Tensor Form Factors Research Articles

Modeling of the Resonant X-ray Response of a Chiral Cubic Phase

The structure of a continuous-grid chiral cubic phase made of achiral constituent molecules is a hot topic in the field of thermotropic liquid crystals. Several structural models have been proposed so far. Resonant X-ray scattering (RXS), which gives information on the molecular orientation in the unit cell, could be applied to select the most appropriate model. We modeled the RXS response for the recently proposed chiral cubic phase structure with an all-hexagon chiral continuous grid. A tensor form factor of a unit cell is constructed, which enables calculation of intensities of peaks for all Miller indices. We find that all the symmetry allowed peaks are resonantly enhanced, and their intensity is much stronger than the intensity of the symmetry forbidden (resonant) peaks. In particular, we predict that a strong resonant enhancement of the symmetry allowed peaks (011) and (002), not observed in a nonresonant scattering, could be observed by RXS at the carbon absorption edge. By RXS at the sulfur absorption edge, one might observe a resonant peak (113) and resonantly enhanced peak (233), and resonant enhancement of all the peaks that are observed in a nonresonant scattering, which probably hide the rest of the predicted resonant peaks.

Kerr-Newman stress-tensor from minimal coupling

In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

Tensor form factors of P→ P, S, V and A transitions within standard and covariant light-front approaches * * Supported by the National Natural Science Foundation of China (11875122) and the Program for Innovative Research Team in University of Henan Province (19IRTSTHN018)

We investigate the tensor form factors of , and A transitions within the standard light-front (SLF) and the covariant light-front (CLF) quark models (QMs). The self-consistency and Lorentz covariance of CLF QM are analyzed via these quantities, and the effects of zero-mode are discussed. For the and A transitions, besides the inconsistency between the results extracted via longitudinal and transverse polarization states, which is caused by the residual -dependent spurious contributions, we find and analyze a “novel” self-consistence problem of the traditional CLF QM, caused by different strategies for dealing with the trace term in CLF matrix element. A possible solution to the problems of traditional CLF QM is discussed and confirmed numerically. Finally, the theoretical predictions for the tensor form factors of some and ( ) induced and A transitions are updated within the CLF QM with a self-consistent scheme.

Isovector and isoscalar tensor form factors of N(1535)→N transition in light-cone QCD

We have applied isovector and isoscalar tensor current to evaluate the tensor form factors of the $ N(1535) \rightarrow N $ transition with the help of the light-cone QCD sum rule method. In numerical computations, have used the most general forms of the interpolating current for the nucleon and the tensor current together with two different sets of the input parameters in the DAs of the $N(1535)$ state. We have obtained that the values of $N(1535) \rightarrow N$ transition tensor form factors very sensitive to the input parameters of the distribution amplitudes of the $N(1535)$ state. We have acquired that the $Q^2$ dependence of $N(1535) \rightarrow$ transition tensor form factors is well defined by a p-pole fit function.

Generalized parton distribution functions of $\rho$ meson

We report our recent studies of generalized parton distribution functions of a \rhoρ meson with the help of a light-front constituent quark model. The electromagnetic form factors and structure functions of the system are discussed. Moreover, we show our results for its gravitational form factors (or energy-momentum tensor form factors) and other mechanical properties, like mass distributions, pressures, shear forces, and D-D−term.

Nucleon\u2019s energy\u2013momentum tensor form factors in light-cone QCD

We use the energy–momentum tensor (EMT) current to compute the EMT form factors of the nucleon in the framework of the light cone QCD sum rule formalism. In the calculations, we employ the most general form of the nucleon’s interpolating field and use the distribution amplitudes (DAs) of the nucleon with two sets of the numerical values of the main input parameters entering the expressions of the DAs. The directly obtained results from the sum rules for the form factors are reliable at Q^2ge 1 GeV^2 : to extrapolate the results to include the zero momentum transfer squared with the aim of estimation of the related static physical quantities, we use some fit functions for the form factors. The numerical computations show that the energy–momentum tensor form factors of the nucleon can be well fitted to the multipole fit form. We compare the results obtained for the form factors at Q^2=0 with the existing theoretical predictions as well as experimental data on the gravitational form factor d_1^q(0). For the form factors M_2^q (0) and J^q(0) a consistency among the theoretical predictions is seen within the errors: our results are nicely consistent with the Lattice QCD and chiral perturbation theory predictions. However, there are large discrepancies among the theoretical predictions on d_1^q(0). Nevertheless, our prediction is in accord with the JLab data as well as with the results of the Lattice QCD, chiral perturbation theory and KM15-fit. Our fit functions well define most of the JLab data in the interval Q^2in [0,0.4] GeV^2 , while the Lattice results suffer from large uncertainties in this region. As a by-product, some mechanical properties of the nucleon like the pressure and energy density at the center of nucleon as well as its mechanical radius are also calculated and their results are compared with other existing theoretical predictions.

CP asymmetry in τ→KSπντ decays within the standard model and beyond

Motivated by the $2.8\sigma$ discrepancy observed between the BaBar measurement and the Standard Model prediction of the CP asymmetry in $\tau\to K_S\pi\nu_\tau$ decays, as well as the prospects of future measurements at Belle II, we revisit this observable in this paper. Firstly, we reproduce the known CP asymmetry due to $K^0 -\bar{K}^0$ mixing by means of the reciprocal basis, which is convenient when a $K_{S(L)}$ is involved in the final state. As the $K\pi$ tensor form factor plays a crucial role in generating a non-zero direct CP asymmetry that can arise only from the interference of vector and tensor operators, we then present a dispersive representation of this form factor, with its phase obtained in the context of chiral theory with resonances, which fulfills the requirements of unitarity and analyticity. Finally, the $\tau\to K_S\pi\nu_\tau$ decays are analyzed both within a model-independent low-energy effective theory framework and in a scalar leptoquark scenario. It is observed that the CP anomaly can be accommodated in the model-independent framework, even at the $1\sigma$ level, together with the constraint from the branching ratio of $\tau^-\to K_S\pi^-\nu_\tau$ decay; it can be, however, marginally reconciled only at the $2\sigma$ level, due to the specific relation between the scalar and tensor operators in the scalar leptoquark scenario. Once the combined constraints from the branching ratio and the decay spectrum of this decay are taken into account, these possibilities are however both excluded, even without exploiting further the stronger bounds from the (semi-)leptonic kaon decays under the assumption of lepton-flavour universality, as well as from the neutron electric dipole moment and $D-\bar{D}$ mixing under the assumption of $SU(2)$ invariance of the weak interactions.

Monopole and quadrupole contributions to the angular momentum density

The energy-momentum tensor form factors contain a wealth of information about the nucleon. It is insightful to visualize this information in terms of 3D or 2D densities related by Fourier transformations to the form factors. The densities associated with the angular momentum distribution were recently shown to receive monopole and quadrupole contributions. We show that these two contributions are uniquely related to each other. The quadrupole contribution can be viewed as induced by the monopole contribution, and contains no independent information. Both contributions however play important roles for the visualization of the angular momentum density.

Tensor form factor of D→π(K)ℓν and D→π(K)ℓℓ decays with Nf=2+1+1 twisted-mass fermions

We present the first lattice Nf=2+1+1 determination of the tensor form factor $f_T^{D \pi(K)}(q^2)$ corresponding to the semileptonic and rare $D \to \pi(K)$ decays as a function of the squared 4-momentum transfer $q^2$. Together with our recent determination of the vector and scalar form factors we complete the set of hadronic matrix elements regulating the semileptonic and rare $D \to \pi(K)$ transitions within and beyond the Standard Model, when a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by ETMC with Nf=2+1+1 flavors of dynamical quarks, which include in the sea, besides two light mass-degenerate quarks, also the strange and charm quarks with masses close to their physical values. We simulated at three different values of the lattice spacing and with pion masses as small as 220 MeV. The matrix elements of the tensor current are determined for plenty of kinematical conditions in which parent and child mesons are either moving or at rest. As in the case of the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed also in the data for the tensor form factor and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum and infinite volume limits we determine the tensor form factor in the whole kinematical region accessible in the experiments. A set of synthetic data points, representing our results for $f_T^{D \pi(K)}(q^2)$ for several selected values of $q^2$, is provided and the corresponding covariance matrix is also available. At zero four-momentum transfer we get $f_T^{D \pi}(0) = 0.506 (79)$ and $f_T^{D K}(0) = 0.687 (54)$, which correspond to $f_T^{D \pi}(0)/f_+^{D \pi}(0) = 0.827 (114)$ and $f_T^{D K}(0)/f_+^{D K}(0)= 0.898 (50)$.

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Phenomenology of {Lambda}_bto {Lambda}_ctau {overline{nu}}_{tau } using lattice QCD calculations

In a recent paper we studied the effect of new-physics operators with different Lorentz structures on the semileptonic {Lambda}_bto {Lambda}_ctau {overline{nu}}_{tau } decay. This decay is of interest in light of the R(D(*)) puzzle in the semileptonic overline{B}to {D}^{left(ast right)}tau {overline{nu}}_{tau } decays. In this work we add tensor operators to extend our previous results and consider both model-independent new physics (NP) and specific classes of models proposed to address the R(D(*)) puzzle. We show that a measurement of Rleft({Lambda}_cright)=mathrm{mathcal{B}}left[{Lambda}_bto {Lambda}_ctau {overline{nu}}_{tau}right]/mathrm{mathcal{B}}left[{Lambda}_bto {Lambda}_cell {overline{nu}}_{ell}right] can strongly constrain the NP parameters of models discussed for the R(D(*)) puzzle. We use form factors from lattice QCD to calculate all {Lambda}_bto {Lambda}_ctau {overline{nu}}_{tau } observables. The Λb → Λc tensor form factors had not previously been determined in lattice QCD, and we present new lattice results for these form factors here.

Nucleon tensor form factors in a relativistic confined quark model

We present results for the isotriplet and isosinglet tensor form factors of the nucleon in the relativistic confined quark model. The model allows us to calculate not only their normalizations at ${Q}^{2}=0$ and the related tensor charges, but also the full ${Q}^{2}$-dependence. Our results are compared to existing data and predictions of other theoretical approaches. We stress the importance of these form factors for the phenomenology of physics beyond the Standard Model.

Tensor form factors of the octet hyperons in QCD

Light-cone QCD sum rules to leading order in QCD are used to investigate the tensor form factors of the $\Sigma-\Sigma$, $\Xi-\Xi$ and $ \Sigma-\Lambda$ transitions in the range $1 GeV^2 \leq Q^2 \leq 10 GeV^2$. The DAs of $\Sigma$, $\Xi$ and $\Lambda$ baryon have been calculated without higher order terms. Then, study including higher order corrections have been done for $\Sigma$ and $\Lambda$ baryon. The result of form factors are obtained using these two DAs. We make a comparison with the predictions of the chiral quark soliton model.

Modification of generalized vector form factors and transverse charge densities of the nucleon in nuclear matter

We investigate the medium modification of the generalized vector form factors of the nucleon, which include the electromagnetic and energy-momentum tensor form factors, based on an in-medium modified $\pi$-$\rho$-$\omega$ soliton model. We find that the vector form factors of the nucleon in nuclear matter fall off faster than those in free space, which implies that the charge radii of the nucleon become larger in nuclear medium than in free space. We also compute the corresponding transverse charge densities of the nucleon in nuclear matter, which clearly reveal the increasing of the nucleon size in nuclear medium.

Heavy-quark-mass expansion of vector and tensor currents and intrinsic charm in nucleon form factors

The framework of the expansion by subgraphs is used to compute asymptotic expansions for the vector and the tensor currents in the limit of large quark masses. We use the results to obtain an estimate for the influence of heavy quarks on the nucleon electromagnetic and tensor form factors.

Form factors of B, Bs → η (′) and D, Ds → η (′) transitions from QCD light-cone sum rules

In the framework of the QCD light-cone sum rules (LCSRs) we present the analysis of all $B, B_{s}\to \eta^{(\prime)}$ and $D, D_{s}\to \eta^{(\prime)}$ form factors ($f^+, f^0$ and $f^T$) by including $m_{\eta^{(\prime)}}^2$ corrections in the leading (up to the twist-four) and next-to-leading order (up to the twist-three) in QCD, and two-gluon contributions to the form factors at the leading twist. The SU(3)-flavour breaking corrections and the axial anomaly contributions to the distribution amplitudes are also consistently taken into account. The complete results for the $f^0$ and $f^T$ form factors of $B,B_s \to \eta^{(\prime)}$ and $D, D_{s} \to \eta^{(\prime)}$ relevant for processes like $B \to \eta^{(\prime)} \tau \nu_{\tau}$ or $B_{s} \to \eta^{(\prime)} l^+ l^-$ are given for the first time, as well as the two-gluon contribution to the tensor form factors. The values obtained for the $f^+$ form factors are as follows: $f^+_{B\eta}(0)= 0.168^{+0.042}_{-0.047}$, $|f^+_{B_s\eta}(0)|= 0.212^{+0.015}_{-0.013}$, $f^+_{B\eta^\prime}(0)= 0.130^{+0.036}_{-0.032}$, $f^+_{B_s\eta^\prime}(0)= 0.252^{+0.023}_{-0.020}$ and $f^+_{D\eta}(0)= 0.429^{+0.165}_{-0.141}$, $|f^+_{D_s\eta}(0)|= 0.495^{+0.030}_{-0.029}$, $f^+_{D\eta^\prime}(0)= 0.292^{+0.113}_{-0.104}$, $f^+_{D_s\eta^\prime}(0)= 0.558^{+0.047}_{-0.045}$. Also phenomenological predictions for semileptonic $B, B_{s}\to \eta^{(\prime)}$ and $D, D_{s}\to \eta^{(\prime)}$ decay modes are given.

B→πll Form Factors for New Physics Searches from Lattice QCD.

The rare decay B→πℓ^{+}ℓ^{-} arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B→π tensor form factor f_{T}. Together with the vector and scalar form factors f_{+} and f_{0} from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B^{+}→π^{+}μ^{+}μ^{-})=20.4(2.1)×10^{-9} in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].

Weak K → π generalized form factors and transverse transition quark-spin density from the instanton vacuum

We investigate the generalized K→π transition vector and tensor form factors, from which we derive the transverse quark spin density in the course of the K→π transition, based on the nonlocal chiral quark model from the instanton vacuum. The results of the transition tensor form factor are in good agreement with recent data of lattice QCD. The behavior of the transverse quark spin density of the K→π transition turns out to be very similar to those of the pion and the kaon.

In-medium modified energy-momentum tensor form factors of the nucleon within the framework of a π - ρ - ω soliton model

We investigate the energy-momentum tensor form factors of the nucleon in nuclear medium, based on an in-medium modified $\pi$-$\rho$-$\omega$ soliton model, with medium modifications of the mesons considered. The results allow us to establish general features of medium modifications of the structure of nucleons bound in a nuclear medium.

Precise calculation of the dilepton invariant-mass spectrum and the decay rate inB±→π±μ+μ−in the SM

We present a precise calculation of the dilepton invariant-mass spectrum and the decay rate for $B^\pm \to \pi^\pm \ell^+ \ell^-$ ($\ell^\pm = e^\pm, \mu^\pm $) in the Standard Model (SM) based on the effective Hamiltonian approach for the $b \to d \ell^+ \ell^-$ transitions. With the Wilson coefficients already known in the next-to-next-to-leading logarithmic (NNLL) accuracy, the remaining theoretical uncertainty in the short-distance contribution resides in the form factors $f_+ (q^2)$, $f_0 (q^2)$ and $f_T (q^2)$. Of these, $f_+ (q^2)$ is well measured in the charged-current semileptonic decays $B \to \pi \ell \nu_\ell$ and we use the $B$-factory data to parametrize it. The corresponding form factors for the $B \to K$ transitions have been calculated in the Lattice-QCD approach for large-$q^2$ and extrapolated to the entire $q^2$-region using the so-called $z$-expansion. Using an $SU(3)_F$-breaking Ansatz, we calculate the $B \to \pi$ tensor form factor, which is consistent with the recently reported lattice $B \to \pi$ analysis obtained at large~$q^2$. The prediction for the total branching fraction ${\cal B} (B^\pm \to \pi^\pm \mu^+ \mu^-) = (1.88 ^{+0.32}_{-0.21}) \times 10^{-8}$ is in good agreement with the experimental value obtained by the LHCb Collaboration. In the low $q^2$-region, heavy-quark symmetry (HQS) relates the three form factors with each other. Accounting for the leading-order symmetry-breaking effects, and using data from the charged-current process $B \to \pi \ell \nu_\ell$ to determine $f_+ (q^2)$, we calculate the dilepton invariant-mass distribution in the low $q^2$-region in the $B^\pm \to \pi^\pm \ell^+ \ell^-$ decay. This provides a model-independent and precise calculation of the partial branching ratio for this decay.