Toward a First-Principles Calculation of Electroweak Box Diagrams

We derive a Feynman-Hellmann theorem relating the second-order nucleon energy shift resulting from the introduction of periodic source terms of electromagnetic and isovector axial currents to the parity-odd nucleon structure function $F_3^N$. It is a crucial ingredient in the theoretical study of the $\gamma W$ and $\gamma Z$ box diagrams that are known to suffer from large hadronic uncertainties. We demonstrate that for a given $Q^2$, one only needs to compute a small number of energy shifts in order to obtain the required inputs for the box diagrams. Future lattice calculations based on this approach may shed new light on various topics in precision physics including the refined determination of the Cabibbo-Kobayashi-Maskawa matrix elements and the weak mixing angle.Comment: Version to appear in PR

Effective Field Theory in The Study of Long Range Nuclear Parity Violation on Lattice

A non-zero signal $A_\gamma^\mathrm{np}=(-3.0\pm1.4\pm0.2)\times 10^{-8}$ of the gamma-ray asymmetry in the neutron-proton capture was recently reported by the NPDGamma Collaboration which provides the first determination of the $\Delta I=1$ parity-odd pion-nucleon coupling constant $h_\pi^1=(2.6\pm 1.2\pm 0.2)\times 10^{-7}$. The ability to reproduce this value from first principles serves as a direct test of our current understanding of the interplay between the strong and weak interaction at low energy. To motivate new lattice studies of $h_\pi^1$, we review the current status of the theoretical understanding of this coupling, which includes our recent work that relates it to a nucleon mass-splitting by a soft-pion theorem. We further investigate the possibility of calculating the mass-splitting on the lattice by providing effective field theory parameterizations of all the involved quark contraction diagrams. We show that the lattice calculations of the easier connected diagrams will provide information of the chiral logarithms in the much harder quark loop diagrams and thus help in the chiral extrapolation of the latter.Comment: 43 pages, 3 figures, 1 table. Accepted by EPJ

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation

The parity-odd effect in the Standard Model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the $\Delta I=1$ channel with the parity-odd pion-nucleon coupling constant $h_\pi^1$. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well-understood. In this Letter we derive a soft-pion theorem relating $h_\pi^1$ and the neutron-proton mass-splitting induced by an artificial parity-even counterpart of the $\Delta I=1$ weak Lagrangian, and demonstrate that the theorem still holds exact at the next-to-leading order in chiral perturbation theory. A considerable amount of simplification is expected in the study of $h_\pi^1$ by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of $h_\pi^1$, and thus a quantitative test of the strangeness-conserving neutral current interaction of the Standard Model is foreseen.Comment: 6 pages, 1 figur

Right-Handed Neutrinos and T-Violating, P-Conserving Interactions

We show that experimental probes of the P-conserving, T-violating triple correlation in polarized neutron or nuclear $\beta$-decay provide a unique probe of possible T-violation at the TeV scale in the presence of right-handed neutrinos. In contrast to other possible sources of semileptonic T-violation involving only left-handed neutrinos, those involving right-handed neutrinos are relatively unconstrained by present limits on the permanent electric dipole moments of the electron, neutral atoms, and the neutron. On the other hand, LHC results for $pp\to e+$ missing transverse energy imply that an order of magnitude of improvement in $D$-coefficient sensitivity would be needed for discovery. Finally, we discuss the interplay with the scale of neutrino mass and naturalness considerations.Comment: 6 pages, 2 figure

Reduced hadronic uncertainty in the determination of VudV_{ud}

We analyze the universal radiative correction $\Delta_R^V$ to neutron and superallowed nuclear $\beta$ decay by expressing the hadronic $\gamma W$-box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the $\gamma W$ interference structure function $F_3^{(0)}$. By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of $\Delta_R^V = 0.02467(22)$, wherein the hadronic uncertainty is reduced. Assuming other Standard Model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of $|V_{ud}| = 0.97366(15)$, raising tension with the first row CKM unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.Comment: 5 pages, 5 figures, references updated; version submitted to PR

Constraints on Disconnected Contributions in ππ\pi\pi Scattering

The accuracy of the lattice QCD computation of hadron-hadron scattering at low isospin depends critically on the ability to compute correlation functions with fermionic disconnected Wick contractions. This happens, for instance, in isospin $I=0$ $\pi\pi$ scattering, which receives contributions from rectangular and vacuum types of contractions among other easier calculable ones. Combining L\"{u}scher's formula and partially-quenched chiral perturbation theory, we provide precise theory predictions of the discrete energy levels extracted from specific linear combinations of lattice correlation functions corresponding to various types of contractions. Expressions are provided for extracting the unphysical low-energy constants in the partially-quenched chiral perturbation theory from the energy levels for these contractions. The predictions for the rectangular and vacuum contractions may serve as solid tests of the accuracy for existing and future lattice studies of $\pi\pi$ scattering.Comment: Version to appear in JHE

Improvement and performance analysis on statistical selection algorithms

Over the years, the distributed database has been developed so fast that there's a need to develop an effective selection algorithm for it. Loo and Choi has proposed a statistical selection algorithm with the same objective and run in multicast / broadcast environment that has been proved that it is the best among others in terms of the number of messages needed to complete the searching process. However, this algorithm has a high probability of failure. A few improvements have been done to this original algorithm. This new algorithm is developed based on the simulation of the real multicast environment. Three modifications have been added in the new algorithm to solve the problem. Two performance measures have been conducted for the purpose of performance analysis between original and new algorithm