28 Search Results

CKM matrix is unitary by construction in the standard model(SM). The recent analyses on the first row of CKM matrix show ≈3σ tension with unitarity. Nonperturbative calculations of the radiative corrections can reduce the theory uncertainty in CKM matrix elements. Here we compute the electroweak box contribution to the pion and kaon β decays using seven Nf = 2 + 1 + 1 HISQ-Clover lattice with various pion mass and lattice spacing. The continuum and chiral limit is taken using the leading dependence on M_π and a, where M_π extrapolation is taken to the physical pion mass and SU(3) symmetricmore » mass for pion and kaon box contribution, respectively. Our results are $$\square^{VA}_{γW}|_{π}$$ = 2.820(28) × 10^–3 and $$\square^{VA}_{γW}|_{K}$$ = 2.384(17) × 10^–3.« less

Abstract not provided.

We present high statistics results for the isovector nucleon charges and form factors using seven ensembles of 2+1-flavor Wilson-clover fermions. The axial and pseudoscalar form factors obtained on each ensemble satisfy the PCAC relation once the lowest energy $$N\pi$$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $$N\pi\pi $$ excited state contributes to the correlation functions with the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parameterization of the experimental electric andmore » magnetic data. Our final estimates for the isovector charges are $$g_{A}^{u-d} = 1.31(06)(05)_{sys}$$, $$g_{S}^{u-d} = 1.06(10)(06)_{sys}$$, and $$g_{T}^{u-d} = 0.95(05)(02)_{sys}$$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, $${\langle r_A^2 \rangle}^{u-d}=0.428(53)(30)_{sys}\ {\rm fm}^2$$, (ii) the induced pseudoscalar charge, $$g_P^\ast=7.9(7)(9)_{sys}$$, (iii) the pion-nucleon coupling $$g_{\pi {\rm NN}} = 12.4(1.2)$$, (iv) the electric charge radius squared, $${\langle r_E^2 \rangle}^{u-d} = 0.85(12)(19)_{sys} \ {\rm fm}^2$$, (v) the magnetic charge radius squared, $${\langle r_M^2 \rangle}^{u-d} = 0.71(19)(23)_{\rm sys} \ {\rm fm}^2$$, and (vi) the magnetic moment $$\mu^{u-d} = 4.15(22)(10)_{\rm sys}$$. All our results are consistent with phenomenological/experimental values but with larger errors. Lastly, we present a Padé parameterization of the axial, electric and magnetic form factors over the range $0.04< Q^2 <1$ GeV$${}^2$$ for phenomenological studies.« less

We present an analysis of the pion-nucleon σ-term σ_πN using six ensembles with 2+1+1-flavor highly improved staggered quark action generated by the MILC Collaboration. The most serious systematic effect in lattice calculations of nucleon correlation functions is the contribution of excited states. We estimate these using chiral perturbation theory (χPT) and show that the leading contribution to the isoscalar scalar charge comes from Nπ and Nππ states. Therefore, we carry out two analyses of lattice data to remove excited-state contamination, the standard one and a new one including Nπ and Nππ states. We find that the standard analysis gives σ_πNmore » = 41.9(4.9) MeV, consistent with previous lattice calculations, while our preferred χPT-motivated analysis gives σ_πN = 59.6(7.4) MeV , which is consistent with phenomenological values obtained using πN scattering data. Our data on one physical pion mass ensemble were crucial for exposing this difference, therefore, calculations on additional physical mass ensembles are needed to confirm our result and resolve the tension between lattice QCD and phenomenology.« less

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, themore » mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.« less

Many physics problems involve integration in multi-dimensional space whose analytic solution is not available. The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in solving the physics problems. We propose a novel numerical multi-dimensional integration algorithm using machine learning (ML). After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral. Then, the difference between the approximation and the true answer is calculated to correct the bias in the approximationmore » of the integral induced by ML prediction errors. Because of the bias correction, the final estimate of the integral is unbiased and has a statistically correct error estimation. Three ML models of multi-layer perceptron, gradient boosting decision tree, and Gaussian process regression algorithms are investigated. The performance of the proposed algorithm is demonstrated on six different families of integrands that typically appear in physics problems at various dimensions and integrand difficulties. The results show that, for the same total number of integrand evaluations, the new algorithm provides integral estimates with more than an order of magnitude smaller uncertainties than those of the VEGAS algorithm in most of the test cases.« less

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms andmore » their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.« less

Abstract not provided.

We present results on the isovector momentum fraction, $$\langle x \rangle_{u–d}$$ , helicity moment, $$\langle x \rangle_{Δ u–Δd}$$ , and the transversity moment, $$\langle x \rangle_{δu–δd}$$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC Collaboration using 2 + 1 + 1 -flavors of dynamical highly improved staggered quarks. The correlation functions are calculated using the Wilson-Clover action, and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI'–MOM scheme. The data have been collected at lattice spacings a ≈ 0.15 , 0.12, 0.09, and 0.06 fm and $$M_π$$more » ≈ 310 , 220, and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $$\overline{\text{MS}}$$ scheme at 2 GeV, are $$\langle$$ x $$\rangle$$ u – d = 0.173 ( 14 ) ( 07 ) , $$\langle x \rangle_{Δu–Δd}$$ = 0.213 ( 15 ) ( 22 ) , and $$\langle x \rangle_{δu–δd}$$ = 0.208 ( 19 ) ( 24 ) , where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.« less

We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumablymore » exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64. The scaling results indicate that a larger number of qubits gives better prediction accuracy.« less