Abstract
We suggest to update the expansion coefficients of 2$\pi$DAs with the distribution amplitudes of light mesons evaluated from lattice QCD, with which we revisit $\overline{B}^0 \to \pi^+\pi^0$ transition form factors from light-cone sum rules approach and extend the predictions from the threshold of dipion invariant mass to high energies with including the resonance intervals. We also derive $B^- \to \pi^0\pi^0$ transition form factors with the isoscalar dipion final state, serving as the supplement to the isovector ones to complete the set of light-cone sum rules prediction of $B \to \pi\pi$ form factors. Our numerics shows that the lowest resonance gives the dominant contribution to $P-$wave form factors, while the resonance contribution in $S-$wave is not so salient.
Highlights
With a large number of angular observables that are sensitive to the spin structure of the underlying short distance operators, B → ππlνl decays have been suggested to probe the V − A nature of weak interaction [1], whose measurement would provide prolific information to test QCD theoretical approaches and to search physics beyond the standard model (SM)
The light-cone sum rules (LCSRs) approach is operative in the regions of large hadronic recoil at low invariant mass, i.e., the S-wave generated B → ππ; Kπ form factors have been calculated [7,8] with the combination of the perturbative theory based on the operator production expansion and the low-energy effective theory inspired by the chiral symmetry, corresponding to the effect from the LCDAs and from the scalar form factors, respectively, and, recently, the B 0 → πþπ0 form factors have been derived from LCSRs approach
In this paper we suggest to update the nonasymptotic coefficients of leading twist 2πDAs with the lattice QCD (LQCD) knowledge of light mesons, which is already quite accurate with the development of the discrete computing technique
Summary
With a large number of angular observables that are sensitive to the spin structure of the underlying short distance operators, B → ππlνl decays have been suggested to probe the V − A nature of weak interaction [1], whose measurement would provide prolific information to test QCD theoretical approaches and to search physics beyond the standard model (SM). The light-cone sum rules (LCSRs) approach is operative in the regions of large hadronic recoil at low invariant mass, i.e., the S-wave generated B → ππ; Kπ form factors have been calculated [7,8] with the combination of the perturbative theory based on the operator production expansion and the low-energy effective theory inspired by the chiral symmetry, corresponding to the effect from the LCDAs and from the scalar form factors, respectively, and, recently, the B 0 → πþπ0 form factors have been derived from LCSRs approach. The LCSRs prediction is always influenced by the high power terms, one of which is the nonasymptotic QCD corrections to hadron distribution amplitudes (DAs); in the literature, most of the calculations of B → ππ form factors use the expansion coefficients of 2πDAs obtained 20 years ago from the instanton model [12].
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