Improved Vcs determination using precise lattice QCD form factors for D→Kℓν

has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the highly improved staggered quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC Collaboration that include the effect of

u

,

d

,

s

, and

c

HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical

u / d

quarks for the first time. Our calculated form factors cover the full

q^{2}

range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of

V_{c s}

from a correlated weighted average over

q^{2}

bins. We obtain

| V_{c s} | = 0.9663 (53)_{latt} (39)_{\exp} (19)_{η_{EW}} (40)_{EM}

, where the uncertainties come from lattice QCD, experiment, short-distance electroweak, and electromagnetic corrections, respectively. This last uncertainty, neglected for

D \to K ℓ ν

hitherto, now needs attention if the uncertainty on

V_{c s}

is to be reduced further. We also determine

V_{c s}

values in good agreement using the measured total branching fraction and the rates extrapolated to

q^{2} = 0

. Our form factors enable tests of lepton flavor universality violation. We find the ratio of branching fractions for

D^{0} \to K^{-}

with

μ

and

e

in the final state to be

R_{μ / e} = 0.9779 (2)_{latt} (50)_{EM}

in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.

Note:

27 pages, 28 figures. Small changes to text to improve readability. Updated to include the BES average for the D to K branching fraction from 2104.08081

correction: electromagnetic
decay: form factor: calculated
quark: staggered
quark: valence
lepton: universality: violation
lepton: flavor: universality
branching ratio: ratio
lattice field theory
gluon
electroweak interaction

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