Short-distance matrix elements for ${D}^{0}$-meson mixing from ${N}_{f}=2+1$ lattice QCD

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Short-distance matrix elements for $D^{0}$ -meson mixing from $N_{f} = 2 + 1$ lattice QCD

A. Bazavov, C. Bernard, C. M. Bouchard, C. C. Chang, C. DeTar, D. Du, A. X. El-Khadra, E. D. Freeland, E. Gámiz, Steven Gottlieb, U. M. Heller, A. S. Kronfeld, J. Laiho, P. B. Mackenzie, E. T. Neil, J. N. Simone, R. Sugar, D. Toussaint, R. S. Van de Water, and R. Zhou (Fermilab Lattice and MILC Collaborations)

Phys. Rev. D 97, 034513 – Published 28 February 2018

Abstract

We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $Δ C = 2$ four-fermion operators that contribute to neutral $D$ -meson mixing both in and beyond the Standard Model. We use the MILC Collaboration’s $N_{f} = 2 + 1$ lattice gauge-field configurations generated with asqtad-improved staggered sea quarks. We also employ the asqtad action for the valence light quarks and use the clover action with the Fermilab interpretation for the charm quark. We analyze a large set of ensembles with pions as light as $M_{π} \approx 180 MeV$ and lattice spacings as fine as $a \approx 0.045 fm$ , thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the $\bar{MS} − NDR$ scheme using the choice of evanescent operators proposed by Beneke et al., evaluated at 3 GeV, $⟨ D^{0} | O_{i} | {\bar{D}}^{0} ⟩ = {0.0805 (55) (16), - 0.1561 (70) (31), 0.0464 (31) (9), 0.2747 (129) (55), 0.1035 (71) (21)} {GeV}^{4}$ ( $i = 1 - 5$ ). The errors shown are from statistics and lattice systematics, and the omission of charmed sea quarks, respectively. To illustrate the utility of our matrix-element results, we place bounds on the scale of $C P$ -violating new physics in $D^{0}$ mixing, finding lower limits of about $10 - 50 \times 10^{3} TeV$ for couplings of $O (1)$ . To enable our results to be employed in more sophisticated or model-specific phenomenological studies, we provide the correlations among our matrix-element results. For convenience, we also present numerical results in the other commonly used scheme of Buras, Misiak, and Urban.

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Received 21 July 2017

DOI:https://doi.org/10.1103/PhysRevD.97.034513

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Flavor changing neutral currents Form factors

Charmed mesons

Lattice QCD

Particles & Fields

Authors & Affiliations

A. Bazavov¹, C. Bernard², C. M. Bouchard³, C. C. Chang^4,5,*, C. DeTar⁶, D. Du⁷, A. X. El-Khadra^4,5,†, E. D. Freeland⁸, E. Gámiz⁹, Steven Gottlieb¹⁰, U. M. Heller¹¹, A. S. Kronfeld^5,12, J. Laiho⁷, P. B. Mackenzie⁵, E. T. Neil^13,14, J. N. Simone⁵, R. Sugar¹⁵, D. Toussaint¹⁶, R. S. Van de Water⁵, and R. Zhou⁵ (Fermilab Lattice and MILC Collaborations)

¹Department of Computational Mathematics, Science and Engineering, Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²Department of Physics, Washington University, St. Louis, Missouri 63130, USA
³School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
⁴Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
⁵Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
⁶Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁷Department of Physics, Syracuse University, Syracuse, New York 13244, USA
⁸Liberal Arts Department, School of the Art Institute of Chicago, Chicago, Illinois 60603, USA
⁹CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, 18071 Granada, Spain
¹⁰Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
¹¹American Physical Society, Ridge, New York 11961, USA
¹²Institute for Advanced Study, Technische Universität München, 85748 Garching, Germany
¹³Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
¹⁴RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
¹⁵Department of Physics, University of California, Santa Barbara, California 93016, USA
¹⁶Department of Physics, University of Arizona, Tucson, Arizona 85721, USA

^*Present address: Lawrence Berkeley National Laboratory, Berkeley, California, 94720, USA. chiachang@lbl.gov
^†axk@illinois.edu

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Issue

Vol. 97, Iss. 3 — 1 February 2018

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