Two-loop QCD corrections toBcmeson leptonic decays

Abstract

The two-loop quantum chromodynamics (QCD) radiative corrections to the B c meson leptonic decay rate are calculated in the framework of the non-relativistic QCD (NRQCD) factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We calculate the short-distance coefficient of the leading matrix element to order α 2 s by matching the full perturbative QCD calculation results to the corresponding NRQCD results. The result presented in this work helps the evaluation of both the B c leptonic decay constant and the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V cb | to the full next-to-next-to-leading-order (NNLO) degree of accuracy.The advent of the non-relativistic quantum chromodynamics (NRQCD) factorization formalism has improved the reliability of investigations on heavy quarkonium [1], thereby also improving the understanding of the strong interaction. It has been noted that for quarkonium production and decays, in many cases, the leading-order calculation in the framework of NRQCD is inadequate. However, the discrepancies between the leading-order calculations and the experimental results can be mostly rectified by including higher-order corrections, which has stimulated various investigations in this respect.The B c meson system, which contains two different flavors of heavy quarks, possesses some peculiar characteristics different from those of heavy quarkonium and has recently attracted considerable interest, especially with the progress of the LHCb experiment [2]. Although the B c meson is highly elusive in experiments, the information obtained from investigations thereof is extremely valuable, including insights into certain aspects of quantum chromodynamics (QCD), the weak interaction and even new physics. In the b c system, the higher excited states will predominantly cascade down into the ground state, the pseudoscalar B c meson, through hadronic or electromagnetic transitions, and this state will then decay into lighter hadrons or leptons via the weak interaction.Using the NRQCD formalism, the B c meson decay amplitude can be expressed in terms of perturbative QCD (pQCD)-calculable shortdistance coefficients multiplied by non-pertubative NRQCD matrix elements. The expression for the leading-order (LO) B c meson leptonic decay width is simple and has long been known, and the next-to-leading-order calculation was completed by Braaten and Fleming two decades ago [3]. In this work, we compute in pQCD the two-loop radiative corrections to the pseudoscalar B c meson leptonic decay rate, i.e., the short-distance coefficient for the leading matrix element at next-to-next-to-leading-order (NNLO), by matching the perturbative result in full QCD with the corresponding perturbative calculation in NRQCD.The calculation of massive two-loop Feynman integrals is rather difficult, especially with two mass scales. For this reason, only a few master integrals with different massive propagators have been successfully calculated [4][5][6]. The method o...

NNLO QCD corrections to γ + η c (η b ) exclusive production in electron-positron collision

“…[13] and [14] respectively, and a few years ago even the NNNLO result for Υ → e + e − process was obtained [15]. In recent years, at the NNLO level many calculations are performed for quarkonium production and decays [16][17][18]. It is interesting to note that in recently, the NNLO corrections to γγ * → η c (η b ) transition form factor and η c (η b ) → light hardrons were calculated numerically [19,20].…”

$$B_c\rightarrow B_{sJ}$$ B c → B s J

“…For the B c meson, the decay constant can in principle be determined by leptonic and radiative-leptonic decays [56][57][58][59], both of which show lack of experimental data yet. Twoloop contributions in the NRQCD framework have been calculated in Ref.…”

“…Twoloop contributions in the NRQCD framework have been calculated in Ref. [58] and the authors have found…”

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

“…To date, perturbative calculations beyond NLO have been conducted only for a few exclusive processes involving quarkonium, exemplified by O(α 2 s ) corrections to Υ(J/ψ) → e + e − [11,12] (Notice the O(α 3 s ) coefficients were also available recently [13,14]), η b,c → γγ [15,16], χ c0,2 → γγ [17], and B c → ℓν [18,19], as well as the O(α 2 s ) correction to the γγ * → η c,b transition form factor [16]. Only two-loop virtual corrections are required in calculating these hard matching coefficients, since they correspond to exclusive quarkonium decays or productions.…”