$B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD

Abstract

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K{\ell }^{+}{\ell }^{-}$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons.

30 pages, 22 figures. Version accepted by Physical Review D

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Cited by in corpus (25)

• FLAG Review 2024
• Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD
• Disentangling new physics in $K\to \pi \bar{\nu }\nu$ and $B\to K(K^{\ast })\bar{\nu }\nu$ observables
• Test of lepton flavor universality in B${}^{\pm }$ $\to$ K${}^{\pm }{\mu }^{+}{\mu }^{-}$ and B${}^{\pm }$ $\to$ K${}^{\pm }$e${}^{+}$e${}^{-}$ decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Review of Semileptonic $B$ Anomalies
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Prospects for searches of $b\to s\nu \bar{\nu }$ decays at FCC-ee
• Disentangling left and right-handed neutrino effects in $B\to K^{(\ast )}\nu \nu$
• The decay $B\to K+\nu +\bar{\nu }$ at Belle II and a massless bino in R-parity-violating supersymmetry
• Impact of new invisible particles on $B\to K^{(\ast )}{E}_{\mathrm{miss}}$ observables
• Observation of $D_s^{+}\to {\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$, Precision Test of Lepton Flavor Universality with $D_s^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$, and First Measurements of $D_s^{+}\to {\eta }^{(\prime )}{\mu }^{+}{\nu }_{\mu }$ Decay Dynamics
• Improved measurements of $D^0\to K^{-}{\ell }^{+}{\nu }_{\ell }$ and $D^{+}\to {\bar{K}}^0{\ell }^{+}{\nu }_{\ell }$
• Charm rescattering in $B^0\to K^0\bar{\ell }\ell$: an improved analysis
• Constructing model-agnostic likelihoods, a method for the reinterpretation of particle physics results
• Constraining inverse moment of $B$-meson distribution amplitude using Lattice QCD data
• Branching ratio and $CP$ violation of $B\to K\pi$ decays in a modified perturbative QCD approach
• Revisiting $B\to K^{\ast }\pi$ and $B\to K\rho$ decays using the modified perturbative QCD approach
• Data-driven analyses and model-independent fits for present $b\to s\ell \ell$ results
• Study of $B\to PP$ decays in the modified perturbative QCD approach
• ${\Xi }_b\to \Xi$ form factors from lattice QCD and Standard-Model predictions for ${\Xi }_b\to \Xi {\mu }^{+}{\mu }^{-}$ and ${\Xi }_b\to \Xi \gamma$ decays
• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach
• Model-agnostic likelihood for the reinterpretation of the $B^{+}\to K^{+}\nu \bar{\nu }$ measurement at Belle II
• First search for $B\to X_s\nu \bar{\nu }$ decays
• Self-consistent optimization of the $z$-Expansion for $B$ meson decays
• Search for the decay $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ using data from the Belle and Belle II experiments