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Register a new userNuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
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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.
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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.
We present a model-independent calculation of hadron matrix elements for all dimension-six operators associated with baryon number violating processes using lattice QCD. The calculation is performed with the Wilson quark action in the quenched approximation at $beta=6/g^2=6.0$ on a $28^2times 48times 80$ lattice. Our results cover all the matrix elements required to estimate the partial lifetimes of (proton,neutron)$to$($pi,K,eta$) +(${bar u},e^+,mu^+$) decay modes. We point out the necessity of disentangling two form factors that contribute to the matrix element; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which could give strong constraints on several GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of chiral lagrangian.
The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.
Matrix elements of six-quark operators are needed to extract new physics constraints from experimental searches for neutron-antineutron oscillations. This work presents in detail the first lattice quantum chromodynamics calculations of the necessary neutron-antineutron transition matrix elements including calculation methods and discussions of systematic uncertainties. Implications of isospin and chiral symmetry on the matrix elements, power counting in the isospin limit, and renormalization of a chiral basis of six-quark operators are discussed. Calculations are performed with a chiral-symmetric discretization of the quark action and physical light quark masses in order to avoid the need for chiral extrapolation. Non-perturbative renormalization is performed, including a study of lattice cutoff effects. Excited-state effects are studied using two nucleon operators and multiple values of source-sink separation. Results for the dominant matrix elements are found to be significantly larger compared to previous results from the MIT bag model. Future calculations are needed to fully account for systematic uncertainties associated with discretization and finite-volume effects but are not expected to significantly affect this conclusion.
We present the ETMC results for the bag parameters describing the neutral kaon mixing in the Standard Model and beyond and preliminary results for the bag parameters controlling the short distance contributions in the D^0-bar{D}^0 oscillations. We also present preliminary results for the B_{Bd}, B_{Bs}, B_{Bs}/B_{Bd} and xi -parameter controlling B^0_-bar{B}^0 oscillations in the Standard Model employing the so-called ratio method. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve both O(a)-improvement and continuum like renormalization pattern. Simulations are performed at three-values of the lattice spacing and several values of quark masses in the light, strange, charm region and above charm up to ~2.5m_c. Our results are extrapolated to the continuum limit and extrapolated/interpolated to the physical quark masses.
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