Abstract
We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$ decays in the presence of neutral-meson mixing. We derive expressions for the time-dependent angular distributions for decays into CP eigenstates, and identify the relevant observables that can be extracted from time-integrated and time-dependent analyses with or without tagging, with a focus on the difference between measurements at $B$-factories and hadronic machines. We construct two observables of interest, which we call $Q_8^-$ and $Q_9$, and which are theoretically clean at large recoil. We compute these two observables in the Standard Model, and show that they have good potential for New Physics searches by considering their sensitivity to benchmark New Physics scenarios consistent with current $b\to s\ell\ell$ data. These results apply to decays such as $B_d\to K^*(\to K_S\pi^0)\ell\ell$, $B_s\to \phi (\to K_SK_L)\ell\ell$ and $B_s\to \phi(\to K^+K^-)\ell\ell$.
Highlights
When dealing with decays of neutral B mesons, experimental observables are affected by particle-antiparticle mixing, with the decaying meson being either a B or a Bdepending on the time of decay
In the case of flavour-non-specific decays –such as decays into CP eigenstates– in which the final state can arise from the decay of both B and Bmesons, the mixing and decay processes interfere quantum-mechanically, leading to interesting phenomenological consequences
In this paper we develop the theoretical framework and study the phenomenological advantages of time-dependent Bd,s → V decays, spelling out the new observables that can be accessed, as well as the opportunities for New Physics searches, both at B-factories and hadronic machines
Summary
We first recall a few elements of the analysis of the exclusive b → s decays of the type B → V (→ M1M2). The operators O1,...,6 and O8 are hadronic operators of the type (sΓb)(qΓ q) and (sσμνTaPRb)Gaμν respectively [43], and contribute to b → s processes through a loop coupled to an electromagnetic current (via b → sγ∗ → s ). If N has spin 1, as the initial decaying particle has spin 0, the only combination of helicity amplitudes allowed are (m, n) = (0, 0), (+1, +1), (−1, −1), (0, t), where t denotes the timelike polarisation. The spin-1 N particle couples to the lepton pair either throughγμPL orγμPR , and we can further separate left- from right-handed components in the amplitudes: AL0 , AR0 , AL|| , AR|| , AL⊥, AR⊥. We stress that this result arises just from the identification of kinematics of CP-conjugate decays, and does not rely on any intrinsic CP-parity of the initial or final states involved
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