Search

The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in the result is needed. We present a Bayesian framework to deal with this problem and discuss first results from a closure test., Comment: 9 pages, 1 figure

The BESIII experiment at the Beijing Electron Positron collider, run as a ``hyperon factory'', recently reported the first measurement of the asymmetry parameter of the $\Lambda\to n\gamma$ decay and updated its branching fraction, which differs from the PDG average by 5.6 sigma. We highlight the impact of this new measurement on our understanding of the puzzle of weak radiative hyperon decays and pinpoint what needs to be done in the future., Comment: 5 pages, 2 figures; to appear in Science Bulletin as a Perspective

We review the study, on the lattice, of the Green-Schwarz gauge-fixed string action describing worldsheet fluctuations about the minimal surface holographically dual to the null cusp Wilson loop, useful to evaluate the cusp anomaly of N = 4 super Yang-Mills (sYM). We comment on discretization, numerical explorations and challenges for the non-perturbative study of this benchmark model of gauge-fixed worldsheet actions., Comment: Invited review to be published on European Physics Journal - Special Topics, 24 pages, 1 figure

In the past two decades, one of the most puzzling phenomena discovered in hadron physics is that a nominal hadronic state can actually correspond to two poles on the complex energy plane. This phenomenon was first noticed for the $\Lambda(1405)$, and then for $K_1(1270)$ and to a less extent for $D_0^*(2300)$. In this Letter, we show explicitly how the two-pole structures emerge from the underlying chiral dynamics describing the coupled-channel interactions between heavy matter particles and Nambu-Goldstone bosons. In particular, the fact that two poles appear between the two dominant coupled channels can be attributed to the particular form of the leading order chiral potentials of the Weinberg-Tomozawa form. Their lineshapes overlap with each other because the degeneracy of the two coupled channels is only broken by explicit chiral symmetry breaking of higher order. We predict that for light-quark~(pion) masses heavier than their physical values, the two-pole structures disappear, which can be easily verified by future lattice QCD simulations. Furthermore, we anticipate similar two-pole structures in other systems, such as the isopin $1/2$ $\bar{K}\Sigma_c-\pi\Xi'_c$ coupled channel, which await for experimental discoveries., Comment: 5 pages, 4 figures

The two gravitational form factors of the pion, $A^{\pi}(t)$ and $D^{\pi}(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\leq -t< 2~\text{GeV}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_{\pi}\approx 170~\text{MeV}$ and $N_f=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange quark contributions is presented in the $\overline{\text{MS}}$ scheme at energy scale $\mu=2~\text{GeV}$, with renormalization factors computed non-perturbatively via the RI-MOM scheme. Using monopole and (modified) $z$-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and $D$-term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for $D^{\pi}(0)$., Comment: 28 pages, 17 figures, 7 tables

For QFT on a lattice of dimension d>=3, the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo N. This fact is related to a problem from number theory about the number of ways to represent a number as a sum of $d$ squares in the ring of residue classes modulo N., 33 pages, 7 figures

The leading jet transport coefficients $\hat{q}$ or $\hat{e}_{2}$ encode transverse or longitudinal momentum broadening of a hard parton traversing a hot medium. Understanding their temperature dependence is key to appreciating the observed suppression of high-transverse momentum probes at RHIC or LHC collision energies. We present a first continuum extrapolated result of $\hat{q}$ computed on pure SU(3) lattices with non-trivial temperature dependence different from the weak-coupling expectation. We discuss our formalism and its challenges and status in view of obtaining $\hat{e}_{2}$ or of unquenching the calculation. We consider a hard quark subject to a single scattering on the plasma. The transport coefficients are factorized in terms of matrix elements given as integrals of non-local gauge-covariant gluon field-strength field-strength correlators. After the analytic continuation to the deep-Euclidean region, the hard scale permits to recast these as a series of local, gauge-invariant operators. The renormalized leading-twist term in this expansion is closely related to static quantities, and is computed on pure SU(3) lattices ($N_τ=4,~6,~8,$ and $10$) for a wide range of temperatures, ranging from 200MeV < T < 1GeV. Our estimate for the unquenched result in $2+1$-flavor QCD has very similar features., 6 pages, 1 figure, HardProbes2023, 26-31 March 2023, Aschaffenburg, Germany

Electromagnetic dipole polarizabilities are fundamental properties of a hadron that represent its resistance to deformation under external fields. For a charged hadron, the presence of acceleration and Landau levels complicates the isolation of its deformation energy in the conventional background field method. In this work, we explore a general method based on four-point functions in lattice QCD that takes into account all photon, quark and gluon interactions. The electric polarizability ($\alpha_E$) has been determined from the method in a previous proof-of-principle simulation. Here we focus on the magnetic polarizability ($\beta_M$) using the same quenched Wilson action on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV. The results from the connected diagrams show a large cancellation between the elastic and inelastic contributions, leading to a relatively small and negative value for $\beta_M$ consistent with chiral perturbation theory. We also discuss the mechanism for $\alpha_E+\beta_M$ from combining the two studies., Comment: 11 pages, 8 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2301.05200

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, $T_c \sim 270$ MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, $\lesssim 1$ GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or $\pm 2\pi/3$ sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an "order parameter" for the confined-deconfined phase transition.

The structure of hadrons relevant for deep-inelastic scattering are completely characterised by the Compton amplitude. A direct calculation of the Compton amplitude in a lattice QCD setup provides a way to accessing the structure functions, circumventing the operator mixing and renormalisation issues of the standard operator product expansion approach. In this contribution, we focus on the QCDSF/UKQCD Collaboration's advances in calculating the forward Compton amplitude via an implementation of the second-order Feynman-Hellmann theorem. We highlight our progress in investigating the moments of nucleon structure functions., Presented at DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related Subjects, Michigan State University, USA, 27-31 March 2023. arXiv admin note: substantial text overlap with arXiv:2212.09197, arXiv:2110.01310

The path integral formulation of quantum mechanical problems including fermions is often affected by a severe numerical sign problem. We show how such a sign problem can be alleviated by a judiciously chosen constant imaginary offset to the path integral. Such integration contour deformations introduce no additional computational cost to the Hybrid Monte Carlo algorithm, while its effective sample size is greatly increased. This makes otherwise unviable simulations efficient for a wide range of parameters. Applying our method to the Hubbard model, we find that the sign problem is significantly reduced. Furthermore, we prove that it vanishes completely for large chemical potentials, a regime where the sign problem is expected to be particularly severe without imaginary offsets. In addition to a numerical analysis of such optimized contour shifts, we analytically compute the shifts corresponding to the leading and next-to-leading order corrections to the action. We find that such simple approximations, free of significant computational cost, suffice in many cases.

We present the key results from the first study of the $x$-dependent nucleon gluon distribution from lattice QCD extrapolated to the physical-continuum limit. We use ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration with clover fermions for the valence action on three different lattice spacings and three different pion masses. We took up to $O(10^6)$ measurements of two-point correlators, obtaining good signal at boost momenta up to 3~GeV. We extrapolated the reduced pseudo-ITD matrix elements to the physical-continuum limit before extracting $xg(x)/\langle x \rangle_g$. Then using the gluon momentum fraction $\langle x \rangle_g$ calculated on the same configurations, we determine the unpolarized nucleon gluon PDF $xg(x)$ and compare results with other lattice and selected global fits., 10 pages, 3 figures, DIS2023 conference proceedings, based on full paper: arXiv:2210.09985

We study the $3$-component $\phi^4$ model on the simple cubic lattice in presence of a cubic perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. First we identify the line of slow flow. The analysis of the RG-flow on this line provides us with the accurate estimate $Y_4 - \omega_2 =0.00081(7)$ for the difference of the RG-eigenvalue $Y_4$ at the $O(3)$-invariant fixed point and the correction exponent $\omega_2$ at the cubic fixed point. Field theory predicts that depending on the sign of the cubic perturbation, the RG-flow is attracted by the cubic fixed point, or runs to an ever increasing amplitude, indicating a fluctuation induced first order phase transition. We demonstrate directly the first order nature of the phase transition for a sufficiently strong breaking of the $O(3)$ symmetry. We obtain accurate results for the latent heat, the correlation length in the disordered phase at the transition temperature and the interface tension for interfaces between one of the ordered phases and the disordered phase. We study how these quantities scale with the RG-flow, allowing quantitative predictions for weaker breaking of the $O(3)$ symmetry., Comment: 34 pages, 6 Figures

We investigate the finite-temperature quantum chromodynamics (QCD) on a rotating lattice with $N_f=2+1$ staggered fermions and the projective plane boundary condition. We observe a negative rotational rigidity (defined in the main text) and a negative quark spin susceptibility associated with the chiral vortical effect. In contrast to most of the effective model predictions, we find that the chiral condensate decreases and the Polyakov loop increases with imaginary rotation, implying a rotational catalysis of chiral symmetry breaking and confinement by real rotation. We determine the phase boundaries for both chiral and confinement-deconfinement phase transitions on the $\Omega_I$-$T$ plane, where $\Omega_I$ is the imaginary angular velocity., Comment: 17 pages, 7 figures

At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. Here, we demonstrate that for a relevant set of parameters considered, Metadynamics can be used to reduce the autocorrelation times of topological quantities in 4-dimensional SU(3) gauge theory by at least two orders of magnitude compared to conventional update algorithms. However, compared to local update algorithms and the Hybrid Monte Carlo algorithm, the computational overhead is significant, and the required reweighting procedure may considerably reduce the effective sample size. To deal with the latter problem, we propose modifications to the Metadynamics bias potential and the combination of Metadynamics with parallel tempering. We test the new algorithm in 4-dimensional SU(3) gauge theory and find, that it can achieve topological unfreezing without compromising the effective sample size. Preliminary scaling tests in 2-dimensional U(1) gauge theory show these modifications lead to improvements of more than an order of magnitude compared to standard Metadynamics, and an improved scaling of autocorrelation times with the lattice spacing compared to standard update algorithms., 20 pages, 12 figures, 7 tables

Gapped fermion theories with gapless boundary fermions can exist in any number of dimensions. When the boundary has even space-time dimensions and hosts chiral fermions, a quantum Hall current flows from the bulk to the boundary in a background electric field. This current compensate for the boundary chiral anomaly. Such a current inflow picture is absent when the boundary theory is odd dimensional. However, in recent work, the idea of quantum Hall current has been generalized to describe odd dimensional boundary theories in continuous Euclidean space-time dimension of infinite volume. In this paper we extend this idea to a lattice regulated finite volume theory of 1+1 dimensional Wilson-Dirac fermions. This fermion theory with a domain wall in fermion mass can host gapless modes on the wall. The number of gapless fermions is equal to the integral of the divergence of the lattice generalized Hall current.

We revisit the simplest Bars-Yankielowicz (BY) model (the $\psi\eta$ model), starting from a model with an additional Dirac pair of fermions in the fundamental representation, together with a complex color-singlet scalar $\phi$ coupled to them through a Yukawa interaction. This model possesses a color-flavor-locked 1-form ${\mathbbm Z}_N$ symmetry, due to the intersection of the color $SU(N)$ and two nonanomalous $U(1)$ groups. In the bulk, the model reduces to the $\psi\eta$ model studied earlier when $\phi$ acquires a nonzero vacuum expectation value and the extra fermions pair up, get massive and decouple (thus we will call our extended theory as the ``X-ray model"), while it provides a regularization of the $\mathbbm Z_2$ fluxes needed to study the $\mathbbm Z_2$ anomaly. The anomalies involving the 1-form ${\mathbbm Z}_N$ symmetry reduce, for $N$ even, exactly to the mixed ${\mathbbm Z}_2$ anomaly found earlier in the $\psi\eta$ model. The present work is a first significant step to clarify the meaning of the mixed ${\mathbbm Z}_2-[{\mathbbm Z}_N^{(1)}]^2$ anomaly found in the $\psi\eta$ and in other BY and Georgi-Glashow type $SU(N)$ models with even $N$., Comment: 26 pages

We describe the picture of physical processes suggested by Edward Nelson's stochastic mechanics when generalized to quantum field theory, after an introductory review of his theory applied to the hydrogen atom. By performing numerical simulations of the relevant stochastic processes, we observe that Nelson's theory provides an intuitive account of how particles can arise from an underlying field ``beable'' -- to use a phrase of John S. Bell -- in the case of free field theory, regularized on a lattice. We then argue that this picture looks qualitatively similar when generalized to interacting scalar field theory. Lastly, we compare the Nelsonian framework to various other proposed ontologies for QFT, and remark upon their relative merits in light of the effective field theory paradigm.

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^+e^-\to\text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the $e^+e^-\to3\pi$ channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and $e^+e^-$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations., Comment: 7 pages, 2 figures

We present the results of a survey meant to assess the opinion of the high-energy physics theory (HET) community on the January 7th postdoc acceptance deadline - specifically, whether there is a preference to shift the deadline to later in January or February. This survey, which served for information-gathering purpose only, is part of a community conversation on the optimal timing of an acceptance deadline and whether the community would be better served by a later date. In addition, we present an analysis of data from the postdoc Rumor Mill, which gives a picture of the current hiring landscape in the field. We emphasize the importance of preserving a universal deadline, and the current results of our survey show broad support for a shift to a later date. A link to the survey, frequently asked questions, a running list of supporters, and next steps can be found on our companion web page., 13 pages, 8 figures and 2 tables webpage: https://het-postdoc-accord.github.io/information/

Effective String Theory (EST) represents a powerful non-perturbative approach to describe confinement in Yang-Mills theory that models the confining flux tube as a thin vibrating string. EST calculations are usually performed using the zeta-function regularization: however there are situations (for instance the study of the shape of the flux tube or of the higher order corrections beyond the Nambu-Goto EST) which involve observables that are too complex to be addressed in this way. In this paper we propose a numerical approach based on recent advances in machine learning methods to circumvent this problem. Using as a laboratory the Nambu-Goto string, we show that by using a new class of deep generative models called Continuous Normalizing Flows it is possible to obtain reliable numerical estimates of EST predictions., 1+28 pages, 11 figures

We investigate the mechanics of the proton by examining the flavor-decomposed proton cosmological constants and generalized vector form factors. The interplay of up, down, and strange quarks within the proton is explored, shedding light on its internal structure. The contributions of strange quarks play a crucial role in the $D$-term and cosmological constants. We find that the flavor blindness of the isovector $D$-term form factor is only valid in flavor SU(3) symmetry., 6 pages, 2 figures

We apply dilaton chiral perturbation theory (dChPT) at next-to-leading order to lattice data from the LatKMI collaboration for the eight-flavor SU(3) gauge theory. In previous work, we found that leading-order dChPT does not account for these data, but that a model extension of leading-order dChPT with a varying mass anomalous dimension describes these data well. Here we calculate the next-to-leading order corrections for the pion mass and decay constant. We focus on these quantities, as data for the dilaton mass are of poorer quality. The application of next-to-leading order dChPT is difficult because of the large number of new low-energy constants, and the the results of our fits turn out to be inconclusive. They suggest -- yet cannot firmly establish -- that the LatKMI mass range might be outside the scope of dChPT., RevTex, 28 pages

Assuming that the $P_c(4312)^+$ is a $I(J^P)=\frac12(\frac32^-)$ compact pentaquark, we study the mass spectrum of its S-wave hidden-charm partner states in a color-magnetic interaction model. Combining the information from their decays obtained in a simple rearrangement scheme, one finds that the quantum numbers of $P_c(4457)^+$, $ P_c(4440)^+$, and $P_c(4337)^+$ can be assigned to be $I(J^P)=\frac12(\frac32^-)$, $\frac12(\frac12^-)$, and $\frac12(\frac12^-)$, respectively, while both $P_{cs}(4338)^0$ and $P_{cs}(4459)^0$ can be interpreted as $I(J^P)=0(\frac12^-)$ $udsc\bar{c}$ compact states. Based on the numerical results, we also find narrow pentaquarks in $ssnc\bar{c}$ ($n=u,d$) and $sssc\bar{c}$ systems. The decay properties of the studied pentaquarks and the searching channels for them can be tested in future experiments., 16 pages, 14 tables, 4 figures

Weak radiative hyperon decays, important to test the strong interaction and relevant in searches for beyond the standard model physics, have remained puzzling both experimentally and theoretically for a long time. The recently updated branching fraction and first measurement of the asymmetry parameter of $\Lambda\to n\gamma$ by the BESIII Collaboration further exacerbate the issue, as none of the existing predictions can describe the data. We show in this letter that the covariant baryon chiral perturbation theory, with constraints from the latest measurements of hyperon non-leptonic decays, can well describe the BESIII data. The predicted branching fraction and asymmetry parameter for $\Xi^-\to\Sigma^-\gamma$ are also in agreement with the experimental data. We note that a more precise measurement of the asymmetry parameter, which is related with that of $\Sigma^+\to p\gamma$, is crucial to test Hara's theorem. We further predict the branching fraction and asymmetry parameter of $\Sigma^0\to n\gamma$, whose future measurement can serve as a highly nontrivial check on our understanding of weak radiative hyperon decay and on the covariant baryon chiral perturbation theory., Comment: 11 pages, 4 figures

The theory of the strong force, quantum chromodynamics, describes the proton in terms of quarks and gluons. The proton is a state of two up quarks and one down quark bound by gluons, but quantum theory predicts that in addition there is an infinite number of quark-antiquark pairs. Both light and heavy quarks, whose mass is respectively smaller or bigger than the mass of the proton, are revealed inside the proton in high-energy collisions. However, it is unclear whether heavy quarks also exist as a part of the proton wavefunction, which is determined by non-perturbative dynamics and accordingly unknown: so-called intrinsic heavy quarks. It has been argued for a long time that the proton could have a sizable intrinsic component of the lightest heavy quark, the charm quark. Innumerable efforts to establish intrinsic charm in the proton have remained inconclusive. Here we provide evidence for intrinsic charm by exploiting a high-precision determination of the quark-gluon content of the nucleon based on machine learning and a large experimental dataset. We disentangle the intrinsic charm component from charm-anticharm pairs arising from high-energy radiation. We establish the existence of intrinsic charm at the 3-standard-deviation level, with a momentum distribution in remarkable agreement with model predictions. We confirm these findings by comparing to very recent data on Z-boson production with charm jets from the LHCb experiment., Comment: 10 pages, 4 figures + Supplementary Information, published version available in https://www.nature.com/articles/s41586-022-04998-2. v2: updated comparison with the MBC model in Fig. 1 right (thanks to Tim Hobbs for the suggestion)

In this work, we study probing for the more general problem of computing the trace of a permutation of $A^{-1}$, say $PA^{-1}$. The motivation comes from Lattice QCD where we need to construct "disconnected diagrams" to extract flavor-separated Generalized Parton functions. In Lattice QCD, where the matrix has a 4D toroidal lattice structure, these non-local operators correspond to a $PA^{-1}$ where $P$ is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement ($p$) but our methods are general. We show that probing on $A^k$ or $(PA)^k$ do not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on $PA^k$ using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed, and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world Lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics is encoded in a one-dimensional Bose--Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigate global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string-breaking, and paves the way for simulating more complex higher-dimensional gauge theories on quantum synthetic matter devices., Accepted version, 6+6 pages, 4+5 figures

The Landau-gauge quark propagator is calculated using overlap fermions on 2+1-flavour dynamical fermion gauge fields from the PACS-CS collaboration with pion mass $m_\pi \sim 156\text{ MeV}$ and spatial volume $\sim (3 \text{ fm})^3.$ The observed features of the mass and renormalisation functions are discussed, including a comparison with recent results using $\mathcal{O}(a)$-improved Wilson fermions on 2-flavour dynamical gauge fields., Comment: 8 pages, 4 figures

Pulsar Timing Arrays (PTAs) have reported evidence for a stochastic gravitational wave (GW) background at nHz frequencies, possibly originating in the early Universe. We show that the spectral shape of the low-frequency (causality) tail of GW signals sourced at temperatures around $T\gtrsim 1$ GeV is distinctively affected by confinement of strong interactions (QCD), due to the corresponding sharp decrease in the number of relativistic species. Bayesian analyses in the NANOGrav 15 years and the previous International PTA datasets reveal a significant improvement in the fit with respect to cubic power-law spectra, previously employed for the causality tail. This suggests that the inclusion of Standard Model effects on GWs can have a potentially decisive impact on model selection., 5+11 pages, 7 figures. v2: Analysis with NANOGrav 15 yrs added, minor corresponding changes in abstract and text, references added

We present a detailed exploration of certain outstanding features of the transversely-projected three-gluon vertex, using the corresponding Schwinger-Dyson equation in conjunction with key results obtained from quenched lattice simulations. The main goal of this study is the scrutiny of the approximate property denominated ``planar degeneracy'', unveiled when the Bose symmetry of the vertex is properly exploited. The planar degeneracy leads to a particularly simple parametrization of the vertex, reducing its kinematic dependence to essentially a single variable. Our analysis, carried out in the absence of dynamical quarks, reveals that the planar degeneracy is particularly accurate for the description of the form factor associated with the classical tensor, for a wide array of arbitrary kinematic configurations. Instead, the remaining three form factors display considerable violations of this property. In addition, and in close connection with the previous point, we demonstrate the numerical dominance of the classical form factor over all others, except in the vicinity of the soft-gluon kinematics. The final upshot of these considerations is the emergence of a very compact description for the three-gluon vertex in general kinematics, which may simplify significantly nonperturbative applications involving this vertex., 39 pages, 10 figures

We present the first data-driven result for $a_\mu^{\rm win,lqc}$, the isospin-limit light-quark connected component of the intermediate-window Hadronic-Vacuum-Polarization contribution to the muon anomalous magnetic moment. Our result, $(198.8\pm 1.1)\times 10^{-10}$, is in significant tension with eight recent mutually compatible high-precision lattice-QCD determinations, and provides enhanced evidence for a puzzling discrepancy between lattice and data-driven determinations of the intermediate window quantity, one driven largely by a difference in the light-quark connected component., Comment: 6 pages, 1 figure

Using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor and the value of gluon condensate $$ from heavy quarkonia, we extract the value of the four-quark condensate : $\rho\alpha_s^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and the dimension eight condensate: $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $\alpha_s^4$. We show the inconsistency in using at the same time the standard SVZ value of the gluon and the vacuum saturation of the four-quark condensates. Using the previous values of the four-quark and $d_8$ condensates, we re-extract $$ from ${\cal R}_{10}$ to be: $(6.12\pm 0.61)\times 10^{-2}$ Gev$^4$ in perfect agreement with the one from heavy quarkonia. We also use the lowest $\tau$-like decay moment ${\cal R}_\tau^{ee}$ to extract the value of the QCD coupling $\alpha_s(M^2_\tau)$=0.3385(145)[resp. 0.3262(86)] (mean of fixed order (FO) and Contour Improved (CI) PT series) to order $\alpha_s^4$ [resp. $\alpha_s^5$] and the standard OPE. The corresponding value of the sum of the non-perturbative contribution is: $\delta_{NP}(M_\tau)=(3.74\pm 0.40)\times 10^{-2}$. Reciprocally, using $\alpha_s(M_\tau)$, $$ and $d_8$ as inputs, we test the stability of the value of the four-quark condensate obtained from the lowest $\tau$-like moment. We complete our analysis by updating our previous determinations of the lowest order hadronic vacuum polarization contributions to the lepton anomalies and to $\alpha(M^2_Z)$. We obtain in Table 2 : $a_\mu\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11}, a_\tau\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $. and $\alpha(M^2_Z)=(2766.3\pm 4.5)\times 10^{-5}$. This new value of $a_\mu$ leads to: $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (142\pm 42_{th}\pm 41_{exp})\times 10^{-11}$., Comment: Latex files, 37 pages, 19 figures, 3 Tables. Inclusion of PT a_s^4 term for the determination of the QCD condensates. Some references added. Complementary discussions on the determination of \alpha_s from $\tau$-like decay and on the muon anomaly. Revised version submitted for publication to the journal

We propose a new method to calculate parton distribution functions (PDFs) from correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used quasi-PDFs defined from gauge-invariant Wilson-line operators, such correlations offer advantages including accessibility to larger off-axis momenta, absence of linear power divergence, and enhanced long-range precision. We verify the validity of this method at next-to-leading order in perturbation theory and use it to calculate the pion valence quark PDF on a lattice with spacing $a=0.06$ fm and valence pion mass $m_\pi=300$ MeV. Our result agrees with that from the gauge-invariant quasi-PDF at similar precision, achieved with only half the computational cost through a large off-axis momentum $|\vec{p}|\sim2.2$ GeV. This opens the door to a more efficient way to calculate parton physics on the lattice., Comment: 5 pages, 4 figures, and the appendix

By extracting the transition amplitudes, we give the first lattice QCD prediction of the two-body decay partial widths of the $1^{-+}$ charmoniumlike hybrid $\eta_{c1}$. Given the calculated mass value $m_{\eta_{c1}}=4.329(36)$ GeV, the $\eta_{c1}$ decay is dominated by the open charm modes $D_1\bar{D}$, $D^*\bar{D}$ and $D^*\bar{D}^*$ with partial widths of $258(133)$ MeV, $88(18)$ MeV and $150(118)$ MeV, respectively. The coupling of $\eta_{c1}$ to $\chi_{c1}$ plus a flavor singlet pseudoscalar is not small, but $\chi_{c1}\eta$ decay is suppressed by the small $\eta-\eta'$ mixing angle. The partial width of $\eta_{c1}\to \eta_c\eta'$ is estimated to be around 1 MeV. We suggest experiments to search for $\eta_{c1}$ in the $P$-wave $D^*\bar{D}$ and $D^*\bar{D}^*$ systems. Especially, the polarization of $D^*\bar{D}^*$ can be used to distinguish the $1^{-+}$ product (total spin $S=1$) from $1^{--}$ products ($S=0$)., Comment: 16 pages, 8 figures

The free scalar field is only conformally invariant when non-minimally coupled to gravity. In flat space this amounts to amending, or improving, the energy momentum tensor. A no-go theorem prohibits the improvement for Goldstone bosons, originating from global internal spontaneous symmetry breaking. It is shown that the no-go theorem can be circumvented in the presence of a dilaton. The latter is a (pseudo) Goldstone boson originating from spontaneous conformal symmetry breaking in a theory with an infrared fixed point. Specifically, the tracelessness of the energy momentum tensor is demonstrated for a generic $d$-dimensional curved space. Additionally, the Goldstone gravitational form factors are shown to obey conformality constraints in the soft limit. The crucial point is that the remainder term of the soft theorem is non-zero due to the presence of the dilaton pole. For Goldstone systems with a trivial infrared fixed point the leading order analysis of this paper ought to be sufficient. Loop effects govern the improvement term outside the fixed point and are scheme-dependent as briefly discussed towards the end of the paper., 14 pages + refs, 1 figure

Non-perturbative results in QCD-like theories can be derived employing positivity of the Euclidean path integral measure, as pioneered by Weingarten, Vafa, Witten. We show that positivity of the measure can be generalized to parity-invariant theories with Yukawa couplings to fundamental scalars, provided the fermions are Dirac and carry a real representation of the gauge group. This result allows us to extend the proof of parity and vector-like flavor symmetries conservation to such theories, as well as to derive exact inequalities among hadrons' masses., 20 pages plus appendix

Physics letters / B 829, 137069 (2022). doi:10.1016/j.physletb.2022.137069, We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with O($a$)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height M$_5$=1+O(g$_0^2$) have the same, approximate, form of the asymptotic cutoff effects: Ka$^2$[$\bar{g}^2$(a$^{−1}$)]$^{0.760}$. A domain wall height M$_5$=1.8, as often used, introduces large mass-dependent K′(m)a$^2$[$\bar{g}^2$(a$^{−1}$)]$^{0.518}$ effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents $\hat{\Gamma}$ of $\bar{g}^2$(a$^{−1}$) but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level O(a$^2$) improvement, which is easy to do [2], should be used in the future – both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases., Published by North-Holland Publ., Amsterdam

Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong inductive bias for the probability distribution described by a machine learning model. However, imposing symmetry on the model sometimes occur a poor acceptance rate in self-learning Monte-Carlo (SLMC). We introduce symmetry equivariant attention to SLMC, which can be systematically improvable. To evaluate our architecture, we apply it to our proposed new architecture on a spin-fermion model (i.e. double exchange model) on a two-dimensional lattice. We find that it overcomes poor acceptance rates of linear models and observe similar scaling law as in large language models, model quality monotonically increased as layers increased., 10 pates, 6 figures

We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale dependence of the finite order perturbative series for the renormalization group (RG) invariant quantities such as spectral function, the second derivative of the polarization function of the pseudoscalar current correlator, and its Borel transformation. In addition, the convergence of the spectral function is significantly improved by summing all running logarithms and kinematical $\pi^2$-terms. Using RGSPT, we find $m_s(2 GeV)=104.34_{-4.21}^{+4.23}\hs\MeV$, and $m_d(2 GeV)=4.21_{-0.45}^{+0.48}\hs\MeV$ leading to $m_u(2 GeV)=2.00_{-0.40}^{+0.33}\hs\MeV$., Comment: 17 pages and 8 figures. Figures updated, new references added, and minor text corrections

Analytic continuation of the perturbative series from spacelike to timelike regions is performed using renormalization group summed perturbation theory (RGSPT). This method provides an all-order summation of kinematic ``$\pi^2$-terms'' accessible from a given order of a perturbative series. The impact of the summation of these terms is studied for Higgs boson decay and electromagnetic R-ratio in the perturbative QCD. Results obtained using RGSPT have improved convergence behavior in addition to significantly reduced renormalization scale dependence compared to fixed-order perturbation theory (FOPT). The higher-order behavior using the Pad\'e approximant is also studied for processes considered., Comment: 25 pages and 10 figures. References added, figures are updated, and minor text corrections

We demonstrate the quantum mean estimation algorithm on Euclidean lattice field theories. This shows a quadratic advantage over Monte Carlo methods which persists even in presence of a sign problem, and is insensitive to critical slowing down. The algorithm is used to compute $\pi$ with and without a sign problem, a toy U(1) gauge theory model, and the Ising model. The effect of $R_{Z}$-gate synthesis errors on a future fault-tolerant quantum computer is investigated., Comment: 14 pages, 18 figures

We formulate $U(1)_k$ Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization, framing, the discrete 1-form symmetry and its 't Hooft anomaly, as well as the electric charge of monopole operators are manifest in our construction. The key technical ingredient is the cup product and its higher generalizations on the (hyper-)cubic lattice, which recently appeared in the literature. All unframed Wilson loops are projected out by a peculiar subsystem symmetry, leaving topological, ribbon-like Wilson loops which have the correct correlation functions and topological spins expected from the continuum theory. Our action can be obtained from a new definition of the theta term in four dimensions which improves upon previous constructions within the modified Villain approach. This bulk action coupled to background fields for the 1-form symmetry is given by the Pontryagin square, which provides anomaly inflow directly on the lattice., 14 pages plus 2 appendices, 14 figures. v2 matches published version

The shear viscosity of strongly interacting dense heavy-quarks plasma is evaluated analytically using a methodology valid for strongly-correlated nonequilibrium dense matter. The shear viscosity turns out to be directly proportional to the zero-frequency limit of the spectral function. By evaluating the latter using lattice QCD data from the literature, the vanishing of interaction-dominated viscosity contribution of heavy quarks to the QGP plasma is demonstrated., arXiv admin note: substantial text overlap with arXiv:2306.05771

We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup. The weakly-coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying SO(5) quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication, focused only on the SO(5) singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone Bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field theory side. But we also find a qualitatively new, unexpected result. When the dimension of the field-theory operator inducing SO(5) breaking is close to half of the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context., 26 pages, 6 figures; Version accepted for publication

We delve deeper into the potential composition of dark matter as stable scalar glueballs from a confining dark $SU(N)$ gauge theory, focusing on $N=\{3,4,5\}$. To predict the relic abundance of glueballs for the various gauge groups and scenarios of thermalization of the dark gluon gas, we employ a thermal effective theory that accounts for the strong-coupling dynamics in agreement with lattice simulations. We compare our methodology with previous works and find that our approach is more comprehensive and reliable. The results are encouraging and show that glueballs can account for the totality of dark matter in many unconstrained scenarios with a phase transition scale $20~{\rm MeV}\lesssim\Lambda\lesssim10^{10}~{\rm GeV}$, thus opening the possibility of exciting future studies., Comment: 12 pages, 6 figures; update and generalization of arXiv:2207.13716

This is the second of two companion papers in which we continue to develop the construction of the doubly heavy pentaquark systems using the gauge/string duality. In this paper, we propose a stringy description of the $Q\bar Qqqq$ system in the case of two light flavors. Our goal is to explore the lower-lying Born-Oppenheimer potentials as a function of the separation distance between the heavy quark-antiquark pair. The analysis shows that the ground state Born-Oppenheimer potential is described in terms of both hadro-quarkonia and hadronic molecules. Meanwhile a standard pentaquark configuration, which describes a genuine five-quark interaction, makes the dominant contribution to a higher lying potential. This configuration has an antiquark-diquark-diquark structure $\bar Q[qq][Qq]$ for separations larger than $0.1\,\text{fm}$. The latter enables us to establish a relation among the masses of hadrons in the heavy quark limit. To describe the structure of the potentials more clear, we define some critical separations that are related to the processes of string reconnection, breaking and junction annihilation. Additionally, we consider the generalized baryon vertices, where more than three strings can meet, and explore their implications for the pentaquark systems., 29 pages, many figures. arXiv admin note: text overlap with arXiv:2211.12305; v2: minor corrections

We present a detailed study of the finite momentum dynamics of the $O(4)$ critical point of QCD, which lies in the dynamic universality class of Model G. The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent $\zeta = 3/2$ of Model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved $O(4)$ charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with $\zeta=3/2$. We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other non-universal amplitudes also reported here) compile all relevant information for further studies of Model G both in and out of equilibrium., Comment: 34 pages, 13 figures

We compute the spectrum of the low-lying mesonic states with vector, scalar and pseudoscalar quantum numbers in QCD with one flavour. With three colours the fundamental and the two-index anti-symmetric representations of the gauge group coincide. The latter is an orientifold theory that maps into the bosonic sector of $\mathcal{N} = 1$ super Yang-Mills theory in the large number of colours limit. We employ Wilson fermions along with tree-level improvement in the gluonic and fermionic parts of the action. In this setup the Dirac operator can develop real negative eigenvalues. We therefore perform a detailed study in order to identify configurations where the fermion determinant is negative and eventually reweight them. We finally compare results with effective field theory predictions valid in the large $N_C$ limit and find reasonably consistent values despite $N_C$ being only three. Additionally,the spin-one sector provides a novel window for supersymmetric dynamics., Version accepted and published by PRD (Phys. Rev. D 107, 114506)

We describe a procedure for alleviating the fermion sign problem in which phase fluctuations are explicitly subtracted from the Boltzmann factor. Several ans\"atze for fluctuations are designed and compared. In the absence of a sufficiently high-quality ansatz, a neural network can be trained to parameterize the fluctuations. Demonstrating on the staggered Thirring model in $1+1$ dimensions, we examine the performance of this method as deeper neural networks are used, and in conjunction with the well-studied contour deformation methods., Comment: 10 pages, 5 figures