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preprint2020arXiv

Ratios of the hadronic contributions to the lepton $g-2$ from Lattice QCD+QED simulations

The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of electron, muon and tau-lepton, $a_{\ell=e,μτ}^{HVP,LO}$, are computed using lattice QCD+QED simulations. The results include the effects at order $O(α_{em}^2)$ as well as the electromagnetic and strong isospin-breaking corrections at orders $O(α_{em}^3)$ and $O(α_{em}^2(m_u-m_d))$, respectively, where $(m_u-m_d)$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range 210 - 450 MeV. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-tau and muon-tau ratios such a cancellation does not occur. For the electron-muon ratio we get $R_{e/μ} \equiv (m_μ/m_e)^2 (a_e^{HVP,LO} / a_μ^{HVP,LO}) = 1.1456~(83)$ with an uncertainty of $\simeq 0.7 \%$. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well wi

preprint2020arXiv

Application of dilaton chiral perturbation theory to $N_f=8$, ${\rm SU}(3)$ spectral data

We extend dilaton chiral perturbation theory (dChPT) to include the taste splittings in the Nambu--Goldstone sector observed in lattice simulations of near-conformal theories with staggered fermions. We then apply dChPT to a recent simulation by the LSD collaboration of the SU(3) gauge theory with 8 fermions in the fundamental representation, which is believed to exhibit near-conformal behavior in the infrared, and in which a light singlet scalar state, nearly degenerate with the pions, has been found. We find that the mesonic sector of this theory can be successfully described by dChPT, including, in particular, the mesonic taste splittings found in the simulation. We confirm that current simulations of this theory are in the "large-mass" regime.

preprint2020arXiv

Walking Dynamics Guaranteed

We report evidence for a continuous transition from an infrared conformal phase to a chirally broken one in four dimensions. We study a model with two Dirac fermions in the adjoint representation of an SU(2) gauge interaction and a chirally symmetric four-fermion interaction. At large four-fermion coupling, the model goes through a transition into a chirally broken phase and infrared conformality is lost. We show strong evidence that this transition is continuous, which would guarantee walking dynamics within the scaling region in the chirally broken phase.

preprint2020arXiv

From spin chains to real-time thermal field theory using tensor networks

One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded equilibrium correlators governing the linear response theory. In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infrared descriptions of quantum Ising chains.We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of nonintegrable interacting quantum field theories.

preprint2020arXiv

Glueball scattering cross section in lattice SU(2) Yang-Mills theory

We calculate the scattering cross section between two $0^{++}$ glueballs in $SU(2)$ Yang-Mills theory on lattice at $β= 2.1, 2.2, 2.3, 2.4$, and 2.5 using the indirect (HAL QCD) method. We employ the cluster-decomposition error reduction technique and use all space-time symmetries to improve the signal. In the use of the HAL QCD method, the centrifugal force was subtracted to remove the systematic effect due to nonzero angular momenta of lattice discretization. From the extracted interglueball potential we determine the low energy glueball effective theory by matching with the one-glueball exchange process. We then calculate the scattering phase shift, and derive the relation between the interglueball cross section and the scale parameter $Λ$ as $σ_{ϕϕ} = (2 - 51) Λ^{-2}$ (stat.+sys.). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter, as $Λ> 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.

preprint2020arXiv

Hybrid static potentials in SU(2) lattice gauge theory at short quark-antiquark separations

We compute hybrid static potentials in SU(2) lattice gauge theory using a multilevel algorithm and three different small lattice spacings. The resulting static potentials, which are valid for quark-antiquark separations as small as 0.05 fm, are important e.g. when computing masses of heavy hybrid mesons in the Born-Oppenheimer approximation. We also discuss and exclude possible systematic errors from topological freezing, the finite lattice volume and glueball decays.

preprint2020arXiv

Spin Order and Entropy in Antiferromagnetic Films Subjected to Magnetic Fields

Using systematic effective field theory, we explore the properties of antiferromagnetic films subjected to magnetic and staggered fields that are either mutually aligned or mutually orthogonal. We provide low-temperature series for the entropy density in either case up to two-loop order. Invoking staggered, uniform and sublattice magnetizations of the bipartite antiferromagnet, we investigate the subtle order-disorder phenomena in the spin arrangement, induced by temperature, magnetic and staggered fields -- some of which are quite counterintuitive. In the figures we focus on the spin-$\frac{1}{2}$ square-lattice antiferromagnet, but our results are valid for any other bipartite two-dimensional lattice.

preprint2020arXiv

Tensor network formulation of two dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the TRG to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Lio

preprint2020arXiv

PDFs and Neutrino-Nucleon Scattering from Hadronic Tensor

We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer ($Q^2 \sim 4\, {\rm GeV^2}$) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents ($V_4$) with the electric form factor calculated from the three-point function and found they agree within errors.

preprint2020arXiv

Hadronic vacuum polarization: $(g-2)_μ$ versus global electroweak fits

Hadronic vacuum polarization (HVP) is not only a critical part of the Standard Model (SM) prediction for the anomalous magnetic moment of the muon $(g-2)_μ$, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in $Δα^{(5)}_\text{had}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $Δα^{(5)}_\text{had}\big|_\text{EW}=270.2(3.0)\times 10^{-4}$. This value actually lies below the range derived from $e^+e^-\to\text{hadrons}$ cross-section data, and thus goes into the opposite direction as would be required if a change in HVP were to bring the SM prediction for $(g-2)_μ$ into agreement with the Brookhaven measurement. Depending on the energy where the bulk of the changes in the cross section occurs, reconciling experiment and SM prediction for $(g-2)_μ$ by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from $(g-2)_μ$ to the EW fit. We briefly explore some options of BSM scenarios that could

preprint2020arXiv

Lattice QCD and baryon-baryon interactions: HAL QCD method

In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories such as QCD. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we formulate a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the Lüscher's formula. We give several theoretical and numerical evidences that the conventional method combined with the naive plateau fitting for the finite volume energies in the literature so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious proble

preprint2020arXiv

Quadrupole pressure and shear forces inside baryons in the large $N_c$ limit

We derive number of relations between quadrupole energy, elastic pressure, and shear force distributions in baryons using the large $N_c$ picture of baryons as chiral solitons. The obtained large $N_c$ relations are independent of particular dynamics and should hold in any picture in which the baryon is the chiral soliton. One of remarkable qualitative predictions of the soliton picture is the nullification of the tangential forces acting on the radial area element for any tensor polarisation of the baryon. The derived relations provide a powerful tool to check the hypothesis that the baryons are chiral solitons, say using lattice QCD.

preprint2020arXiv

Beauty mesons in $N_f=2+1+1+1 $ lattice QCD with exact chiral symmetry

We present the first study of $N_f=2+1+1+1$ lattice QCD with domain-wall quarks. The $(b, c, s)$ quarks are physical, while the $(u, d)$ quarks are heavier than their physical masses, with the pion mass $ \sim 700 $ MeV. The gauge ensemble is generated by hybrid Monte Carlo simulation with the Wilson gauge action for the gluons, and the optimal domain-wall fermion action for the quarks. Using point-to-point quark propagators, we measure the time-correlation functions of quark-antiquark meson interpolators with quark contents $\bar b b$, $\bar b c$, $\bar b s$, and $ \bar c c$, and obtain the masses of the low-lying mesons. They are in good agreement with the experimental values, plus some predictions which have not been observed in experiments. Moreover, we also determine the masses of $(b, c, s)$ quarks.

preprint2020arXiv

Four quark operators for kaon bag parameter with gradient flow

To study the CP-violation using the $K_0-\bar{K}_0$ oscillation, we need the kaon bag parameter which represents QCD corrections in the leading Feynman diagrams. The lattice QCD provides us with the only way to evaluate the kaon bag parameter directly from the first principles of QCD. However, a calculation of relevant four quark operators with theoretically sound Wilson-type lattice quarks had to carry a numerically big burden of extra renormalizations and resolution of extra mixings due to the explicit chiral violation. Recently, the Small Flow-time eXpansion (SFtX) method was proposed as a general method based on the gradient flow to correctly calculate any renormalized observables on the lattice, irrespective of the explicit violations of related symmetries on the lattice. To apply the SFtX method, we need matching coefficients, which relate finite operators at small flow-times in the gradient flow scheme to renormalized observables in conventional renormalization schemes. In this paper, we calculate the matching coefficients for four quark operators and quark bi-linear operators, relevant to the kaon bag parameter.

preprint2020arXiv

Ratio of strange to $u/d$ momentum fraction in disconnected insertions

The ratio of the strange quark momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of light quark $u$ or $d$ in disconnected insertions (DI) is calculated on the lattice with overlap fermions on four domain wall fermion ensembles. These ensembles cover three lattice spacings, three volumes and several pion masses including the physical one, from which a global fitting is carried out. A complete nonperturbative renormalization and the mixing between the quark and glue operators are taken into account. We find the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}} ({\rm DI})=0.795(79)(77)$ at $μ= 2$ GeV in the $\overline{\rm MS}$ scheme. This ratio can be used as a constraint to better determine the strange parton distribution especially in the small $x$ region in the global fittings of PDFs when the connected and disconnected sea are fitted and evolved separately, demonstrating a new way that connects lattice calculations with global analyses.

preprint2020arXiv

Determination of $α(M_z)$ from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $Z_3^F(n_f=3)=2Z_3^V(n_f=3)=0.37(17)$. The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $Λ_{\overline{\rm MS}}$ when fitting to short-distance lattice data of the static energy. We obtain $Λ_{\overline{\rm MS}}^{(n_f=3)}=338(12)$ MeV and $α(M_z)=0.1181(9)$. We have also found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

preprint2020arXiv

't Hooft surface in lattice gauge theory

We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.

preprint2020arXiv

Origin of single transverse-spin asymmetries in high-energy collisions

In this paper we perform the first simultaneous QCD global analysis of data from semi-inclusive deep inelastic scattering, Drell-Yan, $e^+e^-$ annihilation into hadron pairs, and proton-proton collisions. Consequently, we are able to extract a universal set of non-perturbative functions that describes the observed asymmetries in these reactions. The outcome of our analysis indicates single transverse-spin asymmetries in high-energy collisions have a common origin. Furthermore, we achieve the first phenomenological agreement with lattice QCD on the up and down quark tensor charges.

preprint2020arXiv

Proton spin after 30 years: what we know and what we don't?

More than three decades has passed since the European Muon Collaboration published the first surprising result on the spin structure of the proton. Much theoretical and experimental progress has been made in understanding the origins of the proton spin. In this review, we will discuss what we have learned so far, what are still missing, and what we shall expect to learn from the upcoming experiments including JLab 12 GeV and Electron-Ion Collider. In particular, we focus on first principles calculations and experimental measurements of the total gluon helicity $ΔG$, and quark and gluon orbital angular momenta.

preprint2020arXiv

$F_K / F_π$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

We report the results of a lattice quantum chromodynamics calculation of $F_K/F_π$ using Möbius domain-wall fermions computed on gradient-flowed $N_f=2+1+1$ highly-improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from $130 \lesssim m_π\lesssim 400$ MeV, four lattice spacings of $a\sim 0.15, 0.12, 0.09$ and $0.06$ fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the $a\sim0.06$ fm ensemble is helpful, but not necessary to achieve a subpercent determination of $F_K/F_π$. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of $F_{K^\pm}/F_{π^\pm} = 1.1942(45)$ with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchm

preprint2020arXiv

Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo simulation, consequently it usually suffers such problems as the Fermion sign problem and the lack of real-time dynamics. Hopefully they can be avoided by using quantum simulation, which simulates quantum systems by using controllable true quantum processes. The field of quantum simulation is under rapid development. Here we present a circuit-based digital scheme of quantum simulation of quantum $\mathbb{Z}_2$ lattice gauge theory in $2+1$ and $3+1$ dimensions, using quantum adiabatic algorithms implemented in terms of universal quantum gates. Our algorithm generalizes the Trotter and symmetric decompositions to the case that the Hamiltonian varies at each step in the decomposition. Furthermore, we carry through a complete demonstration of this scheme in classical GPU simulator, and obtain key features of quantum $\mathbb{Z}_2$ lattice gauge theory, including quantum phase transitions, topological properties, gauge invariance and duality. Hereby dubbed ps

preprint2020arXiv

Strong Coupling Constants of the Doubly Heavy $ Ξ_{QQ} $ Baryons with $ π$ Meson

The doubly charmed $Ξ_{cc}^{++} (ccu)$ state is the only listed baryon in PDG, which was discovered in the experiment. The LHCb collaboration gets closer to discovering the second doubly charmed baryon $Ξ_{cc}^{+} (ccd)$, hence the investigation of the doubly charmed/bottom baryons from many aspects is of great importance that may help us not only get valuable knowledge on the nature of the newly discovered states, but also in the search for other members of the doubly heavy baryons predicted by the quark model. In this context, we investigate the strong coupling constants among the $Ξ_{cc}^{+(+)}$ baryons and $π^{0(\pm)}$ mesons by means of light cone QCD sum rule. Using the general forms of the interpolating currents of the $Ξ_{cc}^{+(+)}$ baryons and the distribution amplitudes (DAs) of the $π$ meson, we extract the values of the coupling constants $g_{Ξ_{cc} Ξ_{cc} π}$. We extend our analyses to calculate the strong coupling constants among the b-partner baryons with $π$ mesons, as well, and extract the values of the strong couplings $g_{Ξ_{bb} Ξ_{bb} π}$. It is observed that the values of the couplings under study in bottom channels are about 4 times greater than those of the

preprint2020arXiv

Trotter errors in digital adiabatic quantum simulation of quantum $\mathbb{Z}_2$ lattice gauge theory

Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of $2+1$ dimensional quantum $\mathbb{Z}_2$ lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be closely related to the Trotter error usually defined defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.

preprint2020arXiv

Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data

We both review and augment the lightcone conformal truncation (LCT) method. LCT is a Hamiltonian truncation method for calculating dynamical quantities in QFT in infinite volume. This document is a self-contained, pedagogical introduction and "how-to" manual for LCT. We focus on 2D QFTs which have UV descriptions as free CFTs containing scalars, fermions, and gauge fields, providing a rich starting arena for LCT applications. Along our way, we develop several new techniques and innovations that greatly enhance the efficiency and applicability of LCT. These include the development of CFT radial quantization methods for computing Hamiltonian matrix elements and a new SUSY-inspired way of avoiding state-dependent counterterms and maintaining chiral symmetry. We walk readers through the construction of their own basic LCT code, sufficient for small truncation cutoffs. We also provide a more sophisticated and comprehensive set of Mathematica packages and demonstrations that can be used to study a variety of 2D models. We guide the reader through these packages with several examples and illustrate how to obtain QFT observables, such as spectral densities and the Zamolodchikov $C$