To understand the rare decay Bs→π+π−ℓ+ℓ−B_s\to\pi^+\pi^-\ell^+\ell^-

Motivated by the LHCb measurement, we analyze the $B_s\to \pi^+\pi^-\ell^+\ell^-$ decay in the kinematics region where the pion pairs have invariant mass in the range $0.5$-$1.3$ GeV and muon pairs do not originate from a resonance. The scalar $\pi^+\pi^-$ form factor induced by the strange $\bar ss$ current is predicted by the unitarized approach rooted in the chiral perturbation theory. Using the two-hadron light-cone distribution amplitude, we then can derive the $B_s\to \pi^+\pi^-$ transition form factor in the light-cone sum rules approach. Merging these quantities, we present our results for differential decay width which can generally agree with the experimental data. More accurate measurements at the LHC and KEKB in future are helpful to validate our formalism and determine the inputs in this approach.Comment: 8 pages, 4 figures; v2: references added, match the published versio

Radiative Leptonic Bc→γℓνˉB_c\to \gamma \ell\bar\nu Decay in Effective Field Theory beyond Leading Order

We study the radiative leptonic $B_c\to \gamma\ell\bar\nu$ decays in the nonrelativistic QCD effective field theory, and consider a fast-moving photon. As a result the interactions with the heavy quarks can be integrated out, and thus we arrive at a factorization formula for the decay amplitude. We calculate not only the relevant short-distance coefficients at leading order and next-to-leading order in $\alpha_s$, but also the nonrelativistic corrections at the order $|\bold{v}|^2$ in our analysis. We find out that the QCD corrections can sizably decrease the branching ratio and thus is of great importance in extracting the long-distance operator matrix elements of $B_c$. For the phenomenological application, we present our results for the photon energy, lepton energy and lepton-neutrino invariant mass distribution.Comment: 24 pages, 5 figures, and 2 tables;new references and a new table added and typos correcte

Gluon quasidistribution function at one loop

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the $P^z$ evolution equation for quasi parton distribution functions, and find that the $P^z$ evolution kernels are identical to the DGLAP evolution kernels.Comment: 26 pages,8 figures;accepted by Eur.Phys.J

Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions

We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.Comment: 10 pages, 3 figures; v2: accepted for publication in Physical Review D as a rapid communicatio