Hindered magnetic dipole transitions $Υ(nS)\to γη_b(n'S)$ are studied in the covariant light-front approach. Compared with the allowed magnetic dipole transitions, we find that results for hindered magnetic dipole transitions are sensitive to heavy quark mass and shape parameters of the light-front wave functions. It is possible to tune the parameters so that the predictions of branching fractions of $Υ(2S,3S)\toγη_b$ are consistent with the recent experimental data, but the relevant decay constant of $η_b$ is much smaller than that of $Υ(1S)$. We also generalize the investigation to the charmonium sector and find the the same conclusion.
Decay constants and form factors for parity-even (s-wave) and parity-odd (p-wave) mesons are studied within a covariant light-front approach. The three universal Isgur-Wise functions for heavy-to-heavy meson transitions are obtained.
In an explicitly covariant light-front formalism, we analyze transition form factors between pseudoscalar and scalar mesons. Application is performed in case of the $B \to f_0(980)$ transition in the full available transfer momentum range $q^2$.
We discuss the light-front zero-mode issue in the light-front quark model prediction of the twist-3 distribution amplitude of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD.
In this article, we study the radiative transitions among the vector and scalar heavy quarkonium states with the covariant light-front quark model. In calculations, we observe that the radiative decay widths are sensitive to the constituent quark masses and the shape parameters of the wave-functions, and reproduce the experimental data with suitable parameters.
We calculate the predicted width for the radiative decay of a $1^{++}$ heavy meson via the channel $1^{++} \to 1^{--} +γ$ in the covariant light-front quark model. Specifically, we compute the decay widths for $χ_{c1}(1P) \to J/ψ+ γ$ and $χ_{b1}(nP) \to Υ(n'S) + γ$. The results are compared with experimental data and with predictions from calculations based on nonrelativistic models and their extensions to include relativistic effects.
The light-front approach is a relativistic quark model and offers many insights to the internal structures of the hadronic bound states. In this study, we apply the covariant light-front approach to ground-state heavy quarkonium. The pesudoscalar and vector meson decay constants are discussed. We present a detailed study of two-photon annihilation P \to γγand magnetic dipole transition V \to P γprocesses. The numerical predictions of the light-front approach are consistent with the experimental data and those in other approaches. The relations of the light-front approach with the other methods…
The light-front (LF) canonical quantization of quantum chromodynamics in covariant gauge is discussed. The Dirac procedure is used to eliminate the constraints in the gauge-fixed front form theory quantum action and to construct the LF Hamiltonian formulation. The physical degrees of freedom emerge naturally. The propagator of the dynamical $ψ_+$ part of the free fermionic propagator in the LF quantized field theory is shown to be causal and not to contain instantaneous terms. Since the relevant propagators in the covariant gauge formulation are causal, rotational invariance---including the Co…
Light-Front Field Theory (LFFT) is a good candidate to describe bound states. In LFFT covariance is non-manifest. Burkardt and Langnau claim that, even for scattering amplitudes, rotational invariance is broken. We will take a different path of obtaining rules for light-front time-ordered diagrams. Covariance depends on the choice of a regulator $α$. We need to apply some regularisation scheme to render physical amplitudes finite. This is done by applying minus regularisation. In this process all ambiguities related to the regulator $α$ are removed. Therefore there is equivalence between the p…
This work is the first check of gauge invariance for nonperturbative calculations in light-front QED. To quantize QED in an arbitrary covariant gauge, we use a light-front analog of the equal-time Stueckelberg quantization. Combined with a Pauli-Villars regularization, where massive, negative-metric photons and fermions are included in the Lagrangian, we are then able to construct the light-front QED Hamiltonian and the associated mass eigenvalue problem in a Fock-space representation. The formalism is applied to the dressed-electron state, with a Fock-space truncation to include at most one p…
We study the decay constants and form factors of the ground-state s-wave and low-lying p-wave mesons within a covariant light-front approach. Numerical results of the B to D** transition form factors, where D** denotes generically a p-wave charmed meson, are compared with other model calculations. Predictions on the decay rates for Bbar to D** pi, D** rho, Dbar**_s D* by using these decay constants and form factors are in agreement with the experimental data. The universal Isgur-Wise functions, xi, tau_{1/2}, tau_{3/2} are obtained and are used to test the Bjorken and Uraltsev sum rules.
In this paper we construct a covariant light-front model of heavy mesons within the framework of heavy quark effective theory (HQET). The covariant model consists of the light-front heavy meson bound states constructed in the heavy quark limit with heavy quark symmetry and heavy quark effective theory as its basis. Within this model, the Isgur-Wise function and decay constants in the infinite quark mass limit can be evaluated in a very simple and the most general way. The results are ensured to be consistent with heavy quark symmetry. From the heavy-quark-limit bound states, we can further dev…
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +γ$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy qua…
Although the meson decay amplitude described by a two-point function may be regarded as one of the simplest possible physical observable, it is interesting that this apparently simple amplitude bears abundant fundamental informations on QCD vacuum dynamics and chiral symmetry. The light-front zero-mode issue of the vector meson decay constant $f_V$ is in this respect highly non-trivial and deserves careful analyses. We discuss the zero-mode issue in the light-front quark model (LFQM) prediction of $f_V$ from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. …
In the covariant light-front quark model, we investigate the $B_c\to h_c, χ_{c0,1,2}$ form factors. The form factors are evaluated in space-like kinematic region and are recasted to the physical region by adopting the exponential parametrization. We also study the semileptonic $B_c$ decays and find that branching fractions for the $B_c\to (h_c,χ_{c0,1,2})l\barν(l=e,μ)$ decays have the order $10^{-3}$ while branching fractions for $B_c\to (h_c,χ_{c0,1,2})τ\barν_τ$ are suppressed by one order. These predictions will be tested at the forthcoming hadron colliders.
The generalized parton distributions of the pion are studied within different light-front approaches for the quark-hadron and quark-photon vertices, exploring different kinematical regions in both the valence and non-valence sector. Moments of the generalized parton distributions which enter the definition of generalized form factors are also compared with recent lattice calculations.
We study the implications of Lorentz symmetry for hadronic structure by formulating a manifestly covariant constituent quark model and find full covariance for any Lorentz transformation requires utilizing a variable quantization surface. Even though time-reversal invariance mandates a unique orientation for the surface's direction, we investigated alternative choices and find small numerical sensitivity to different directions. We also calculate the static properties of the low lying pseudoscalar mesons and compare results with existing noncovariant calculations. We conclude that there is a l…
In this paper we discuss the relation between the standard covariant quantum field theory and light-front field theory. We define covariant theory by its Feynman diagrams, whereas light-front field theory is defined in terms of light-cone time-ordered diagrams. A general algorithm is proposed that produces the latter from any Feynman diagram. The procedure is illustrated in several cases. Technical problems that occur in the light-front formulation and have no counterpart in the covariant formulation are identified and solved.
Light-front perturbation theory has been proposed as an alternative to covariant perturbation theory. Light-front perturbation theory is only acceptable if it produces invariant S-matrix elements. Doubts have been raised concerning the equivalence of light-front and covariant perturbation theory. One of the obstacles to a rigorous proof of equivalence is the occurrence of longitudinal divergences not present in covariant perturbation theory. We show in the case of the Yukawa model of fermions interacting with scalar bosons at the one-loop level how to deal with the longitudinal divergences. In…
The rho-meson eletromagnetic form factors are calculated, both in covariant and light-front framework with constituintes quarks. The effect of the breakdown rotational symmetry for the one-body current operador in the null-plane is investigate by comparing calculations within ligth-front and covariant approaches.
We discuss the equivalence between light-front time-ordered-perturbation theory and covariant quantum field theory in light-front quantization, in the case of quantum electrodynamics at one-loop level. In particular, we review the one-loop calculation of the vertex correction, fermion self-energy and vacuum polarization. We apply the procedure of integration by residue over the light-front energy in the loop to show how the perturbative expansion in covariant terms can be reduced to a sum of propagating and instantaneous diagrams of light-front time-ordered perturbation theory. The detailed pr…
We investigate the model dependence of no-helicity flip generalized parton distribution of the pion upon different approaches for the quark-hadron and quark-photon vertexes, in the spacelike region. In order to obtain information on contributions from both the valence and non-valence regions, we compare results for spacelike momentum transfers obtained from i) an analytic covariant model with a bare quark-photon vertex, ii) a Light-front approach with a quark-photon vertex dressed through a microscopic vector-meson model and iii) a Light-front approach based on the Relativistic Hamiltonian Dyn…
We reanalyzed nonleptonic charmless two-body B decays involving tensor mesons in final state motivated by the disagreement between current experimental information and theoretical predictions obtained in ISGW2 model for some $\mathcal{B}(B \to P(V)T)$ (where $P$, $V$ and $T$ denote a pseudoscalar, a vector and a tensor meson, respectively). We have calculated branching ratios of charmless $B \to PT$ and $B\to VT$ modes, using $B \to T$ form factors obtained in the covariant light-front (CLF) approach and the full effective Hamiltonian. We have considered the $η-η^{\prime}$ two-mixing angle for…
We study the light-front covariance of a vector-meson decay constant using a manifestly covariant fermion field theory model in $(3+1)$ dimensions. The light-front zero-mode issues are analyzed in terms of polarization vectors and method of identifying the zero-mode operator and of obtaining the light-front covariant decay constant is discussed.
The light-front dynamics is an efficient approach to study of field theory and of relativistic composite systems (nuclei at relativistic relative nucleon momenta, hadrons in the quark models). The explicitly covariant version of this approach is briefly reviewed and illustrated by some applications.
We suggest to study the $B_{s}$ and its excitations $B_{sJ}$ in the $B_c$ decays. We calculate the $B_c\to B_{sJ}$ and $B_c\to B_{J}$ form factors within the covariant light-front quark model, where the $B_{sJ}$ and $B_{J}$ denote an s-wave or p-wave $\bar bs$ and $\bar bd$ meson, respectively. The form factors at $q^2=0$ are directly computed while their $q^2$-distributions are obtained by the extrapolation. The derived form factors are then used to study semileptonic $B_c\to (B_{sJ},B_{J})\bar\ellν$ decays, and nonleptonic $B_c\to B_{sJ}π$. Branching fractions and polarizations are predicted…
The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a simple one-gluon exchange model and investigate various physical observables: decay constant, charge radius, electromagnetic and transition form factors. We discuss the influence of the full relativistic structure of the pion wave function for an overall good description of all these observables, including both low and high momentum scales.
We reanalyze the decay constants of s-wave and p-wave mesons and D, B ->M form factors, where M represents a pseudoscalar meson, a vector meson, a scalar meson, or an axial vector meson within a covariant light-front quark model. The parameter βfor wave-functions of most of s-wave mesons and of a few axial-vector mesons are fixed with latest experimental information, wherever available or using the lattice calculations. The treatment of masses and mixing angles for strange axial vector mesons is improved for the purpose. We extend our analysis to determine the form factors appearing in the tra…
We consider the three fundamental one loop Feynman diagrams of QED viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge and discuss the equivalence of their standard covariant expressions with the light-front expressions obtained using light-cone time-ordered Hamiltonian perturbation theory. Although this issue has been considered by us and others previously, our emphasis in this article is on addressing the ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We generalize our earlier results and show, …
We discuss the light-front zero-mode issue in the light-front quark model (LFQM) prediction of a vector meson decay constant from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. We extend the exactly solvable manifestly covariant Bethe-Salpeter model calculation to the more phenomenologically accessible realistic LFQM and present a self-consistent covariant description of the vector meson decay constant analyzing the twist-2 and twist-3 quark-antiquark distribution amplitudes with even chirality.
In this paper, a study of two-photon and two-gluon decays in the context of p-wave heavy quarkonia is presented. Within the covariant light-front framework, the annihilation rates of scalar and tensor quarkonium states are derived. In the absence of free parameters in this case, the results for the charmonium decay widths are consistent with the experimental data. However, in comparison to other theoretical calculations, there are large discrepancies in our results regarding bottomonia.
In the covariant light-front quark model, we calculate the form factors of $B_c^-\to J/ψ$ and $B_c^-\to X(3872)$. Since the factorization of the exclusive processes $B_c^- \to J/ψπ^-(K^-)$ and $B_c^- \to X(3872)π^-(K^-)$ can be proved in the soft-collinear effective theory, we can get the branching ratios for these decays easily from the form factors. Taking the uncertainties into account, our results for the branching ratio of $B_c^-\to J/ψπ^-(K^-)$ are consistent with the previous studies. By identifying X(3872) as a $1^{++}$ charmonium state, we obtain ${\cal BR}(B_c^-\to X(3872)π^-)=(1.7^{…
The masses and vertex functions of heavy and heavy-light mesons, described as quark-antiquark bound states, are calculated with the Covariant Spectator Theory (CST). We use a kernel with an adjustable mixture of Lorentz scalar, pseudoscalar, and vector linear confining interaction, together with a one-gluon-exchange kernel. A series of fits to the heavy and heavy-light meson spectrum were calculated, and we discuss what conclusions can be drawn from it, especially about the Lorentz structure of the kernel. We also apply the Brodsky-Huang-Lepage prescription to express the CST wave functions fo…
In several preceding studies, the explicitly covariant formulation of light front dynamics was developed and applied to many observables. In the present study we show how in this approach the renormalization procedure for the first radiative correction can be carried out in a standard way, after separating out the contributions depending on the orientation of the light-front plane. We calculate the renormalized QED vertices $γe^-\to e^-$ and $e^+e^-\to γ$ and the electron self-energy and recover, in a straightforward way, the well known analytical results obtained in the Feynman approach.
We revisit the proof of equivalence of one loop expressions for fermion self-energy and vertex correction in light-front QED and Covariant QED at the Feynman diagram level and generalize, to all components, the proof of equivalence for the one loop vertex correction diagram which was presented earlier by us only for the $+$ component of $Λ^μ$. We demonstrate, in the general case also, that the equivalence cannot be established without the third term in the three-term photon propagator in light cone gauge.
In this paper, we test the self-consistencies of the standard and the covariant light-front quark model and study the zero-mode issue via the decay constants of pseudoscalar ($P$), vector ($V$) and axial-vector ($A$) mesons, as well as the $P\to P$ weak transition form factors. With the traditional type-I correspondence between the manifestly covariant and the light-front approach, the resulting $f_{V}$ as well as $f_{^1\!A}$ and $f_{^3\!A}$ obtained with the $\lbd=0$ and $\lbd=\pm$ polarization states are different from each other, which presents a challenge to the self-consistency of the cov…
We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector $ω^μ.$ The LFWFs with definite total angular momentum are eigenstates of a {\it kinematic} angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents $M^2_0= (\sum k^μ)^2$ and the light-cone momentum fractions $x_i= {k_i\cd ω/ p \cd ω}$ multiplied by invariants const…
Based on the predictions of the relevant form factors from the covariant light-front quark model, we show the branching fractions for the $D (D_s) \to (P,\,S,\,V,\,A)\,\ellν_\ell$ ($\ell=e$ or $μ$) decays, where $P$ denotes the pseudoscalar meson, $S$ the scalar meson with a mass above 1 GeV, $V$ the vector meson and $A$ the axial-vector one. Comparison with the available experimental results are made, and we find an excellent agreement. The predictions for other decay modes can be tested in a charm factory, e.g., the BESIII detector. The future measurements will definitely further enrich our …
Light-front dynamics can only become a viable alternative to the covariant approach if doubts about its covariance can be taken away. As a minimal requirement we take that the physical quantities calculated with light-front perturbation theory are the same as those obtained using covariant perturbation theory. If this situation occurs, we use the word equivalent to characterize it. For quantities that involve the calculation of superficially convergent diagrams, proofs of equivalence exist. For some types of divergent diagrams the proof of equivalence is complicated. Longitudinal divergences w…
We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states that leads to results which resemble those obtained within the covariant light-front formalism of Carbonell et al. Our starting points are the physical processes in which such form factors are measured, i.e. electron scattering off the bound state, or the semileptonic weak decay of the bound state. These processes are treated by means of a coupled-channel framework for a Bakamjian-Thomas type mass operator. A current with the correct covariance properties is then derived from …
In the covariant light-front quark model, we investigate the form factors of $B_c$ decays into $D, D^*, D_s, D_s^*, η_c, J/ψ, B, B^*, B_s, B_s^*$ mesons. The form factors in the spacelike region $q^2<0$ are directly evaluated. To extrapolate the form factors to the full kinematic region, we fit the form factors by adopting a three-parameter form from the spacelike region. $b\to u,d,s$ transition form factors at maximally recoiling point ($q^2=0$) are smaller than $b\to c$ and $c\to d,s$ transition form factors, while the $b\to d,s,c$ form factors at zero recoiling point are close to each other…
We study the transition form factors between pseudoscalar and vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing the light-front calculation in the $q^+ =0$ frame in parallel with the manifestly covariant calculation, we note that the suspected nonvanishing zero-mode contribution to the light-front current $J^+$ does not exist in our analysis of transition form factors. We also perform the light-front calculation in a purely longitudinal $q^+ > 0$ frame and confirm that the form factors obtained directly from the timelike region are identical to the on…
Study of $B_{(s)}$ meson decays to $D_{0}^{\ast}(2300) ,D_{s0}^{\ast}(2317) , D_{s1}(2460)$ and $D_{s1}(2536)$ within the covariant light-front approach
Within the framework of the covariant formulation of Light-Front Dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the "bare" fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the Light-Cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that in Light-Front Dynamics, to restore the rotational invariance, an ex…
We investigate the transition form factors between nucleon and $Δ$(1232) particles by using a covariant quark-spectator-diquark field theory model in (3+1) dimensions. Performing a light-front calculation in parallel with the manifestly covariant calculation in light-front helicity basis, we examine the light-front zero-mode contribution to the helicity components of light-front good ("+") current matrix elements. Choosing the light-front gauge ($ε^+_{h=\pm}=0$) with circular polarization in Drell-Yan-West frame, we find that only the helicity components $({1\over 2}, {1\over 2})$ and $({1\ove…
In this paper, we investigate the tensor form factors of $P\to P,\,S,\,V$ 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 $P\to V$ and $A$ transitions, besides the inconsistence between the results extracted via longitudinal and transverse polarization states, which is caused by the residual $ω$-dependent spurious contributions, we find and analyze a "new" self-consistence problem of the tr…
Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.
We study the form factors of vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing a light-front calculation in the $q^+ =0$ frame in parallel with a manifestly covariant calculation, we note the existence of a nonvanishing zero-mode contribution to the light-front current $J^+$ and find a way of avoiding the zero-mode in the form factor calculations. Upon choosing the light-front gauge ($\ep^+_{h=\pm}=0$) with circular polarization and with spin projection $h=\uparrow\downarrow=\pm$, only the helicity zero to zero matrix element of the plus current recei…
Exclusive radiative B decays, B to K* gamma, K_1(1270) gamma, K_1(1400) gamma and K*_2(1430) 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 B to K* gamma, is found to be 0.24, substantially smaller than what 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 B to K* gamma agrees with experiment, while most of the existing models predict too large B to K* gamma compa…
We explore skewed parton distributions for two-body, light-front wave functions. In order to access all kinematical regimes, we adopt a covariant Bethe-Salpeter approach, which makes use of the underlying equation of motion (here the Weinberg equation) and its Green's function. Such an approach allows for the consistent treatment of the non-wave function vertex (but rules out the case of phenomenological wave functions derived from ad hoc potentials). Our investigation centers around checking internal consistency by demonstrating time-reversal invariance and continuity between valence and non-…
A fully covariant model for describing the electromagnetic decay of Vector Mesons, both in light and in heavy sectors, is presented. The main ingredients of our approach are i) an Ansatz for the Bethe-Salpeter vertex for Vector Mesons, and ii) a Mandelstam-like formula for the electromagnetic decay constant. The free parameters of our approach are fixed through a comparison with the transverse momentum distribution obtained within a Light-Front Hamiltonian Dynamics framework with constituent quarks. Preliminary results for both the decays constants and the probability of the valence component …
We study the decay constants and form factors of the ground-state s-wave and low-lying p-wave mesons within a covariant light-front approach. Numerical results of the form factors for transitions between a heavy pseudoscalar meson and an s-wave or p-wave meson and their momentum dependence are presented in detail. In particular, form factors for heavy-to-light and B to D** transitions, where D** denotes generically a p-wave charmed meson, are compared with other model calculations. The experimental measurements of the decays B^- to D** pi^- and B to D D**_s are employed to test the decay const…
We present a consistent calculation of the structure functions within a light-front constituent quark model of the nucleon. Relativistic effects and the relevance of the covariance constraints are analyzed for both polarized and unpolarized parton distributions. Various models, which differ in their gluonic structure at the hadronic scale, are investigated. The results of the full covariant calculation are compared with those of a non-relativistic approximation to show the structure and magnitude of the differences.
As a test of the new light-front coupled-cluster method in a gauge theory, we apply it to the nonperturbative construction of the dressed-electron state in QED, for an arbitrary covariant gauge, and compute the electron's anomalous magnetic moment. The construction illustrates the spectator and Fock-sector independence of vertex and self-energy contributions and indicates resolution of the difficulties with uncanceled divergences that plague methods based on Fock-space truncation.
