The B → K* transition form factors within the QCD lightcone sum rules and their application to the semileptonic decay B → K* μ ^{+} μ ^{}
Abstract
We present a detailed calculation on the B\to {K}^{*} transition form factors (TFFs), {A}_{{0,1,2}}, V and {T}_{{1,2,3}}, within the QCD lightcone sum rules (LCSRs). To suppress the contributions from hightwist lightcone distribution amplitudes, we adopt a righthanded chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leadingtwist distribution amplitude {φ }_{2;{K}^{*}}^{\perp } provides over 90% contribution, thus those TFFs provide good platforms for testing the property of {φ }_{2;{K}^{*}}^{\perp }. We suggest a model for {φ }_{2;{K}^{*}}^{\perp }, in which two parameters {B}_{2;{K}^{*}}^{\perp } and {C}_{2;{K}^{*}}^{\perp } dominantly control its longitudinal distribution. With a proper choice of {B}_{2;{K}^{*}}^{\perp } and {C}_{2;{K}^{*}}^{\perp }, our predictions on B\to {K}^{*} TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the Bmeson rare decay B\to {K}^{*}{μ }^{+}{μ }^{}. The predicted differential branching fraction {{d}}{B}/{{d}}{q}^{2}(B\to {K}^{*}{μ }^{+}{μ }^{}) is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q ^{2}region, we get the branching fraction, {B}(B\to {K}^{*}{μ }^{+}{μ }^{})=≤ft({1.088}_{0.205}^{+0.261}\right)× {10}^{6}, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of {φ }_{2;{K}^{*}}^{\perp }.
 Publication:

Journal of Physics G Nuclear Physics
 Pub Date:
 August 2016
 DOI:
 10.1088/09543899/43/1/015002
 Bibcode:
 2016JPhG...43a5002F