Branching Fraction of the Decay $B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-}$ and Lepton Flavor Universality Test via the Ratio $R_{\pi }(\tau /\mu )$

Abstract

Among (semi)leptonic rare $B$-decays induced by the $b\to d$ flavor changing neutral current, the decay $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ is the only one observed so far experimentally. Related decays involving the $e^{+}{e}^{-}$ and ${\tau }^{+}{\tau }^{-}$ pairs are the targets for the ongoing experiments at the LHC, in particular LHCb, and Belle II. The muonic and electronic semileptonic decays have almost identical branching fractions in the Standard Model (SM). However, the tauonic decay $B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-}$ differs from the other two due to the higher reaction threshold which lies slightly below the $\psi (2S)$-resonance. We present calculations of the ditauon (${\tau }^{+}{\tau }^{-}$) invariant-mass distribution and the branching fraction $\mathrm{Br}(B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-})$ in the SM based on the Effective Electroweak Hamiltonian approach, taking into account also the so-called long-distance contributions. The largest theoretical uncertainty in the short-distance part of the decay rates is due to the $B\to \pi$ form factors, which we quantify using three popular parametrizations. The long-distance contribution can be minimized by a cut on the ditauon mass $m_{{\tau }^{+}{\tau }^{-}}>M_{\psi (2S)}$. Once available, the branching fractions in the tauonic and muonic (and electronic) modes provide stringent test of the lepton flavor universality in the $b\to d$ transitions. We illustrate this by calculating the ratio $R_{\pi }(\tau /\mu )\equiv \mathrm{Br}(B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-})/\mathrm{Br}(B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-})$ in the SM for the total and binned ratios of the branching fractions.

arXiv comment11 pages, 5 figures, 11 tables. v2. References added, matches version published in Physics Letters B

References in corpus (32)

• Weak Decays Beyond Leading Logarithms
• Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• More Model-Independent Analysis of b->s Processes
• Measurement of the $\tau$ lepton polarization and $R(D^{\ast })$ in the decay $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$
• On the Standard Model predictions for $R_K$ and $R_{K^{\ast }}$
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• Test of lepton universality in beauty-quark decays
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• B-decay discrepancies after Moriond 2019
• Exclusive radiative and electroweak b->d and b->s penguin decays at NLO
• Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ with a semileptonic tagging method
• Importance of Loop Effects in Explaining the Accumulated Evidence for New Physics in B Decays with a Vector Leptoquark
• Scalar leptoquarks from GUT to accommodate the $B$-physics anomalies
• Test of lepton-flavor universality in $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ decays at Belle
• Searching for New Physics with $b\to s{\tau }^{+}{\tau }^{-}$ processes
• Precise Calculation of the Dilepton Invariant-Mass Spectrum and the Decay Rate in $B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$ in the SM
• Gauge-invariant implications of the LHCb measurements on Lepton-Flavour Non-Universality
• Measurement of the phase difference between short- and long-distance amplitudes in the $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ decay
• Search for $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ at the BaBar experiment
• $B\to \pi \ell \ell$ form factors for new-physics searches from lattice QCD
• Hadronic effects and observables in $B\to \pi {\ell }^{+}{\ell }^{-}$ decay at large recoil
• Unitarity Bounds for Semileptonic Decays in Lattice QCD
• Disentangling Lepton Flavour Universal and Lepton Flavour Universality Violating Effects in $b\to s{\ell }^{+}{\ell }^{-}$ Transitions
• Virtual- and bremsstrahlung corrections to b -> d l+ l- in the standard model
• Test of the universality of $\tau$ and $\mu$ lepton couplings in $W$-boson decays from $t\bar{t}$ events with the ATLAS detector
• Rates and Asymmetries of B --> pi l+ l- Decays
• Study of the rare $B_s^0$ and $B^0$ decays into the ${\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ final state
• Rare $B\to \pi l\bar{l}$ and $B\to \rho l\bar{l}$ decays in the relativistic quark model
• The LFU Ratio $R_{\pi }$ in the Standard Model and Beyond
• A general effective field theory description of $b\to s{l}^{+}{l}^{-}$ lepton universality ratios