$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond

Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gamiz, E.; Gottlieb, Steven; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J.; Sugar, R.; Toussaint, D.; Van de Water, R. S.; Zhou, Ran

doi:10.1103/PhysRevD.93.113016

Title: $$B^0_{(s)}$$-mixing matrix elements from lattice QCD for the Standard Model and beyond

Journal Article · Tue Jun 28 00:00:00 EDT 2016 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.93.113016· OSTI ID:1260383

Bazavov, A. ^[1]; Bernard, C. ^[2]; Bouchard, C. M. ^[3]; Chang, C. C. ^[4]; DeTar, C. ^[5]; Du, Daping ^[6]; El-Khadra, A. X. ^[4]; Freeland, E. D. ^[7]; Gamiz, E. ^[8]; Gottlieb, Steven ^[9]; Heller, U. M. ^[10]; Kronfeld, A. S. ^[11]; Laiho, J. ^[6]; Mackenzie, P. B. ^[12]; Neil, E. T. ^[13]; Simone, J. ^[12]; Sugar, R. ^[14]; Toussaint, D. ^[15]; Van de Water, R. S. ^[12]; Zhou, Ran ^[12]

Univ. of Iowa, Iowa City, IA (United States)
Washington Univ., St. Louis, MO (United States)
The College of William and Mary, Williamsburg, VA (United States)
Univ. of Illinois, Urbana, IL (United States)
Univ. of Utah, Salt Lake City, UT (United States)
Syracuse Univ., Syracuse, NY (United States)
School of the Art Institute of Chicago, Chicago, IL (United States)
Univ. de Granada, Granada (Spain)
Indiana Univ., Bloomington, IN (United States)
American Physical Society, Ridge, NY (United States)
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Technische Univ. Munchen, Garching (Germany)
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Univ. of Colorado, Boulder, CO (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
Univ. of California, Santa Barbara, CA (United States)
Univ. of Arizona, Tucson, AZ (United States)

We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B⁰- and B_s-meson mixing in and beyond the Standard Model. In this paper, we present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |V_td|=8.00(34)(8)×10^-3, |V_ts|=39.0(1.2)(0.4)×10^-3, and |V_td/V_ts|=0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. Lastly, these results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States). RIKEN Research Center

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Organization:: Fermilab Lattice; MILC; Fermilab Lattice and MILC Collaborations

Grant/Contract Number:: AC02-07CH11359; FG02-91ER40628; FC02-06ER41446; SC0010120; SC0010005; FG02-91ER40661; FG02-13ER42001; FG02-13ER41976; SC0012704; SC00112704

OSTI ID:: 1260383

Alternate ID(s):: OSTI ID: 1259736; OSTI ID: 1336071

Report Number(s):: FERMILAB-PUB-16-030-T; arXiv:1602.03560; BNL-112445-2016-JA; PRVDAQ; 1421164

Journal Information:: Physical Review D, Vol. 93, Issue 11; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 112 works

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Publisher’s Note: Improved measurement of $C P$ -violation parameters $\sin 2 ϕ_{1}$ and $\| λ \|$ , $B$ meson lifetimes, and $B^{0} - {\bar{B}}^{0}$ mixing parameter $Δ m_{d}$ [Phys. Rev. D 71 , 072003 (2005) ] Abe, K.; Abe, K.; Adachi, I. Physical Review D, Vol. 71, Issue 7 https://doi.org/10.1103/PhysRevD.71.079903	journal	April 2005
Measurement of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mtext>–</mml:mtext><mml:msup><mml:mrow><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> oscillation frequency <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math> with the decays <mml:math altimg="si3.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math> and <mml:math altimg="si4.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> Aaij, R.; Abellan Beteta, C.; Adametz, A. Physics Letters B, Vol. 719, Issue 4-5 https://doi.org/10.1016/j.physletb.2013.01.019	journal	February 2013
Observation of $B_{s}^{0} - {\bar{B}}_{s}^{0}$ Oscillations Abulencia, A.; Adelman, J.; Affolder, T. Physical Review Letters, Vol. 97, Issue 24 https://doi.org/10.1103/PhysRevLett.97.242003	journal	December 2006
Measurement of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mtext>–</mml:mtext><mml:msubsup><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> oscillation frequency <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> in <mml:math altimg="si3.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>−</mml:mo></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mi>π</mml:mi></mml:math> decays Aaij, R.; Adeva, B.; Adinolfi, M. Physics Letters B, Vol. 709, Issue 3 https://doi.org/10.1016/j.physletb.2012.02.031	journal	March 2012
Precision measurement of the B ⁰ _s –$\overline{\rm B}{}^0_{\rm s}$ oscillation frequency with the decay B ⁰ _s → D ⁻ _s π ⁺ Aaij, R.; Abellan Beteta, C.; Adeva, B. New Journal of Physics, Vol. 15, Issue 5 https://doi.org/10.1088/1367-2630/15/5/053021	journal	May 2013
Observation of $B^{0}_{s}$ – $\overline{B}{}^{0}_{s}$ mixing and measurement of mixing frequencies using semileptonic B decays Aaij, R.; Adeva, B.; Adinolfi, M. The European Physical Journal C, Vol. 73, Issue 12 https://doi.org/10.1140/epjc/s10052-013-2655-8	journal	December 2013
Precision Measurement of $C P$ Violation in $B_{S}^{0} \to J / Ψ K^{+} K^{-}$ Decays Aaij, R.; Adeva, B.; Adinolfi, M. Physical Review Letters, Vol. 114, Issue 4 https://doi.org/10.1103/PhysRevLett.114.041801	journal	January 2015
Search for $B^0_s-\overline{B^0_s}$ oscillations and a measurement of $B^0_d-\overline{B^0_d}$ oscillations using events with an inclusively reconstructed vertex al., J. Abdallah et The European Physical Journal C, Vol. 28, Issue 2 https://doi.org/10.1140/epjc/s2003-01183-7	journal	May 2003
Limits on the Decay-Rate Difference of Neutral $B$ Mesons and on $C P$ , $T$ , and $C P T$ Violation in $B^{0} {\bar{B}}^{0}$ Oscillations Aubert, B.; Barate, R.; Boutigny, D. Physical Review Letters, Vol. 92, Issue 18 https://doi.org/10.1103/PhysRevLett.92.181801	journal	May 2004
Limits on the decay-rate difference of neutral B mesons and on CP , T , and CPT violation in $B^{0} B^{0}$ oscillations Aubert, B.; Barate, R.; Boutigny, D. Physical Review D, Vol. 70, Issue 1 https://doi.org/10.1103/PhysRevD.70.012007	journal	July 2004
Search for time-dependent $C P T$ violation in hadronic and semileptonic $B$ decays Higuchi, T.; Sumisawa, K.; Adachi, I. Physical Review D, Vol. 85, Issue 7 https://doi.org/10.1103/PhysRevD.85.071105	journal	April 2012
Measurements of the B +, B 0, $ B_s^0 $ meson and $ \Lambda_b^0 $ baryon lifetimes Aaij, R.; Adeva, B.; Adinolfi, M. Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)114	journal	April 2014
Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set Aaltonen, T.; Álvarez González, B.; Amerio, S. Physical Review Letters, Vol. 109, Issue 17 https://doi.org/10.1103/PhysRevLett.109.171802	journal	October 2012
Measurement of the $C P$ -violating phase $ϕ_{s}^{J / ψ ϕ}$ using the flavor-tagged decay $B_{s}^{0} \to J / ψ ϕ$ in $8 {fb}^{- 1}$ of $p \bar{p}$ collisions Abazov, V. M.; Abbott, B.; Acharya, B. S. Physical Review D, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevD.85.032006	journal	February 2012
Flavor tagged time-dependent angular analysis of the $B_{s}^{0} \to J / ψ ϕ$ decay and extraction of $Δ Γ_{s}$ and the weak phase $ϕ_{s}$ in ATLAS Aad, G.; Abajyan, T.; Abbott, B. Physical Review D, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevD.90.052007	journal	September 2014
Measurement of the CP-violating weak phase ϕs and the decay width difference ΔΓs using the $B_{s}^{0} \to J / ψ ϕ (1020)$ decay channel in pp collisions at $\sqrt{s} = 8 TeV$ Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A. Physics Letters B, Vol. 757 https://doi.org/10.1016/j.physletb.2016.03.046	journal	June 2016
Phenomenology of semileptonic $B$ -meson decays with form factors from lattice QCD Du, Daping; El-Khadra, A. X.; Gottlieb, Steven Physical Review D, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevD.93.034005	journal	February 2016
Differential branching fractions and isospin asymmetries of B → K (*) μ + μ − decays Aaij, R.; Adeva, B.; Adinolfi, M. Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)133	journal	June 2014
First measurement of the differential branching fraction and CP asymmetry of the B ± → π ± μ + μ − decay Aaij, R.; Adeva, B.; Adinolfi, M. Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)034	journal	October 2015
$B \to π l l$ Form Factors for New Physics Searches from Lattice QCD Bailey, Jon A.; Bazavov, A.; Bernard, C. Physical Review Letters, Vol. 115, Issue 15 https://doi.org/10.1103/PhysRevLett.115.152002	journal	October 2015
Relations between ΔMs,d and Bs,d→μμ̄ in models with minimal flavour violation Buras, Andrzej J. Physics Letters B, Vol. 566, Issue 1-2 https://doi.org/10.1016/S0370-2693(03)00561-6	journal	July 2003
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Branching ratio measurements of $B_{s}$ decays De Bruyn, Kristof; Fleischer, Robert; Knegjens, Robert Physical Review D, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevD.86.014027	journal	July 2012
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