$$V_{us}$$ from $$K_{\ell 3}$$ decay and fourflavor lattice QCD
Abstract
Using highly improved staggered quark (HISQ) Nf=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→πℓν vector form factor at zero momentum transfer, f+K0π(0)=0.9696(15)stat(12)syst. This is the first calculation that includes the dominant finitevolume effects, as calculated in chiral perturbation theory at nexttoleading order. Our result for the form factor provides a direct determination of the CabibboKobayashiMaskawa (CKM) matrix element Vus=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 fK+/fπ+, which uses Vud as input. Our value of Vus is in tension at the 2–2.6σ 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 Vud, although a recent determination of the nucleusindependent radiative corrections to superallowed nuclear β decays could reduce the Vud2 uncertainty nearly to that of Vus2. Alternative unitarity tests using only kaon decays, for which improvementsmore »
 Authors:

 Northwestern U.
 Washington U., St. Louis
 Utah U.
 Syracuse U.
 Fermilab
 Art Inst. of Chicago
 Granada U., Theor. Phys. Astrophys.
 Indiana U.
 APS, New York
 TUMIAS, Munich
 RIKEN BNL
 Arizona U.
 UC, Santa Barbara
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Contributing Org.:
 Fermilab Lattice; MILC
 OSTI Identifier:
 1529039
 Alternate Identifier(s):
 OSTI ID: 1478015
 Report Number(s):
 arXiv:1809.02827; FERMILABPUB18439T
1693293
 Grant/Contract Number:
 AC0207CH11359; AC0205CH11231; AC0206CH11357; FG0291ER40628; FC0212ER41879; SC0010120; FG0291ER40661; FG0213ER42001; SC0015655; SC0010005; FG0213ER41976; SC0012704; FQM101
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 Phys.Rev.
 Additional Journal Information:
 Journal Volume: D99; Journal Issue: 11
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Bazavov, A., Bernard, C., DeTar, C., Du, Daping, ElKhadra, A. X., Freeland, E. D., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Primer, T., Simone, J. N., Sugar, R., Toussaint, D., Van de Water, R. S., and Zhou, Ran. $V_{us}$ from $K_{\ell 3}$ decay and fourflavor lattice QCD. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.114509.
Bazavov, A., Bernard, C., DeTar, C., Du, Daping, ElKhadra, A. X., Freeland, E. D., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Primer, T., Simone, J. N., Sugar, R., Toussaint, D., Van de Water, R. S., & Zhou, Ran. $V_{us}$ from $K_{\ell 3}$ decay and fourflavor lattice QCD. United States. doi:10.1103/PhysRevD.99.114509.
Bazavov, A., Bernard, C., DeTar, C., Du, Daping, ElKhadra, A. X., Freeland, E. D., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Primer, T., Simone, J. N., Sugar, R., Toussaint, D., Van de Water, R. S., and Zhou, Ran. Tue .
"$V_{us}$ from $K_{\ell 3}$ decay and fourflavor lattice QCD". United States. doi:10.1103/PhysRevD.99.114509.
@article{osti_1529039,
title = {$V_{us}$ from $K_{\ell 3}$ decay and fourflavor lattice QCD},
author = {Bazavov, A. and Bernard, C. and DeTar, C. and Du, Daping and ElKhadra, A. X. and Freeland, E. D. and Gámiz, E. and Gottlieb, Steven and Heller, U. M. and Komijani, J. and Kronfeld, A. S. and Laiho, J. and Mackenzie, P. B. and Neil, E. T. and Primer, T. and Simone, J. N. and Sugar, R. and Toussaint, D. and Van de Water, R. S. and Zhou, Ran},
abstractNote = {Using highly improved staggered quark (HISQ) Nf=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→πℓν vector form factor at zero momentum transfer, f+K0π(0)=0.9696(15)stat(12)syst. This is the first calculation that includes the dominant finitevolume effects, as calculated in chiral perturbation theory at nexttoleading order. Our result for the form factor provides a direct determination of the CabibboKobayashiMaskawa (CKM) matrix element Vus=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 fK+/fπ+, which uses Vud as input. Our value of Vus is in tension at the 2–2.6σ 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 Vud, although a recent determination of the nucleusindependent radiative corrections to superallowed nuclear β decays could reduce the Vud2 uncertainty nearly to that of Vus2. 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+Kπ(0) due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the fullQCD and the partially quenched cases. We also obtain the combination of lowenergy constants in the chiral effective Lagrangian [C12r+C34r(L5r)2](Mρ)=(2.92±0.31)×106.},
doi = {10.1103/PhysRevD.99.114509},
journal = {Phys.Rev.},
number = 11,
volume = D99,
place = {United States},
year = {2019},
month = {6}
}