Search

The many-body entanglement between two finite (size-$d$) disjoint vacuum regions of non-interacting lattice scalar field theory in one spatial dimension -- a $(d_A \times d_B)_{\rm mixed}$ Gaussian continuous variable system -- is locally transformed into a tensor-product "core" of $(1_A \times 1_B)_{\rm mixed}$ entangled pairs. Accessible entanglement within these core pairs exhibits an exponential hierarchy, and as such identifies the structure of dominant region modes from which vacuum entanglement could be extracted into a spatially separated pair of quantum detectors. Beyond the core, remaining modes of the "halo" are determined to be AB-separable in isolation, as well as separable from the core. However, state preparation protocols that distribute entanglement in the form of $(1_A \times 1_B)_{\rm mixed}$ core pairs are found to require additional entanglement in the halo that is obscured by classical correlations. This inaccessible (bound) halo entanglement is found to mirror the accessible entanglement, but with a step behavior as the continuum is approached. It remains possible that alternate initialization protocols that do not utilize the exponential hierarchy of core-pair entanglement may require less inaccessible entanglement. Entanglement consolidation is expected to persist in higher dimensions and may aid classical and quantum simulations of asymptotically free gauge field theories, such as quantum chromodynamics., Comment: 11 pages, 3 figures, 10 pages supplemental material. The manuscript has been re-organized and elaborated to improve clarity

In this work we present perturbative results for the renormalization of the supercurrent operator, $S_\mu$, in ${\cal N} =1$ Supersymmetric Yang-Mills theory. At the quantum level, this operator mixes with both gauge invariant and noninvariant operators, which have the same global transformation properties. In total, there are 13 linearly independent mixing operators of the same and lower dimensionality. We determine, via lattice perturbation theory, the first two rows of the mixing matrix, which refer to the renormalization of $S_\mu$, and of the gauge invariant mixing operator, $T_\mu$. To extract these mixing coefficients in the ${\overline{\rm MS}}$ renormalization scheme and at one-loop order, we compute the relevant two-point and three-point Green's functions of $S_\mu$ and $T_\mu$ in two regularizations: dimensional and lattice. On the lattice, we employ the plaquette gluonic action and for the gluinos we use the fermionic Wilson action with clover improvement., Comment: 9 pages, 3 figures, 1 table, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\"at Bonn, Bonn, Germany

We report progress in the calculation of the thermal interquark potential of bottomonium using the HAL QCD method applied to bottom quarks in the non-relativistic approximation (i.e. NRQCD). We exploit the fast Fourier transform algorithm, using a momentum space representation, to efficiently calculate NRQCD correlation functions of non-local mesonic S-wave states, and thus obtain the potential for temperatures in both the hadronic and plasma phases. This work was performed on our anisotropic 2+1 flavour ''Generation 2'' FASTSUM ensembles., 8 pages, 3 figures. Submitted in the proceedings of The 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universitaet Bonn, Bonn, Germany

After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we decompose the nonabelian gauge field into the Abelian field created by Abelian monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentials in the fundamental representation and show that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. Comparison with other ways of decomposition is made., 5 pages, 2 figures

Local gauge symmetry is intriguing for the study of quantum thermalization breaking. For example, in the high-spin lattice Schwinger model (LSM), the local U(1) gauge symmetry underlies the disorder-free many-body localization (MBL) dynamics of matter fields. This mechanism, however, would not work in a spin-1/2 LSM due to the absence of electric energy in the Hamiltonian. In this paper, we show that the spin-1/2 LSM can also exhibit disorder-free MBL dynamics, as well as entropy prethermalization, by introducing a four-fermion interaction into the system. The interplay between the fermion interaction and U(1) gauge symmetry endows the gauge fields with an effectively disordered potential which is responsible for the thermalization breaking. It induces anomalous (i.e., non-thermal) behaviors in the long-time evolution of such quantities as local observables, entanglement entropy, and correlation functions. Our work offers a new platform to explore emergent non-thermal dynamics in state-of-the-art quantum simulators with gauge symmetries.

We use three-flavor chiral perturbation theory ($\chi$PT) to calculate the pressure, light and $s$-quark condensates of QCD in the confined phase at finite temperature to ${\cal O}(p^6)$ in the low-energy expansion. We also include electromagnetic effects to order $e^2$, where the electromagnetic coupling $e$ counts as order $p$. Our results for the pressure and the condensates suggest that $\chi$PT converges very well for temperatures up to approximately 150 MeV. We combine $\chi$PT and the Hadron Resonance Gas (HRG) model by adding heavier baryons and mesons. Our results are compared with lattice simulations an d the agreement is very good for temperatures below {170} MeV, in contrast to the results from $\chi$PT which agree with the lattice only up to $T\approx120$ MeV. Our value for the chiral crossover temperature is 160.1 MeV, which compares favorably to the lattice result of $157.3$ MeV., Comment: 21 pages. 8 figures V2 matches published version in PRD

Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome. One of the key features of the method is the possibility to expand around non-trivial vacua. While this idea has been around for a while, and it has been implemented in the case of the (non-trivial) background of the Schr\"odinger functional, NSPT expansions around instantons have not yet been fully worked out. Here we present computations for the double well potential in quantum mechanics. We compute a few orders of the expansion of the ground-state energy splitting in the one-instanton sector. We discuss how (already) known two-loop results are reproduced and present the current status of higher-order computations., Comment: 10 pages, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

The dynamics of the gauge sector of QCD give rise to nonperturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole and the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations., 57 pages, 23 figures

The heavy quark diffusion coefficient is encoded in the spectral functions of the chromo-electric and the chromo-magnetic correlators, of which the latter describes the T/M contribution. We study these correlators at two different temperatures $T=1.5T_c$ and $T=10^4T_c$ in the deconfined phase of SU(3) gauge theory. We use gradient flow for noise reduction. We perform both continuum and zero flow time limits to extract the heavy quark diffusion coefficient. Our results imply that the mass suppressed effects in the heavy quark diffusion coefficient are 20% for bottom quarks and 34% for charm quark at $T=1.5T_c$., Comment: 9 pages, 6 figures, Contribution to the 39th International Symposium on Lattice Field theory (LATTICE2022),8th-13th August, 2022, Bonn, Germany

The stochastic Laplacian Heaviside (LapH) method has proven to be successful in hadronic calculations. In this work, with charm-light spectroscopy in mind, we set up and optimise the LapH procedure limiting ourselves to the evaluation of two-point mesonic correlation functions. The calculations are performed on CLS ensembles with $N_f=2+1$ Wilson-Clover fermions on a $32^3\times64$ lattice with open boundary conditions. We analyse the interplay between the LapH parameters and the boundary effects, and implement a fitting procedure to isolate excitations coming from the border., Comment: 8 pages, 5 figures, Proceedings contribution to the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany

The generation of ensembles of gauge configurations is a considerable expense. The preservation and curation of these ensembles constitutes a valuable shared resource for the lattice field theory community. The organizers of Lattice 2022 dedicated a parallel session to the presentation of gauge ensembles and their generation, plans for ensemble publication and data management/storage activities of different collaborations. A summary of the twelve contributions is presented here., Comment: Contribution to the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8-13 August, 2022, Bonn, Germany, 23 pages

Two-dimensional $O(N)$ non-linear sigma models are exactly solvable theories and have many applications, from statistical mechanics to their use as QCD toy models. We consider a supersymmetric extension, the non-linear sigma model on the supersphere~$S^{N+2m-1|2m}\equiv \frac{OSP(N+2m|2m)}{OSP(N+2m-1|2m)}$. We briefly describe its renormalization properties and lattice discretization, and present a strategy for numerical simulations together with some preliminary numerical results., 8 pages, 3 figures, Contribution to the Proceedings of the 39th International Symposium on Lattice Field Theory

In this paper we present an improved RI-type prescription appropriate for the non-perturbative renormalization of gauge invariant nonlocal operators. In this prescription, the non-perturbative vertex function is improved by subtracting unwanted finite lattice spacing ($a$) effects, calculated in lattice perturbation theory. The method is versatile and can be applied to a wide range of fermion and gluon actions, as well as types of nonlocal operators. The presence of operator mixing can also be accommodated. Compared to the standard RI' prescription, this variant can be recast as a supplementary finite renormalization, whose coefficients bring about corrections of higher order in $a$; consequently, it coincides with standard RI' as $a\to 0$, however it can afford us a smoother and more controlled extrapolation to the continuum limit. In this proof-of-concept calculation we focus on nonlocal fermion bilinear operators containing a straight Wilson line. In the numerical implementation we use Wilson/clover fermions and Iwasaki improved gluons. The finite-$a$ terms were calculated to one-loop level in lattice perturbation theory, and to all orders in $a$, using the same action as the non-perturbative vertex functions. We find that the method leads to significant improvement in the perturbative region indicated by small and intermediate values of the length of the Wilson line. This results in a robust extraction of the renormalization functions in that region. We have also applied the above method to operators with stout-smeared links. We show how to perform the perturbative correction for any number of smearing iterations, and evaluate its effect on the power divergent renormalization coefficients., 15 pages, 8 figures, 1 table

We show that the phase structure of certain staggered fermion theories can be understood on the basis of exact anomalies. These anomalies arise when staggered fermions are coupled to gravity which can be accomplished by replacing them by discrete K\"{a}hler-Dirac fermions. We first show the existence of a perturbative anomaly in even dimensions which breaks an exact $U(1)$ symmetry of the massless theory down to $Z_4$. If we attempt to gauge this $Z_4$ symmetry we find a 't Hooft anomaly which can only be cancelled for multiples of two K\"{a}hler-Dirac fields. This result is consistent with the cancellation of a further mixed non-perturbative 't Hooft anomaly between the global $Z_4$ and a reflection symmetry. In four dimensional flat space, theories of two staggered fields yield eight Dirac or sixteen Majorana fermions in the continuum limit and this critical number of fermions agrees with results in condensed matter theory literature on the fermion content required to gap boundary fermions in $4+1$ dimensional topological superconductors. It is also consistent with constraints stemming from the cancellation of spin-$Z_4$ anomalies of Weyl fermions. Indeed, cancellation of 't Hooft anomalies is a necessary requirement for symmetric mass generation and this result gives a theoretical explanation of recent numerical work on the phase diagram of interacting staggered fermions. As an application of these ideas we construct a lattice model whose low energy continuum limit is conjectured to yield the Pati-Salam GUT theory., Comment: 8 pages. Minor edits. Version published in PRD

The thermodynamics of QCD with sufficiently heavy dynamical quarks can be described by a three-dimensional Polyakov loop effective theory, obtained after a truncated character and hopping expansion. We investigate the resulting phase diagram for low temperatures by mean field methods. Taking into account chemical potentials for both baryon number and isospin, we obtain clear signals for a liquid-gas type transition to baryon matter at $\mu_I=0$ and a Bose-Einstein condensation transition at $\mu_B=0$, as well as for their connection when both chemical potentials are non-zero., Comment: 8 pages, 3 figures

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential equations, supplemented with techniques from twisted cohomology. We derive differential equations for the variation with the coupling or -- more generally -- with the parameters of the action. Already simple examples show that the differential equation with respect to the coupling has an essential singularity at zero coupling and a regular singularity at infinite coupling. The properties of the differential equation at zero coupling can be used to prove that the perturbative series is only an asymptotic series., 6 pages, v2: version to be published

Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof of principle for simple models in two dimensions. However, further studies indicate that the training cost can be, in general, very high for large lattices. The poor scaling traits of current models indicate that moderate-size networks cannot efficiently handle the inherently multi-scale aspects of the problem, especially around critical points. We explore current models with limited acceptance rates for large lattices and examine new architectures inspired by effective field theories to improve scaling traits. We also discuss alternative ways of handling poor acceptance rates for large lattices., 10 pages, 6 figures; contribution to the 39th International Symposium on Lattice Field Theory, 2022, Bonn, Germany

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in 2+1+1 dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\rightarrow\mathrm{U}(1)\otimes \mathrm{U}(1)$ symmetry breaking; we analyse the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension $\eta_\psi\approx 3$ at the critical point, in stark contrast with the Gross-Neveu model in 3$d$ and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalisable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions., Comment: 27 + 12 pages, 13 + 6 figures; code and data available (https://doi.org/10.17638/datacat.liverpool.ac.uk/1959)

Motivated by the existence of two-body hadronic molecules composed of $\Omega\Omega$, $\Omega_{ccc}\Omega_{ccc}$ and $\Omega_{bbb}\Omega_{bbb}$ predicted by lattice QCD simulations, we employ the Gaussian expansion method to study whether three-body systems composed of $\Omega\Omega\Omega$, $\Omega_{ccc}\Omega_{ccc}\Omega_{ccc}$ and $\Omega_{bbb}\Omega_{bbb}\Omega_{bbb}$ can bind with the two-body $^1S_0$ interactions provided by lattice QCD. Our results show that none of the three-body systems binds. On the other hand, we find that supplemented with a synthetic $^5S_2$ potential, the $\Omega\Omega\Omega$ system develops a bound state, for which both the $^1S_0$ and $^5S_2$ interactions play an important role. Our predictions are further corroborated by explicit studies employing the one-boson exchange potentials constrained by the lattice QCD simulations. Our studies support the existence of the $\frac{3}{2}^+$ $\Omega\Omega\Omega$ bound state and the non-existence of the $\frac{3}{2}^+$ $\Omega_{ccc}\Omega_{ccc}\Omega_{ccc}$ and $\Omega_{bbb}\Omega_{bbb}\Omega_{bbb}$ bound states, due to the suppressed $^5S_2$ interactions in heavier systems., Comment: 5 pages, 2 figures, 4 tables

To elucidate the internal structure of exotic states is one of the central purposes of hadron physics. Motivated by this, we study the electromagnetic properties of $\bar D^{(*)}Ξ^{\prime}_c$, $\bar D^{(*)}Λ_c$, $\bar D_s^{(*)}Λ_c$ and $\bar D_s^{(*)}Ξ_c$ pentaquarks without strange, with strange and with double strange through QCD light-cone sum rules. We have also evaluated electric quadrupole and magnetic octupole moments of the $\bar D^{*}Ξ^{\prime}_c$, $\bar D^{*}Λ_c$, $\bar D_s^{*}Λ_c$ and $\bar D_s^{*}Ξ_c$ pentaquark states. The magnetic dipole moment is the leading-order response of a bound system to a soft external magnetic field. Thus, it ensures a prominent platform for examination of the internal organizations of hadrons governed by the quark-gluon dynamics of QCD. We look forward to that the present study can stimulate the interest of experimentalist in investigating the electromagnetic properties of the hidden-charmed pentaquark states., 19 pages, 3 tables and 2 figures

Using lattice QCD we extract $ππ$ scattering amplitudes with isospin--0,1,2 in low partial-waves at two values of the light quark mass corresponding to $m_π\sim 283$ and $330$ MeV. We confirm expectations of weak repulsion in isospin--2, and the presence of a narrow $ρ$ resonance in isospin--1, and study the pion mass dependence of these channels. In isospin--0 we find that the two pion masses considered straddle the point at which the $σ$ transitions from being a stable bound-state to being either a virtual bound-state or a subthreshold resonance. We discuss the ability of lattice calculations like these to precisely determine the $σ$ pole location when it is a resonance, and propose an approach in which the full complement of amplitudes computed in this paper can be used simultaneously to provide more constraint., 18 pages, 17 figures, 1 table

The lowest-lying charmonium-like tetraquarks $c\bar{c}q\bar{q}$ $(q=u,\,d)$ and $c\bar{c}s\bar{s}$, with spin-parity $J^P=0^+$, $1^+$ and $2^+$, and isospin $I=0$ and $1$, are systematically investigated within the theoretical framework of complex-scaling range for a chiral quark model that has already been successfully applied in former studies of various tetra- and penta-quark systems. A four-body $S$-wave configuration which includes meson-meson, diquark-antidiquark and K-type arrangements of quarks, along with all possible color wave functions, is comprehensively considered. Several narrow resonances are obtained in each tetraquark channel when a fully coupled-channel computation is performed. We tentatively assign theoretical states to experimentally reported charmonium-like signals such as $X(3872)$, $Z_c(3900)$, $X(3960)$, $X(4350)$, $X(4685)$ and $X(4700)$. They can be well identified as hadronic molecules; however, other exotic components which involve, for instance, hidden-color channels or diquark-antidiquark structures play a considerable role. Meanwhile, two resonances are obtained at $4.04$ GeV and $4.14$ GeV which may be compatible with experimental data in the energy interval $4.0-4.2$ GeV. Furthermore, the $X(3940)$ and $X(4630)$ may be identified as color compact tetraquark resonances. Finally, we also find few resonance states in the energy interval from $4.5$ GeV to $5.0$ GeV, which would be awaiting for discovery in future experiments., Comment: 22 pages, 10 figures, 21 tables. arXiv admin note: text overlap with arXiv:2101.04933, arXiv:2204.08556, arXiv:2109.04311

The topological $θ$-angle is central to the understanding of a plethora of phenomena in condensed matter and high-energy physics such as the strong CP problem, dynamical quantum topological phase transitions, and the confinement--deconfinement transition. Difficulties arise when probing the effects of the topological $θ$-angle using classical methods, in particular through the appearance of a sign problem in numerical simulations. Quantum simulators offer a powerful alternate venue for realizing the $θ$-angle, which has hitherto remained an outstanding challenge due to the difficulty of introducing a dynamical electric field in the experiment. Here, we report on the experimental realization of a tunable topological $θ$-angle in a Bose--Hubbard gauge-theory quantum simulator, implemented through a tilted superlattice potential that induces an effective background electric field. We demonstrate the rich physics due to this angle by the direct observation of the confinement--deconfinement transition of $(1+1)$-dimensional quantum electrodynamics. Using an atomic-precision quantum gas microscope, we distinguish between the confined and deconfined phases by monitoring the real-time evolution of particle--antiparticle pairs, which exhibit constrained (ballistic) propagation for a finite (vanishing) deviation of the $θ$-angle from $π$. Our work provides a major step forward in the realization of topological terms on modern quantum simulators, and the exploration of rich physics they have been theorized to entail., $7+7$ pages, $4+7$ figures, $1+0$ table

The correlation function of meson interpolators in $N_f=2+1+1$ lattice QCD with optimal domain-wall quarks at the physical point are studied for six temperatures in the range $ T \sim$ 190-770 MeV. The meson interpolators include a complete set of Dirac bilinears, and each for six combinations of quark flavors. In this paper, we focus on the meson correlators of $u$ and $d$ quarks, and discuss their implications for the effective restoration of $U(1)_A$ and $SU(2)_L \times SU(2)_R$ chiral symmetries, as well as the emergence of the approximate $SU(2)_{CS}$ chiral spin symmetry., Comment: 44 pages, v2: published version

In their seminal work, Lellouch and L\"uscher derived a conversion factor relating a finite-volume matrix element, calculable using numerical lattice QCD, with the infinite-volume decay amplitude for $K \to \pi \pi$. The conversion factor depends on the $\pi \pi \to \pi \pi$ scattering amplitude with the same total isospin (either zero or two) as the $\pi \pi$ decay channel. Although an infinite tower of $\pi \pi \to \pi \pi$ partial-wave components affect the conversion factor, the $S$-wave ($\ell=0$) component is expected to dominate, and only this contribution is included in the well-known Lellouch-L\"uscher factor, with other $\pi \pi \to \pi \pi$ partial-wave amplitudes formally set to zero. However, as the precision of lattice calculations increases, it may become important to assess the systematic uncertainty arising from this approximation. With this motivation, we compare the $S$-wave-only results with those truncated at the next contaminating partial wave: the $G$-wave ($\ell=4$) for zero total momentum in the finite-volume frame and the $D$-wave ($\ell=2$) otherwise. Using the general framework for $1 \overset{\mathcal J}{\to} 2$ transitions, we quantify the effect of higher partial waves for systems with zero and non-zero total momentum as well as with anti-periodic boundary conditions, presenting both generic numerical examples and results for realistic $\pi \pi$ amplitudes taken from chiral perturbation theory and dispersive analysis. We also consider the accidental degeneracy occurring in the 8$^{\text {th}}$ excited state of the zero-momentum system. This exhibits qualitatively new features at $\ell=4$, not seen in the $\ell=0$ truncation., Comment: 31 pages, 6 figures, 2 tables

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudo-scalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton., Comment: 24 pages, 19 figures

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field $ϕ(x)$ locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional $λϕ^4$ terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling $λ$. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the $λϕ^4$ QFT.

Quark confinement and dynamical chiral symmetry breaking are two of the most important emergent properties of the theory of quantum chromodynamics. We review recent results studying centre vortices in SU(3) lattice gauge theory with dynamical quarks. Through a vortex identification procedure, vortex-removed and vortex-only fields are obtained from the usual Monte Carlo generated gauge fields. Several comparisons between the untouched fields and the vortex-modified fields support the notion that centre vortices are fundamental to both confinement and dynamical chiral symmetry breaking in full QCD., Comment: 10 pages, 6 figures; Proceedings of the 39th International Symposium on Lattice Field Theory, 8-13 August 2022, Bonn, Germany

We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320 MeV. For temperatures 195 MeV

We calculate the nucleon electric dipole moment (EDM) from the $θ$ term with overlap fermions on three domain wall lattices with different sea pion masses at lattice spacing 0.11 fm. Due to the chiral symmetry conserved by the overlap fermions, we have well defined topological charge and chiral limit for the EDM. Thus, the chiral extrapolation can be carried out reliably at nonzero lattice spacings. We use three to four different partially quenched valence pion masses for each sea pion mass and find that the EDM dependence on the valence and sea pion masses behaves oppositely, which can be described by partially quenched chiral perturbation theory. With the help of the cluster decomposition error reduction (CDER) technique, we determine the neutron and proton EDM at the physical pion mass to be $d_{n}=-0.00148\left(14\right)\left(31\right)\barθ$ e$\cdot$fm and $d_{p}=0.0038\left(11\right)\left(8\right)\barθ$ e$\cdot$fm. This work is a clear demonstration of the advantages of using chiral fermions in the nucleon EDM calculation and paves the road to future precise studies of the strong $CP$ violation effects., 6 pages, 4 figures, and supplementary materials

A novel approach is introduced for obtaining precise solutions of the pairing Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite dimensions. The parameters involved in the transition phase are calibrated based on potential tetraquark candidates derived from phenomenology. Our investigation shows that the rotation and vibration transitional theory delivers a more accurate explanation for heavy tetraquarks compared to other methods utilizing the same formalism. To illustrate the concept, we compute the spectra of several tetraquarks, namely charm, bottom, bottom-charm and open charm and bottom systems, and contrast them with those of other particles., Comment: 13 pages, 4 figures, 4 Tables. Invited contribution to a Special Issue of Few Body Systems: "Emergence and Structure of Baryons -- Selected Contributions from the International Conference Baryons 2022"

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $\Lambda\sim400\;$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $\Lambda$, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to $\gamma^*\gamma^*$ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level $\gamma^*\gamma^*\to e^+e^-$ cross-section, we predict the expected lattice-QCD integrand resulting from the $\gamma^*\gamma^*\to\pi^0$ process., Comment: 29 pages, 6 figures; text matches the published version

There is growing evidence that extraordinary-log critical behavior emerges on the open surfaces of critical systems in a semi-infinite geometry. Here, using extensive Monte Carlo simulations, we observe extraordinary-log critical behavior on the plane defects of O(2) critical systems in an infinite geometry. In this extraordinary-log critical phase, the large-distance two-point correlation $G$ obeys the logarithmic finite-size scaling $G \sim ({\rm ln}L)^{-\hat{q}}$ with the linear size $L$, having the critical exponent $\hat{q}=0.29(2)$. Meanwhile, the helicity modulus $\Upsilon$ follows the scaling form $\Upsilon \sim \alpha({\rm ln}L)/L$ with the universal parameter $\alpha=0.56(3)$. The values of $\hat{q}$ and $\alpha$ do not fall into any known universality class of critical phenomena, yet they conform to the scaling relation of extraordinary-log universality. We also discuss the extension of current results to a quantum system that is experimentally accessible. These findings reshape our understanding of extraordinary-log critical phenomena., Comment: 15 pages, 7 figures

We find a simple spin Hamiltonian to describe physical states of $2+1$ dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation of the electric field representation at $j_{\rm max}=\frac{1}{2}$. The simple spin Hamiltonian only contains local products of Pauli matrices, even though Gauss's law has been completely integrated out., Comment: 16 pages, 3 figures

Using the technique of supervised neural networks (NN), we study the phase transitions of two-dimensional (2D) 6- and 8-state clock models on the square lattice. The employed NN has only one input layer, one hidden layer of 2 neurons, and one output layer. In addition, the NN is trained without any prior information about the considered models. Interestingly, despite its simple architecture, the built supervised NN not only detects both the two Berezinskii--Kosterlitz--Thouless (BKT) transitions but also determines the transition temperatures with reasonable high accuracy. It is remarkable that a NN, which has an extremely simple structure and is trained without any input from the studied models, can be employed to study topological phase transitions. The outcomes shown here as well as those previously demonstrated in the literature suggest the feasibility of constructing a universal NN that is applicable to investigate the phase transitions of many systems., Comment: 6 pages, 7 figures

We study the impact of the Glasma fields, used to describe the very early stage of heavy-ion collisions, on the transport of hard probes, namely heavy quarks and jets. We perform numerical simulations of the strong classical fields using techniques from real-time lattice gauge theory. The resulting fields are used as background for the classical transport of ensembles of particles, described by Wong's equations. For this purpose, we develop a numerical solver for the transport of the probes, based on colored particle-in-cell methods. We focus on the dynamics of heavy quarks and jets in the classical colored fields. To quantify the effect of the Glasma, we extract the momentum broadening of hard probes and evaluate the anisotropy transfer from the Glasma to the probes. Lastly, we evaluate the heavy quark $κ$ and jet $\hat{q}$ transport coefficients in the Glasma, which turn out to be large and exhibit a peak, irrespective of the particle initialization., 7 pages, 2 figures, proceedings for the 11th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2023)

The first calculation of the response of the momentum space quark propagator to center vortices in the ground state fields of QCD is presented. Center vortices are identified on 2+1-flavour dynamical gauge fields with $m_\pi \simeq 156$ MeV to obtain the vortex-removed and vortex-only quark propagator. Dynamical mass generation is found to vanish upon vortex removal, while the vortex-only field is able to generate dynamical mass. These new signatures significantly strengthen evidence that center vortices underpin both dynamical chiral symmetry breaking and quark confinement., Comment: 6 pages, 2 figures

We compute the electromagnetic mass difference for the $B$-, $D$- and $K$-mesons using QCD sum rules with double dispersion relations. For the $B$- and $D$-mesons we also compute the linear quark mass correction, whereas for the $K$ the standard soft theorems prove more powerful. The mass differences, which have not previously been computed via a double dispersion, are fully consistent with experiment, albeit with large uncertainties., Comment: pp17 plus refs and 2 figures

We propose a chiral quark model including the $\omega$ and $\rho$ meson contributions in addition to the $\pi$ and $\sigma$ meson contributions. We show that the masses of the ground state baryons such as the nucleon, $\Lambda_c$ and $\Lambda_b$ are dramatically improved in the model with the vector mesons compared with the one without them. The study of the tetraquark $T_{cc}$ is also performed in a coupled channel calculation and the resultant mass is much closer to its experimental value than the result without vector meson contribution. This approach can be applied to the future study of multi-quark systems., Comment: 6 pages, 4 figures

We consider the problem of magnetic charges in $(2+1)$ dimensions for a torus geometry in real-space, subjected to an inverted Lorentz force due to an external electric field applied normal to the surface of the torus. We compute the Hall conductivity associated with transport of these charges for the case of negligible gapless excitations and global $\mathrm{U}(1)$ charge conservation symmetry, and find it is proportional to an integer-valued topological invariant $\mathcal{Q}$, corresponding to a magnetic quantum Hall effect (MQHE). We identify a lattice model realizing this physics in the absence of an external electric field. Based on this, we identify a generalization of the MQHE to be quantized transport of magnetic skyrmions, the quantum skyrmion Hall effect (QSkHE), with a $\mathrm{U}(1)$ easy-plane anisotropy of magnetic skyrmions and effective conservation of charge associated with magnetic skyrmions yielding incompressibility, provided a hierarchy of energy scales is respected. As the lattice model may be characterized both by a total Chern number and the topological invariant $\mathcal{Q}$, we furthermore outline a possible field theory for electric charges, magnetic charges, and correlations between magnetic and electric charges approximated as composite particles, on a two-torus, to handle the scenario of intermediate-strength correlations between electric and magnetic charges modeled as composite particles. We map this problem to a generalized $(4+1)$D theory of the quantum Hall effect for the composite particles., Comment: 9 pages, 6 figures

Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The polynomials are developed from the GMRES algorithm for solving linear equations. To reduce orthogonalization expense, the highest degree polynomial is a composite or double polynomial found with a polynomial preconditioned GMRES iteration. Added to some of the Monte Carlo pieces is deflation of eigenvalues that reduces the variance. Deflation is also used for finding a reduced degree deflated polynomial. The new Multipolynomial Monte Carlo method can significantly improve the trace computation for matrices that have a difficult spectrum due to small eigenvalues.

I examine the high-energy behavior of the Ioffe-time distribution for the quark bi-local space-like separated operator using the high-energy operator product expansion. These findings have significant implications for lattice calculations, which require extrapolation for large Ioffe-time values. I perform an explicit Fourier transform for both the pseudo-PDF and quasi-PDF, and investigate their behavior within the first two leading twist contributions. I show that the quark pseudo-PDF captures the BFKL resummation (resummation of all twists) and exhibits a rising behavior for small $x_B$ values, while the quasi-PDF presents a different behavior. I demonstrate that an appropriate small-$x_B$ behavior cannot be achieved solely through DGLAP dynamics, emphasizing the importance of all-twist resummation. This study provides valuable insights into quark non-local operators' high-energy behavior and the limitations of lattice calculations in this context., Comment: 41 pages, 14 figures; results added, appendix extended, typos corrected; it matches the version published in JHEP

The magnetic and quadrupole moments of the $Z_{c}(4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ states are calculated within the QCD light-cone sum rules. To extract the magnetic and quadrupole moments of these states the compact diquark-antidiquark interpolating currents and distribution amplitudes of the on-shell photon are employed. The magnetic moments are acquired as $\mu_{Z_{c}} = 0.55 ^{+0.23}_{-0.22}~\mu_N$, $\mu_{Z^{1}_{c}}=1.11 ^{+0.27}_{-0.29}~\mu_N$, $\mu_{Z^2_{c}}=2.44 ^{+0.53}_{-0.48}~\mu_N$ for the $Z_{c}(4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ states, respectively. We see that the magnetic moment results evaluated for the $Z_{c}4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ states are large enough to be measured experimentally. We get a nonzero however small value for the quadrupole moments of $Z_c$ states indicating a nonspherical charge distribution. The comparison of any future experimental data on the magnetic and quadrupole moments of the $Z_{c}(4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ states together with the results of the present study can shed light on the nature and inner structure of these states., Comment: 12 pages, 2 tables and 1 figure

We discuss the chiral fermion in the Hamiltonian formalism of lattice gauge theory. Although the naive chiral charge operator does not commute with the Hamiltonian, the commutable one can be defined for the overlap fermion. The eigenvalues of the energy and the chiral charge can be defined simultaneously. We study how the eigenvalue spectrum reflects chiral properties of systems, such as a chiral chemical potential and the axial anomaly. We also show that the Wilson fermion is a chiral fermion in one dimension.

International audience; We present a systematic study demonstrating the impact of lattice QCD data on the extraction of generalised parton distributions (GPDs). For this purpose, we use a previously developed modelling of GPDs based on machine learning techniques fulfilling the theoretical requirements of polynomiality, a form of positivity constraint and known reduction limits. A special care is given to estimate the uncertainty stemming from the ill-posed character of the connection between GPDs and the experimental processes usually considered to constrain them, like deeply virtual Compton scattering (DVCS). Mock lattice QCD data inputs are included in a Bayesian framework to the prior model which is fitted to reproduce the most experimentally accessible information of a phenomenological model by Goloskov and Kroll. We highlight the impact of the precision, correlation and kinematic coverage of lattice data on GPD extraction at moderate $\xi$ which has only been brushed in the literature so far, paving the way for a joint extraction of GPDs.

We study the interactions between 't Hooft-Polyakov magnetic monopoles and the domain walls formed by the same order parameter within an $SU(2)$ gauge theory. We observe that the collision leads to the erasure of the magnetic monopoles, as suggested by Dvali, Liu, and Vachaspati. The domain wall represents a layer of vacuum with un-Higgsed $SU(2)$ gauge symmetry. When the monopole enters the wall, it unwinds, and the magnetic charge spreads over the wall. We perform numerical simulations of the collision process and in particular analyze the angular distribution of the emitted electromagnetic radiation. As in the previous studies, we observe that erasure always occurs. Although not forbidden by any conservation laws, the monopole never passes through the wall. This is explained by entropy suppression. The erasure phenomenon has important implications for cosmology, as it sheds a very different light on the monopole abundance in post-inflationary phase transitions and provides potentially observable imprints in the form of electromagnetic and gravitational radiation. The phenomenon also sheds light on fundamental aspects of gauge theories with coexisting phases, such as confining and Higgs phases. Additionally to the figures, the results of the numerical simulations can be found in the following video: https://youtu.be/JZaXUYikQbo, Comment: 10 pages, 10 figures, 1 video (https://youtu.be/JZaXUYikQbo)

We determine the axial, scalar and tensor isovector charges of the nucleon, sigma and cascade baryons as well as the difference between the up and down quark masses, $m_u-m_d$. We employ gauge ensembles with $N_f=2+1$ non-perturbatively improved Wilson fermions at six values of the lattice spacing in the range $a\approx (0.039 - 0.098) \,$fm, generated by the Coordinated Lattice Simulations (CLS) effort. The pion mass $M_\pi$ ranges from around $430 \, $MeV down to a near physical value of $130 \, $MeV and the linear spatial lattice extent $L$ varies from $6.5\,M_{\pi}^{-1}$ to $3.0\,M_{\pi}^{-1}$, where $L M_\pi \geq 4$ for the majority of the ensembles. This allows us to perform a controlled interpolation/extrapolation of the charges to the physical mass point in the infinite volume and continuum limit. Investigating SU(3) flavour symmetry, we find moderate symmetry breaking effects for the axial charges at the physical quark mass point, while no significant effects are found for the other charges within current uncertainties., Comment: 47 pages, 47 figures

Physical review / D 107(5), 054504 (2023). doi:10.1103/PhysRevD.107.054504, We present the first calculation of the Mellin moments of the transverse quark spin densities in the nucleon using lattice QCD simulations with physical values of the pion mass and in the continuum limit. Specifically, we use three $N_f=2+1+1$ twisted mass fermion gauge ensembles each at different lattice spacings. The densities are extracted from the unpolarized and transversity generalized form factors. The first moment of transversely polarized quarks in an unpolarized nucleon shows an interesting distortion, which can be traced back to the sharp falloff of the transversity generalized form factor $\bar{B}_{Tn0}(Q^2)$. The isovector tensor anomalous magnetic moment is determined to be $κ_T=1.051(94)$, which confirms a negative and large Boer-Mulders function, $h_1^⊥$, in the nucleon., Published by Inst., Woodbury, NY

Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through large-momentum $P^z$ expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale $P^z|1-y|$ and a pair of heavy-light Sudakov form factors at scale $P^z$. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-$x$ PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes., Comment: 53 pages, 7 figures

Following the publication of the new measurement of the anomalous magnetic moment of the muon, the discrepancy between experiment and the theory prediction from the $g-2$ theory initiative has increased to $4.2\,\sigma$. Recent lattice QCD calculations predict values for the hadronic vacuum polarization contribution that are larger than the data-driven estimates, bringing the Standard Model prediction closer to the experimental measurement. Euclidean time windows in the time-momentum representation of the hadronic vacuum polarization contribution to the muon $g-2$ can help clarify the discrepancy between the phenomenological and lattice predictions. We present our calculation of the intermediate distance window contribution using $N_\mathrm{f}=2+1$ flavors of O$(a)$ improved Wilson quarks. We employ ensembles at six lattice spacings below $0.1\,$fm and pion masses down to the physical value. We present a detailed study of the continuum limit, using two discretizations of the vector current and two independent sets of improvement coefficients. Our result at the physical point displays a tension of $3.9\,\sigma$ with a recent evaluation of the intermediate window based on the data-driven method., Comment: 10 pages, 5 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany