$B_c\to J/\psi$ Form Factors for the full $q^2$ range from Lattice QCD

Abstract

We present the first lattice QCD determination of the $B_c\to J/\psi$ vector and axial-vector form factors. These will enable experimental information on the rate for $B_c$ semileptonic decays to $J/\psi$ to be converted into a value for $V_{cb}$. Our calculation covers the full physical $q^2$ range of the decay and uses non-perturbatively renormalised lattice currents. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks on the second generation MILC ensembles of gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks. Our HISQ heavy quarks have masses ranging upwards from that of $c$; we are able to reach that of the $b$ on our finest lattices. This enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the $b$. We use our form factors to construct the differential rates for $B_c^{-}\to J/\psi {\mu }^{-}{\bar{\nu }}_{\mu }$ and obtain a total rate with $7\%$ uncertainty: $\Gamma (B_c^{-}\to J/\psi {\mu }^{-}{\bar{\nu }}_{\mu })/|{\eta }_{\mathrm{EW}}{V}_{cb}{|}^2=1.73(12)\times 10^{13}{\mathrm{s}}^{-1}$. Including values for $V_{cb}$, ${\eta }_{\mathrm{EW}}$ and ${\tau }_{B_c}$ yields a branching fraction for this decay mode of 0.0150(11)(10)(3) ~with uncertainties from lattice QCD, ${\eta }_{\mathrm{EW}}{V}_{cb}$ and ${\tau }_{B_c}$ respectively.

arXiv comment23 pages, 14 Figures, Version accepted for publication in Phys. Rev. D

References in corpus (50)

• The NumPy array: a structure for efficient numerical computation
• Evidence for an excess of B -> D(*) Tau Nu decays
• Measurement of an Excess of B -> D(*) Tau Nu Decays and Implications for Charged Higgs Bosons
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Mesons with Beauty and Charm: Spectroscopy
• Measurement of the Differential Branching Fraction and Forward-Backword Asymmetry for B->K(*)l+l-
• Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Measurement of the ratio of branching fractions $\mathcal{B}(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })$/$\mathcal{B}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })$
• Constrained Curve Fitting
• Precision Corrections to Dispersive Bounds on Form Factors
• Twisted Boundary Conditions in Lattice Simulations
• Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ with a semileptonic tagging method
• Spectroscopy of B_c Mesons in the Relativized Quark Model
• Measurement of Branching Fractions and Rate Asymmetries in the Rare Decays B -> K(*) l+ l-
• Scaling studies of QCD with the dynamical HISQ action
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• Weak decays of the B_c meson to charmonium and D mesons in the relativistic quark model
• Leptonic and Semileptonic Decays of Charm and Bottom Hadrons
• A fresh look at the determination of |V_cb| from B-> D^* l nu
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD
• Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea
• The $V_{cb}$ puzzle: an update
• Neutral B-meson mixing from full lattice QCD at the physical point
• Update of $|V_{cb}|$ from the $\bar{B}\to D^{\ast }\ell \bar{\nu }$ form factor at zero recoil with three-flavor lattice QCD
• Theory determination of $\bar{B}\to D^{(\ast )}{\ell }^{-}\bar{\nu }$ form factors at $\mathcal{O}(1/m_c^2)$
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Observation of two excited B${}_{\mathrm{c}}^{+}$ states and measurement of the B${}_{\mathrm{c}}^{+}$(2S) mass in pp collisions at $\sqrt{s}=$ 13 TeV
• High-Precision $f_{B_s}$ and HQET from Relativistic Lattice QCD
• The hadronic vacuum polarization contribution to $a_{\mu }$ from full lattice QCD
• The B -> D* l nu form factor at zero recoil from three-flavor lattice QCD: A model independent determination of |V_cb|
• $B_s\to D_s\ell \nu$ Form Factors for the full $q^2$ range from Lattice QCD with non-perturbatively normalized currents
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Lattice QCD calculation of the $B_{(s)}\to D_{(s)}^{\ast }\ell \nu$ form factors at zero recoil and implications for $|V_{cb}|$
• $R(J/\psi )$ and $B_c^{-}\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell }$ Lepton Flavor Universality Violating Observables from Lattice QCD
• Observation of an excited $B_c^{+}$ state
• Lattice study of semileptonic form factors with twisted boundary conditions
• Lattice QCD form factor for $B_s\to D_s^{\ast }l\nu$ at zero recoil with non-perturbative current renormalisation
• V_cs from D_s to ϕlν semileptonic decay and full lattice QCD
• Measurement of the lifetime of the $B_c^{+}$ meson using the $B_c^{+}\to J/\psi {\pi }^{+}$ decay mode
• Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks
• Model-Independent Bounds on $R(J/\psi )$
• $B_c\to B_{s(d)}$ form factors from lattice QCD
• Renormalising vector currents in lattice QCD using momentum-subtraction schemes
• Observation of $B_c^{+}\to J/\psi D^{(\ast )}{K}^{(\ast )}$ decays
• Tests of the Standard Model in $B\to D\ell {\nu }_{\ell }$, $B\to D^{\ast }\ell {\nu }_{\ell }$ and $B_c\to J/\psi \ell {\nu }_{\ell }$
• Measurement of b hadron lifetimes in pp collisions at $\sqrt{s}=$ 8 TeV
• Measurement of the $B_c^{\pm }$ production cross section in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

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• FLAG Review 2021
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• Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Next-to-next-to-leading order matching of beauty-charmed meson $B_c$ and $B_c^{\ast }$ decay constants
• Searching for doubly charmed tetraquark candidates $T_{cc}$ and $T_{cc\bar{s}}$ in $B_c$ decays
• Right-handed interactions in puzzling $B$-decays
• Toward accurate form factors for $B$-to-light meson decay from lattice QCD
• Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay
• New physics footprints in the angular distribution of $B_s\to D_s^{\ast }(\to D_s\gamma ,D_s\pi )\tau \nu$ decays
• Systematic analysis of the form factors of $B_c\to {\eta }_c$, $J/\psi$ and corresponding weak decays
• Next-to-leading order QCD calculation of $B_c$ to charmonium tensor form factors
• First lattice QCD calculation of $J/\psi$ semileptonic decay containing $D$ and $D_s$ particles
• New physics in the angular distribution of $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decay
• Extra gauge bosons and lepton flavor universality violation in ${\rm Y}$ and $B$ meson decays
• Quark flavor physics and lattice QCD
• Impact of $b\to c$ measurements on ${\Lambda }_b\to p\tau \bar{\nu }$ decay in $U_1$ leptoquark model
• Study of angular observables in exclusive semileptonic $B_c$ decays
• Systematic analysis of the form factors of $B_c$ to $P$-wave charmonia and corresponding weak decays
• Prospects for $B_c^{+}\to {\tau }^{+}{\nu }_{\tau }$ at FCC-ee
• Recent progress in decays of $b$ and $c$ hadrons