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R(D) ratios in line at LHCb

24 January 2025

A report from the LHCb experiment.

LHCb figure 1

The accidental symmetries observed between the three generations of leptons are poorly understood, with no compelling theoretical motivation in the framework of the Standard Model (SM). The b  cτντ transition has the potential to reveal new particles or forces that interact primarily with third-generation particles, which are subject to the less stringent experimental constraints at present. As a tree-level SM process mediated by W-boson exchange, its amplitude is large, resulting in large branching fractions and significant data samples to analyse.

The observable under scrutiny is the ratio of decay rates between the signal mode involving τ and ντ leptons from the third generation of fermions and the normalisation mode containing μ and νμ leptons from the second generation. Within the SM, this lepton flavour universality (LFU) ratio deviates from unity only due to the different mass of the charged leptons – but new contributions could change the value of the ratios. A longstanding tension exists between the SM prediction and the experimental measurements, requiring further input to clarify the source of the discrepancy.

The LHCb collaboration analysed four decay modes: B0 D(*)+ν, with ℓ representing τ or μ. Each is selected using the same visible final state of one muon and light hadrons from the decay of the charm meson. In the normalisation mode, the muon originates directly from the B-hadron decay, while in the signal mode, it arises from the decay of the τ lepton. The four contributions are analysed simultaneously, yielding two LFU ratios between taus and muons – one using the ground state of the D+ meson and one the excited state D*+.

The control of the background contributions is particularly complicated in this analysis as the final state is not fully reconstructible, limiting the resolution on some of the discriminating variables. Instead, a three-dimensional template fit separates the signal and the normalisation from the background versus: the momentum transferred to the lepton pair (q2); the energy of the muon in the rest frame of the B meson (Eμ*); and the invariant mass missing from the visible system. Each contribution is modelled using a template histogram derived either from simulation or from selected control samples in data.

This constitutes the world’s second most precise measurement of R(D)

To prevent the simulated data sample size from becoming a limiting factor in the precision of the measurement, a fast tracker-only simulation technique was exploited for the first time in LHCb. Another novel aspect of this work is the use of the HAMMER software tool during the minimisation procedure of the likelihood fit, which enables a fast, but exact, variation of a template as a function of the decay-model parameters. This variation is important to allow the form factors of both the signal and normalisation channels to vary as the constraints derived from the predictions that use precise lattice calculations can have larger uncertainties than those obtained from the fit.

The fit projection over one of the discriminating variables is shown in figure 1, illustrating the complexity of the analysed data sample but nonetheless showcasing LHCb’s ability to distinguish the signal modes (red and orange) from the normalisation modes (two shades of blue) and background contributions.

The measured LFU ratios are in good agreement with the current world average and the predictions of the SM: R(D+) = 0.249 ± 0.043 (stat.) ± 0.047 (syst.) and R(D*+) = 0.402 ± 0.081(stat.) ± 0.085 (syst.). Under isospin symmetry assumptions, this constitutes the world’s second most precise measurement of R(D), following a 2019 measurement by the Belle collaboration. This analysis complements other ongoing efforts at LHCb and other experiments to test LFU across different decay channels. The precision of the measurements reported here is primarily limited by the size of the signal and control samples, so more precise measurements are expected with future LHCb datasets.

Further reading

LHCb Collab. 2024 arXiv:2406.03387.
F Bernlochner et al. 2020 Eur. Phys. J. C 80 883.

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