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Register a new userHadronic matrix elements for B-mixing in the Standard Model and beyond
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C.M. Bouchard
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We use lattice QCD to calculate the B-mixing hadronic matrix elements for a basis of effective four-quark operators that spans the space of all possible contributions in, and beyond, the Standard Model. We present results for the SU(3)-breaking ratio and discuss our ongoing calculation of the mixing matrix elements, including the first calculation of the beyond the Standard Model matrix elements from unquenched lattice QCD.
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We calculate---for the first time in three-flavor lattice QCD---the hadronic matrix elements of all five local operators that contribute to neutral $B^0$- and $B_s$-meson mixing in and beyond the Standard Model. 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 $xi = 1.206(18)(6)$, 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 $|V_{td}| = 8.00(34)(8) times 10^{-3}$, $|V_{ts}| = 39.0(1.2)(0.4) times 10^{-3}$, and $|V_{td}/V_{ts}| = 0.2052(31)(10)$, which differ from CKM-unitarity expectations by about 2$sigma$. 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.
Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.
At the Forschungszentrum Juelich (FZJ) we have started a long-term program that aims to determine beyond-the-Standard-Model (BSM) matrix elements using the gradient flow, and to understand the impact of BSM physics in nucleon and nuclear observables. Using the gradient flow, we propose to calculate the QCD component of key beyond the Standard Model (BSM) matrix elements related to quark and strong theta CP violation and the strange content within the nucleon. The former set of matrix elements impacts our understanding of Electric Dipole Moments (EDMs) of nucleons and nuclei (a key signature of BSM physics), while the latter contributes to elastic recoil of Dark Matter particles off nucleons and nuclei. If successful, these results will lay the foundation for extraction of BSM observables from future low-energy, high-intensity and high-accuracy experimental measurements.
We report on an ongoing calculation of hadronic matrix elements needed to parameterize K-Kbar mixing in generic BSM scenarios, using domain wall fermions (DWF) at two lattice spacings. Recent work by the SWME collaboration shows a significant disagreement with our previous results for two of these quantities. Since the origin of this disagreement is unknown, it is important to reduce the various uncertainties. In this work, we are using N_f=2+1 DWF with Iwasaki gauge action at inverse lattice spacings of 2.31 and 1.75 GeV, with multiple unitary pions on each ensemble, the lightest being 290 and 330 MeV on the finer and coarser of the two ensembles respectively. This extends previous work by the addition of a second lattice spacing (a^{-1}approx 1.75 GeV). Renormalization is carried out non-perturbatively in the RI/MOM scheme and converted perturbatively to MSbar.
Neutral-meson mixing is loop suppressed in the Standard Model, leading to the possibility of enhanced sensitivity to new physics. The uncertainty in Standard Model predictions for $B$-meson oscillation frequencies is dominated by theoretical uncertainties within the short-distance $B$-meson hadronic matrix elements, motivating the need for improved precision. In $D$-meson mixing, the Standard Model short-distance contributions are further suppressed by the GIM mechanism allowing for the possibility of large new physics enhancements. A first-principle determination of the $D$-meson short-distance hadronic matrix elements will allow for model-discrimination between the new physics theories. I review recently published and ongoing lattice calculations of hadronic matrix elements in $B$ and $D$-meson mixing with emphasis on the Fermilab lattice and MILC collaboration effort on the determination of the $B$ and $D$-meson mixing hadronic matrix elements using the methods of lattice QCD.
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