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Register a new userRevisiting radiative leptonic $B$ decay
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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 $B to gamma ell u$ 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.
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Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B to gamma ell u$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $alpha_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B to gamma$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30% correction to the leading-power direct photon effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of ${cal O} (3 sim 5%)$ with the light-cone sum rule approach. We further predict the partial branching fractions of $B to gamma ell u $ with a photon-energy cut $E_{gamma} geq E_{rm cut}$, which are of interest for determining the inverse moment of the leading-twist $B$-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.
Radiative and leptonic decays of B-mesons represent an excellent laboratory for the search for New Physics. I present here recent results on radiative and leptonic decays from the Belle and BABAR collaborations.
We reconsider the QCD predictions for the radiative decay $Bto gamma ell u_ell$ with an energetic photon in the final state by taking into account the $1/E_gamma, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $phi_+(omega)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of $phi_+(omega)$, including the first inverse moment, $1/lambda_B$, from the expected high-statistics data of the BELLE II experiment.
Pure leptonic radiative decays of heavy-light mesons are calculated using a very simple non-relativistic model. Dominant contribution originates from photon emission from light initial quark. We find $BR(B^pmtoell ugamma)sim3.5times10^{-6}$ and $BR(D_sto ell ugamma)sim1.7 times10^{-4}$. The importance of these reactions to clarify the dynamics of the annihilation graph is emphasized.
We present a lattice NRQCD study of the B meson decay constant in the quenched approximation with emphasis given to the scaling behavior. The NRQCD action and the heavy-light axial current we use include all terms of order 1/M and the perturbative $O(alpha_s a)$ and $O(alpha_s/M)$ corrections. Using simulations at three value of couplings $beta$=5.7, 5.9 and 6.1 on lattices of size $12^3times 32, 16^3times 48$ and $24^3times 64$, we find no significant $a$ dependence in $f_B$ if the $O(alpha_s a)$ correction is included in the axial current. We obtain $f_B = 167(7)(15)$ MeV, $f_{B_s}= 191(4)(17)(^{+4}_{-0})$ MeV and $f_{B_s}/f_B =1.15(3)(1)(^{+3}_{-0})$, with the first error being statistical, the second systematic, and the third due to uncertainty of strange quark mass, while quenching errors being not included.
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