The crown jewel of particle physics, the Standard Model (SM), has withstood numerous experimental trials. However, there are still some observations it cannot explain. Examples such as dark matter and the matter-antimatter imbalance in the Universe come to mind. The SM may be extended, by including additional particles and interactions, so as to explain such phenomena. These new particles and interactions are collectively referred to as “new physics” (NP), and the results covered by this article provide a promising lead for their discovery.

In the past decade, a pattern has been emerging in the study of *b*-quark decays with leptons in the final state. They are collectively referred to as “flavour anomalies”, and they typically feature tensions at the level of 2–3 standard deviations between experimental results and SM predictions. As such, individual anomalies are not sufficiently significant to claim discovery of NP. However, the anomalies are often treated collectively in an Effective Field Theory (EFT) framework, whereby short distance contributions are separated from their long distance counterparts. This is similar to the 4-point approximation used to describe beta decay, where the process is observed at long enough distances to regard the *W* boson propagator as point-like.

The EFT approach leads to the formulation of an effective Lagrangian, *L*** _{eff}** = Σ

Two examples of EFT analyses of flavour anomalies are shown in Figure 1 [1-3]. In the plot on the left-hand side, the 1σ and 2σ confidence levels for the best-fit point for the considered anomalies are shown in red. On the right-hand side, the best-fit 1σ, 2σ, and 3σ confidence levels are shown in green. The two analyses make different assumptions on the presence of NP in the coefficients *C*_{i} (as shown by the axes), however they both find that the flavour anomalies prefer *C*_{i} values that are significantly different from the ones predicted by the SM (the origin in each plot).

There are several types of anomalous flavour observables, such as differential branching fractions and angular coefficients. They are predicted in the SM with various degrees of precision, and so particularly important are the flavour anomalies that are theoretically clean. Recently, at the Electroweak session of the Moriond 2021 conference, the LHCb collaboration has presented the most precise individual measurements to date of two such theoretically-clean anomalous observables. The first one is the ratio of branching fractions *R_{K}* = B(

The branching fraction of *B*** _{s}^{0}** →

Despite the unambiguous SM predictions, experimental results on *B*** _{(s) }**→

**Measurement of R _{K}**

Highly anticipated updates to the *R_{K}* and

where *N*(*X*) and *ε*(*X*) represent respectively the yields and efficiencies of selecting the decay of a *B*** ^{+}** meson into

Several cross-checks are performed to ensure the selection efficiencies are well understood. Among these checks are the ratios *r_{J/ψ}* and

The value of *R_{K}* is extracted from an unbinned maximum likelihood fit to the selected

As expected, the uncertainty on the result is dominated by the statistical component, rather than the systematic one. The dominant systematic effect is the choice of the fit model, which contributes by around 1%. By comparison, effects induced by the calculation of efficiencies are reduced to the permille level by the double ratio

Thanks to the excellent mass resolution of muons, the signature of *B*** _{(s) }**→

where *N*** _{sig}** and

The fit for the *B*** _{(s) }**→

The branching fraction of *B*** _{(s) }**→

Like *R_{K}*, the measurement of B(

The updaded results on *R_{K}* and the

Since all presented measurements are dominated by the statistical uncertainty, future updates are crucial to the better understanding of the flavour puzzle. In Table 1 are summarised the projected improvements on the precision of the measurements of *R_{K }*and

**Table 1: Extrapolation, based on Run 1 results, of statistical uncertainties on R_{K, }B(B_{s}^{0}_{ }→ μ^{+}μ^{−}) (expressed in units of their SM predictions), and the expected electron-mode yield at the end of future detector upgrades. The b-quark production cross-section is assumed to scale linearly with centre-of-mass energy, and the detector performance is assumed to be unchanged with respect to Run 1. Adapted from Ref. [21].**

The EFT interpretation in terms of shifts in muonic Wilson Coefficients ∆*C*_{i}**^{μ}** from their SM value, in light of the new results of

In light of the recent results from LHCb, the flavour puzzle has become even more intriguing. LHCb will continue to improve the precision on its anomalous flavour measurements, whilst also investigating related observables that could provide complementary information. Verification from other experiments, such as Belle II, is expected in the near future, so exciting times lay ahead of the particle physics community!

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