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We present a lattice QCD calculation of the unpolarized isovector quark parton distribution function (PDF) of the proton utilizing a perturbative matching at next-to-next-to-leading-order (NNLO). The calculations are carried out using a single ensemble of gauge configurations generated with $N_f = 2 + 1$ highly-improved staggered quarks with physical masses and a lattice spacing of $a = 0.076$ fm. We use one iteration of hypercubic smearing on these gauge configurations, and the resulting smeared configurations are then used for all aspects of the subsequent calculation. For the valence quarks, we use the Wilson-clover action with physical quark masses. We consider several methods for extracting information on the PDF. We first extract the lowest four Mellin moments using the leading-twist operator product expansion approximation. Then, we determine the $x$ dependence of the PDF through a deep neural network within the pseudo-PDF approach and additionally through the framework of large-momentum effective theory utilizing a hybrid renormalization scheme. This is the first application of the NNLO matching coefficients for the nucleon directly at the physical point., 20 pages, 17 figures, and 3 tables; version accepted for publication in PRD

This paper explores the effects of system frequency on electromagnetic (EM) remote sensing of atmospheric refractivity. A frequency range of 2-40 GHz covering S to Ka bands is analyzed. A multi-frequency inversion algorithm is developed to estimate the evaporation duct heights using a parabolic wave equation propagation model. The capabilities of a theoretical multi-frequency system are explored for high and low signal to noise ratios for varying numbers of frequencies and bands. Experimental data were collected using the Lower Atmospheric Propagation Ultra-Wide Band (LATPROP-UWB) system deployed during the Coupled Air-Sea Processes and EM Ducting Research (CASPER) East Campaign. Range-dependent propagation loss measurements at 53 frequencies ranging from 2 to 40 GHz were made. The evaporation duct refractivity profiles estimated from the multi-frequency LATPROP-UWB data were compared to the profiles inferred from the concurrent meteorological and oceanographic measurements. Inversion results show that the optimal refractivity retrieval can be achieved using 10 frequencies and results in a fourfold reduction in the estimation RMSE compared to a single-frequency inversion.

It is often taken for granted that Generalized Parton Distributions (GPDs) are defined in the "symmetric" frame, where the transferred momentum is symmetrically distributed between the incoming/outgoing hadrons. However, such frames pose computational challenges for the lattice QCD practitioners. In these proceedings, we lay the foundation for lattice QCD calculations of GPDs in "asymmetric" frames, where the transferred momentum is not symmetrically distributed between the incoming/outgoing hadrons. The novelty of our work relies on the parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which not only helps in establishing relations between the said frames but also helps in isolating higher-twist contaminations. As an example, we focus on the unpolarized GPDs for spin-1/2 particles., Comment: 10 pages, 1 figure, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

We present lattice QCD calculations of valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching. Our calculations are based on three gauge ensembles of 2+1 flavor highly improved staggered quarks and Wilson--Clover valance quarks, corresponding to pion mass $m_\pi=140$~MeV at a lattice spacing $a=0.076$~fm and $m_\pi=300$~MeV at $a=0.04, 0.06$~fm. This enables us to present, for the first time, continuum-extrapolated lattice QCD results for NNLO valence PDF of the pion at the physical point. Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bi-local pion matrix elements with NNLO Wilson coefficients we extract $2^{\mathrm{nd}}$, $4^{\mathrm{th}}$ and $6^{\mathrm{th}}$ Mellin moments of the PDF. We reconstruct the Bjorken-$x$ dependence of the NNLO PDF from real-space RGI ratios using a deep neural network (DNN) as well as from momentum-space matrix elements renormalized using a hybrid-scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations., Comment: 25 pages, 29 figures, version published in PRD

In this work, we present a numerical investigation of a novel Lorentz-covariant parametrization to extract $x$-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of an asymmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements into Lorentz-invariant amplitudes. The amplitudes can then be related to the standard light-cone GPDs. GPDs are defined in the symmetric frame, which requires a separate calculation for each value of the momentum transfer, increasing the computational cost significantly. The proposed method is powerful, as one can extract the GPDs at multiple values of the momentum transfer at the computational cost of a single value. For this proof-of-concept calculation, we use one ensemble of $N_f=2+1+1$ twisted mass fermions and a clover improvement with a pion mass of 260 MeV to calculate the proton unpolarized GPDs., 10 pages, 5 figures, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

Parabolic wave equation (PWE) propagation models using multiple phase screens (MPS) are widely used to predict the log-amplitude variance of the signal propagating in tropospheric turbulence. Previous literature demonstrates the limitations of the MPS technique, usable only when the signal frequency is low (typically below 5 GHz for radio-wave propagation in the troposphere). In this article, we demonstrate that the accuracy of the MPS technique depends not only on the signal frequency but also on the outer scale length ( $L_{os}$ ) of the turbulent eddy. For example, when $L_{os}$ is on the order of tens of meters (e.g., in most terrestrial communication links), the MPS method is indeed unusable at high frequencies, but, when $L_{os}$ is on the order of hundreds of meters (e.g., in air–ground and satellite links), the method can be used even at millimeter-wave frequencies. Next, a correlated phase screen (CPS) implementation within the PWE is introduces, which avoids the condition of statistical noncorrelation of the phase screens in the MPS technique, and as such, it can be used for any signal frequency. Finally, an ad hoc error metric is provided, allowing for the selection of the appropriate phase screen model based on the signal frequency, turbulence outer scale length, and the electromagnetic (EM) link distance. The simulated signal log-amplitude variances as a function of range at microwave and millimeter-wave frequencies using the CPS method are reported here for the first time and are shown to be in excellent agreement with the analytically obtained values.

We investigate the criticality of chiral phase transition manifested in the first and second order derivatives of Dirac eigenvalue spectrum with respect to light quark mass in (2+1)-flavor lattice QCD. Simulations are performed at temperatures from about 137 MeV to 176 MeV on $N_{\tau}=8$ lattices using the highly improved staggered quarks and the tree-level improved Symanzik gauge action. The strange quark mass is fixed to its physical value $m_s^{\text{phy}}$ and the light quark mass is set to $m_s^{\text{phy}}/40$ which corresponds to a Goldstone pion mass $m_{\pi}=110$ MeV. We find that in contrast to the case at $T\simeq 205$ MeV $m_l^{-1} \partial \rho(\lambda, m_l)/\partial m_l$ is no longer equal to $\partial ^2\rho(\lambda, m_l)/\partial m_l^2$ and $\partial ^2\rho(\lambda, m_l)/\partial m_l^2$ even becomes negative at certain low temperatures. This means that as temperature getting closer to $T_c$ $\rho(\lambda, m_l)$ is no longer proportional to $m_l^2$ and thus dilute instanton gas approximation is not valid for these temperatures. We demonstrate the temperature dependence can be factored out in $\partial \rho(\lambda, m_l)/ \partial m_l$ and $\partial^2 \rho(\lambda, m_l)/ \partial m_l^2$ at $T \in [137, 153]$ MeV, and then we propose a feasible method to estimate the power $c$ given $\rho \propto m_l^{c}$., Comment: Talk presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021, 26th-30th, July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_\pi=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi distribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the $\overline{\rm MS}$ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yield a reliable determination of the valence quark distribution for $0.03\lesssim x \lesssim 0.80$ with 5-20\% uncertainties., Comment: 4 pages, 4 figures and appendix

Taylor expansion in powers of baryon chemical potential ($\mu_B$) is an oft-used method in lattice QCD to compute QCD thermodynamics for $\mu_B>0$. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of $\mu_B$ where such an expansion around $\mu_B=0$ can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in $\mu_B$ that is based on the $n$-point correlation functions of the conserved current ($D_n$). The method resums the contributions of the first $N$ correlation function $D_1,\dots,D_N$ to the Taylor expansion of the QCD partition function to all orders in $\mu_B$. We show that the resummed partition function is an approximation to the reweighted partition function at $\mu_B\ne0$. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on $32^3\times8$ lattices and for temperatures $T\approx145$-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of our scheme to include resummation of powers of temperature and quark masses in addition to $\mu_B$, and show that the alternative expansion scheme of [S. Bors\'anyi et al., Phys. Rev. Lett. 126, 232001 (2021).] is a special case of this generalized resummation., Comment: Resubmitted to match with the journal version of the paper

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasi-distribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame-independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f$=2+1+1 twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$., Comment: 39 pages, 19 figures, matches with published version

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report., Comment: 57 pages, 1 figure. Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). Topical Group Report for TF05 - Lattice Gauge Theory

We present our results on the electromagnetic form factor of pion over a wide range of $Q^2$ using lattice QCD simulations with Wilson-clover valence quarks and HISQ sea quarks. We study the form factor at the physical point with a lattice spacing $a=0.076$ fm. To study the lattice spacing and quark mass effects, we also present results for 300 MeV pion at two different lattice spacings $a=0.04$ and 0.06 fm. The lattice calculations at the physical quark mass appear to agree with the experimental results. Through fits to the form factor, we estimate the charge radius of pion for physical pion mass to be $\langle r_{\pi}^2 \rangle=0.42(2)~{\rm fm}^2$., Comment: 14 pages, 14 figures, revised version accepted by PRD

We explore the interactions between a quark anti-quark pair in a thermal medium based on lattice QCD ensembles with $N_f = 2+1$ dynamical HISQ flavors. Our dataset spans the phenomenologically relevant temperature range between T=140MeV-2GeV based on lattice sizes $N_\tau=10,12$ and $16$, with an aspect ratio of $N_\sigma/N_\tau=4$. The peak position $\Omega$ and the width $\Gamma$ of the spectral function of Wilson-line correlators in Coulomb gauge is computed. We assess the information content in the correlation functions and deploy three complementary strategies to reconstruct spectral information: model fits, Pad\'e approximation and the Bayesian BR method. Limitations of each approach are carefully assessed., Comment: Contribution to The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology, 9 pages, 7 figure, LaTeX, uses PoS class

For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory based computations of the equation of state. Recently, in arXiv:2106.03165, a new resummation scheme was proposed for such an expansion that resums contributions of correlation functions of conserved currents to all orders in the chemical potential. Here, we study the efficacy of this resummation scheme using a solvable low energy model, namely the mean-field quark-meson model. After adapting the scheme for a mean-field analysis, we confront the results of this scheme with the direct solution of the model at finite density as well as compare with results from Taylor expansions. We study to what extent the two methods capture the analytical properties of the equation of state in the complex chemical potential plane. As expected, the Taylor expansion breaks down as soon as the baryon chemical potential reaches the radius of convergence defined by the Yang-Lee edge singularity. Encouragingly, the resummation not only captures the location of the Yang-Lee edge singularity accurately, but is also able to describe the equation of state for larger chemical potentials beyond the location of the edge singularity for a wide range of temperatures., 9 pages, 9 figures

The goal of this work is to develop a numerical EM tool based on a parabolic wave equation (PWE) model that can accurately predict propagation losses over a wide range of frequencies, geometries, atmospheric and ocean conditions, including very small elevation angles. The code is specifically written for accurate field computations in ducted environments for low grazing angle air-to-ground links (typically less than 4-5°). It can run as a hybrid model with upper atmosphere is modeled using fast simpler models and lower marine atmospheric boundary layer is simulated by a discrete mixed Fourier transform-based PWE. It also include a Monte Carlo module that allows statistical estimation of realistic effects of varying sea surface, and turbulence by providing both the coherent and incoherent components of the field.

We report on a preliminary study of static quark anti-quark potential at non-zero temperature in $2+1$ flavor QCD using $96^3\times N_{\tau}$ lattices with lattice spacing $a=0.028$fm, physical strange quark mass and light quark masses corresponding to pion mass of about $300$ MeV. We use $N_\tau=32,~24,~20$ and $16$ that correspond to temperature range $T=220-441$ MeV. The in order to obtain the potential we calculate the Wilson line correlator in Coulomb gauge with additional HYP smearing to reduce the noise at large quark anti-quark separations. We apply $0$, $5$ and $10$ steps of HYP smearing to ensure that there is no physical effect from over-smearing. At the two highest temperatures we also consider a noise reduction technique that is based on an interpolation in the spatial separation between the static quark and anti-quark., Comment: Contribution to The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology, 7 pages, 4 figure, LaTeX, uses PoS class, typos corrected

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real ($V_R(T,r)$) and imaginary ($V_I(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain $V_R(T,r)$ and $V_I(T,r)$ in a model-independent fashion. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-334$~MeV. For $T=151-334$~MeV, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations., Comment: 16 pages, 10 figures; Published version; Data for plots enclosed

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks, which can be characterized by real (VR(T, r)) and imaginary (VI(T, r)) potentials, as functions of temperature and spatial separation. Recently, the masses and thermal widths of up to 3S and 2P bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network (DNN), here, we obtain model-independent results for VR(T, r) and VI(T, r). The temperature dependence of VR(T, r) was found to be very mild between T ≈ 0 − 330 MeV. Meanwhile, VI(T, r) shows rapid increase with T and r, which is much larger than the perturbation theory based expectations.

We present results on the in-medium interactions of static quark anti-quark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles., 7 pages, 4 figures, talk given at the XVth Quark confinement and the Hadron spectrum conference, Aug. 1st - 6th, 2022, Stavanger, Norway. Date of presentation Aug. 5th 2022

The boundaryless beam propagation method has been reported to suffer from reflections due to frequency aliasing. We propose an alternate explanation of reflection in the method, based on eikonal analysis of the wave equation in the mapped space, and show that reflection starts much before aliasing happens. We theoretically predict the reflection coefficient profile in a simulation and introduce an internal absorbing boundary condition (ABC), where reflection becomes appreciable. The a priori knowledge of the window size of the ABC does away with the arbitrariness in the design of such boundaries. Finally, we use the boundaryless scheme with the ABC to successfully model a dielectric bend. � 1983-2012 IEEE.

The Coupled Air–Sea Processes and Electromagnetic Ducting Research (CASPER) project aims to better quantify atmospheric effects on the propagation of radar and communication signals in the marine environment. Such effects are associated with vertical gradients of temperature and water vapor in the marine atmospheric surface layer (MASL) and in the capping inversion of the marine atmospheric boundary layer (MABL), as well as the horizontal variations of these vertical gradients. CASPER field measurements emphasized simultaneous characterization of electromagnetic (EM) wave propagation, the propagation environment, and the physical processes that gave rise to the measured refractivity conditions. CASPER modeling efforts utilized state-of-the-art large-eddy simulations (LESs) with a dynamically coupled MASL and phase-resolved ocean surface waves. CASPER-East was the first of two planned field campaigns, conducted in October and November 2015 offshore of Duck, North Carolina. This article highlights the scientific motivations and objectives of CASPER and provides an overview of the CASPER-East field campaign. The CASPER-East sampling strategy enabled us to obtain EM wave propagation loss as well as concurrent environmental refractive conditions along the propagation path. This article highlights the initial results from this sampling strategy showing the range-dependent propagation loss, the atmospheric and upper-oceanic variability along the propagation range, and the MASL thermodynamic profiles measured during CASPER-East.

Fading depth due to tropospheric scintillation in satellite to ground-station link is obtained from combined electromagnetic and large eddy simulations for low elevation angles. The numerically obtained fading depth is compared to previously established models and variability of fading depth with range and height is shown.

In this paper an ultra-wideband filter is designed using periodic defected ground structures as low pass filter and Slot SRRs in the conducting strip as a band reject filter to prevent interference from WLAN. The high pass characteristic is obtained by an interdigital capacitor in the conducting strip. The average insertion loss is 1.6 dB in the passband. The band stop filter rejects frequencies from 5.21 GHz to 5.9 GHz with maximum rejection being -33.46 dB at 5.4 GHz and stopband rejection is upto -68.61 dB and -60dB in the upper and lower stop-bands respectively. Keywords-communication systems, ultrawideband technology, microwave filters, SRRs, WLAN.

In this paper, a theoretical model is proposed to estimate the resonant frequency of a circular split ring resonator (C-SRR) in which the outer ring is rotated. The variation in the resonant frequency with angle of rotation of the SRR is theoretically calculated. The computed values are then compared with the simulated results using an electromagnetic simulator. Also, the magnetic polarizability for different angle of rotation is extracted from the simulated data.

We propose a new variant of the operator method for the computation of the equation of state of QCD, which yields positive pressure for all temperatures and all values of temporal lattice spacings. Using this new method, we calculate the continuum limit of pressure, energy density, entropy density, specific heat, and the speed of sound, in quenched QCD, for 0.9 \le T/T_c \le 3., Talk given at Lattice 2005 (nonzero temperature and density), uses PoS.cls

We have studied finite temperature complex static quark-antiquark potentials for 2+1 flavor QCD using highly improved staggered action with physical strange quark masses and light quark masses corresponding to a pion mass of 161 MeV. We calculated the potential using Wilson line correlators fixed in Coulomb gauge. For the extraction, we have used HTL motivated parametrization of the correlators. We found that the real part of the potential is screened above the crossover temperature and it's close to singlet free energies, whereas the imaginary part is increasing with both distance and temperature., Comment: 9 pages, 4 figures, Contribution to the 38th International Symposium on Lattice Field Theory, 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

A new technique is proposed to solve the problem of frequency aliasing reported in the Boundaryless Beam Propagation Method (BPM). A dielectric bend is simulated using the new approach, and compared with theoretical calculations.