Exploiting the Symmetries of P and S wave for B --> K^* mu^+ mu^-

Abstract

After summarizing the current theoretical status of the four-body decay B --> K^*(--> K pi) mu^+ mu^-, we apply the formalism of spin-symmetries to the full angular distribution, including the S-wave part involving a broad scalar resonance K0^*. While we recover in the P-wave sector the known relation between the angular observables Pi('), we find in the S-wave sector two new relations connecting the coefficients of the S-wave angular distribution and reducing the number of independent S-wave observables from six to four. Included in the experimental data analysis, these relations can help to reduce the background from S-wave pollution. We further point out the discriminative power of the maximum of the angular observable P2 as a charm-loop insensitive probe of right-handed currents. Moreover, we show that in absence of right-handed currents the angular observables P4' and P5' fulfill the relation P4' = beta P5' at the position where P2 reaches its maximum.