Tensor Form Factors Research Articles

Study of τ− → ωπ−ντ decay in resonance chiral theory with tensor sources

In this work, we make a study of the τ− → ωπ−ντ decay in the framework of low-energy effective field theory. The JPG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {J}^{\\mathcal{P}G} $$\\end{document} decompositions of the quark currents and the ωπ final state show that, besides the Standard Model vector interaction, only the non-standard tensor interaction can have a non-zero contribution to the decay. To discuss its effect, a reliable calculation of the ωπ tensor form factors is necessary. After constructing the Lagrangian of resonance chiral theory with external tensor sources, we calculate both the vector and tensor form factors with the relevant resonance couplings determined by combining the QCD short-distance constraints, the fit to the spectral function of τ− → ωπ−ντ decay, as well as the matching between the Op4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^4\\right) $$\\end{document} odd-intrinsic-parity operators after integrating out the vector resonances and the Op6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^6\\right) $$\\end{document} operators of chiral perturbation theory. The new physics effect is then investigated in the distributions of the spectral function and the forward-backward asymmetry of τ− → ωπ−ντ decay. We find that the spectral function is dominated by the Standard Model, and the non-standard tensor contribution is negligible. However, since the forward-backward asymmetry can be only generated with a non-zero tensor interaction, the observable is quite sensitive to this kind of new physics. A future measurement of the observable at the Belle II experiment as well as at the proposed Tera-Z and STCF facilities is, therefore, strongly called for to check the existence of such a non-standard tensor interaction.

Hyperon semileptonic decays in QCD sum rules

We investigate the hyperon semileptonic decays within the framework of QCD sum rules. The flavor SU(3) symmetry breaking effects are analyzed via the relevant form factors and corresponding branching fractions. Employing the z-series parameterization to capture the q2 dependence of form factors, we calculate the hyperon semileptonic decay rates and confront them with the recent experimental measurements. Moreover, we calculate as well the non-standard tensor form factors, which involve certain new physics beyond the standard model.

B→D* and Bs→Ds* vector, axial-vector and tensor form factors for the full q2 range from lattice QCD

We compute the complete set of Standard Model (SM) and tensor B→D*ℓν¯ and Bs→Ds*ℓν¯ semileptonic form factors across the full kinematic range of the decays using second generation MILC nf=2+1+1 highly improved staggered quark (HISQ) gluon field configurations and HISQ valence quarks, with the method. Lattice spacings range from 0.09 to 0.044 fm with pion masses from ≈300 MeV down to the physical value and heavy quark masses ranging between ≈1.5mc and 4.1mc≈0.9mb; currents are normalized nonperturbatively. Using the recent untagged B→D*ℓν¯ℓ data from Belle and Bs→Ds*μν¯μ from LHCb together with our form factors, we determine a model independent value of Vcb=39.03(56)exp(67)latt×10−3, in agreement with previous exclusive determinations and in tension with the most recent inclusive result at the level of 3.6σ. We also observe a ≈1σ tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a purely theoretical Standard Model value for the ratio of semitauonic and semimuonic decay rates, R(D*)=0.273(15), which we find to be closer to the recent Belle measurement and heavy flavor averaging group average than theory predictions using fits to experimental differential rate data for B→D*ℓν¯ℓ. Determining Vcb from our form factors and the experimental total rate for B→D*ℓν also gives a value in agreement with inclusive results. We also compute the longitudinal polarization fraction for the semitauonic mode, FLD*=0.395(24), which is in tension at the level of 2.2σ with the recent Belle measurement. Our calculation combines B→D* and Bs→Ds* lattice results in a simultaneous chiral continuum extrapolation, maintaining correlations between both modes. We then give results for both B→D* and Bs→Ds*, with the Bs→Ds* results superseding our previous lattice computation. We also give the chiral perturbation theory needed to analyze the tensor form factors. Published by the American Physical Society 2024

Four-gluon vertex from the Curci-Ferrari model at one-loop order

We compute the four-gluon vertex from the Curci-Ferrari model at one-loop order for a collinear configuration. Our results display a good agreement with the first lattice data for this vertex, released very recently []. A noteworthy novelty of our work is that we can provide analytical expressions for the four-gluon vertex in collinear configurations, together with a renormalization scheme that allows us to perform reliable perturbative computations even in the infrared regime. We observe an infrared suppression in the form factor associated with the tree-level four-gluon tensor with a possible zero crossing in the deep infrared which demands new lattice investigations to be confirmed. Moreover, we report an infrared divergence in the completely symmetric tensor form factor due to the ghost-loop contributions. These results come as predictions, since previous two-point correlations fix all the available parameters of the model, up to an overall constant factor. Published by the American Physical Society 2024

Proton’s gluon GPDs at large skewness and gravitational form factors from near threshold heavy quarkonium photoproduction

We study the exclusive near threshold photoproduction of heavy quarkonium in the framework of the generalized parton distribution (GPD) factorization, taking the J/ψ production as an example. Because of the threshold kinematics, the Compton-like amplitudes are related to gluon GPDs at large skewness ξ, distinct from the common kinematics in asymptotic high energy where the skewness is typically small. We discuss the nature of large-ξ expansion of these amplitudes in terms of the moments of gluon GPDs in the large-ξ limit. Based on that, we propose several ways to extract the first few moments of the gluon GPDs from these amplitudes, with the leading ones corresponding to the gluonic gravitational or energy-momentum tensor form factors (GFFs). We apply these methods to analyze the recent near threshold J/ψ production measurements by the J/ψ 007 experiment and GlueX Collaboration and find that the ξ scaling of the measured differential cross sections is consistent with the asymptotic behavior. However, the current data are not accurate enough yet for a complete determination of the gluonic GFFs, and therefore we consider some prospects for better extractions in the future. Published by the American Physical Society 2024

Parity-odd 3-point functions from CFT in momentum space and the chiral anomaly

We illustrate how the Conformal Ward Identities (CWI) in momentum space for parity-odd correlators determine the structure of a chiral anomaly interaction, taking the example of the VVA (vector/vector/axial-vector) and AAA correlators in momentum space. Only the conservation and the anomalous WIs, together with the Bose symmetry, are imposed from the outset for the determination of the correlators. We use a longitudinal/transverse decomposition of tensor structures and form factors. The longitudinal (L) component is fixed by the anomaly content and the anomaly pole, while in the transverse (T) sector we define a new parameterization. We relate the latter both to the Rosenberg original representation of the VVA and to the longitudinal/transverse (L/T) one, first introduced in the analysis of g-2 of the muon in the investigation of the diagram in the chiral limit of QCD. The correlators are completely identified by the conformal constraints whose solutions are fixed only by the anomaly coefficient, the residue of the anomaly pole. In both cases, our CFT result matches the one-loop perturbative expression, as expected. The CWIs for correlators of mixed chirality J_L J J_R generate solutions in agreement with the all-orders nonrenormalization theorems of perturbative QCD and in the chiral limit.

B→K and D→K form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K\ell^+\ell^-$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons.

Scrutinizing new physics in semi-leptonic B c → J/ψτν decay

We perform a global analysis of the b → cτν data using the recent lattice results on the B c → J/ψ vector and axial-vector form factors. To explore the effects from the tensor operator of new physics beyond the Standard Model, we determine the tensor form factors by using the non-relativistic QCD (NRQCD) relations between tensor and (axial-)vector form factors. Based on the lattice + NRQCD form factors, we fit the Wilson coefficients and the new physics couplings in R 2, S 1 and U 1 leptoquark models by including the recently measured R(Λ c ) and imposing the relaxed constraint in light of the recent studies on LEP1 data and B c lifetime. We give predictions for the experimental observables including R(J/ψ), P τ (J/ψ), F L (J/ψ) and as well as their q 2 distribution in new physics scenarios/models. Our results suggest that the longitudinal τ polarization fraction P τ (J/ψ) and the forward–backward asymmetry are useful for testing the R 2 leptoquark model.

Parametrization of transition energy-momentum tensor form factors

While the Lorentz structures of the N→Δ transition matrix element of the vector current are well-known, that of the symmetric energy-momentum tensor current is unknown. In this letter, we first reproduce the Lorentz structures of the 12±→12±, 12∓→12±, and 12∓→32± transition matrix elements of the vector current. We also repeat the parametrizations of the symmetric energy-momentum tensor current for the 12±→12± and 12∓→12± transitions. We then consider both 12±→32± and 12∓→32± matrix elements of the symmetric energy-momentum tensor current (say, N→Δ transition) for the first time. We found that there are five independent conserved and four independent non-conserved energy-momentum tensor form factors.

Energy-Momentum Tensor Form Factors in QED

We present the results for the Energy-Momentum Tensor (EMT) form factor D(t) at one-loop accuracy in quantum electrodynamics for an electron state. We report the the results in the case of both zero and nonzero photon mass. Moreover, individual electron and photon contributions to the EMT are investigated.

Next-to-leading order QCD calculation of Bc to charmonium tensor form factors

We present a next-to-leading order (NLO) QCD corrections to $B_c\to \eta_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end.

Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD

We present a calculation of the scalar, vector, and tensor form factors for the pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a strange and a charm quark (${N}_{f}=2+1+1$) of maximally twisted mass fermions with clover improvement. The corresponding pion and kaon masses are about 265 MeV and 530 MeV, respectively. The calculation is done in both rest and boosted frames obtaining data for four-vector momentum transfer squared up to $\ensuremath{-}{q}^{2}=2.5\text{ }\text{ }{\mathrm{GeV}}^{2}$ for the pion and $3\text{ }\text{ }{\mathrm{GeV}}^{2}$ for the kaon. The excited-states effects are studied by analyzing six values of the source-sink time separation for the rest frame (1.12--2.23 fm) and for four values for the boosted frame (1.12--1.67 fm). The lattice data are renormalized nonperturbatively and the results for the scheme- and scale-dependent scalar and tensor form factors are presented in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We apply different parametrizations to describe ${q}^{2}$-dependence of the form factors to extract the scalar, vector, and tensor radii, as well as the tensor anomalous magnetic moment. We compare the pion and kaon form factors to study SU(3) flavor symmetry breaking effects. By combining the data for the vector and tensor form factors we also obtain the lowest moment of the densities of transversely polarized quarks in the impact parameter space. Finally, we give an estimate for the average transverse shift in the $y$ direction for polarized quarks in the $x$ direction.

Form factor counting and HQET matching for new physics in Λb→Λc*lν

We calculate the $\Lambda_b \to \Lambda_c^*(2595) l \nu$ and $\Lambda_b \to \Lambda_c^*(2625) l \nu$ form factors and decay rates for all possible $b \to c l \bar\nu$ four-Fermi interactions in and beyond the Standard Model (SM), including nonzero charged lepton masses and terms up to order $\mathcal{O}(\alpha_s, 1/m_{c,b})$ in the heavy quark effective theory (HQET). We point out a subtlety involving the overcompleteness of the representation of the spin-parity $1/2^+ \to 3/2^-$ antisymmetric tensor form factors, relevant also to other higher excited-state transitions, and present a general method for the counting of the physical form factors for any hadronic transition matrix element and their matching onto HQET. We perform a preliminary fit of a simple HQET-based parametrization of the $\Lambda_b \to \Lambda_c^*$ form factors at $\mathcal{O}(\alpha_s, 1/m_{c,b})$ to an existing quark model, providing preliminary predictions for the lepton universality ratios $R(\Lambda_c^*)$ beyond the SM. Finally, we examine the possible incompatibility of recent lattice QCD results with expectations from the heavy-quark expansion and available experimental data.

Three-gluon vertex in Landau-gauge from quenched-lattice QCD in general kinematics

We report on a novel and extensive lattice QCD analysis for the three-gluon vertex from quenched lattice-QCD simulations. Using standard Wilson action, we have computed the three-gluon vertex beyond the usual kinematic restriction to the symmetric (q2 = r2 = p2) and soft-gluon (p = 0) cases where it depends on a single momentum scale. The so-dubbed bisectoral case (r2 = q2 ≠ p2), where the transversely projected vertex can be cast in terms of three independent tensors, have been the object of a recent exhaustive scrutiny [1], also shown in this communication. Herein, beyond this special case, results for kinematic configurations with three different squared momenta are also presented. All data considered, the lattice estimate of the three-gluon vertex exhibits a clear dominance of the tree-level tensor form factor.

Generalized parton distributions and spin structures of light mesons from a light-front Hamiltonian approach

We present the generalized parton distributions (GPDs) for the valence quarks of the pion and the kaon in both momentum space and position space within the basis light-front quantization framework. These GPDs are obtained from the eigenvectors of a light-front effective Hamiltonian consisting of the holographic quantum chromodynamics (QCD) confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu-Jona--Lasinio interactions for the valence quarks of mesons. We then calculate the generalized form factors of the pion and the kaon from the moments of these GPDs. Combining the tensor form factors with the electromagnetic form factors, we subsequently evaluate the impact parameter dependent probability density of transversely polarized quarks inside the pion and the kaon. The numerical results for the generalized form factors, corresponding charges, as well as those for the probability densities and the transverse shift of the polarized densities are consistent with lattice QCD simulations and with chiral quark models.

Bc → J/ψ tensor form factors at large momentum recoil

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

Nucleon mass radii and distribution: Holographic QCD, lattice QCD, and GlueX data

We briefly review and expand our recent analysis for all three invariant $A$, $B$, $D$ gravitational form factors of the nucleon in holographic QCD. They compare well to the gluonic gravitational form factors recently measured using lattice QCD simulations. The holographic $A$-term is fixed by the tensor $T={2}^{++}$ (graviton) Regge trajectory, and the $D$-term by the difference between the tensor $T={2}^{++}$ (graviton) and scalar $S={0}^{++}$ (dilaton) Regge trajectories. The $B$-term is null in the absence of a tensor coupling to a Dirac fermion in bulk. A first measurement of the tensor form factor $A$-term is already accessible using the current GlueX data, and therefore the tensor gluonic mass radius, pressure, and shear inside the proton, thanks to holography. The holographic $A$-term and $D$-term can be expressed exactly in terms of harmonic numbers. The tensor mass radius from the holographic threshold is found to be $⟨{r}_{GT}^{2}⟩\ensuremath{\approx}(0.57--0.60\text{ }\text{ }\mathrm{fm}{)}^{2}$, in agreement with $⟨{r}_{GT}^{2}⟩\ensuremath{\approx}(0.62\text{ }\text{ }\mathrm{fm}{)}^{2}$ as extracted from the overall numerical lattice data, and empirical GlueX data. The scalar mass radius is found to be slightly larger $⟨{r}_{GS}^{2}⟩\ensuremath{\approx}(0.7\text{ }\text{ }\mathrm{fm}{)}^{2}$.

Tensor form factors of [formula omitted] state via light-cone QCD

We have achieved the isovector and isoscalar tensor form factors of the N(1535) state in the framework of the light-cone QCD sum rule approach. In numerical computations, we have considered the most general forms of the interpolating current for the nucleon and the tensor current together with the distribution amplitudes of the N(1535) resonance. We have shown that the squared momentum transfer, Q2, dependence of N(1535) tensor form factors is characterized by a multipole fit function. Our results provide a perspective of the momentum dependence of the tensor form factors and can help to improve our understanding of the internal structure of nucleon states.

Two-meson form factors in unitarized chiral perturbation theory

We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays Bs→ π+π−ℓ+ℓ− and the τ lepton decay τ → π−π0ντ, in searches for physics beyond the Standard Model.

Heavy Quark Expansion of Λb→Λ*(1520) Form Factors beyond Leading Order

I review the parametrisation of the full set of Λb→Λ*(1520) form factors in the framework of Heavy Quark Expansion, including next-to-leading-order O(αs) and, for the first time, next-to-leading-power O(1/mb) corrections. The unknown hadronic parameters are obtained by performing a fit to recent lattice QCD calculations. I investigate the compatibility of the Heavy Quark Expansion and the current lattice data, finding tension between these two approaches in the case of tensor and pseudo-tensor form factors, whose origin could come from an underestimation of the current lattice QCD uncertainties and higher order terms in the Heavy Quark Expansion.