Symmetry breaking radiative corrections to B to tensor meson form factors at large recoil

Abstract

In heavy-to-light $B$ decays, the heavy-quark/large-energy symmetry reduces the number of QCD form factors. At large final state meson energy, these form factors receive sizeable perturbative corrections. The hard-gluon vertex corrections are absorbed in the coefficients of soft-form factors, while the hard-spectator interactions generate symmetry-breaking corrections and end-point singularities. At an order of $1/m_b$, using the heavy-quark/large-energy symmetry, the end-point singularities can also be absorbed in the soft form factors, whereas the symmetry breaking corrections add separately to the form factors. In this work, we calculate these perturbative corrections for $B\rightarrow T\mu^{+}\mu^{-}$ decays, with $T$ representing the tensor mesons $K^*_2,\; f_2,\; a_2$ all having $J^P=2^+$. We find that the values of the branching ratio $(Br)$ and the zero-position of the forward-backward asymmetry $(\mathcal{A}_{FB})$ of $B\to K^*_2 \mu^{+}\mu^{-}$ decay receive nearly $5\%$ and $14\%$ contributions, respectively, from these radiative corrections. Compared to these observables, the radiative corrections change the averaged longitudinal lepton polarization asymmetry ($\langle P_L\rangle$) by $13\%$. Therefore, prior to attributing any deviation from the SM predictions of these asymmetries as a hint of NP, one has to take into account the contributions of vertex and hard-spectator corrections.

Radiative B to tensor meson decays at NLO in SCET

“…n p is the large component of the total outgoing n-hard-collinear momentum and n • p γ is the momentum of an outgoing photon. Similarly, the relevant SCET I operators for ¢-B type currents and their corresponding WCs are The index j in ¢-B type WCs refer to the two types of operators represented by equations (14) and equation (15). The variable ( ¯) u u denotes the fraction of the large component of the nhard-collinear momentum carried by the quark (gluon) field.…”

“…The seven form-factors for B → T can be related to z T by invoking the heavy quark symmetry, therefore, to determine z T at zero momentum transfer i.e. q 2 = 0, any one of them can be used [15]. Using this liberty, let us use the vector form-factor V(q 2 ), which is calculated by using LCSR [9,11], to determine the z T , i.e.…”

“…, where ( ) * K 1430 2 is a tensor mesons, is studied using a perturbative Quantum Chromodynamics (QCD) approach [9], light-cone sum rules [10,11], Light front quark model (LFQM) [12,13], heavy quark effective theory (HQET) [14], and LEET [15]. Also, the experimental averaged value of the branching ratio of ( )g  * B K 1430 2 is measured to be (1.24 ± 0.24) × 10 −5 [16].…”