Precise Calculation of the Dilepton Invariant-Mass Spectrum and the Decay Rate in $B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$ in the SM

Abstract

We present a precise calculation of the dilepton invariant-mass spectrum and the decay rate for $B^{\pm }\to {\pi }^{\pm }{\ell }^{+}{\ell }^{-}$ (${\ell }^{\pm }=e^{\pm },{\mu }^{\pm }$) in the Standard Model (SM) based on the effective Hamiltonian approach for the $b\to d{\ell }^{+}{\ell }^{-}$ transitions. With the Wilson coefficients already known in the next-to-next-to-leading logarithmic (NNLL) accuracy, the remaining theoretical uncertainty in the short-distance contribution resides in the form factors $f_{+}(q^2)$, $f_0(q^2)$ and $f_T(q^2)$. Of these, $f_{+}(q^2)$ is well measured in the charged-current semileptonic decays $B\to \pi \ell {\nu }_{\ell }$ and we use the $B$-factory data to parametrize it. The corresponding form factors for the $B\to K$ transitions have been calculated in the Lattice-QCD approach for large-$q^2$ and extrapolated to the entire $q^2$-region using the so-called $z$-expansion. Using an $SU(3{)}_F$-breaking Ansatz, we calculate the $B\to \pi$ tensor form factor, which is consistent with the recently reported lattice $B\to \pi$ analysis obtained at large~$q^2$. The prediction for the total branching fraction $\mathcal{B}(B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-})=(1.88_{-0.21}^{+0.32})\times 10^{-8}$ is in good agreement with the experimental value obtained by the LHCb Collaboration. In the low $q^2$-region, heavy-quark symmetry (HQS) relates the three form factors with each other. Accounting for the leading-order symmetry-breaking effects, and using data from the charged-current process $B\to \pi \ell {\nu }_{\ell }$ to determine $f_{+}(q^2)$, we calculate the dilepton invariant-mass distribution in the low $q^2$-region in the $B^{\pm }\to {\pi }^{\pm }{\ell }^{+}{\ell }^{-}$ decay. This provides a model-independent and precise calculation of the partial branching ratio for this decay.

23 pages, RevTeX, 11 figures. The subsection VI-C is included concerning the $SU(3{)}_F$-breaking and several references added

References in corpus (69)

• Weak Decays Beyond Leading Logarithms
• Heavy Quark Symmetry
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Systematic approach to exclusive B ->V l^+l^-, V gamma decays
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• The three loop relation between the \bar {MS} and the pole quark masses
• A Comparative Study of the Decays $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ in Standard Model and Supersymmetric Theories
• QCD at Low Energies
• Charm-loop effect in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }\gamma$
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• Updated Values of Running Quark and Lepton Masses
• Asymptotics of Heavy-Meson Form Factors
• Theoretical Update of Pseudoscalar Meson Distribution Amplitudes of Higher Twist: The Nonsinglet Case
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• Constraints on Form Factors For Exclusive Semileptonic Heavy to Light Meson Decays
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit of QCD
• Precision Corrections to Dispersive Bounds on Form Factors
• Comment on the heavy-->light form factors
• Improved Model-Independent Analysis of Semileptonic and Radiative Rare B Decays
• The B-Meson Distribution Amplitude in QCD
• Short Distance Mass of a Heavy Quark at Order α_s^3
• $B\to K{\ell }^{+}{\ell }^{-}$ decay at large hadronic recoil
• B Meson Semileptonic Form Factors from Unquenched Lattice QCD
• B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks
• Light-cone sum rules for $B\to \pi$ form factors revisited
• Calculation of two-loop virtual corrections to b --> s l+ l- in the standard model
• Comment on form factor shape and extraction of |V_ub| from B --> pi l nu
• $B\to \pi \ell {\nu }_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment
• General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil
• Model-Independent Extraction of |V_{cb}| Using Dispersion Relations
• Two-loop virtual corrections to B --> X_s l^+ l^- in the standard model
• The rare decay B --> X_s l^+ l^- to NNLL precision for arbitrary dilepton invariant mass
• A Precision Model Independent Determination of |Vub| from B -> pi e nu
• Twist-4 Distribution Amplitudes of the K${}^{\ast }$ and $\varphi$ Mesons in QCD
• Rare decay B -> K ll form factors from lattice QCD
• Measurement of the decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and determination of $|V_{ub}|$
• Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays
• Next-to-leading-order corrections to $B\to \pi$ form factors in $k_T$ factorization
• Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
• Model-Independent Properties of the B-Meson Distribution Amplitude
• Lattice-Constrained Unitarity Bounds for ${\bar{B}}^0\to {\pi }^{+}{l}^{-}{\bar{\nu }}_l$ Decays
• Standard Model predictions for B -> Kll with form factors from lattice QCD
• The semileptonic decays $B/B_s\to (\pi ,K)(l^{+}{l}^{-},l\nu ,\nu \bar{\nu })$ in the perturbative QCD approach beyond the leading-order
• Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu
• Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region
• First observation of the decay $B_c^{+}\to J/\psi K^{+}$
• Precise B, B_s and B_c meson spectroscopy from full lattice QCD
• The Decay $B\to \pi \ell \nu$ in Heavy Quark Effective Theory
• Two-loop Corrections to the B to pi Form Factor from QCD Sum Rules on the Light-Cone and |V(ub)|
• BELLE Data on the ${\pi }^0\gamma \ast \gamma$ Form Factor: A Game Changer?
• Operator Relations for SU(3) Breaking Contributions to K and K* Distribution Amplitudes
• First observation of the decay $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$
• Analytic two-loop virtual corrections to $b-->d{l}^{+}{l}^{-}$
• Measurement of the B^0 --> pi^-ell^+nu and B^+ --> eta^(')ell^+nu Branching Fractions, the B^0 --> pi^-ell^+nu and B^+ --> eta ell^+nu Form-Factor Shapes, and Determination of |V_{ub}|
• Virtual- and bremsstrahlung corrections to b -> d l+ l- in the standard model
• The rare decays $B_u^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$, ${\rho }^{+}{\ell }^{+}{\ell }^{-}$ and $B_d^0\to {\ell }^{+}{\ell }^{-}$ in the R-parity violating supersymmetry
• Extracting $B\to K^{\ast }$ Form Factors from Data
• Branching fraction measurement of B -> omega l nu decays
• A lattice calculation of B -> K(*) form factors
• B and Bs semileptonic decay form factors with NRQCD/HISQ quarks
• Form factors for $B$ to $Kll$ semileptonic decay from three-flavor lattice QCD
• Lattice Calculations of B to K/K*l+l- form factors
• Form factors for semi-leptonic B decays

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