Search

We accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the exclusive electroweak penguin decays $B \to \left \{K, \pi \right \} \ell^{+} \ell^{-}$ with an energetic light-flavour meson, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulae from the short-distance fluctuations at the two distinct scales $m_b$ and $\sqrt{m_b \, \Lambda}$ are determined at ${\cal O}(\alpha_s)$ with the soft-collinear factorization technique. We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the CP asymmetries and the isospin asymmetry in the $B \to \pi \ell^{+} \ell^{-}$ decays., Comment: 8 pages, 3 figures

We determine for the first time the renormalization-group (RG) evolution equation for the $B$-meson soft function dictating the non-perturbative strong interaction dynamics of the long-distance penguin contributions to the exclusive $b \to q \ell^{+} \ell^{-}$ and $b \to q \gamma$ decays. The distinctive feature of the ultraviolet renormalization of this fundamental distribution amplitude consists in the novel pattern of mixing positive into negative support for an arbitrary initial condition. The exact solution to this integro-differential RG evolution equation of the bottom-meson soft function is then derived with the Laplace transform technique, allowing for the model-independent extraction of the desired asymptotic behaviour at large/small partonic momenta., Comment: 8 pages, 2 figures

We calculate the next-to-leading order QCD corrections to $B$ to scalar meson form factors from QCD light-cone sum rules with $B$ meson light-cone distribution amplitudes. We demonstrate that the $B$ meson-to-vacuum correlation functions can be factorized into the convolution of short-distance coefficients and light-cone distribution amplitudes at the one-loop level and find that only $\phi_B^+(\omega,\mu)$ contributes to the form factors. We then employ the $z$-parameterization combined with constraints from strong coupling constants to reconstruct the $q^2$ dependence of the form factors in the whole kinematic allowed regions. Due to the large cancellations between the hard functions and the jet functions, the next-to-leading order results show a modest increase of approximately 5\% compared to the leading order results. Based on the results of form factors, we predict the branching ratios of semi-leptonic $B\to S\ell\bar{\nu}_\ell$ and $B\to S\nu_\ell\bar{\nu}_\ell$ processes, as well as several angular observables, such as forward-backward asymmetries, "flat terms" and lepton polarization asymmetries. We compare these results with calculations from other methods. Experimental verification of these results is required in future experiments., Comment: 47 pages, 13 figures

The radiative leptonic $B\to \gamma\ell\nu_{\ell}$ decay serves as an ideal platform to determine the $B$-meson inverse moment which is a fundamental nonperturbative parameter for the $B$ meson. In this paper, we explore precise QCD contributions to this decay with an energetic photon. We reproduce the next-to-next-to-leading-logarithmic resummation formula for the decay amplitude at leading power in $\Lambda_{\rm QCD}/m_b$. Employing operator identities, we calculate subleading-power contributions from the expansion of the hard-collinear propagator of the internal up quark and the heavy-quark expansion of the bottom quark. We update the contributions from the hadronic structure of the photon to the $\decay$ process with the dispersion technique. Together with other yet known power corrections, phenomenological applications including the partial branching fraction and ratio of the branching fractions of the radiative $B$ decay are investigated., Comment: 29 pages, 6 figures

Motivated by a dynamical enhancement of the electromagnetic corrections by a power of $\Lambda_{\mathrm{QCD}}/m_b$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$ at next-to-leading order (NLO), we extend the QED factorization effects on the leptonic $B$ meson decays with light muon leptons to tauonic final states, $B_{d,s} \, \to\, \tau^+\, \tau^-$, using soft-collinear effective theory (SCET). This extension is necessary owing to the appearance of the large $\tau$ mass, which will lead to different power counting in SCET and also different results. We provide a complete NLO electromagnetic corrections to $B_{d,s} \, \to\, \tau^+\, \tau^-$, which include hard functions and hard-collinear functions below the bottom quark mass scale $\mu_b$. The power enhanced electromagnetic effects from hard-collinear contributions on $B_{d,s}\, \to\, \mu^+\, \mu^-$ discussed before also exist in $B_{d,s} \, \to\, \tau^+\, \tau^-$. However the logarithm term arising from contributions of hard-collinear photon and lepton virtualities for $B_{d,s}\, \to\, \tau^+\, \tau^-$ is not large as it is in muon case due to the hard-collinear scale of $\tau$ mass, which lead to only approximately $0.04\%$ QED corrections to the branching fraction of $B_{d,s} \, \to\, \tau^+\, \tau^-$ compared with overall reduction about $0.5\%$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$., Comment: 29 pages, 3 figures

We improve QCD calculations of the $B_{d, s} \to \pi, K$ form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at ${\cal O}(\alpha_s^0)$, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term in the ${\rm SCET_{I}}$ representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes, and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive $B$-meson decay form factors, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist $B$-meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch parametrization for the semileptonic $B_{d, s} \to \pi, K$ form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive $B$-meson decay form factors to both the achieved SCET sum rule predictions and the available lattice QCD results., Comment: 74 pages, 15 figures

We compute for the first time the long-distance penguin contribution to the double radiative $B$-meson decays due to the purely hadronic operators acting with the electromagnetic current in the background soft-gluon field from first field-theoretical principles by introducing a novel subleading $B$-meson distribution amplitude. The numerically dominant penguin amplitude arises from the soft-gluon radiation off the light up-quark loop rather than the counterpart charm-loop effect on account of the peculiar analytical behaviour of the short-distance hard-collinear function. Importantly the long-distance up-quark penguin contribution brings about the substantial cancellation of the known factorizable power correction possessing the same multiplication CKM parameters, thus enabling $B_{d, \, s} \to \gamma \gamma$ to become new benchmark probes of physics beyond the Standard Model., Comment: 7 pages, 2 figures

In this work, we calculate the transition form factors of $\Lambda_b$ decaying into $\Lambda_c$ within the framework of light-cone sum rules with the distribution amplitudes (DAs) of $\Lambda_b$-baryon. In the hadronic representation of the correlation function, we have isolated both the $\Lambda_c$ and the $\Lambda_c^*$ states so that the $\Lambda_b \rightarrow \Lambda_c$ form factors can be obtained without ambiguity. We investigate the P-type and A-type current to interpolate the light baryons for a comparison since the interpolation current for the baryon state is not unique. We also employ three parametrization models for DAs of $\Lambda_b $ in the numerical calculation. We present the numerical predictions on the $\Lambda_b \rightarrow \Lambda_c$ form factors and the branching fractions, the averaged forward-backward asymmetry , the averaged final hadron polarization and the averaged lepton polarization of the $\Lambda_b \to \Lambda_c \ell\mu$ decays, as well as the ratio of branching ratios $R_{\Lambda_c}$, and the predicted $R_{\Lambda_c}$ can be consistent with the LHCb data., Comment: 22 pages, 2figure

In this work we calculate the transition form factors of $\Lambda_b$ decaying into proton and $N^*(1535)$ ($J^P={1/2}^+$ and ${1/2}^-$ respectively), within the framework of light-cone sum rules with the distribution amplitudes (DAs) of $\Lambda_b$-baryon. In the hadronic representation of the correlation function, we have isolated both the proton and the $N^*(1535)$ states so that the $\Lambda_b \rightarrow p, N^*(1535)$ form factors can be evaluated simultaneously. Due to the less known properties of baryons, we investigate three interpolating currents of the light baryons and five parametrization models for DAs of $\Lambda_b $. Numerically, our predictions on the $\Lambda_b \rightarrow p$ form factors and the branching fractions of $\Lambda_b\to p\ell \nu$ from the Ioffe or the tensor currents are consistent with the Lattice simulation and the results from the light-baryon sum rules, as well as the experimental data of $Br(\Lambda_b^0\to p\mu^-\bar\nu)$. The predictions on the form factors of $\Lambda_b \rightarrow N^*(1535)$ are very sensitive to the choice of the interpolating currents so that the relevant measurement could be helpful to clarify the properties of baryons., Comment: 29 pages, 3figures

In this paper we investigate the next-to-leading power contribution to the $B_s \to \gamma\gamma$ and $B_s \to \gamma\ell\bar{\ell}$ decays from the strange quark mass effect with the dispersion approach which is QCD inspired and more predictive. We have presented the analytic expression of the quark mass contribution in the $B_s \to \gamma\gamma$ and $B_s \to \gamma\ell\bar{\ell}$ decays, together with a new term that is missed in the previous study. The numerical results of the strange quark mass contribution to the $B_s \to \gamma\gamma$ decay is about 6% relative to the total branching ratio, while it is relatively small in the $B_s \to \gamma\ell\bar{\ell}$ decay due to the large resonance contribuiton, Comment: 17 pages, 6 figures

We accomplish the analytical computation of the pure weak annihilation non-leptonic $B$-meson decay amplitudes at leading power in the heavy quark expansion. The novel observation regarding such fundamental hadronic quantities is that adding the missing hard-collinear contribution on top of the hard gluon exchange effect eliminates rapidity divergences entering the convolution integrals of factorization formulae. Subsequently we identify the perturbative enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables., Comment: 5+2 pages, 1 figure

We reanalyze the $\Lambda_b\to p$ transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $\Lambda_b$ baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $\Lambda_b$ baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 $\Lambda_b$ baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays $\Lambda_b\to p\ell\bar{\nu}_\ell$ and the hadronic decay $\Lambda_b\to p\pi$ are also close to the data. It implies that the $b$ quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of $B$ meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach., Comment: 37 pages, 7 figures, version to be published in Eur.Phys.J.C

In this review, we discuss the calculation of the $B\to P,V$ form factors within the framework of the light-cone sum rules with the light-cone distribution amplitudes of the $B$ meson. A detailed introduction to the definition, scale evolution, and phenomenological models of the $B$-meson distribution amplitudes is presented. We show two equivalent approaches of calculating the next-to-leading order QCD corrections to the sum rules for the form factors, i.e., the method of regions and the step-by-step matching in the soft-collinear effective theory. The power suppressed corrections to the $B\to P,V$ form factors especially the contributions from the higher-twist $B$-meson distribution amplitudes are displayed. We also present numerical results of the form factors including both the QCD and the power corrections, and phenomenological applications of the predicted form factors such as the determination of the CKM matrix element $|V_{ub}|$., Comment: 37 pages, 7 figures

Using the perturbative QCD approach, we studied the effects from hadronic structure of photon on the pure annihilation rediative decays $B\to\phi\gamma$ and $B_s\to(\rho^0,\omega)\gamma$. These decays have small branching fractions due to the power suppression by the $\Lambda/m_B$, which make them very sensitive to the next-leading power corrections. The quark components and the related two-particle distribution amplitudes of a final state photon are introduced. The branching fractions can be enhanced remarkably by the factorizable and nonfactorizable emission diagrams. The branching fraction of $B\to \phi\gamma$ even increases by about 40 times, and those of $B_s \to \rho^0\gamma$ and $B_s \to \omega\gamma$ are at the order of ${\cal O}(10^{-10})$. We also note that the ratio of branching fractions of $B_s \to \rho^0\gamma$ and $B_s \to \omega\gamma$ is very sensitive to the effects from hadronic structure of photon. All above results could be tested in future., Comment: 9 pages, 1 figure, to be published in Chinese Physics C

We investigate the pure annihilation type radiative $B$ meson decays $B^0 \to \phi \gamma$ and $B_s \to \rho^0(\omega)\gamma$ in the soft-collinear effective theory. We consider three types of contributions to the decay amplitudes, including the direct annihilation topology, the contribution from the electro-magnetic penguin operator and the contribution of the neutral vector meson mixings. The numerical analysis shows that the decay amplitudes are dominated by the $\omega-\phi$ mixing effect in the $B^0 \to \phi\gamma$ and $B_s \to \omega\gamma$ modes. The corresponding decay branching ratios are enhanced about three orders of magnitudes relative to the pure annihilation type contribution in these two decay channels. The decay rate of $B_s \to \rho^0\gamma$ is much smaller than that of $B_s \to \omega\gamma$ because of the smaller $\rho^0-\phi$ mixing. The predicted branching ratios $B(B^{0}\rightarrow\phi\gamma)=(3.99^{+1.67}_{-1.46} )\times10^{-9},\,B(B_s\rightarrow\omega\gamma)=(2.01^{+0.81}_{-0.71} )\times10^{-7}$ are to be tested by the Belle-II and LHC-b experiments., Comment: radiative decay, annihilation topology, vector meson mixing

In this work, the full leading order results of the form factors for $\Xi_{b}\to\Xi_{c}$ and $\Lambda_{b}\to\Lambda_{c}$ are obtained in QCD sum rules. Contributions from up to dim-5 have been considered. For completeness, we also study the two-point correlation function to obtain the pole residues of $\Xi_{Q}$ and $\Lambda_{Q}$, and higher accuracy is achieved. For the three-point correlation function, since stable Borel regions can not be found, about $20\%$ uncertainties are introduced for the form factors of $\Xi_{b}\to\Xi_{c}$ and $\Lambda_{b}\to\Lambda_{c}$. Our results for the form factors are consistent with those of the Lattice QCD within errors., Comment: 17 pages, 5 figures

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist $B$-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors $F_{A,V}$ in the $B \to \gamma \ell\nu$ decay at leading power in $\Lambda/m_b$. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by $1/E_\gamma$ and $1/m_b$), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data., Comment: 15 pages, 4 figures

Employing the systematic framework of soft-collinear effective theory (SCET) we perform an improved calculation of the leading-power contributions to the double radiative $B_{d, \, s}$-meson decay amplitudes in the heavy quark expansion. We then construct the QCD factorization formulae for the subleading power contributions arising from the energetic photon radiation off the constituent light-flavour quark of the bottom meson at tree level. Furthermore, we explore the factorization properties of the subleading power correction from the effective SCET current $J^{(A2)}$ at ${\cal O} (\alpha_s^0)$. The higher-twist contributions to the $B_{d, \, s} \to \gamma \gamma $ helicity form factors from the two-particle and three-particle bottom-meson distribution amplitudes are evaluated up to the twist-six accuracy. In addition, the subleading power weak-annihilation contributions from both the current-current and QCD penguin operators are taken into account at the one-loop accuracy. We proceed to apply the operator-production-expansion-controlled dispersion relation for estimating the power-suppressed soft contributions to the double radiative $B_{d, \, s}$-meson decay form factors. Phenomenological explorations of the radiative $B_{d, \, s} \to \gamma \, \gamma$ decay observables in the presence of the neutral-meson mixing, including the CP-averaged branching fractions, the polarization fractions and the time-dependent CP asymmetries, are carried out subsequently with an emphasis on the numerical impacts of the newly computed ingredients together with the theory uncertainties from the shape parameters of the HQET bottom-meson distribution amplitudes., Comment: 58 pages, 7 figures