Tensor Form Factors Research Articles

Nucleon form factors with2+1flavor dynamical domain-wall fermions

We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axial-vector currents: the vector, induced tensor, axial-vector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with ${N}_{f}=2+1$ dynamical domain-wall fermions and Iwasaki gauge actions at $\ensuremath{\beta}=2.13$, corresponding to a cutoff ${a}^{\ensuremath{-}1}=1.73\text{ }\text{ }\mathrm{GeV}$, and a spatial volume of $(2.7\text{ }\text{ }\mathrm{fm}{)}^{3}$. The up and down-quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, $0.2<{q}^{2}<0.75\text{ }\text{ }{\mathrm{GeV}}^{2}$. The vector and induced tensor form factors are well described by the conventional dipole forms and result in significant underestimation of the Dirac and Pauli mean-squared radii and the anomalous magnetic moment compared to the respective experimental values. We show that the axial-vector form factor is significantly affected by the finite spatial volume of the lattice. In particular in the axial charge, ${g}_{A}/{g}_{V}$, the finite-volume effect scales with a single dimensionless quantity, ${m}_{\ensuremath{\pi}}L$, the product of the calculated pion mass and the spatial lattice extent. Our results indicate that for this quantity, ${m}_{\ensuremath{\pi}}L>6$ is required to ensure that finite-volume effects are below 1%.

Radiative corrections on theB→Pform factors with chiral current in the light-cone sum rules

Based on the approach of the vector form factor F(B ->pi,K)(+)(q(2)) in our previous papers, we extend the calculation of the radiative corrections to the B -> P (P stands pi, K, and all light pseudoscalar mesons) scalar and tensor form factors F(B -> P)(0,T)(q(2)) with chiral current in the light-cone sum rules (LCSRs). The most uncertain twist-3 contributions to the B -> P form factors can be naturally eliminated through a properly designed correlator. We present the next-leading-order formulas of F(B -> P)(+,0,T)(q(2)) with the b-quark pole mass that is universal. It has been shown that our results are simpler and less uncertain under the same parameter regions since we only need to calculate the next-leading order on the twist-2 part from the obtained LCSR. Second, we obtain f(B ->pi)(+,0)(0)=0.260(-0.040)(+0.059), f(B ->pi)(T)(0)=0.276(-0.039)(+0.052), f(B -> K)(+,0)(0)=0.334(-0.069)(+0.094), and f(B -> K)(T)(0)=0.379(-0.077)(+0.092) at q(2)=0 and the SU(f)(3)-breaking effects are discussed too.

Study of second-class currents effects on polarization characteristics in quasi-elastic neutrino (anti-neutrino) scattering by nuclei

The differential cross section of quasi-elastic neutrino scattering by nuclei is computed. The numerical analysis of energy dependence of the spin asymmetry, the angular electron-neutrino (e\nu) correlation and the charge asymmetry coefficients shows that the relative contribution of the second-class current (SCC) tensor form factor can reach some tens of percents in the case of particular values of final nuclei alignment and polarization.

Nucleon form factors from quenched lattice QCD with domain wall fermions

We present a quenched lattice calculation of the weak nucleon form factors: vector [${F}_{V}({q}^{2})$], induced tensor [${F}_{T}({q}^{2})$], axial vector [${F}_{A}({q}^{2})$] and induced pseudoscalar [${F}_{P}({q}^{2})$] form factors. Our simulations are performed on three different lattice sizes ${L}^{3}\ifmmode\times\else\texttimes\fi{}T={24}^{3}\ifmmode\times\else\texttimes\fi{}32$, ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$, and ${12}^{3}\ifmmode\times\else\texttimes\fi{}32$ with a lattice cutoff of ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.3\text{ }\text{ }\mathrm{GeV}$ and light quark masses down to about $1/4$ the strange quark mass (${m}_{\ensuremath{\pi}}\ensuremath{\approx}390\text{ }\text{ }\mathrm{MeV}$) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about $(3.6\text{ }\text{ }\mathrm{fm}{)}^{3}$, where the finite volume effects on form factors become negligible and the lower momentum transfers (${q}^{2}\ensuremath{\approx}0.1\text{ }\text{ }{\mathrm{GeV}}^{2}$) are accessible. The ${q}^{2}$ dependences of form factors in the low ${q}^{2}$ region are examined. It is found that the vector, induced tensor, and axial-vector form factors are well described by the dipole form, while the induced pseudoscalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling ${g}_{A}/{g}_{V}={F}_{A}(0)/{F}_{V}(0)=1.219(38)$ and the pseudoscalar coupling ${g}_{P}={m}_{\ensuremath{\mu}}{F}_{P}(0.88{m}_{\ensuremath{\mu}}^{2})=8.15(54)$, where the errors are statistical errors only. These values agree with experimental values from neutron $\ensuremath{\beta}$ decay and muon capture on the proton. However, the root mean-squared radii of the vector, induced tensor, and axial vector underestimate the known experimental values by about 20%. We also calculate the pseudoscalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.

Gravitational form factors of vector mesons in an AdS/QCD model

We calculate gravitational form factors of vector mesons using a holographic model of QCD. These provide restrictions on the generalized parton distributions of vector mesons, via the sum rules connecting stress tensor form factors to generalized parton distributions. We concentrate on the traceless part of the stress tensor, which suffices to fix the momentum and angular momentum sum rules. The vector mesons appear noticeably more compact measured by the gravitational form factors than by the charge form factor.

Form factors in the radiative pion decay

We perform an analysis of the form factors that rule the structure-dependent amplitude in radiative pion decay. The resonance contributions to π→eνeγ decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions 〈VVP〉 and 〈VAP〉, and by demanding the smoothening of the form factors at high transfer of momentum. A comparison between theoretical and experimental determination of the form factors is also carried out. We also consider and evaluate the role played by a non-standard tensor form factor. We conclude that, at present and due to the hadronic uncertainties, the search for new physics in this process is not feasible.

Thermal-motion-induced resonant reflections at the Ge K-edge: calculation of the intensity dependence on atomic displacements

In the Ge-structure, the forbidden Bragg reflections hk0 (h + k = 4n + 2) can be excited at the Ge K-edge due to both dipole-quadrupole scattering and dipole-dipole scattering of thermally vibrating atoms. The dipole-dipole contribution is referred to as TMI (Thermal Motion Induced) and is caused by the dependence of the atomic tensor form factors on the relative atomic displacements. This effect explains the strong increase of the 600 forbidden reflection intensity with temperature observed in experiments. In the present paper, both the dipole-quadrupole and the TMI contributions to the structure factor of the 600 reflection are calculated using the FDMNES code. Two models are considered, one assuming only displacements of the scattering atom, the other assuming all atoms in a supercell randomly displaced. Both approaches reveal a strong dependence of the dipole-dipole contribution to the tensor atomic factor on the atomic displacements and thus give a qualitative explanation of the temperature behavior of the forbidden reflection 600 observed in Ge.

POLARIZATION OF TAU LEPTONS PRODUCED IN QUASIELASTIC NEUTRINO–NUCLEON SCATTERING

A numerical analysis of the polarization vector of τ's produced through quasielastic ντ and [Formula: see text] interactions with nucleons is given with two models for vector electromagnetic form factors of proton and neutron. The impact of G parity violating axial and vector second-class currents is investigated by applying a simple heuristic model for the induced scalar and tensor form factors.

Covariant light-front approach forB→K*γ,K1γ,K2*γdecays

Exclusive radiative B decays $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma},$ ${K}_{1}(1270)\ensuremath{\gamma},$ ${K}_{1}(1400)\ensuremath{\gamma},$ and ${K}_{2}^{*}(1430)\ensuremath{\gamma}$ are studied in the framework of a covariant light-front quark model. The tensor form factor ${T}_{1}{(q}^{2})$ at ${q}^{2}=0,$ which is relevant to the decay $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma},$ is found to be 0.24, substantially smaller than what was expected from the conventional light-front model or light-cone sum rules. Taking into account the sizable next-to-leading order (NLO) corrections, the calculated branching ratio of $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ agrees with experiment, while most of the existing models predict too large $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ compared to the data. The relative strength of $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{1}(1270)\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{1}(1400)\ensuremath{\gamma}$ rates is very sensitive to the sign of the ${K}_{1}(1270)\ensuremath{-}{K}_{1}(1400)$ mixing angle. Contrary to the other models in which ${K}_{1}(1270)\ensuremath{\gamma}$ and ${K}_{1}(1400)\ensuremath{\gamma}$ rates are predicted to be comparable, it is found that one of them is strongly suppressed owing to a large cancellation between two different form factor terms. The calculated branching ratio of $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{2}^{*}\ensuremath{\gamma}$ is in a good agreement with experiment and this may imply the smallness of NLO corrections to this radiative decay mode.

β Decays of Nucleons and Quarks Embedded in the Nucleus

The β-ray angular distributions from purely spin aligned 1 2 B and 1 2 N nuclei were precisely remeasured to determine a new limit of the G-parity irregular induced tensor form factor in weak nucleon axial vector currentsand to study the in-medium mass renormalization of nucleons through the axial charge. A more reliable result on the induced tensor term was obtained as -0.31 < 2M f T /f A < 0.02 at a 90% confidence level. This result is consistent with the theoretical prediction in the framework of which the form factor is proportional to the mass difference between the up and down quarks. The axial charge of the axial vector current was determined to be y = 4.9 ′ 0.10, which may disclose an in-medium mass reduction of the decaying nucleon of (16 ′ 4)% at a 90% confidence level.

New limit of the G-parity irregular weak nucleon current detected in β decays of spin aligned 12B and 12N

The G-parity irregular induced tensor form factor in the weak nucleon axial vector current has been precisely determined by measuring the alignment correlation terms in the $\ensuremath{\beta}$-ray angular distributions of the purely spin aligned mirror pair ${}^{12}\mathrm{B}{(I}^{\ensuremath{\pi}}{=1}^{+},$ ${T}_{1/2}=20.2$ ms) and ${}^{12}\mathrm{N}{(I}^{\ensuremath{\pi}}{=1}^{+},$ ${T}_{1/2}=11.0$ ms) in order to place a new limit on the applicability of the G-parity conservation law. The coefficient of the induced tensor term was determined to be ${2Mf}_{T}{/f}_{A}=\ensuremath{-}0.21\ifmmode\pm\else\textpm\fi{}0.09$ (stat.) \ifmmode\pm\else\textpm\fi{}0.07 (syst.)\ifmmode\pm\else\textpm\fi{}0.05 (theory) at a 90% confidence level. The previously obtained data in the year 1996 was reanalyzed to be added to the present result. The combined result is ${2Mf}_{T}{/f}_{A}=\ensuremath{-}0.15\ifmmode\pm\else\textpm\fi{}0.12\ifmmode\pm\else\textpm\fi{}0.05$ (theory) at a 90% confidence level. The obtained induced tensor coefficient is vanishingly small and is consistent with the theoretical prediction based on QCD in the framework of which the induced tensor form factor is proportional to the mass difference between up and down quarks. Also we set constraints on the Kubodera-Delorme-Rho parameters from the present result together with the results of correlation-type experiments in the mass $A=8$ and 20 systems as $\ensuremath{\zeta}=\ensuremath{-}(0.12\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3} {\mathrm{MeV}}^{\ensuremath{-}1}$ and $\ensuremath{\lambda}=+(0.30\ifmmode\pm\else\textpm\fi{}0.88)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in the $1\ensuremath{\sigma}$ level.

Mesonic tensor form factors with the light front quark model

We study the tensor form factors for $P \to P$ and $P \to V$ transitions in the light-front quark model with $P$ and $V$ being pseudoscalar and vector mesons, respectively. We explore the behaviors of these form factors in the entire physical range of $0\leq p^2\leq (M_i - M_f)^2$. At the maximum recoil of $p^2=0$, we compare our results of the form factors in $B\to \pi,K,\rho,K^*$ with various other calculations in the literature.

Quark orbital angular momentum from lattice QCD

We calculate the quark orbital angular momentum of the nucleon from the quark energy-momentum tensor form factors on the lattice. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30 \pm 0.07$. From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17 \pm 0.06$ which is $\sim 34$% of the proton spin. We further predict that the gluon angular momentum to be $0.20 \pm 0.07$, i. e. $\sim$ 40% of the proton spin is due to the glue.

B¯→K*γfromD→K*l¯ν

The $\overline{B}\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$ branching fraction is predicted using heavy quark spin symmetry at large recoil to relate the tensor and (axial-)vector form factors, using heavy quark flavor symmetry to relate the B decay form factors to the measured $\stackrel{\ensuremath{\rightarrow}}{D}{K}^{*}\overline{l}\ensuremath{\nu}$ form factors, and extrapolating the semileptonic B decay form factors to large recoil assuming nearest pole dominance. This prediction agrees with data surprisingly well, and we comment on its implications for the extraction of $|{V}_{\mathrm{ub}}|$ from $\overline{B}\ensuremath{\rightarrow}\ensuremath{\rho}l\overline{\ensuremath{\nu}}.$

New limit of the G-parity irregular induced tensor current and of the axial charge in the weak nucleon current detected in alignment correlation terms of 12B and 12N β decays

The β-ray angular distributions from purely spin aligned 12 B and 12 N were precisely remeasured using a further refined spin-manipulation technique. We determined the amount of a G -parity violating induced tensor form factor in a weak axial vector current as 2 M f T /f A = + 0.22 ± 0.05 (stat) ± 0.15 (syst) ± 0.05 (theor.). The result is consistent with the theoretical prediction in the framework of which induced tensor form factor is proportional to the u- and d-quark mass difference. We also determined the axial charge of the weak nucleon current to be y = 4.66 ± 0.06 (stat) ± 0.13 (syst), which can be explained mainly in terms of the impulse value y 1A and soft pion exchange effect y EX . There, however, remains 18 % unexplained part of the experimental value relative to the theoretical value y th = y 1A + y EX = 4.12. An in medium mass reduction of 12 ± 4 % may explain the unexplained part if there is such an effect for the decaying nucleon.

Spin control and structure of weak nucleon currents in A= 8, 12, 20 and 41

The β-ray angular distributions from purely spin aligned 12B and 12N were precisely remeasured using a further refined spin-manipulation technique. We determined the amount of a g-parity violating induced tensor form factor in a weak axial vector current as 2M fT/fA= +0.22 ± 0.05\ (stat.) ± 0.15\ (syst.) ± 0.05\ (theor.). The result is consistent with the theoretical prediction in the framework of which induced tensor form factor is proportional to u- and d-quark mass difference. To study the g-parity violation in weak nucleon current systematically, we have started to measure the alignment correlation terms of 8Li, 8B, 20F and 41Sc.

Reduction of one-loop tensor form factors to scalar integrals: a general scheme

A general method for reducing tensor form factors, which appear in one-loop calculations in dimensional regularization, to scalar integrals is presented. The method is an extension of the reduction scheme introduced by Passarino and Veltman [Nucl. Phys. B 160 (1979) 151] and is applicable in all regions of parameter space including those where the kinematic Gram determinant vanishes. New relations between the form factors that are valid for the vanishing Gram determinant play a key rôle in the extended scheme.

Meson substructure and the ϱNN and ωNN couplings

Estimates are made of the ϱNN and ωNN vector and tensor coupling constants and form factors by consideration of vector qq correlations as producted by a quark model nucleon source. Attention is paid to the finite extent of the qq correlations and to their departure from true bound state form at space-like momenta.

Order-α radiative correction to 6He and 32Ar β decay recoil spectra

Order-α model independent radiative correction results to the 6He → 6Li and 32Ar → 32Cl β decay recoil spectra are presented. The effects of these corrections on the electron-neutrino correlation parameter ( a eν ) and the induced tensor form factor are discussed (taking into account the most important experimental details of these measurements). In the case of 6He beta decay, the shift of the a eν value due to our radiative correction calculation is larger than the total experimental error of the last, precise measurement. The order- Zα 2 radiative correction of the recoil spectrum is also estimated. Recoil-order formulae are given for the beta energy - recoil energy Dalitz distribution and the recoil spectrum.

Determination of ||Vts|| from D-->K*l nu and B-->K* gamma data via heavy quark symmetry and perturbative QCD.

We use heavy quark effective theory (HQET) and perturbative QCD to study the heavy-meson--light-vector-meson transitions involved in D and B decays. HQET is used to relate the measured D\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$l\ensuremath{\nu} vector and axial-vector form factors at four-momentum transfer ${\mathit{q}}^{2}$=0 to the B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma} tensor and axial-tensor form factors at ${\mathit{q}}^{2}$=16.5 ${\mathrm{GeV}}^{2}$. Perturbative QCD is then used to find matching conditions for the B-meson form factors at ${\mathit{q}}^{2}$=0. A five parameter ``vector-dominance''-type fit of the two HQET form factors, consisting of single pole, double pole, and subtraction terms, is used to match the data at ${\mathit{q}}^{2}$=16.5 ${\mathrm{GeV}}^{2}$ to QCD at ${\mathit{q}}^{2}$=0. The values at ${\mathit{q}}^{2}$=0 are compared with recent data on the exclusive rate for B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma} decay to extract a value for the Cabibbo-Kobayashi-Maskawa matrix element \ensuremath{\Vert}${\mathit{V}}_{\mathit{t}\mathit{s}}$\ensuremath{\Vert}=0.026, with 23% experimental uncertainty, and 29% theoretical uncertainty from higher order QCD effects and violations of heavy quark symmetry.