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Title: $$|V_{us}|$$ from $$K_{\ell 3}$$ decay and four-flavor 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 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 |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 nucleus-independent radiative corrections to superallowed nuclear β decays could reduce the |Vud|2 uncertainty nearly to that of |Vus|2. Alternative unitarity tests using only kaon decays, for which improvementsmore » 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 full-QCD and the partially quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian [C12r+C34r-(L5r)2](Mρ)=(2.92±0.31)×10-6.« less

Authors:
 [1];  [2];  [3];  [4];  [5];  [6]; ORCiD logo [7];  [8];  [9];  [10];  [10];  [4];  [5];  [11];  [12];  [5];  [13];  [12];  [5];  [5]
  1. Northwestern U.
  2. Washington U., St. Louis
  3. Utah U.
  4. Syracuse U.
  5. Fermilab
  6. Art Inst. of Chicago
  7. Granada U., Theor. Phys. Astrophys.
  8. Indiana U.
  9. APS, New York
  10. TUM-IAS, Munich
  11. RIKEN BNL
  12. Arizona U.
  13. 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) (SC-25)
Contributing Org.:
Fermilab Lattice; MILC
OSTI Identifier:
1529039
Alternate Identifier(s):
OSTI ID: 1478015
Report Number(s):
arXiv:1809.02827; FERMILAB-PUB-18-439-T
1693293
Grant/Contract Number:  
AC02-07CH11359; AC02-05CH11231; AC02-06CH11357; FG02-91ER40628; FC02-12ER41879; SC0010120; FG02-91ER40661; FG02-13ER42001; SC0015655; SC0010005; FG02-13ER41976; SC0012704; FQM-101
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, El-Khadra, 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 four-flavor lattice QCD. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.99.114509.
Bazavov, A., Bernard, C., DeTar, C., Du, Daping, El-Khadra, 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 four-flavor lattice QCD. United States. doi:10.1103/PhysRevD.99.114509.
Bazavov, A., Bernard, C., DeTar, C., Du, Daping, El-Khadra, 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 four-flavor lattice QCD". United States. doi:10.1103/PhysRevD.99.114509.
@article{osti_1529039,
title = {$|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD},
author = {Bazavov, A. and Bernard, C. and DeTar, C. and Du, Daping and El-Khadra, 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 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 |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 nucleus-independent radiative corrections to superallowed nuclear β decays could reduce the |Vud|2 uncertainty nearly to that of |Vus|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+Kπ(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 [C12r+C34r-(L5r)2](Mρ)=(2.92±0.31)×10-6.},
doi = {10.1103/PhysRevD.99.114509},
journal = {Phys.Rev.},
number = 11,
volume = D99,
place = {United States},
year = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevD.99.114509

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