data.

Structure of the Ω baryon and the kaon cloud

Abstract We investigate the effects of the kaon cloud on the electromagnetic and axial-vector form factors of the Ω− baryon within the framework of the chiral quark-soliton model. We first derive the profile function of the chiral soliton in such a way that the kaon Yukawa tail is properly produced self-consistently. Then, we compute the electromagnetic form factors of the Ω− baryon. The results for the electromagnetic form factors are compared with the lattice data. We find that the results with the kaon tail are in better agreement with the lattice data than those obtained with the pion tail. We also study the axial-vector form factors of the Ω− baryon, examining the effects of the kaon cloud.

Decay parameters and the axial-vector form factors for strangeness changing as well as strangeness conserving semileptonic decays of the hyperons

We have calculated the axial-vector form factors for the hyperon semileptonic decays Bi → Bflv̄ in the chiral constituent quark model (χCQM). The decays considered here are the strangeness changing as well as strangeness conserving semileptonic decays of the hyperons. The conventional dipole form of parametrization has been used to analyse the Q2 dependence of the axialvector form factors (giBiBf (Q2)) as well their decay constants.

The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g − 2

We revisit well-known short-distance constraints relating the hadronic light-by light Green’s function to the ⟨VVA⟩ one, that have been a subject of debate over the past years in the context of the muon (g − 2). Specifically, we identify a relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly that, by contrast, has not received attention in the past. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors, but further applications are discussed as well, with special focus on the role of axial-vector mesons in the HLbL contribution to the muon (g − 2). Our results should also contribute to a better understanding of the, so far, controversial interplay among short-distance constraints with longitudinal and transverse degrees of freedom, such as axial-vector mesons. This is key to confront the theoretical and experimental result for the muon (g − 2) that, currently, exhibits a 4.2σ tension.

Calculation of the derivative of nucleon form factors in Nf=2+1 lattice QCD at Mπ=138 MeV on a (5.5 fm)3 volume

We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer ${q}^{2}$ using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the ${N}_{f}=2+1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass ${M}_{\ensuremath{\pi}}=138\text{ }\text{ }\mathrm{MeV}$, on a $(5.5\text{ }\text{ }\mathrm{fm}{)}^{4}$ lattice at a single lattice spacing of $a=0.085\text{ }\text{ }\mathrm{fm}$. In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the ${q}^{2}$ extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the ${q}^{2}$ extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of ${M}_{\ensuremath{\pi}}=510\text{ }\text{ }\mathrm{MeV}$. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.

The three-loop singlet contribution to the massless axial-vector quark form factor

We compute the three-loop corrections to the quark axial vector form factor in massless QCD, focusing on the pure-singlet contributions where the axial vector current couples to a closed quark loop. Employing the Larin prescription for γ5, we discuss the UV renormalization of the form factor. The infrared singularity structure of the resulting singlet axial-vector form factor is explained from infrared factorization, defining a finite remainder function.

Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data

We present a comparison of existing experimental data for the radiative leptonic decays $P\to\ell\nu_\ell\gamma$, where $P=K$ or $\pi$ and $\ell=e$ or $\mu$, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, $F_V$ and $F_A$ respectively. These were obtained using lattice QCD+QED simulations at order $O(\alpha_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to e\nu_e\gamma$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $K\to\mu\nu_\mu\gamma$ decays we observe differences of up to 3\,-\,4 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor $F^+$. The discrepancy between the theoretical and experimental values of the form factor $F^-=F_V-F_A$ is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors $F^+$ and $F^-$, as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond $V - A$ and/or non-universal corrections to the lepton couplings.

Quasielastic production of polarized τ leptons in ντ and ν¯τ scattering from nucleons

The cross sections and polarization components of the $\tau$ leptons produced in the charged current induced quasielastic $\nu_\tau~(\bar\nu_\tau) - N$ scattering have been studied. The theoretical uncertainties arising due to the use of different vector form factors and the axial dipole mass in the axial vector form factor have been investigated. Due to the high mass of $\tau$ lepton, the contributions from the term containing pseudoscalar and second class current form factors are non-negligible and contribute to the uncertainty in the cross section and polarization observables as these form factors are not well known. In view of the currently proposed experiments by DUNE, SHiP and DsTau collaborations to study the production of $\tau$ lepton, an updated calculation of the cross sections and polarizations of tau leptons in the case of quasielastic production have been done and the numerical results have been presented along with a discussion of the theoretical uncertainties.

Singlet, triplet, and octet axial-vector form factors of the spin−32+ decuplet baryons in the chiral quark constituent model

The axial-vector form factors of the $\mathrm{spin}\ensuremath{-}{\frac{3}{2}}^{+}$ decuplet baryons are investigated in the chiral constituent quark model using their explicit quark spin polarizations. The quark sea arises from the chiral symmetry breaking, which results in the Goldstone bosons mediating the interaction between constituent quarks. The axial-vector form factors, which have some physical significance corresponding to the flavor singlet current, flavor isovector (triplet) current, and the flavor hypercharge axial (octet) current at zero momentum transfer, are, respectively ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{0}(0)$, ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{3}(0)$, and ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{8}(0)$. In order to further understand the ${Q}^{2}$ dependence of these form factors, we have used the dipole form of parametrization. The qualitative and quantitative contribution of the quark sea has also been investigated by varying the transition probability of the chiral fluctuation.

Bc→J/ψ form factors for the full q2 range from lattice QCD

We present the first lattice QCD determination of the $B_c \rightarrow J/\psi$ vector and axial-vector form factors. These will enable experimental information on the rate for $B_c$ semileptonic decays to $J/\psi$ to be converted into a value for $V_{cb}$. Our calculation covers the full physical $q^2$ range of the decay and uses non-perturbatively renormalised lattice currents. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks on the second generation MILC ensembles of gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks. Our HISQ heavy quarks have masses ranging upwards from that of $c$; we are able to reach that of the $b$ on our finest lattices. This enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the $b$. We use our form factors to construct the differential rates for $B_c^- \rightarrow J/\psi \mu^- \bar{\nu}_\mu$ and obtain a total rate with $7\%$ uncertainty: $\Gamma(B_c^-\rightarrow J/\psi \mu^-\bar{\nu}_{\mu})/|\eta_{\mathrm{EW}}V_{cb}|^2 = 1.73(12)\times 10^{13} ~\mathrm{s}^{-1}$. Including values for $V_{cb}$, $\eta_{\mathrm{EW}}$ and $\tau_{B_c}$ yields a branching fraction for this decay mode of 0.0150(11)(10)(3) ~with uncertainties from lattice QCD, $\eta_\mathrm{EW}V_{cb}$ and $\tau_{B_c}$ respectively.

Axial-vector form factors of the baryon decuplet with flavor SU(3) symmetry breaking

The axial-vector form factors and axial-vector constants of the baryon decuplet are investigated within a pion mean-field approach, which is also known as the chiral quark-soliton model. Given an axial-vector current with a specified flavor, there are four different form factors of a decuplet baryon. When we consider the singlet, triplet, and octet axial-vector currents, we have twelve different form factors for each member of the baryon decuplet. We compute all these axial-vector form factors of the baryon decuplet, taking into account the rotational $1/N_c$ corrections and effects of flavor SU(3) symmetry breaking. We find that, for a given flavor, two of the form factors for a decuplet baryon are only independent within the present approach. We first examine properties of the axial-vector form factors of the $\Delta^+$ isobar and $\Omega^-$ hyperon. We also compare the results of the triplet axial-vector form factors of $\Delta^+$ with those from lattice QCD and those of the present work for the axial-vector constants of the baryon decuplet with the lattice data. All the results for other members of the baryon decuplet are then presented. The results of the axial charges are compared with those of other works. The axial masses and axial radii are also discussed.

On the axial-vector form factor of the nucleon and chiral symmetry

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at hbox {N}^3LO for the baryon masses and at hbox {N}^2LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

Erratum: Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point [Phys. Rev. D 99 , 014510 (2019)

We present the nucleon form factors and root-mean-square (RMS) radii measured on a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors at small momentum transfer region in $q^2\le 0.102$ GeV$^2$ with the standard plateau method choosing four source-sink separation times $t_{\rm sep}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large $t_{\rm sep}$ dependence in our lattice setup. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.

Polarized mathrm{q}overline{mathrm{q}} \u2192 Z+Higgs amplitudes at two loops in QCD: the interplay between vector and axial vector form factors and a pitfall in applying a non-anticommuting \u03b35

We consider QCD corrections to two loops for the polarized amplitudes of qoverline{q} → Z + Higgs boson. First we show how the polarized amplitudes of boverline{b} → Zh associated with a non-vanishing b-quark Yukawa coupling and a scalar or pseudoscalar Higgs boson h can be built up solely from vector form factors (FF) of properly grouped classes of diagrams, bypassing completely the need of explicitly manipulating γ5 in dimensional regularization (up to a few “anomalous”, i.e., triangle diagrams). We determine the contributions of the triangle diagrams in the heavy top limit. We present the analytic results of the vector FF and the triangle-diagram contributions to the axial vector FF, which are sufficient for deriving the two-loop QCD amplitudes for boverline{b} → Zh with a CP-even and CP-odd Higgs boson h. We derive the respective Ward identity for these amplitudes, which are subsequently verified to two-loop order in QCD using these FF. In addition, the FF of a class of corrections to qoverline{q} → ZH proportional to the top-Yukawa coupling are obtained analytically to two-loop order in QCD in the heavy-top limit using the Higgs-gluon effective Lagrangian where the top quark is integrated out. We address a pitfall that occurs when applying the non-anticommutating γ5 prescription to this class of contributions that has been overlooked so far in the literature. We attribute this issue to the fact that the absence of certain heavy-mass expanded diagrams in the infinite-mass limit of a scattering amplitude with an axial vector current depends on the particular γ5 prescription in use.