Relativistic Constituent Quark Model Research Articles

The exclusive rare decays $$B \rightarrow k{\bar l}l$$ and $$B_c \rightarrow D(D^*){\bar l}l$$ in a relativistic quark model

We study the exclusive rare decay $$B \rightarrow k{\bar l}l$$ . We calculate the relevant form factors within a relativistic constituent quark model, for the first time without employing the impulse approximation. The calculated form factors are used to evaluate differential decay rates and polarization observables. We present results on the q2-dependence of a set of observables with and without long-distance contributions. A similar analysis is done for the exclusive rare decays $$B_c \rightarrow D(D^*){\bar l}l$$ with special emphasis on the cascade decay $$B_c\to D^\ast(\to D\pi){\bar l} l$$ . We derive a four-fold angular decay distribution for this process in terms of helicity amplitudes including lepton mass effects. The four-fold angular decay distribution allows to define a number of physical observables which are amenable to measurement. We compare our results with the results of other studies.

The kaon form factor in the light-cone quark model

The electromagnetic form factor of the kaon meson is calculated in the light-cone formalism of the relativistic constituent quark model. The calculated K+ form factor is consistent with almost all of the available experimental data at low-energy scale, while other properties of the kaon could also be interrelated in this representation with reasonable parameters. Predictions of the form factors for the charged and neutral kaons at a higher-energy scale are also given, and we find the non-zero K0 form factor at Q2≠ 0 due to the mass difference between the strange and down quarks inside K0.

Q2independence ofQF2/F1,Poincaré invariance, and the nonconservation of helicity

A relativistic constituent quark model is found to reproduce the recent data regarding the ratio of proton form factors, $F_2(Q^2)/F_1(Q^2)$. We show that imposing Poincare invariance leads to substantial violation of the helicity conservation rule, as well as an analytic result that the ratio $F_2(Q^2)/F_1(Q^2)\sim 1/Q$ for intermediate values of $Q^2$.

Semileptonic decays of theBcmeson

We study the semileptonic transitions B_c to \eta_c, J/\psi, D, D^*, B, B^*, B_s, B_s^* in the framework of a relativistic constituent quark model. We use experimental data on leptonic J/\psi decay, lattice and QCD sum rule results on leptonic B_c decay, and on radiative \eta_c transitions to adjust the quark model parameters. We compute all form factors of the above semileptonic B_c-transitions and give predictions for various semileptonic B_c decay modes including their \tau-modes when they are kinematically accessible. The implications of heavy quark symmetry for the semileptonic decays are discussed and are shown to be manifest in our explicit relativistic quark model calculation. A comparison of our results with the results of other calculations is performed.

The Kalman-Tran-D'Souza model and the semileptonic decay rates of heavy baryons

We present an investigation of the inclusive semileptonic decay widths of the heavy baryons Λ Q , Σ Q and Ξ Q , ( q = b, c) performed within a relativistic constituent quark model, formulated on the light-front. In a way conceptually similar to the deep-inelastic scattering case, the H Q -baryon inclusive width is expressed as the integral of the free Q-quark partial width multiplied by a bound-state factor related to the Q-quark distribution function in the H Q . The non-perturbative meson structure is described through the quark-model wave functions, constructed via the Hamiltonian light-front formalism using as input the Kalman-Tran-D'Souza equal time wave functions. A link between spectroscopic quark models and the H Q decay physics is obtained in this way. It is shown that the bound-state effects and the Fermi motion of the b-quark remarkably reduce the decay rate with respect to the free-quark result. Our predictions for the BR(Λ c → X sl ν e ) and BR(Λ b → X cl ν e ) decays are in good agreement with existing data.

Instanton effects in meson spectroscopy

In this contribution, the results on the spectra and semileptonic decays of light and heavy mesons in a relativistic constituent quark model incorporating a confinement potential as well as a residual interaction induced by instantons are reported.

Connection between inclusive semileptonic decays of bound and free heavy quarks

A relativistic constituent quark model, formulated on the light front, is used to derive a new parton approximation for the inclusive semileptonic decay width of the B meson. A simple connection between the decay rate of a free heavy quark and the one of a heavy quark bound in a meson or in a baryon is established. The main features of the new approach are the treatment of the b quark as an on-mass-shell particle and the inclusion of the effects arising from the b quark transverse motion in the B meson. In a way conceptually similar to the deep-inelastic scattering case, the B meson inclusive width is expressed as the integral of the free b quark partial width multiplied by a bound-state factor related to the b-quark distribution function in the B meson. The nonperturbative meson structure is described through various quark-model wave functions, constructed via the Hamiltonian light front formalism, using as input both relativistic and nonrelativistic potential models. A link between spectroscopic quark models and B-meson decay physics is obtained in this way. Our predictions for the $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{c}l{\ensuremath{\nu}}_{l}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}l{\ensuremath{\nu}}_{l}$ decays are used to extract the CKM parameters $|{V}_{\mathrm{cb}}|$ and $|{V}_{\mathrm{ub}}|$ from available inclusive data. After averaging over the various quark models adopted and including leading-order perturbative QCD corrections, we obtain $|{V}_{\mathrm{cb}}|=(43.0\ifmmode\pm\else\textpm\fi{}{0.7}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{1.8}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $|{V}_{\mathrm{ub}}|=(3.83\ifmmode\pm\else\textpm\fi{}{0.48}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.14}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3},$ implying $|{V}_{\mathrm{ub}}{/V}_{\mathrm{cb}}|=0.089\ifmmode\pm\else\textpm\fi{}{0.011}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.005}_{\mathrm{th}},$ in nice agreement with existing predictions.

Light-cone quark model analysis of radially excited pseudoscalar and vector mesons

We present a relativistic constituent quark model to analyze the mass spectrum and hadronic properties of radially excited u and d quark sector mesons. Using a simple Gaussian function as a trial wave function for the variational principle of a QCD motivated Hamiltonian, we obtain a mass spectrum consistent with the experimental data. To do the same for several observables such as decay constants and form factors, it seems necessary to include both Dirac and Pauli form factors on the level of constituent quarks. Taking into account the quark form factors, we thus present the generalized formulas for the rho meson decay constant and form factors as well as the $\ensuremath{\pi}\ensuremath{\gamma}$ transition form factor. We also predict several hadronic properties for the radially excited states.

Leptonic and semileptonic decays of pseudoscalar mesons

We employ the relativistic constituent quark model to give a unified description of the leptonic and semileptonic decays of pseudoscalar mesons ( π, K, D, D s , B, B s ). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and other approaches. We reproduce the results of spin-flavor symmetry in the heavy quark limit.

The Bc meson lifetime in the light-front constituent quark model

We present an investigation of the total decay rate of the (ground state) B c meson within the framework of the relativistic constituent quark model formulated on the light-front (LF). The exclusive semileptonic (SL) and nonleptonic (NL) beauty and charm decays of the B c meson are described through vector and axial hadronic form factors, which are calculated in terms of quark model LF wave functions. The latter ones are derived via the Hamiltonian LF formalism using as input the update constituent quark models. The inclusive SL and NL partial rates are calculated within a convolution approach inspired by the partonic model and involving the same B c wave function which is used for evaluation of the exclusive modes. The framework incorporates systematically 84 exclusive and 44 inclusive partial rates corresponding to the underlying b ̄ → c ̄ and c→ s quark decays. We find τ B c =0.59±0.06 ps where the theoretical uncertainty is dominated by the uncertainty in the choice of LF wave functions and the threshold values for the hadron continuum. For the branching fractions of the B + c → J/ ψμ + ν μ and B c +→ J/ ψπ + decays we obtain 1.6% and 0.1%, respectively.

Semileptonic Decays of Heavy Mesons to Light Pseudoscalar Mesons in the BS Formalism**The project supported in part by National Natural Science Foundation of China, the State Education Commission of China and the State Commission of Science and Technology of China

The decay processes from heavy to light pseudoscalar mesons such as are studied in a relativistic constituent quark model based on the BS formalism. It is emphasized that the negative energy projector operators's contributions in the BS wavefunctions for light pseudoscalar mesons have to be considered. By taking into account these contributions, the previously encountered difficulties in calculating the decay constants and form factors are found to be removed. A11 the form factors for transitions such as are estimated and the branching ratios for these semileptonic decays are calculated. The results of our calculations are consistent with experimental values.

Nucleon generalized polarizabilities within a relativistic constituent quark model

Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $\beta_{para}(q)$, as a function of the virtual-photon three-momentum transfer $ q,$ is explicitly evaluated within a relativistic constituent quark model by adopting transition form factors obtained in the light-front formalism. The discussion is focussed on the role played by the effects due to the relativistic approach and to the transition form factors, derived within different models.

The nucleon Drell-Hearn-Gerasimov sum rule within a relativistic constituent quark model

The Drell-Hearn-Gerasimov sum rule for the nucleon is investigated within a relativistic constituent quark model formulated on the light-front. The contribution of the N − Δ (1232) transition is explicitly evaluated using different forms for the baryon wave functions and adopting a one-body relativistic current for the constituent quarks. It is shown that the N − Δ (1232) contribution to the sum rule is sharply sensitive to the introduction of anomalous magnetic moments for the constituent quarks, at variance with the findings of non-relativistic and relativized quark models. The experimental value of the isovector-isovector part of the sum rule is almost totally reproduced by the N − Δ (1232) contribution, when the values of the quark anomalous magnetic moments are fixed by fitting the experimental nucleon magnetic moments. Our results are almost independent of the adopted form of the baryon wave functions and only slightly sensitive to the violation of the angular condition caused by the use of a one-body current. The calculated average slope of the generalized sum rule around the photon point results to be only slightly negative at variance with recent predictions of relativized quark models.

Bcmeson weak decays andCPviolation

The form factors for ${B}_{c}$ transitions are calculated with a relativistic constituent quark model based on the Bethe-Salpeter formalism. The rates for some semileptonic and nonleptonic ${B}_{c}$ weak decays and $\mathrm{CP}$-violating asymmetries for two-body hardonic ${B}_{c}$ decays are estimated as well. The calculated widths are compared with those predicted in other quark models of mesons. For the most promising signatures for the discovery of ${B}_{c}:$ ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}l\ensuremath{\nu}\ensuremath{\rightarrow}{(l}^{\ensuremath{'}+}{l}^{\ensuremath{'}\ensuremath{-}})l\ensuremath{\nu}$ and ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}\ensuremath{\pi}\ensuremath{\rightarrow}{(l}^{\ensuremath{'}+}{l}^{\ensuremath{'}\ensuremath{-}})\ensuremath{\pi}$ (with ${l}^{\ensuremath{'}}=e$ or $\ensuremath{\mu})$, the combined branching ratios are, respectively, estimated to be $1.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${4.8a}_{1}^{2}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ for ${\ensuremath{\tau}}_{{B}_{c}}=0.5$ ps and as large as $2.56\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${1.15a}_{1}^{2}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\ensuremath{\tau}}_{{B}_{c}}=1.2$ ps. There are large $\mathrm{CP}$-violating effects in some ${B}_{c}$ decay modes, and the rates for some of these (e.g., ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}{D}^{*},{\ensuremath{\eta}}_{c}D$, and ${\ensuremath{\eta}}_{c}{D}^{*}$, etc.) are large too.

1/mQcorrections to form factors and extraction of|Vcb|

Form factors for ${0}^{\ensuremath{-}}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ and ${0}^{\ensuremath{-}}\ensuremath{\rightarrow}{1}^{\ensuremath{-}}$ mesonic transitions in the heavy quark limit and the ${1/m}_{Q}$ corrections are analyzed model independently within the Bethe-Salpeter (BS) formalism. The analysis shows that the BS formalism has spin-flavor symmetry in the heavy quark limit and respects Luke's theorem when the ${1/m}_{Q}$ corrections are taken into account. All form factors for $B\ensuremath{\rightarrow}{D}^{(*)}$ transitions beyond the zero recoil point are estimated in a relativistic constituent quark model based on the BS formalism. Using these form factors we calculate the branching ratios for the semileptonic decays $B\ensuremath{\rightarrow}{D}^{(*)}{l}^{+}{\ensuremath{\nu}}_{l}$ and extract the Cabibbo-Kobayashi-Maskawa matrix element ${|V}_{\mathrm{cb}}|.$ We get ${|V}_{\mathrm{cb}}|=0.042\ifmmode\pm\else\textpm\fi{}0.003$ which is consistent with the current world average.

Weak Decays of D and Ds Mesons in a Relativistic Quark Model**The project supported in part by National Natural Science Foundation of China and the State Education Commission of China

The transitions of D and Ds, mesons to light vector states are studied in a relativistic constituent quark model based on the Bethe–Salpeter formalism. The form factors are calculated, and the branching fractions for both semileptonic and nonleptonic decays are given. The results show that the form factors for these transitions deviate substantially from the request of heavy quark symmetry. All the branching ratios for D and Ds semileptonic decays are found to be consistent with data, whereas the calculations of nonleptonic D and Ds decays under the factorization assumption do not agree with experiments. This confirms the conjecture that the factorization scheme is much less applicable in D and Ds decays than in B and Bs decays.

Light-cone quark model predictions for radiative meson decays

We investigate the radiative decay of pseudoscalar (π, K, η, η′), vector (ϱ, K ∗ , ω, ƒ) and axial-vector ( A 1) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock state expansion of meson wave functions are not contaminated by the vacuum fluctuation, (2) the problem of assigning quantum numbers J PC to mesons is circumvented by the Melosh transformation. Except the well-known constituent quark masses of ( u, d, s) quarks and the spin-averaged meson masses, the only parameter in the model is the Gaussian parameter β which determines the broadness (or sharpness) of the radial wave function. Our overall predictions of pseudoscalar, vector and axial-vector meson radiative decay processes are in remarkably good agreement with the experimental data.

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ϕ) and axial vector (A 1) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA 1 → πγ* at 0≤Q 2≤5 GeV2 and π0(η) → γ*γ at 0≤Q 2≤3 GeV2 are in a remarkably good agreement with the experimental data and the result forA 1 + → π+ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.

Weak decay form factors of heavy pseudoscalar mesons within a light-front constituent quark model

The transition form factors describing the semileptonic decays of heavy pseudoscalar mesons are investigated within a relativistic constituent quark model formulated on the light-front. For the first time the form factors are calculated in the whole accessible kinematical region, adopting meson wave functions derived from various effective q q interactions able to describe the meson mass spectra. It is shown that the decay rates of the B → Dℓ ν ℓ, D → Kℓ ν ℓ and D → πℓ ν ℓ weak decays are mainly governed by the effects of the confinement scale, whereas the B → πℓ ν ℓ decay rate is sensitive to the high-momentum components generated in the meson wave functions by the effective one-gluon-exchange interaction. Our results are consistent with available experimental data and predictions of lattice QCD calculations and QCD sum rules.

The [formula omitted] amplitudes extracted from the γp → π+π−p reaction and comparison to quark models

The γp → π + π − p reaction, in combination with data from the πN → ππN reaction has been recently analyzed and allows one to obtain the s- and d-wave amplitudes for the N ∗ (1520) decay into Δπ with absolute sign with respect to the N ∗ (1520) → Nγ helicity amplitudes. In addition one obtains the novel information on the momentum dependence of the amplitudes. In the present paper we show how this new information poses new constraints to quark models of hadron structure. In particular we show that the signs and the momentum dependence of these amplitudes coincide with those given by non relativistic constituent quark models. The absolute values provided by these models agree only qualitatively, and a discussion is done on the reasons for it and possible ways to improve.