High Energy Physics Lattice

We calculate the low-energy constantL10in a two-representation SU(4) lattice gauge theory that is close to a composite-Higgs model. From this we obtain the contribution of the new strong sector to theSparameter. This leads to an upper bound on the vacuum misalignment parameterξwhich is similar to current estimates of this bound. Our result agrees with large-Ncscaling expectations, within large systematic uncertainties.

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-xdependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken-x) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small-xreliably. This means that very fine lattice spacing to minimize lattice artifacts at order(Pza)nwill become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements (in finer lattice units), increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning (ML) algorithms can make correlator predictions to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon andηsunpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different fit quality and systematic errors. The predictions from smaller displacementzto larger ones work better than those for momentumpdue to the higher correlation among the data.

We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, if the algorithm aimed to predict the Polyakov loop as the deconfining order parameter, it builds a trace of the gauge group matrices along a closed loop in the time direction. As a result, the neural network, trained at one unphysical value of the lattice couplingβpredicts the order parameter in the whole region of theβvalues with good precision. We thus demonstrate that the machine learning techniques may be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.

Conventional hadron interpolating fields, which utilise gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from theSU(3)×U(1)eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provides the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarisability of both the proton and neutron is calculated using this method on the323×64dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarisabilities ofβp=2.79(22)(+13−18)×10−4fm3andβn=2.06(26)(+15−20)×10−4fm3, where the numbers in parantheses describe statistical and systematic uncertainties.

We determine the magnetic susceptibility of thermal QCD matter by means of first principles lattice simulations using staggered quarks with physical masses. A novel method is employed that only requires simulations at zero background field, thereby circumventing problems related to magnetic flux quantization. After a careful continuum limit extrapolation, diamagnetic behavior (negative susceptibility) is found at low temperatures and strong paramagnetism (positive susceptibility) at high temperatures. We revisit the decomposition of the magnetic susceptibility into spin- and orbital angular momentum-related contributions. The spin term -- related to the normalization of the photon lightcone distribution amplitude at zero temperature -- is calculated non-perturbatively and extrapolated to the continuum limit. Having access to both the full magnetic susceptibility and the spin term, we calculate the orbital angular momentum contribution for the first time. The results reveal the opposite of what might be expected based on a free fermion picture. We provide a simple parametrization of the temperature- and magnetic field-dependence of the QCD equation of state that can be used in phenomenological studies.

The mass anomalous dimension is determined in SU(2) gauge theory coupled toNffermions in the adjoint representation forNf=2,3/2,1and1/2, where half-integer flavor numbers correspond to Majorana fermions. The numerical method is based on gradient flow. The results show near-conformal behavior forNf=2,3/2and1. Particular emphasis is placed onNf=2, which is relevant for a strongly interacting extension of the Standard Model and has been studied in several previous investigations. We check whether the method is able to resolve discrepancies in earlier results for this theory. Overall, the method based on the gradient flow delivers reliable results in qualitative agreement with previously known numerical data.

We studied the temporal correlation function of mesons in the pseudo-scalar channel in (2+1)-flavor QCD in the presence of external magnetic fields at zero temperature. The simulations were performed on323×96lattices using the Highly Improved Staggered Quarks (HISQ) action withmπ≈230 MeV. The strength of magnetic fields|eB|ranges from 0 to around 3.3 GeV2(∼60m2π). We found that the masses of neutral pseudo-scalar particles, e.g. neutral pion and kaon, monotonouslly decrease as the magnetic field grows and then saturate at a nonzero value. It is observed that heavier neutral pseudo-scalars are less affected by magnetic fields. Moreover, we found a non-monotonous behavior of charged pion and kaon mass in magnetic field for the first time. In the case of small magnetic field (0≤ |eB|≲0.3 GeV2 ∼6m2π) the mass of charged pseudo-scalar grows with magnetic field and can be well described by the Lowest Landau Level approximation, while for|eB|larger than 0.3 GeV2the mass starts to decrease. The possible connection between|eB|dependences of neutral pion mass and the decreasing behavior of pseudo-critical temperature in magnetic field is discussed. Due to the nonzero value of neutral pion mass our simulation indicates that the superconducting phase of QCD does not exist in the current window of magnetic field.

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the largeNlimit (withNf/N⟶0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values ofN(169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with largeNvolume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

Lattice QCD calculations of resonant meson-meson scattering amplitudes have improved significantly due to algorithmic and computational advances. However, progress in meson-nucleon scattering has been slower due to difficulties in computing the necessary correlation functions, the exponential signal-to-noise problem, and the finite-volume treatment of scattering with fermions. Nonetheless, first benchmark calculations have now been performed. The status of lattice QCD calculations of meson-nucleon scattering amplitudes is reviewed together with comments on future prospects.

In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion toO((μ/T)2), in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices withNf=2+1flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.