Covariant Light-front Quark Model Research Articles

Revisiting radiative decays of 1^{+-} heavy quarkonia in the covariant light-front approach

We revisit the calculation of the width for the radiative decay of a 1^{+-} heavy Q bar{Q} meson via the channel 1^{+-} rightarrow 0^{-+} +gamma 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-quark mass and wave function structure parameter. We analyze the specific decays h_{mathrm{c}}(1P) rightarrow eta _{mathrm{c}}(1S) + gamma and h_{mathrm{b}}(1P) rightarrow eta _{mathrm{b}}(1S) + gamma . We compare our results with experimental data and with other theoretical predictions from calculations based on non-relativistic models and their extensions to include relativistic effects, finding reasonable agreement.

$$B_c\rightarrow B_{sJ}$$ B c → B s J form factors and $$B_c$$ B c decays into $$B_{sJ}$$ B s J in covariant light-front approach

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 $B_c\to (B_{sJ},B_{J})\bar\ell\nu$ decays, and nonleptonic $B_c\to B_{sJ}\pi$. Branching fractions and polarizations are predicted in the standard model. We find that the branching fractions are sizable and might be accessible at the LHC experiment and future high-energy $e^+e^-$ colliders with a high luminosity at the $Z$-pole. The future experimental measurements are helpful to study the nonperturbative QCD dynamics in the presence of a heavy spectator and also of great value for the spectroscopy study.

Exclusive decaysJ/ψ→D(s)(*)−ℓ+νℓin a covariant constituent quark model with infrared confinement

We investigate the exclusive semileptonic decays $J/\psi \to D_{(s)}^{(*)-} {\ell}^+ \nu_{\ell}$, where $\ell=e,\mu$, within the Standard Model. The relevant transition form factors are calculated in the framework of a relativistic constituent quark model with built-in infrared confinement. Our calculations predict the branching fractions $\mathcal{B}(J/\psi \to D_{(s)}^{(*)-} {\ell}^+ \nu_{\ell})$ to be of the order of $10^{-10}$ for $D_s^{(*)-}$ and $10^{-11}$ for $D^{(*)-}$. Most of our numerical results are consistent with other theoretical studies. However, some branching fractions are larger than those calculated in QCD sum rules approaches but smaller than those obtained in the covariant light-front quark model by a factor of about $2-3$.

Radiative Transitions Among the Vector and Scalar Heavy Quarkonium States with Covariant Light-Front Quark Model

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.

Radiative D(D s ) decays in the covariant light front approach

In the covariant light-front quark model, we investigate the D→V,A,T tensor form factors induced by c→u transition, which can contribute to radiative D(D s ) decays. The short distance contribution is much smaller than the experimental data, thus radiative D(D s ) decays is dominated by nonperturbative effect. We also include the weak annihilation contributions and the long distance contributions to D→Vγ. Our results for D→(K ∗0,ϕ)γ decays can approach the data and the other predictions should be checked with the BEPCII experiment.

Decay constants and form factors of s-wave and p-wave mesons in the covariant light-front quark model

We reanalyze the decay constants of s-wave and p-wave mesons and the 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 β for wavefunctions of most of s-wave mesons and that of a few axial-vector mesons are fixed with the 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 Ds, Bs → M transitions, and to the isoscalar final state mesons. Numerical results of the form factors for transitions between a heavy pseudoscalar meson and an s-wave or a p-wave light meson and their momentum dependence are presented in detail. Further, their sensitivity to uncertainties of the β parameters of the initial as well as the final mesons is investigated. Some experimental measurements of the charmed and bottom meson decays are employed to compare the decay constants and transition form factors obtained in this and other works.

Bs→Ds(3040)form factors andBsdecays intoDs(3040)

Under the assignment of ${D}_{s}(3040)$ as a radially excited $p$-wave $\overline{c}s$ state with ${J}^{P}={1}^{+}$, we compute the ${B}_{s}\ensuremath{\rightarrow}{D}_{s}(3040)$ form factors within the covariant light-front quark model. Two classification schemes for the $p$-wave $\overline{c}s$ meson are adopted. We also use our results to predict the branching ratios (BRs), polarization fractions, and angular asymmetries in semileptonic ${B}_{s}\ensuremath{\rightarrow}{D}_{s}(3040)\ensuremath{\ell}\overline{\ensuremath{\nu}}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$). The BRs are found at the order of ${10}^{\ensuremath{-}3}$ for $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, and ${10}^{\ensuremath{-}5}$ for $\ensuremath{\ell}=\ensuremath{\tau}$. We find that the polarization fractions and angular asymmetries could be useful to pin down the ambiguities in theoretical prescriptions for ${D}_{s}(3040)$. In addition, we investigate the nonleptonic ${B}_{s}\ensuremath{\rightarrow}{D}_{s}(3040)M$ decays under the factorization method, where $M$ denotes a charged pseudoscalar or a vector meson. The BRs of ${B}_{s}\ensuremath{\rightarrow}{D}_{s}(3040)\ensuremath{\rho}$ and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}(3040){D}_{s}^{*}$ reach the order of ${10}^{\ensuremath{-}3}$, while the other channels are typically smaller by 1--2 orders.

Erratum:B→V,A,Ttensor form factors in the covariant light-front approach: Implications on radiativeBdecays [Phys. Rev. D81, 114006 (2010)

We reanalyze the $B\to M$ tensor form factors in a covariant light-front quark model, where $M$ represents a vector meson $V$, an axial-vector meson $A$, or a tensor meson $T$. The treatment of masses and mixing angles in the $K_{1A,1B}$ systems is improved, where $K_{1A}$ and $K_{1B}$ are the $^3P_1$ and $^1P_1$ states of the axial-vector meson $K_1$, respectively. Rates of $B\to M\gamma$ decays are then calculated using the QCD factorization approach. The updated $B\to K^*\gamma$, $B\to K_1(1270)\gamma$, $K_1(1400)\gamma$ and $K_2\gamma$ rates agree with the data. The $K_1(1270)$--$K_1(1400)$ mixing angle is found to be about $51^\circ$. The sign of the mixing angle is fixed by the observed relative strength of $B\to K_1(1270)\gamma$ and $K_1(1400)\gamma$. The formalism is then applied to $B_s\to M$ tensor form factors. We find that the calculated $B_s\to \phi\gamma$ rate is consistent with experiment, though in the lower end of the data. The branching fractions of $B_s\to f_1(1420)\gamma$ and $f'_2(1525)\gamma$ are predicted to be of order $10^{-5}$ and it will be interesting to search for these modes. Rates on $B_s\to f_1(1285)\gamma$, $h_1(1380)\gamma$, $h_1(1170)\gamma$, $f_2(1270)\gamma$ decays are also predicted.

B→V,A,Ttensor form factors in the covariant light-front approach: Implications on radiativeBdecays

We reanalyze the $B\ensuremath{\rightarrow}M$ tensor form factors in a covariant light-front quark model, where $M$ represents a vector meson $V$, an axial-vector meson $A$, or a tensor meson $T$. The treatment of masses and mixing angles in the ${K}_{1A,1B}$ systems is improved, where ${K}_{1A}$ and ${K}_{1B}$ are the $^{3}P_{1}$ and $^{1}P_{1}$ states of the axial-vector meson ${K}_{1}$, respectively. Rates of $B\ensuremath{\rightarrow}M\ensuremath{\gamma}$ decays are then calculated using the QCD factorization approach. The updated $B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$, $B\ensuremath{\rightarrow}{K}_{1}(1270)\ensuremath{\gamma}$, ${K}_{1}(1400)\ensuremath{\gamma}$, and ${K}_{2}\ensuremath{\gamma}$ rates agree with the data. The ${K}_{1}(1270)--{K}_{1}(1400)$ mixing angle is found to be about 51\ifmmode^\circ\else\textdegree\fi{}. The sign of the mixing angle is fixed by the observed relative strength of $B\ensuremath{\rightarrow}{K}_{1}(1270)\ensuremath{\gamma}$ and ${K}_{1}(1400)\ensuremath{\gamma}$. The formalism is then applied to ${B}_{s}\ensuremath{\rightarrow}M$ tensor form factors. We find that the calculated ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\gamma}$ rate is consistent with experiment, though in the lower end of the data. The branching fractions of ${B}_{s}\ensuremath{\rightarrow}{f}_{1}(1420)\ensuremath{\gamma}$ and ${f}_{2}^{\ensuremath{'}}(1525)\ensuremath{\gamma}$ are predicted to be of order ${10}^{\ensuremath{-}5}$ and it will be interesting to search for these modes. Rates on ${B}_{s}\ensuremath{\rightarrow}{f}_{1}(1285)\ensuremath{\gamma}$, ${h}_{1}(1380)\ensuremath{\gamma}$, ${h}_{1}(1170)\ensuremath{\gamma}$, ${f}_{2}(1270)\ensuremath{\gamma}$ decays are also predicted.

Erratum: Covariant light-front approach forB→K*γ,K1γ,K2γdecays [Phys. Rev. D69, 094007 (2004)

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 compared to the data. The relative strength of B to K_1(1270) gamma and B to K_1(1400) gamma rates is very sensitive to the sign of the K_1(1270)-K_1(1400) mixing angle. Contrary to the other models in which K_1(1270) gamma and K_1(1400) gamma rates are predicted to be comparable, it is found that one of them is strongly suppressed owing to a large cancellation between two different form factor terms. The calculated branching ratio of B to K*_2 gamma is in a good agreement with experiment and this may imply the smallness of NLO corrections to this radiative decay mode.

Bctop-wave charmonia transitions in the covariant light-front approach

In the covariant light-front quark model, we investigate the B{sub c}{yields}h{sub c}, {chi}{sub c0,1,2} form factors. The form factors are evaluated in the spacelike kinematic region and are recasted to the physical region by adopting the exponential parametrization. We also study the semileptonic B{sub c} decays and find that branching fractions for the B{sub c}{yields}(h{sub c},{chi}{sub c0,1,2})l{nu}(l=e,{mu}) decays have the order 10{sup -3}, while branching fractions for B{sub c}{yields}(h{sub c},{chi}{sub c0,1,2}){tau}{nu}{sub {tau}} are suppressed by one order. These predictions will be tested on the forthcoming hadron colliders.

Covariant light-front approach forBctransition form factors

In the covariant light-front quark model, we investigate the form factors of $B_c$ decays into $D, D^*, D_s, D_s^*, \eta_c, J/\psi, B, B^*, B_s, B_s^*$ 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. In the fitting procedure, we find the parameters for the form factors $A_2(B_c\to B^*)$ and $A_2(B_c\to B^*_s)$ strongly depend on the decay constants of $B^*$ and $B_s^*$ mesons. Fortunately, the semileptonic and nonleptonic $B_c$ decays are not sensitive to these form factors. With the form factors, we also investigate the branching fractions, polarizations of the semileptonic $B_c\to Ml\nu$ decays. Semileptonic $B_c\to (\eta_c,J/\psi)l\nu$ and $B_c\to (B_s,B_s^*)l\nu$ decays have much larger branching fractions than $B_c\to (D,D^*,B,B^*)l\nu$. In the three kinds of $B_c\to Vl\nu$ decays, contributions from the longitudinal polarized vector is comparable with those from the transversely polarized vector. These predictions will be tested at the ongoing and forthcoming hadron colliders.

J/ψweak decays in the covariant light-front quark model

In the covariant light-front quark model, we study $J/\ensuremath{\psi}\ensuremath{\rightarrow}{D}_{(s)}$ transition form factors and utilize them to evaluate the branching fractions of various $J/\ensuremath{\psi}$ weak decay channels. For the Cabbibo allowed semileptonic decay modes $J/\ensuremath{\psi}\ensuremath{\rightarrow}{D}_{s}l\ensuremath{\nu}$, the predicted branching ratios are at the order of ${10}^{\ensuremath{-}10}$, which may be marginally measured at BESIII. The results for the semileptonic decay modes presented here are about 2--8 times larger than those calculated in the QCD sum rules approach, which is mainly due to the different treatment of nonperturbative QCD dynamics between these two approaches. Furthermore, we also give a rough estimation of the nonleptonic modes within the framework of the factorization approach, whose branching fraction numbers can be as large as ${10}^{\ensuremath{-}9}$ and are consistent with that obtained in the QCD sum rules within the theoretical uncertainties.

Ds→K,K*,ϕform factors in the Covariant Light-Front Approach and ExclusiveDsDecays

In the covariant light-front quark model, we investigate the form factors of D{sub s}{yields}K, K*, {phi} transitions and compare our results with the experimental data and the previous theoretical studies. The semileptonic D{sub s} decays are studied: our result for the branching ratio of D{sub s}{yields}{phi}l{sup +}{nu} is consistent with the data; while the other predictions, such as BR(D{sub s}{sup +}{yields}K{sup 0}l{sup +}{nu}), the branching ratio and the polarization of D{sub s}{yields}K*{sup 0}l{sup +}{nu}, will be tested at the future experiments. Utilizing the results for form factors, we then calculate the two-body nonleptonic D{sub s} decays and find: up to the leading power accuracy, theoretical predictions on branching ratios of nonleptonic D{sub s} decays are typically smaller than the experimental data by a factor of 1.5-2.0. Large contributions from weak annihilation diagrams, together with the s, t-channel final state interactions, are expected to resolve this problem. The D{sub s}{yields}K{sup +}K*{sup 0} decay, which can be easily measured in the K{sup +}K{sup +}{pi}{sup -} final state, can directly shed light on internal information of the doubly Cabibbo-suppressed decay amplitudes.

Study of Bc -→X(3872)π-(K-) decays in the covariant light-front approach

In the covariant light-front quark model, we calculate the form factors of Bc -→J/ψ and Bc -→X(3872). Since the factorization of the exclusive processes Bc -→J/ψπ-(K-) and Bc -→X(3872)π-(K-) can be proved in the soft-collinear effective theory, we can easily get the branching ratios for these decays from the form factors. Taking the uncertainties into account, our results for the branching ratio of Bc -→J/ψπ-(K-) are consistent with previous studies. By identifying X(3872) as a 1++ charmonium state, we obtain BR(Bc -→X(3872)π-)=(1.7+0.7+0.1+0.4 -0.6-0.2-0.4)×10-4 and BR(Bc -→X(3872)K-)=(1.3+0.5+0.1+0.3 -0.5-0.2-0.3)×10-5. Assuming X(3872) to be a 1– state, the branching ratios will be one order of magnitude larger than those of the 1++ state. These results can easily be used to test the charmonium description for this mysterious meson X(3872) at the LHCb experiment.

Production ofP-wave charmed mesons in hadronicBdecays

Production of even-parity charmed mesons in hadronic $B$ decays is studied. Specifically, we focus on the Cabibbo-allowed decays $\overline{B}\ensuremath{\rightarrow}{D}^{**}\ensuremath{\pi}$ and ${\overline{D}}_{s}^{**}{D}^{(*)}$, where ${D}^{**}$ denotes generically a $P$-wave charmed meson. While the measured color-allowed decays ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{**+}{\ensuremath{\pi}}^{\ensuremath{-}}$ are consistent with the theoretical expectation, the experimental observation of ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{**0}{\ensuremath{\pi}}^{\ensuremath{-}}$ for the broad ${D}^{**}$ states is astonishing as it requires that the color-suppressed contribution dominates over the color-allowed one, even though the former is $1/{m}_{b}$ suppressed in the heavy quark limit. In order to accommodate the data of $\overline{B}\ensuremath{\rightarrow}{D}^{**}{\ensuremath{\pi}}^{\ensuremath{-}}$, it is found that the real part of ${a}_{2}/{a}_{1}$ has a sign opposite to that in $\overline{B}\ensuremath{\rightarrow}D\ensuremath{\pi}$ decays, where ${a}_{1}$ and ${a}_{2}$ are the effective parameters for color-allowed and color-suppressed decay amplitudes, respectively. The decay constants and form factors for ${D}^{**}$ and the Isgur-Wise functions ${\ensuremath{\tau}}_{1/2}(\ensuremath{\omega})$ and ${\ensuremath{\tau}}_{3/2}(\ensuremath{\omega})$ are extracted from the data of $B\ensuremath{\rightarrow}{D}^{**}\ensuremath{\pi}$ decays. The Isgur-Wise functions calculated in the covariant light-front quark model are in good agreement with experiment. The neutral modes ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{**0}{\ensuremath{\pi}}^{0}$ for ${D}^{**}={D}_{0}^{*}(2400)$, ${D}_{1}^{\ensuremath{'}}(2430)$, and ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}_{1}^{\ensuremath{'}0}(2430)\ensuremath{\omega}$ are predicted to have branching ratios of order ${10}^{\ensuremath{-}4}$ which are also supported by the isospin argument. The decay constants of ${D}_{s0}^{*}(2317)$ and ${D}_{s1}^{\ensuremath{'}}(2460)$ are inferred from the measurements of $\overline{B}\ensuremath{\rightarrow}{D}_{s}^{**\ensuremath{-}}D$ to be 58\char21{}86 MeV and 130\char21{}200 MeV, respectively. Contrary to the decay constants ${f}_{{D}_{0}^{*}}$ and ${f}_{{D}_{1}^{\ensuremath{'}}}$ which are similar in size, the large disparity between ${f}_{{D}_{s0}^{*}}$ and ${f}_{{D}_{s1}^{\ensuremath{'}}}$ is surprising and unexpected.

Covariant light-front approach forB→K*γ,K1γ,K2*γdecays

Exclusive radiative B decays $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma},$ ${K}_{1}(1270)\ensuremath{\gamma},$ ${K}_{1}(1400)\ensuremath{\gamma},$ and ${K}_{2}^{*}(1430)\ensuremath{\gamma}$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma},$ is found to be 0.24, substantially smaller than what was 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 $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ agrees with experiment, while most of the existing models predict too large $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ compared to the data. The relative strength of $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{1}(1270)\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{1}(1400)\ensuremath{\gamma}$ rates is very sensitive to the sign of the ${K}_{1}(1270)\ensuremath{-}{K}_{1}(1400)$ mixing angle. Contrary to the other models in which ${K}_{1}(1270)\ensuremath{\gamma}$ and ${K}_{1}(1400)\ensuremath{\gamma}$ rates are predicted to be comparable, it is found that one of them is strongly suppressed owing to a large cancellation between two different form factor terms. The calculated branching ratio of $\stackrel{\ensuremath{\rightarrow}}{B}{K}_{2}^{*}\ensuremath{\gamma}$ is in a good agreement with experiment and this may imply the smallness of NLO corrections to this radiative decay mode.