Speaker
Description
Semileptonic $B$ decays involving multiple final-state hadrons play a crucial role as backgrounds to studies of lepton flavour universality or recent anomaly observed in $B \rightarrow K\nu\nu$. Furthermore, these poorly understood decays constitute sizeable signal components in measurements of inclusive $B \rightarrow X_{u/c} \ell\nu$ decays and the subsequent extraction of inclusive $V_{xb}$.
Current theoretical models describing decays such as $B\rightarrow D\pi\ell\nu$ or $B\rightarrow \pi\pi\ell\nu$ rarely take contributions beyond dominant resonances into account, while neglecting non-resonant components.
In this talk, we present a novel, model-independent parameterization of three-hadron form factors.
The challenge is the dependence of the form-factors on two additional variables beyond the usual $q^2$-dependence: they can be chosen to correspond to the invariant mass and the helicity angle of the final state hadron system. Using dispersive methods we derive a systematic expansion in all three kinematic variables, generalizing the standard $z$-expansion, and bound the expansion coefficients through unitarity. Our method treats the two-hadron lineshapes in a model-independent manner using Omnès functions, thus allowing for a data-driven determination of all expansion parameters.
