Looking forward to $B^+ o τ^+ ν_τ$ and $B_c^+ o τ^+ ν_τ$

These proceedings present the outcome of a feasibility study using RapidSim simulation software that demonstrates that the LHCb experiment will be capable of observing the decays $B^+\to τ^+ ν_τ$ and $B_c^+\to τ^+ ν_τ$ using the data that is being collecting during Run 3 of the LHC. The proposed analysis exploits the small distance of only 5.1 millimetres between the sensing elements of LHCb’s innermost silicon pixel detector, the VELO, and the LHC’s proton beams to identify direct pixel hits in the VELO that can be associated with the charged $B^+$, $B_c^+$ or $τ^+$ particles. By using this extra information, the limitations due to the missing momentum and vertex information will be significantly reduced. This provides enough statistical power to pursue the measurements of these two decay channels at the LHC. In particular for the decay $B_c^+\to τ^+ ν_τ$, which has been identified by the high energy physics community as a key objective for experiments at the planned next-generation particle accelerators, this means we do not need to wait for the 2030s or beyond to get first experimental constraints.

💡 Research Summary

The paper presents a feasibility study showing that the LHCb experiment can observe the purely leptonic decays B⁺→τ⁺ν and B_c⁺→τ⁺ν using data collected during Run 3 of the LHC. These decays are of great interest because they are sensitive probes of physics beyond the Standard Model (BSM) and, in the case of B_c⁺→τ⁺ν, provide complementary information to the long‑standing R(D^{(*)}) anomalies in semileptonic B decays. The main experimental challenge is the presence of at least two neutrinos in the final state, which removes crucial momentum and vertex information and makes background discrimination difficult in the busy environment of proton–proton collisions.

The authors propose to exploit a unique feature of the upgraded LHCb vertex detector (VELO): the silicon pixel sensors are positioned only 5.1 mm from the LHC beam. Because B⁺, B_c⁺ and the τ⁺ each have lifetimes of order 1 ps and travel several centimeters at LHC energies, there is a non‑negligible probability that one of these charged particles traverses a VELO sensor before decaying. When this happens, a direct “VELO‑hit” is recorded. The location of the first VELO‑hit between the primary vertex (PV) and the τ decay vertex (TV) provides a more accurate estimate of the B‑meson flight direction than the conventional PV‑TV line, thereby improving the reconstruction of the missing transverse momentum.

The study uses RapidSim, a fast phase‑space generator, to produce signal events (B⁺→τ⁺ν, B_c⁺→τ⁺ν with τ⁺→π⁺π⁻π⁺ν̄) and three classes of background that mimic the three‑pion topology: D→τν, B→D 3π, and B→D Y (where Y denotes additional particles such as τν or D_s). After applying geometric acceptance cuts, the authors require: (i) at least one VELO‑hit between PV and TV, (ii) 3π invariant mass between 0.5 and 1.8 GeV, (iii) opposite‑charge pion pair mass ≤ 1.67 GeV, and (iv) transverse momentum of the 3π system > 5 GeV. An isolation factor ε_iso = 10 % is assumed for backgrounds that contain extra detectable particles, reflecting a conservative estimate based on existing LHCb performance.

Signal extraction is performed with an extended two‑dimensional binned maximum‑likelihood fit to the corrected mass (m_corr) and the output of a boosted decision tree (BDT). The corrected mass is defined as m_corr = √(m_{3π}² + |p⊥^{3π}|²) + |p⊥^{3π}|, where the transverse momentum is calculated with respect to the line connecting the PV to the first VELO‑hit. The BDT is trained on kinematic and topological variables of the three‑pion system, including momentum, impact parameter, flight distance, and invariant mass.

A set of 2000 pseudo‑experiments is generated for integrated luminosities ranging from 5 fb⁻¹ to 30 fb⁻¹. For each luminosity the mean relative uncertainty σ_fit / n_fit on the fitted signal yields is computed. The results show that, assuming only statistical uncertainties, a 3σ observation of B_c⁺→τ⁺ν can be achieved with ≈10 fb⁻¹, while a 5σ discovery requires slightly more than 20 fb⁻¹. When systematic uncertainties are taken to be comparable to the statistical ones, the required luminosity rises to just above 20 fb⁻¹. LHCb has already collected about 10 fb⁻¹ since 2024, and is expected to reach the necessary dataset by mid‑2026. For B⁺→τ⁺ν, the study finds that a relative precision better than 5 % is attainable for all considered luminosities, indicating that the decay can already be measured with the existing data.

The paper concludes that LHCb, by leveraging VELO‑hit information, can provide the first experimental constraints on B_c⁺→τ⁺ν and a precise measurement of B⁺→τ⁺ν well before next‑generation lepton colliders become operational. This will supply valuable, complementary input to the ongoing tests of lepton‑flavour universality in R(D^{(*)}) and to broader searches for BSM physics in the b→cτν sector. The authors note that further work will be needed to validate the VELO‑hit efficiency, refine background modeling, and incorporate realistic detector effects, but the feasibility study presents a compelling case for the proposed analysis.