dc.contributor.author Cooper, LJ dc.contributor.author Davies, CTH dc.contributor.author Wingate, M dc.date.accessioned 2022-01-29T00:31:09Z dc.date.available 2022-01-29T00:31:09Z dc.date.issued 2022 dc.identifier.issn 2470-0010 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/333414 dc.description.abstract We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^+ \to D^0 \ell^+ \nu_{\ell}$, $B_c^+ \to D_s^+ \ell^+ \ell^-$ and $B_c^+ \to D_s^+ \nu \overline{\nu}$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu}) /\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12} \mathrm{~s}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find $\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu )/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to D}(18)_{B_c \to J/\psi}$. We calculate the differential decay widths of $B_c^+ \to D_s^+ \ell^+ \ell^-$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u \overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2 = 1 \; \mathrm{GeV}^2 - 6 \; \mathrm{GeV}^2$ for $B_c^+ \to D_s^+ \mu^+ \mu^-$ and $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to J/\psi} \times 10^{-6}$. We also give results for the branching fraction of $B_c^+ \to D_s^+ \nu \overline{\nu}$. Prospects for reducing our errors in the future are discussed. dc.publisher American Physical Society (APS) dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.subject hep-lat dc.subject hep-lat dc.subject hep-ph dc.title Form factors for the processes Bc+ →d0ℓ+νℓ and Bc+ → Ds+ ℓ+ℓ- (ν ν ¯) from lattice QCD FORM FACTORS for the PROCESSES Bc+ →d0ℓ+νℓ ⋯ COOPER, DAVIES, and WINGATE dc.type Article dc.publisher.department Department of Applied Mathematics And Theoretical Physics dc.date.updated 2022-01-28T16:16:33Z prism.issueIdentifier 1 prism.number ARTN 014503 prism.publicationDate 2022 prism.publicationName Physical Review D prism.startingPage 014503 prism.volume 105 dc.identifier.doi 10.17863/CAM.80838 dcterms.dateAccepted 2021-12-06 rioxxterms.versionofrecord 10.1103/PhysRevD.105.014503 rioxxterms.version VoR dc.contributor.orcid Wingate, Matthew [0000-0001-6568-988X] dc.identifier.eissn 2470-0029 dc.publisher.url http://dx.doi.org/10.1103/PhysRevD.105.014503 rioxxterms.type Journal Article/Review pubs.funder-project-id Science and Technology Facilities Council (ST/P000681/1) pubs.funder-project-id Science and Technology Facilities Council (ST/R002452/1) pubs.funder-project-id Science and Technology Facilities Council (ST/R00689X/1) pubs.funder-project-id Science and Technology Facilities Council (ST/M007065/1) pubs.funder-project-id STFC (ST/M007073/1) pubs.funder-project-id STFC (ST/T000694/1) cam.issuedOnline 2022-01-05 cam.depositDate 2022-01-28 pubs.licence-identifier apollo-deposit-licence-2-1 pubs.licence-display-name Apollo Repository Deposit Licence Agreement
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