LHCb sheds light on V_ub puzzle

The Cabibbo–Kobayashi–Maskawa (CKM) matrix element V_ub describes the coupling between u and b quarks in the weak interaction, and is one of the fundamental parameters of the Standard Model (SM). Though it was first observed to be non-zero 30 years ago, its value is still debated. |V_ub| determines the length of the least well-known side of the corresponding unitarity triangle, and is therefore a key ingredient for testing the consistency of the SM in the flavour sector. LHCb has recently published a new result on |V_ub| using the first ever measurement of the B_s⁰ → K^–μ⁺ν_μ decay.

|V_ub| and |V_cb| are the focus of a longstanding puzzle. When comparing the world-average values derived from inclusive and exclusive B-meson decays, respectively, the inclusive and exclusive measurements disagree by more than three standard deviations, for measurements of both |V_ub| and |V_cb|. Traditionally, the exclusive |V_ub| determination requires the reconstruction of the semileptonic b → u decay B⁰ → π^–μ⁺ν_μ. LHCb also has access to B_s⁰ meson and b-baryon decays, but the missing neutrino makes it difficult to isolate the signal from the copious background. Defying expectations, however, in 2015 LHCb managed to observe the Λ_b⁰ → pμ^–ν_μ decay, and used the normalisation channel Λ_b⁰ → Λ⁺_cμ^–ν_μ to determine |V_ub|/ |V_cb|. The main difficulty in this type of analysis resides in the fact that only two charged particles are reconstructed in decays such as B_s⁰ → K^–μ⁺ν_μ and Λ_b⁰ → pμ^–ν_μ. A huge background arising from other sources dominates the selected data sample. Machine-learning algorithms are therefore used to isolate the signal from the various background categories consisting of decays with additional charged and/or neutral particles in the final state. The remaining irreducible background is modelled by using both simulation and control samples extracted from data.

This is the first experimental test of the form-factor calculations

First observation

In a recent paper, the LHCb collaboration presented the first observation of the decay B_s⁰ → K^–μ⁺ν_μ. The decay B_s⁰ → D_s^– μ⁺ν_μ is used as a normalisation channel to minimise experimental systematic uncertainties. The study was performed in two regions of the squared invariant mass (or momentum transfer) q² of the muon and the neutrino below and above 7 GeV². The observed total yield was about 13,000 events, corresponding to a branching fraction of (1.06 ± 0.10) × 10^–4, of which about one third stemmed from the low q² range (figure 1).

The extraction of the ratio |V_ub|/|V_cb| requires external knowledge of the form factors describing the strong B_s⁰ → K^– and B_s⁰ → D_s^– transitions, to account for the interactions of the quarks bound in mesons. These vary with the momentum transfer and are calculated using non-perturbative techniques, such as lattice QCD (LQCD) and light-cone sum rules (LCSR). As LQCD and LCSR calculations are more accurate at high and low q², respectively, they are used in the corresponding q² regions. The obtained value of |V_ub|/|V_cb| = 0.095 ± 0.008 in the high q² interval shows agreement with the world average of exclusive measurements, and with the LHCb result using Λ_b⁰ → pμ^–ν_μ decays, while in the low q² region, |V_ub|/|V_cb| = 0.061 ± 0.004 is significantly lower (figure 2). This is the first experimental test of the form-factor calculations, and new results are expected in the near future. These will help settle the exclusive versus inclusive debate surrounding the values of |V_ub| and |V_cb|, and provide further constraints on the unitarity triangle.