@misc{10481/57369,
year = {2019},
month = {6},
url = {http://hdl.handle.net/10481/57369},
abstract = {Using highly improved staggered quark (HISQ) 
N
f
=
2
+
1
+
1
 MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we perform the most precise computation to date of the 
K
→
π
ℓ
ν
 vector form factor at zero momentum transfer, 
f
K
0
π
−
+
(
0
)
=
0.9696
(
15
)
stat
(
12
)
syst
. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element 
|
V
u
s
|
=
0.22333
(
44
)
f
+
(
0
)
(
42
)
exp
, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio 
f
K
+
/
f
π
+
, which uses 
|
V
u
d
|
 as input. Our value of 
|
V
u
s
|
 is in tension at the 
2
–
2.6
σ
 level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in 
|
V
u
d
|
, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear 
β
 decays could reduce the 
|
V
u
d
|
2
 uncertainty nearly to that of 
|
V
u
s
|
2
. Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions and could be further improved by taking correlations between the theory inputs. As part of our analysis, we calculated the correction to 
f
K
π
+
(
0
)
 due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian 
[
C
r
12
+
C
r
34
−
(
L
r
5
)
2
]
(
M
ρ
)
=
(
2.92
±
0.31
)
×
10
−
6
.},
organization = {This work was supported in part by the U.S. Department of
Energy under Grants No. DE-FG02-91ER40628 (C. B.),
No. DE-FC02-12ER41879 (C. D.), No. DE-SC0010120
(S. G.), No. DE-FG02-91ER40661 (S. G.), No. DE-FG02-
13ER42001 (A. X. K.), No. DE-SC0015655 (A. X. K.),
No. DE-SC0010005 (E. T. N.), No. DE-FG02-
13ER41976 (D. T.); by the U.S. National Science
Foundation under Grants No. PHY14-14614 and
No. PHY17-19626 (C. D.), No. PHY14-17805 (J. L.),
and No. PHY13-16748 and No. PHY16-20625 (R. S.);
by the MINECO (Spain) under Grants No. FPA2013-
47836-C-1-P and No. FPA2016-78220-C3-3-P (E. G.); by
the Junta de Andalucía (Spain) under Grant No. FQM-101
(E. G.); by the European Commission (EC) under Grant
No. PCIG10-GA-2011-303781 (E. G.); by the U.K. Science
and Technology Facilities Council (J. K.); by the German
Excellence Initiative and the European Union Seventh
Framework Program under Grant No. 291763 as well as
the European Union Marie Curie COFUND program (J. K.,
A. S. K.). Brookhaven National Laboratory is supported by
the United States Department of Energy, Office of Science,
Office of High Energy Physics, under Contract No. DESC0012704.
Fermilab is operated by Fermi Research
Alliance, LLC, under Contract No. DE-AC02-
07CH11359 with the United States Department of
Energy, Office of Science, Office of High Energy Physics.},
publisher = {Physical Review D},
title = {|Vus| from Kℓ3 decay and four-flavor lattice QCD},
doi = {10.1103/PhysRevD.99.114509},
author = {Bazavov, A. and Gámiz Sánchez, María Elvira},
}