Invariant Form Factors Research Articles

Semileptonic decay of the triply heavy Ωccb to the observed Ξcc++ state

We investigate the weak semileptonic decay of the Ωccb+→Ξcc++ℓν¯ℓ, where a triply heavy baryon with spin 1/2 decays into the observed doubly heavy baryon with spin 1/2, using quantum chromodynamics (QCD) sum rule method in all lepton channels. We compute the six relevant vector and axial vector form factors entering the low energy matrix elements in full theory. The invariant form factors are building blocks, using the fit faction of which in terms of q2 in whole physical region, we calculate the exclusive widths in three lepton channels. Our predictions may help the present and future experiments in the course of their search for doubly and triply heavy baryons. Published by the American Physical Society 2025

Exclusive rare semileptonic decays of B and Bc mesons in the relativistic independent quark model

We investigate the exclusive rare semileptonic decays B(Bc)→K(D(s))ll¯/νlνl¯ (l=μ, τ) in the framework of relativistic independent quark model based on an average flavor independent confining potential in equally mixed scalar-vector harmonic form. The invariant weak form factors, parametrizing the matrix elements between participating meson states, are calculated in the parent meson rest frame. The momentum transfer dependence of the form factors is reliably determined in the whole accessible kinematical range qmin2≤0≤qmax2. Our predicted branching fractions for B→Kμ+μ−/τ+τ−(νlνl¯), Bc→D(Ds)μ+μ−, Bc→D(Ds)τ+τ−, and Bc→D(Ds)νlνl¯, obtained in order of 10−7(10−6), 10−9(10−7), 10−9(10−8), and 10−8(10−7), respectively, are in reasonable agreement with other Standard Model predictions and Lattice QCD results. The averaged values of the lepton polarization asymmetries for decay modes are obtained as ⟨PL(B→Kμ+μ−)⟩=−0.97, ⟨PL(Bc→D(s)μ+μ−)⟩=−0.972, ⟨PL(B→Kτ+τ−)⟩=−0.224, ⟨PL(Bc→Dτ+τ−)⟩=−0.275, and ⟨PL(Bc→Dsτ+τ−)⟩=−0.194. Published by the American Physical Society 2024

Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD

We present the first full analytic evaluation of the scattering amplitude for the process qq → Qoverline{Q} up-to two loops in Quantum Chromodynamics, for a massless (q) and a massive (Q) quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant.

Exclusive semileptonic B_c-meson decays to radially excited charmonium and charm meson states

In the wake of recent measurements of ratios of semileptonic branching fractions: {mathscr {R}}_{J/psi }, {mathscr {R}}_D and {mathscr {R}}_{D^{*}} reported by the LHCb, BELLE and HFLAV Collaborations, we calculate invariant form factors for the exclusive semileptonic B_c-meson decays to radially excited charmonium and charm meson states in the full kinematical region within the framework of relativistic independent quark (RIQ) model. We evaluate the lepton mass effect in the decay processes induced by brightarrow c,u transition at the quark level. Our predictions on branching fractions for B_crightarrow eta _c/psi (nS) are found sim 10^{-2}-10^{-4} and that for B_crightarrow D^{*}(nS) are sim 10^{-4} in their e^{-} decay modes, which lie within the detection accuracy of current experiment. Our predictions on branching fractions, forward backward asymmetry and asymmetry parameter are found in reasonable agreement with other model predictions; which can hopefully be tested in future experiments at LHC and Tevatron. Our predicted observable {mathscr {R}} in this sector are found comparable to other standard model (SM) predictions that violate the lepton flavor universality hinting at new physics beyond SM.

РАСЧЕТ РАСПАДОВ ДВАЖДЫ ОЧАРОВАННЫХ БАРИОНОВ

We calculated a subclass of four nonleptonic two-body weak decays of the double charm baryon ground states Ξcc++. Nonleptonic decays can be dividedinto two group: factorizable and nonfactorizable decays. The first one can be easily calculated from first principles. Therefore, its good example understands all pros and cons of a model. We focused on a weak two-body nonleptonic decay consists only fromthe factorizing contribution precluding a contamination from W-exchange. We use the covariant confined quark model previously developed by us to calculate the various helicity amplitudes which describe the dynamics of the transition induced by the Cabibbo-favored effective currents. Achievement of CCQM is that only size parameter Λvarying can describe all tree diagrams of nonleptonic decay. We then proceed to calculate the rates of the decay. The rates, branching ratios and helicity amplitude were calculated using dimensionless invariant form factors. Also, we calculated leptonic constant for scalar and vector mesons which has good agreement with experimental data. There isn’t any experimental data about the decay so we waiting for new experimental observation in the heavy baryon sector.

Elastic scattering of electrons by nuclei of half-integer spin and discrete symmetries

Analytical expression is obtained for the right-left asymmetry A RL (3/2) for the process of elastic scattering of the longitudinally polarized electrons by nuclei with spin 3/2, described in the framework of Rarita-Schwinger formalism by invariant form factors of electromagnetic and weak vertex functions. It is shown, that this asymmetry directly depends on the nuclear anapole form factors G 1 (n), and structurally is equivalent to asymmetry A RL (1/2), which arises in electron scattering by proton.

Extraction of Compton Form Factors in Scalar QED

When deeply virtual Compton scattering is used as a tool to study the structure of hadrons in an exclusive process, one way to analyze this process is to express the amplitudes in terms of generalized parton distributions (GPDs). The definition of the latter quantities requires a special kinematics, that cannot always be realized in experiments. Therefore, one may use the expression of the scattering amplitudes in terms of the invariant Compton form factors (CFFs) as a stepping stone to finding the GPDs. In a simple case we illustrate the influences of making approximations in the extraction of CFFs on the values obtained.

Twist Expansion of Forward Drell--Yan Process

We present a twist expansion of differential cross-sections of the forward Drell-Yan process at the high energies. The expansion of all invariant form-factors is performed assuming GBW saturation model and the saturation scale plays the role of the hadronic scale of OPE. Some expilicit predictions for LHC experiments are given. It is shown also how the Lam-Tung relation is broken at twist 4 what provides a sensitive probe for searching of higher twists.

A framework for the calculation of the [formula omitted] transition form factors on the lattice

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the ΔNγ⁎ transition form factors from lattice data. A counterpart of the Lüscher approach for the matrix elements of unstable states is formulated. In particular, we thoroughly discuss various kinematic settings, which are used in the calculation of the above matrix element on the lattice. The emerging Lüscher–Lellouch factor and the analytic continuation of the matrix elements into the complex plane are also considered in detail. A full group-theoretical analysis of the problem is made, including the partial-wave mixing and projecting out the invariant form factors from data.

Determination of theΔ(1232)axial and pseudoscalar form factors from lattice QCD

We present a lattice QCD calculation of the $\ensuremath{\Delta}(1232)$ matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out, and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for $2+1$ domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman--type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Using lattice QCD results on the axial charges of the nucleon and the $\ensuremath{\Delta}$, as well as the nucleon-to-$\ensuremath{\Delta}$ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached.

Studies onπ+π−phase motion in theΨ′→J/Ψπ+π−process

We propose a measurement of the elastic $\ensuremath{\pi}\ensuremath{\pi}$ scattering phase-shift difference ${\ensuremath{\delta}}_{0}^{0}\ensuremath{-}{\ensuremath{\delta}}_{0}^{2}$ through the ${\ensuremath{\Psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}J/\ensuremath{\Psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ process in the future high statistics BES-III experiment. The decay amplitude is constructed with seven Lorentz invariant form factors and is compared with their theoretical estimation. Based on a Monte Carlo study, it is found that the phase-shift difference can be indeed recovered and, hence, it is expected to be measured in the energy region between 350 and 550 MeV at future BES-III.

Study of the decayDs+→K+K−e+νe

Using 214 fb-1 of data recorded by the Babar detector at the PEPII electron-positron collider, we study the decay Ds+ --> K+ K- e+ nu. Except for a small S-wave contribution, the events with K+K- masses in the range 1.01-1.03 GeV/c2 correspond to phi mesons. For Ds+ --> phi e+ nu decays, we measure the relative normalization of the Lorentz invariant form factors at q2=0, rV=V(0)/A1(0)=1.849 +/- 0.060 +/- 0.095, r2=A2(0)/A1(0)=0.763 +/- 0.071 +/- 0.065 and the pol e mass of the axial-vector form factors mA=(2.28^{+0.23}_{-0.18}+/- 0.18) GeV/c2. Within the same K+K- mass range, we also measure the relative branching fraction B(Ds+ --> K + K- e+ nu)/B(Ds+ --> K+ K- pi+)=0.558 +/- 0.007 +/- 0.016, from which we obtain the total branching fraction B(Ds+ --> phi e+ nu) = (2.61 +/- 0.03 +/- 0.08 +/- 0.15)* 10^{-2}. By comparing this value with the predicted decay rate, we extract A1(0) = 0.607 +/- 0.011 +/- 0.019 +/- 0.018. The stated uncertainties are statistical, systematic, and from external inputs.

Exclusive nonleptonic decays ofBmesons

The energetic exclusive two-body nonleptonic decays of B mesons are investigated in the relativistic independent quark model based on the confining potential in scalar-vector harmonic form within the factorization approximation. The branching ratios for B decays to $\mathrm{PP}$ and $\mathrm{PV}$ channels with at least one charm meson in the final states are calculated from Lorentz invariant form factors and meson decay constants. The model predictions are found to be in reasonable agreement with the available experimental data.

Point form relativistic quantum mechanics and electromagnetic form factors

A relativistic quantum mechanics of constituents is formulated in which particles are bound states of a mass operator. The point form of relativistic dynamics is used, in which Lorentz transformations are kinematic, and the four-momentum operator carries all the interactions. A general covariant expression for matrix elements of the electromagnetic current operator is given in which the invariant form factors are reduced matrix elements of the Poincar\'e group. A point form relativistic impulse approximation is formulated, in which invariant form factors of particles are given in terms of their underlying constituents.

Quantitative predictions forBsemileptonic decays intoD,D*,and the orbitally excitedD**in quark models in the manner of Bakamjian and Thomas

Once chosen the dynamics in one frame, the rest frame in this paper, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the infinite quark mass limit, fully covariant current form factors as matrix elements of the quark current operator. In this paper we use the rest frame dynamics fitted from the meson spectrum by various authors, already shown to provide a reasonable value for $\rho^2$. From the general formulae for the scaling invariant form factors $\xi^{(n)}(w)$, $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$, we predict quantitavely the $B$ semileptonic branching ratios to the ground state and orbitally excited charmed mesons $D, D^\ast$ and $D^{\ast\ast}$. We check Bjorken's sum rule and discuss the respective contributions to it. We find $\xi(w)\simeq (2/(1+w)) ^2$, resulting from the fact that the ground state wave function is Coulomb-like. We also find $\tau_{3/2}\simeq 0.5 (2/(1+w))^3$ and $\tau_{1/2}(w)\ll \tau_{3/2}(w)$. Very small branching ratios into $j=1/2$ orbitally excited $D$'s results. The overall agreement with experiment is rather good within the present accuracy which is poor for the orbitally excited charmed mesons. We predict a ratio $Br(B\to D^\ast_2 l \nu)/Br(B\to D_1 l \nu)=1.55\pm 0.15$ as a mere consequence of the heavy quark symmetry. If some faint experimental indications that $Br(B\to D_1 l \nu)\simeq Br(B\to D^\ast_2 l \nu)$ were confirmed, it would indicate a sizeable $O(1/m_c)$ correction.

Formula omitted] semileptonic decay in covariant quark models à la Bakamjian-Thomas

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter p 3 > 3 4 for all the possible choices of the dynamics. In this paper we study the L = 1 excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors τ 1 2 (n)(w) and τ 3 2 (n)(w) . We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models.

Radiative gluon effects in quark-antiquark production in collisions of polarized electrons and positrons

The cross section in terms of three independent radiative gluon correction form factors related to angular dependence and angular asymmetry is calculated as functions of the maximum recorded scaled gluon momentumXg, with 0<X g ≤1. The effects of longitudinal and transversal polarization of the initial electron and positron are taken into account. For the same geometry the two independent thrust form factors are obtained as functions of the minimum thrustT m recorded, with 2/3≤T m <1. Similarly the related invariant mass form factors are obtained. In particular, the regions of infrared gluons,\(X_g<< {{m^2 } \mathord{\left/ {\vphantom {{m^2 } s}} \right. \kern-\nulldelimiterspace} s}\), and of near infrared gluons,\({{m^2 } \mathord{\left/ {\vphantom {{m^2 } s}} \right. \kern-\nulldelimiterspace} s}<< X_g<< {m \mathord{\left/ {\vphantom {m {\sqrt s }}} \right. \kern-\nulldelimiterspace} {\sqrt s }}\), are discussed.

Electromagnetic form factors in the light-front dynamics

It is shown that the electromagnetic vertex of a nucleus (and of any bound system), expressed through the wave function in the light-front dynamics at relativistic values of momentum transfer, contains a contribution of nonphysical form factors which increases the total number of invariant form factors (for the deuteron from 3 up to 11). This fact explains an ambiguity in the form factors calculated previously. The physical and nonphysical form factors are covariantly separated. Explicit expressions for physical form factors of systems with spin 0, 1 2 and 1 through the vertex functions are obtained.

DIZET — Electroweak one-loop corrections for e ++e -→f ++f - around the Z 0 peak

The use of five gauge invariant form factors allows a dense notation of electroweak one-loop effects for the fermion pair production in e+e- annihilation. Based on this notation a program package (DIZET) has been developed to calculate the differential cross section for these processes. It is evaluated as a function of the energy of the process, the production angle, the longitudinal polarization of the beam particles, and the helicities of the final fermions.

Exclusive semileptonic B-meson decays

We study the semileptonic processes B → D l ν and B → D ∗ l ν and show that the invariant hadronic form factors describing the decays can be measured directly by observing the angular correlations of the decay products. We emphasize that this allows an almost model-independent determination of the V cb quark mixing-matrix element. We examine the theoretical models for the form factors in terms of the spectator quark approach. We present a general formalism for semileptonic decays which includes lepton mass effects, since the decay into τ-leptons may be important as background events in the search for rare decay modes involving missing particles.