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

TL;DR

The paper assesses the feasibility of observing the purely leptonic decays $B^+\to \tau^+\nu_\tau$ and $B_c^+\to \tau^+\nu_\tau$ at LHCb Run 3. Using RapidSim for fast kinematic simulations and exploiting the VELO's close proximity to the beam to identify VELO-hits, the study constructs a strategy around $\tau$ decays to $\pi^+\pi^-\pi^+$ and a corrected mass $m_{\text{corr}}$ together with a boosted decision tree to separate signal from backgrounds. Backgrounds from $D\to\tau\nu$, $B\to D\,3\pi$, and $B\to D\,Y$ are modeled with an iso-efficiency factor $\varepsilon_{\rm iso}$ to reflect undetected activity. A sensitivity study with 2000 pseudo-experiments shows that, under plausible luminosities and systematic scenarios, both decays are within reach, with $B_c^+$ requiring more data and $B^+$ able to achieve sub-5% precision, enabling new tests of the SM and potential BSM effects related to the $R(D^{(*)})$ anomalies.

Abstract

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.

Figures (4)

• Figure 1: Leading-order Feynman diagrams for the purely leptonic decay $B_c^+\to \tau^+ \nu_\tau$ (left) and the semileptonic decay $B^0 \to D^{(*)-} \tau^+ \nu_\tau$ (right).
• Figure 2: Schematic illustration of a $B_{(c)}^+$ meson decaying to a $\tau^+$ lepton, which subsequently decays to three pions. The gray vertical lines represent the VELO sensor modules, with red crosses indicating hits between PV and TV. The dashed lines represent neutrinos, which are not detected in the LHCb experiment.
• Figure 3: Distributions of $m_{corr}$ (left) and the BDT classifier output (right), showing the projections of the two-dimensional fit on a representative pseudo-dataset generated with an integrated luminosity of $10\,\mathrm{fb}^{-1}$.
• Figure 4: Mean relative precision on the fitted $B_c^+\to \tau^+ \nu_\tau$ (left) and $B^+\to \tau^+ \nu_\tau$ (right) yields as a function of integrated luminosity, based on 2000 pseudo-experiments per point. Different curves correspond to scenarios where the systematic uncertainty is assumed to be 0, 25%, 50%, or 100% of the statistical uncertainty. These scenarios are included to illustrate the impact of potential systematic effects not explicitly evaluated in this study. For the $B_c^+\to \tau^+ \nu_\tau$ decay, the dashed red line indicates the $3\sigma$ significance level threshold, while the solid red line corresponds to $5\sigma$.