Hadrons containing a b quark can decay via a virtual W boson to semileptonic final states through the transitions b→c and b→u accompanied by a W boson, which in turn decays into a charged lepton and neutrino pair. These transitions involve the CKM matrix elements Vcb and Vub, respectively. While the Standard Model (SM) does not predict the values of the parameters of the CKM matrix, the measurements of these parameters in different processes should be consistent with each other. If they are not, it may be a sign of physics beyond the SM. 

The measurement of the decay rates (branching fractions) of the Bₛ⁰→ K⁻μ⁺ν decay, depending on the |Vub| parameter and the Bₛ⁰→ Dₛ⁻μ⁺ν decay, depending on the |Vcb| parameter determines the |Vub|/|Vcb| ratio. The analysis of LHCb data collected in 2012 has provided the first observation of the Bₛ⁰→ K⁻μ⁺ν decay and a measurement of the |Vub|/|Vcb| ratio in two regions of q², the momentum transfer, or invariant mass squared, of the muon and the neutrino. The new analysis will use three times more data aiming at a measurement of the differential decay rate that will allow a powerful comparison with theory prediction of the decay form factors (that describe how a Bₛ⁰ meson turns into either a K⁻ or a Dₛ⁻ meson) and a more precise measurement of  |Vub|.

The B→µνɣ decay is considered the best probe of the structure of the B meson. A measurement of its branching ratio would be of crucial importance in calculating other B meson observables. However, this task is extremely challenging and was never achieved by any experiment. Indeed, only about one in a million B mesons decays to µνɣ because the decay amplitude is suppressed by the |Vub| matrix element and the electromagnetic coupling. Furthermore, the B→µνɣ final state is very hard to identify because it includes only one charged track (the muon). 

We proposed a new technique to find this decay in the large LHCb data sample by using the events where the photon materialises as a pair of electrons. This can happen either because the photon interacts with the detector material or because it has some virtuality. Since the beginning of 2023, the Bicocca group has been developing a novel analysis of the large Run-2 LHCb dataset that aims to observe this decay for the first time or at least place the most stringent upper limit on its rate.

In the Standard Model (SM), all charged leptons, such as τ or μ, have the same gauge couplings. This property is called Lepton Universality. However, differences in mass between the leptons must be accounted for. The ratio R(D⁽*⁾) of the B⁰→D⁽*⁾τν and B⁰→D⁽*⁾µν branching fractions can be used to precisely test this symmetry.  Any measurement exhibiting a conclusive violation of lepton universality, after mass-related effects are accounted for, would be a clear sign of physics beyond the SM. The ratio R(D⁽*⁾) is particularly interesting since a large class of SM extensions contains new interactions that involve the third generation of quarks and leptons, like a b quark as well as τ and ν_τ leptons. Previous measurements from different experiments exhibit a deviation from the SM expectation of about 3 sigmas. The ongoing measurement will provide the first R(D⁽*⁾) result from LHCb using B⁰→D⁺ℓ⁻ν and B⁰→ D*⁺ℓ⁻ν decays.

B decays to final states containing τ leptons, which in turn decay hadronically in three charged pions, represent an excellent candidate for testing the Standard Model (SM). The measurement of the ratio R(D*) of the B⁰→D*⁻τν and B⁰→D*⁻µν branching fractions τ hadronic decays is indeed a crucial result which can provide important information on the possible NP scenarios. Previous measurements performed on this decay channel was found to be in agreement with the SM expectation and now LHCb is working on an update of this measurement with an increased statistics.
Another discriminating observable, not fully explored at the moment, is the longitudinal D* polarization fraction (Fld) which is expected to be very sensible to the NP effects.  The relevance of this measurement lies in the fact that it could provide additional information on the SM extensions even when the ratio R(D*), measured on the same channel, is found to be compatible with the SM value. The on-going measurement, performed on  B⁰→D*⁻τν hadronic  decays, will provide the first LHCb Fld result.