Resumen de Looking for new physics in the (—) B0 d → (—) K∗0(→ Kπ) ℓ+ℓ− decay mode at large recoil
Over the last decade flavour physics has become a precision testing field of Standard Model (SM), providing extremely accurate measurements which severely constrain the New Physics (NP) models that can be build to explain particle physics phenomena at the TeV scale. Moreover, the suppression of flavour-changing neutral currents in the SM turns heavy-flavoured meson decays into extremely useful instruments for the indirect search of NP signals.
From the theoretical point of view the calculation of inclusive decays suffer less from hadronic uncertainties than exclusive decays, but the latter are easier to measure experimentally. The commissioning of the LHC accelerator at CERN, with its experiment dedicated to the study of flavour through the decays of B mesons (LHCb), has created the need for a good theoretical control over these exclusive modes. This thesis will deal with one of the rarest B decays ever measured experimentally: $\bar{B}_d^0 ¿¿>\bar{ K}^{*0} (\to K \pi) \ell^+ \ell^-$ .
This thesis is organised in two blocks. We first discuss how to calculate the differential decay amplitude of this decay mode in a pedagogical way, reviewing briefly the effective Hamiltonian formalism and some techniques to obtain the non-perturbative parameters that arise in transition matrix elements of effective operators. The QCD factorisation (QCDf) framework is introduced as a formalism to account for both factorisable and non-factorisable order $\alpha_s$ corrections at leading order in $\Lambda_{\rm{QCD}}/m_b$. Also the kinematics of a generic four-body decay and the dynamics of this process are reviewed thoroughly.
The second part of the thesis contains the four original articles published, which deal with the construction of observables free from form factor uncertainties at leading order in $\alpha_s$ (named ¿FFI observables¿) and explain the importance of getting rid of this source of uncertainties. The benefits and drawbacks of this way of proceeding are studied in depth. Simulations of the signal that could be detected at LHCb at integrated luminosities of 10 and 100 fb-1 are performed using a toy Monte Carlo model for the CP-conserving and CP-violating observables proposed. The explicit form of uniangular distributions in terms of these observables is also given. Sensitivity to certain kinds of NP (mainly chirally-flipped currents and scalars) is also studied using benchmark scenarios with NP contributions in the Wilson coefficients of the effective Hamiltonian. The allowed regions for these contributions in the parameter space of Wilson coefficients is deduced using both experimental and theoretical constraints from different observables. Finally, we obtain the symmetries of the differential decay distribution in the massless lepton, massive lepton and massive leptons + scalars scenarios, and use them to establish the minimum amount of FFI observables needed to characterise the decay completely and extract the maximum amount of useful information from it.
