If you have ever had Neapolitan gelato, you know how important it is to combine three different flavours, each in just the right size. And the Standard Model (SM) of particle physics is not less tasty than that! In the SM, leptons are some of the fundamental building blocks that make up the known universe. Besides the familiar electrons, there are two other types of charged leptons: muons and taus. Although these charged leptons share many properties, their differences define their “flavour”, just like the ice cream scoops of a Neapolitan gelato. The vanilla, chocolate and strawberry flavours are simply replaced by the electron, muon and tau flavours. 

 Regardless of their flavour, in the SM the three leptons are expected to have the same coupling to electroweak force carriers. This principle is known as Lepton Flavour Universality (LFU). It is not a formal symmetry of the SM, since the Higgs boson likes certain flavors over others (and this results in different masses for these particles). As a result, there is a wide mass spectrum of these three leptons, with taus about 3500 times heavier than electrons and 17 times heavier than muons. 

 Experimentally, LFU can be tested in semileptonic decays of B mesons, in which a beauty (b) quark can be transformed into a charm (c) quark through a weak decay that also produces a lepton pair, composed of a charged lepton and its neutrino companion: b→c ℓ 𝜈_ℓ. If Nature respects LFU, the only difference in the B meson decays to, say, muons and taus should come from the lepton masses, which can be accounted for by the theory. The CMS Collaboration recently presented a new test of LFU between these two leptons by measuring the ratio of branching fractions R(J/𝜓)=Br(B_c→J/𝜓 𝜏 𝜈_𝜏) / Br(B_c→J/𝜓 𝜇 𝜈_𝜇 ), predicted to be 0.2582 ± 0.0038 in the SM. This ratio is particularly interesting because many theoretical models extending the SM, such as those with leptoquarks, include new interactions that are stronger for taus than muons, differentiating the two flavors. So, a significant increase in the measured ratio could be evidence of new physics, as indicated in Fig. 1.  

The LHCb experiment measured this ratio in 2018 and saw an increase with respect to the SM, at the level of 2 standard deviations.  Similar quark transition studies using B⁰ decays to D^(*) mesons at BaBar, Belle (II), and LHCb showed together a disagreement with the SM at the level of 3.3 standard deviations. Although not significant enough to claim a discovery, this observation baffled the scientific community and motivated further studies.

Figure 1: New physics (right) could lead to a considerable deviation from the SM expectation (left) for the b→c ℓ 𝜈_ℓ quark transition.

Taking advantage of an excellent muon reconstruction, the measurement focuses on events where particles ultimately decay to muons and neutrinos, i.e., 𝜏 →𝜇 𝜈_𝜇 𝜈_𝜏 and J/𝜓 →𝜇𝜇 . The only differences between the numerator and the denominator is that there are more neutrinos in the numerator and the tau lepton is much heavier than the muon. One of the most discriminating variables is the squared four-momentum transfer to the lepton pair (q²). As seen in Fig. 2, the B_c→J/𝜓 𝜏 𝜈_𝜏 (violet) and B_c→J/𝜓 𝜇 𝜈_𝜇 (light blue) decays have different q² distributions.

Figure 2: Measured q2 distribution. The B_c→J/𝜓 𝜏 𝜈_𝜏 (violet) and B_c→J/𝜓 𝜇 𝜈_𝜇 (light blue) contributions are significantly different.

The measurement yields R(J/𝜓) = 0.17 ± 0.33, in agreement with the SM. Is this the end of the story? Not quite! As even in the best Neapolitan gelato, different scoops can mix, making it harder to distinguish the flavour. We need a more precise result to better separate the tau and muon flavours. Stay tuned and, in the meantime, enjoy this first CMS flavour gelato!

Read more about these results:

• CMS Physics Analysis Summary (BPH-22-012): "Test of lepton flavor universality violation in semileptonic B_c⁺ meson decays at CMS "

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