arXiv subjects

Xu Feng

Publications and source records attributed to Xu Feng.

At least 91 records · Page 5Linked to original sources

arXiv2019

Lattice QCD study of the rare kaon decay $K^+\toπ^+ν\barν$ at a near-physical pion mass

The rare kaon decay $K^+\toπ^+ν\barν$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude at the near-physical pion mass $m_π=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small.

hep-lat↗

arXiv2019

Long-distance Contributions to Neutrinoless Double Beta Decay $π^- \toπ^+ e e$

Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, then $π^-π^-\to ee$ and $π^-\toπ^+ ee$ (or equivalently $π^-e^+\toπ^+ e^-$) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to the $π^-\toπ^+ee$ transition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constant $g_ν^{ππ}(m_ρ)=-10.89(28)_\text{stat}(74)_\text{sys}$, which is close to $g_ν^{ππ}(m_ρ)=-11.96(31)_\text{stat}$ determined from the crossed-channel $π^-π^-\to ee$ decay.

hep-lat↗

arXiv2019

Parton distribution functions of $Δ^+$ on the lattice

We present results for renormalized matrix elements related to the unpolarized quasi-distribution function of the $Δ^+$ baryon making use of the large momentum effective theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions with a clover term and pion masses of 250 MeV and 330 MeV are analyzed. We employ momentum smearing to improve the overlap with the boosted $Δ$ state significantly reducing in this way the statistical error of both two- and three-point functions.

hep-lat↗

arXiv2019

Light-Neutrino Exchange and Long-Distance Contributions to $0\nu2β$ Decays: An Exploratory Study on $ππ\to ee$

We present an exploratory lattice QCD calculation of the neutrinoless double beta decay $ππ\to ee$. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses $m_π=420$ and 140 MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are $24\%$ and $9\%$ smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.

hep-lat↗

arXiv2018

QED self energies from lattice QCD without power-law finite-volume errors

Using the infinite-volume photon propagator, we developed a method which allows us to calculate electromagnetic corrections to stable hadron masses with only exponentially suppressed finite-volume effects. The key idea is that the infinite volume hadronic current-current correlation function with large time separation between the two currents can be reconstructed by its value at modest time separation, which can be evaluated in finite volume with only exponentially suppressed errors. This approach can be extended to other possible applications such as QED corrections to (semi-)leptonic decays and some rare decays.

hep-lat↗

arXiv2018

Fast Randomized PCA for Sparse Data

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA algorithm for processing large sparse data. The algorithm has similar accuracy to the basic randomized SVD (rPCA) algorithm (Halko et al., 2011), but is largely optimized for sparse data. It also has good flexibility to trade off runtime against accuracy for practical usage. Experiments on real data show that the proposed algorithm is up to 9.1X faster than the basic rPCA algorithm without accuracy loss, and is up to 20X faster than the svds in Matlab with little error. The algorithm computes the first 100 principal components of a large information retrieval data with 12,869,521 persons and 323,899 keywords in less than 400 seconds on a 24-core machine, while all conventional methods fail due to the out-of-memory issue.

cs.LG↗

arXiv2018

Faster Matrix Completion Using Randomized SVD

Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly, two fast randomized algorithms (rSVD-PI and rSVD- BKI) are proposed for handling sparse matrix. They make use of an eigSVD procedure and several accelerating skills. Then, with the rSVD-BKI algorithm and a new subspace recycling technique, we accelerate the singular value thresholding (SVT) method in [1] to realize faster matrix completion. Experiments show that the proposed rSVD algorithms can be 6X faster than the basic rSVD algorithm [2] while keeping same accuracy. For image inpainting and movie-rating estimation problems, the proposed accelerated SVT algorithm consumes 15X and 8X less CPU time than the methods using svds and lansvd respectively, without loss of accuracy.

cs.LG↗

arXiv2018

Exploratory lattice QCD study of the rare kaon decay $K^+\toπ^+ν\barν$

In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\toπ^+ν\barν$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^+\toπ^+ν\barν$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3\times32$) and at unphysical pion, kaon and charm quark masses, $m_π=420$ MeV, $m_K=563$ MeV and $m_c^{\overline{\mathrm{MS}}}(\mbox{2 GeV})=863$ MeV, the techniques presented in this work can readily be applied to a future realistic calculation.

hep-lat↗

arXiv2018

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 $ΔI=1$ channel with the parity-odd pion-nucleon coupling constant $h_π^1$. 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 $h_π^1$ and the neutron-proton mass-splitting induced by an artificial parity-even counterpart of the $ΔI=1$ 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 $h_π^1$ 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 $h_π^1$, and thus a quantitative test of the strangeness-conserving neutral current interaction of the Standard Model is foreseen.

nucl-th↗

arXiv2017

Including electromagnetism in $K\toππ$ decay calculations

Because of the small size of the ratio A_2/A_0 of the I=2 to I=0 K -> pipi decay amplitudes (the Delta I=1/2 rule) the effects of electromagnetism on A_2 may be a factor of 20 larger than given by a naive O(alpha) estimate. Thus, if future calculations of A_2 and epsilon'/epsilon are to achieve 10% accuracy, these effects need to be included. Here we present the first steps toward including electromagnetism in a calculation of the standard model K -> pipi decay amplitudes using lattice QCD.

hep-lat↗

arXiv2017

Recent progress in applying lattice QCD to kaon physics

Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic $K\toππ$ decay and long-distance processes including $K^0$-$\overline{K^0}$ mixing and rare kaon decays.

hep-lat↗

arXiv2017

Effects of finite volume on the $K_L$-$K_S$ mass difference

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher, and Lellouch and Lüscher, which determine the leading order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second order mixing of the $K^0$ and $\overline{K^0}$ states. We extend the methods of Kim, Sachrajda and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the $K_L$-$K_S$ mass difference $ΔM_K$ and the CP violating parameter $ε_K$ are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.

hep-lat↗

arXiv2017

Exploratory Lattice QCD Study of the Rare Kaon Decay $K^+\toπ^+ν\barν$

We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

hep-lat↗

arXiv2017

First exploratory calculation of the long-distance contributions to the rare kaon decays $K\toπ\ell^+\ell^-$

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. The CP conserving $K\toπ\ell^+\ell^-$ decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long-distance contributions to these rare decay amplitudes using lattice QCD and present the numerical results of the first exploratory studies of these decays in which all but the disconnected diagrams are evaluated. The domain wall fermion ensembles of the RBC and UKQCD collaborations are used, with a pion mass of $M_π\sim 430\,\mathrm{MeV}$ and a kaon mass of $M_{K}\sim 625\,\mathrm{MeV}$. In particular we determine the form factor, $V(z)$, of the $K^+\toπ^+\ell^+\ell^-$ decay from the lattice at small values of $z=q^2/M_{K}^{2}$, obtaining $V(z)=1.37(36),\, 0.68(39),\, 0.96(64)$ for the three values of $z=-0.5594(12),\, -1.0530(34),\, -1.4653(82)$ respectively.

hep-lat↗

arXiv2016

Prospects for a lattice computation of rare kaon decay amplitudes II $K\toπν\barν$ decays

The rare kaon decays $K\toπν\barν$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\toπν\barν$ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on $K^+\toπ^+ν\barν$. Our methodology covers the calculation of both $W$-$W$ and $Z$-exchange diagrams. We discuss the estimation of the power-law, finite-volume corrections and two methods to consistently combine the long distance contribution determined by the lattice methods outlined here with the short distance parts that can be reliably determined using perturbation theory. It is a subsequent work of our first methodology paper on $K\toπ\ell^+\ell^-$, where the focus was made on the $γ$-exchange diagrams.

hep-lat↗

arXiv2016

Long distance contributions to the rare kaon decay $K\toπ\ell^{+}\ell^{-}$

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. To discern such New Physics one must be able to control the errors on the Standard Model prediction of the decay amplitude. These particular decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long distance contributions to these rare decay amplitudes using lattice QCD, and present the numerical results of some exploratory studies using the Domain Wall Fermion ensembles of the RBC and UKQCD collaborations.

hep-lat↗

arXiv2015

Leading-order hadronic contributions to the lepton anomalous magnetic moments from the lattice

The hadronic leading-order (hlo) contribution to the lepton anomalous magnetic moments $a_l^\mathrm{hlo}$ of the Standard Model leptons still accounts for the dominant source of the uncertainty of the Standard Model estimates. We present the results of an investigation of the hadronic leading order anomalous magnetic moments of the electron, muon and tau lepton from first principles in twisted mass lattice QCD. With lattice data for multiple pion masses in the range $230 \mathrm{~MeV} \lesssim m_{PS} \lesssim 490 \mathrm{~MeV}$, multiple lattice volumes and three lattice spacings we perform the extrapolation to the continuum and to the physical pion mass and check for all systematic uncertainties in the lattice calculation. As a result we calculate $a_{l}^\mathrm{hlo}$ for the three Standard Model leptons with controlled statistical and systematic error in agreement with phenomenological determinations using dispersion relations and experimental data. In addition, we also give a first estimate of the hadronic leading order anomalous magnetic moments from simulations directly at the physical value of the pion mass.

hep-lat↗

arXiv2015

Timelike pion form factor in lattice QCD

We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2+1-flavor overlap fermion at pion masses m_pi = 380 and 290 MeV. By calculating the I = 1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.

hep-lat↗