Momentum Fraction Research Articles

Power corrections to quasidistribution amplitudes of a heavy meson

It has been recently demonstrated that light cone distribution amplitudes (LCDAs) for a heavy meson, defined in the heavy quark limit, can be extracted by simulating quasidistribution amplitudes on the lattice with a large meson momentum Pz. This extraction involves a two-step procedure. In the first step, the quasidistribution amplitudes are matched onto the QCD LCDAs in the large Pz limit. In the second step, the QCD LCDAs are matched onto the desired LCDAs defined in heavy quark effective theory. In this work, we present the mH2n/(Pz)2n and ΛQCD2/(xPz)2 and ΛQCD2/((1−x)Pz)2 corrections in the first step with mH being the heavy meson mass and x being the momentum fraction of the light quark. To account for mH2n/(Pz)2n corrections, we employ two methods: the moment relation that can provide mass corrections to all orders, and a leading-twist projector that gives the leading-order mass corrections. For the ΛQCD2/(Pz)2 corrections, we employ a renormalon model that addresses the renormalon ambiguity stemming from the divergence of the perturbative series. We adopt two parametrizations for QCD LCDAs to conduct a numerical analysis. The results suggest that these corrections are typically smaller than 20% in the region 0.2<x<0.8, and should be included in a precision analysis. These findings will serve as a valuable guide for future studies on heavy meson LCDAs, particularly in the context of lattice QCD, where accounting for such corrections is crucial for improving the accuracy and reliability of the results. Published by the American Physical Society 2024

Deciphering twist-3 chiral-even GPDs in the light-front quark-diquark model

We investigate quantum chromodynamics (QCD) in this study by computing chiral-even generalized parton distributions (GPDs) at twist-3 in the framework of the light-front quark-diquark model, particularly in the zero skewness scenario. We provide a detailed examination of twist-3 chiral-even GPDs, illustrating their behavior through extensive two-dimensional (2-D) and three-dimensional (3-D) visualizations, which demonstrate their dependence on the longitudinal momentum fraction (x) and the momentum transfer (t). Our investigation also reveals the intricate relationships between these GPDs and other distribution functions such as generalized transverse-momentum dependent distributions, transverse momentum-dependent parton distributions, and parton distribution functions (PDFs). Our study also includes the connected form factors at this twist, which are crucial in understanding the internal structure of hadrons. Additionally, we provide impact parameter-dependent PDF plots to offer insights into the spatial distribution of partons. Published by the American Physical Society 2024

Impressions of Parton Distribution Functions

Abstract Parton distribution functions (DFs) have long been recognised as key measures of hadron structure. Today, theoretical prediction of such DFs is becoming possible using diverse methods for continuum and lattice analyses of strong interaction (QCD) matrix elements. Recent developments include a demonstration that continuum and lattice analyses yield mutually consistent results for all pion DFs, with behaviour on the far valence domain of light-front momentum fraction that matches QCD expectations. Theory is also delivering an understanding of the distributions of proton mass and spin amongst its constituents, which varies, of course, with the resolving scale of the measuring probe. Aspects of the pion DF and proton spin developments are sketched herein, along with some novel perspectives on gluon and quark orbital angular momentum.

Heavy flavor-asymmetric pseudoscalar mesons on the light front

We extract the leading Fock-state light front wave functions of heavy flavor-asymmetric pseudoscalar mesons D, B, and Bc from their Bethe-Salpeter wave functions, based on the Dyson-Schwinger equations approach. We then study their leading-twist parton distribution amplitudes, generalized parton distribution functions, and transverse momentum-dependent parton distributions. The spatial distributions of the quark and antiquark on the transverse plane are presented, along with their charge and energy distributions on the light front. We find that in the considered mesons, the heavier quarks carry most of the longitudinal momentum fraction, resulting in narrow x distributions, while the lighter quarks play an active role in shaping the transverse distributions in both spatial and momentum space, exhibiting a duality that embodies characteristics of both light mesons and heavy quarkonium. Published by the American Physical Society 2024

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Unraveling subleading twist GTMDs of proton using light-front quark-diquark model

This study investigates the subleading twist generalized transverse momentum dependent distributions (GTMDs) of a proton within the light-front quark-diquark model framework. We solve the parametrization equations for the Dirac matrix structure, yielding explicit GTMD expressions for both scalar and vector diquark configurations, leading to expressions for active u and d quarks. This analysis addresses the multidimensional nature of GTMDs by exploring their dependencies on one or two variables while keeping others fixed. Additionally, we extract transverse momentum dependent form factors from GTMDs by integrating over the longitudinal momentum fraction x. The study uses three-dimensional plots to illustrate the variation of transverse momentum dependent form factors with the quark’s transverse momentum p⊥ and the transverse momentum transfer to the proton Δ⊥. Published by the American Physical Society 2024

Hard jet substructure in a multistage approach

We present predictions and postdictions for a wide variety of hard jet-substructure observables using a multistage model within the framework. The details of the multistage model and the various parameter choices are described in []. A novel feature of this model is the presence of two stages of jet modification: a high-virtuality phase [modeled using the modular all twist transverse-scattering elastic-drag and radiation model ()], where modified coherence effects diminish medium-induced radiation, and a lower virtuality phase [modeled using the linear Boltzmann transport model ()], where parton splits are fully resolved by the medium as they endure multiple scattering induced energy loss. Energy-loss calculations are carried out on event-by-event viscous fluid dynamic backgrounds constrained by experimental data. The uniform and consistent descriptions of multiple experimental observables demonstrate the essential role of modified coherence effects and the multistage modeling of jet evolution. Using the best choice of parameters from [], and with no further tuning, we present calculations for the medium modified jet fragmentation function, the groomed jet momentum fraction zg and angular separation rg distributions, as well as the nuclear modification factor of groomed jets. These calculations provide accurate descriptions of published data from experiments at the Large Hadron Collider. Furthermore, we provide predictions from the multistage model for future measurements at the BNL Relativistic Heavy Ion Collider. Published by the American Physical Society 2024

Numerical Simulation and Neural Network Model for Hydromagnetic Nanofluid Convection in a Porous Wavy Channel with Thermal Non-Equilibrium Model

Abstract The present study aims to analyze the nonfluid MHD convective heat transfer in a porous wavy channel with a local thermal non-equilibrium (LTNE) model. Such a model finds applications related to enhancement in thermal performance, increasing the heat transfer coefficient in the compact design of heat exchangers for the aerospace and automotive industries and elevation in the efficiency of the solar collector. A sinusoidal porous wavy LTNE channel containing nanofluid and subjected to the induced and applied magnetic fields is considered. A uniform magnetic field is applied orthogonal to the channel and the induced magnetic field effects are considered due to the large magnetic Reynolds number. The momentum, continuity, energy, and nanoparticle volume fraction equations constitute the coupled nonlinear system of differential equations and are solved using the Galerkin finite element method. The reliability of the technique is assessed by comparing the proposed procedure with the results from earlier sources. A detailed analysis is presented to determine the effects of different physical parameters arising in the system on temperature, nanoparticle concentration, and velocity profiles. As an illustration, the findings exhibit that increasing the modified diffusivity ratio increases the values of the nanoparticle volume fraction whereas, reducing the modified diffusivity ratio enhances the temperature distribution. A higher value of thermal Rayleigh number presents a significant involvement of buoyancy forces, potentially resulting in the development of convective currents. A higher Nield number indicates more effective heat transport from the solid surface to the nanofluid. Consequently, there is a minimal thermal difference between the solid surface and the bulk nanofluid. Effective heat transmission enhances the nanofluid ability to absorb heat and generates a more consistent dispersion of temperature inside the fluid. The performance of the designed algorithms of the artificial neural network, namely, the Levenberg – Marquardt algorithm, in the problem under consideration is evaluated and the methodology is found reasonably precise with the matching of order around 6 to 7 decimal places of accuracy.

Security-Enhanced and High-Resolution Fractional Orbital Angular Momentum Multiplexing Holography

Security-Enhanced and High-Resolution Fractional Orbital Angular Momentum Multiplexing Holography

Beam test of n-type Silicon pad array detector at PS CERN

This work reports the test of an n-type silicon pad array detector at the CERN PS in the context of the future Forward Calorimeter (FoCal) detector. FoCal is a proposed upgrade in the ALICE detector operating within the pseudorapidity range of 3.2 < η < 5.8. It aims to measure direct photons, neutral hadrons, vector mesons, and jets for the study of gluon saturation effects in the unexplored region of low momentum fraction x (∼ 10-5–10-6). The prototype is a 8×9 n-type Si pad array detector with each pad occupying one cm2 area, fabricated on a 6-in, 325 ± 10 μm thick, and high-resistivity (∼ 7 kΩ cm) Si wafer, which is readout using the HGCROCv2 chip. The detector is tested using pion beams of energy 10 GeV and electron beams of energy 1–5 GeV. The measurements of the Minimum Ionizing Particle (MIP) response of pions and the shower profiles of electrons are reported.

Numerical Study of Cavitation Phenomenon in a Venturi Tube

This research aims to understand and numerically analyze the cavitation phenomenon that occurs in Venturi tubes with variations in throat length and pressure changes. This research uses Ansys Fluent 2023 R2 numerical simulation with venturi tube geometries of 25 mm, 30 mm, and 35 mm and pressures of 300,000, 600,000, and 900,000 Pa. A multiphase flow model with water liquid and water vapor is applied to predict cavitation using a mixture model. RANS steady state conditions with the k-ε turbulence model are used to solve the continuity, momentum, energy and volume fraction equations. The Schnerr-Sauer cavitation model calculates the phase transition between water-liquid and water vapor. Geometry varies by reference journal with different converging and diverging angles, outlined in tables and figures. 2D simulations are carried out using a pressure based solver with specified boundary conditions, using the Presto! for pressure solutions, and upwind and Quick schemes for discretization. The results of this research show that 1) Length throat 25 mm has the most stable distribution compared to 30 and 35 mm geometries at a pressure of 600,000 Pa. 2) The cavitation phenomenon is influenced by changes in geometry where at 35 mm geometry greater cavitation occurs in the area near the wall inlet convergent. 3) At a pressure of 900,000 Pa, the cavitation area that forms becomes larger and becomes a critical point in this journal.

Numerical Analysis of the Submerged Horizontal Plate Device Subjected to Representative Regular and Realistic Irregular Waves of a Sea State

This study numerically analyzes a submerged horizontal plate (SHP) device subjected to both regular and irregular waves. This device can be used either as a breakwater or a wave energy converter (WEC). The WaveMIMO methodology was applied for the numerical generation and wave propagation of the sea state of the Rio Grande coast in southern Brazil. The finite volume method was employed to solve conservation equations for mass, momentum, and volume fraction transport. The volume of fluid model was employed to handle the water-air mixture. The SHP length (Lp) effects were carried out in five cases. Results indicate that relying solely on regular waves in numerical studies is insufficient for accurately determining the real hydrodynamic behavior. The efficiency of the SHP as a breakwater and WEC varied depending on the wave approach. Specifically, the SHP demonstrates its highest breakwater efficiency in reducing wave height at 2.5Lp for regular waves and 3Lp for irregular waves. As a WEC, it achieves its highest axial velocity at 3Lp for regular waves and 2Lp for irregular waves. Since the literature lacks studies on SHP devices under the incidence of realistic irregular waves, this study significantly contributes to the state of the art.

Quark spin-orbit correlations in spin-0 and spin-1 mesons using the light-front quark model

We investigate the spin-orbital angular momentum correlations for the active quark inside the light and heavy mesons for both the spin-0 and spin-1 cases. These correlations can be derived from the generalized transverse-momentum-dependent distributions as well as the generalized parton distributions. We employ the overlap representation of light-front wave functions in the light-front quark model to calculate our analytical results. The dependence of spin-orbit correlations (SOCs) on the longitudinal momentum fraction x as well as the transverse-momentum-dependence k⊥ is graphically presented. Even though the SOCs have already been studied for the spin-0 pions and kaons in other approaches, no calculations for the other light and heavy spin-0 mesons have been reported in the literature. Further, the correlations for any of the light and heavy spin-1 mesons are studied for the first time in the present work. Published by the American Physical Society 2024

Four-loop splitting functions in QCD – The quark-to-gluon case

We present the even-N moments N≤20 of the fourth-order (N3LO) contribution Pgq(3)(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analytically computing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N≤10 derived before from structure functions in deep-inelastic scattering. Using the new moments and the available endpoint constraints, we construct approximations for Pgq(3)(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x>0.1. The resulting errors of the convolution of Pgq at N3LO with a typical quark distribution are small at x≳10−3 and exceed 1% only at x≲10−4 for a strong coupling αs=0.2. The present results for Pgq(3)(x) should thus be sufficient for most collider-physics applications.

Contact interaction study of proton parton distributions

Using a symmetry-preserving formulation of a vector×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ imes \\,$$\\end{document}vector contact interaction (SCI) and treating the proton as a quark + interacting-diquark bound state, whose structure is obtained by solving a Poincaré-covariant Faddeev equation, we provide a comprehensive, coherent set of predictions for unpolarised and polarised proton parton distribution functions (DFs): valence, glue, and four-flavour separated sea. The results enable many themes to be addressed, including: the asymmetry of antimatter in the proton; the neutron:proton structure function ratio; helicity retention in hard scattering processes; the charm quark momentum fraction; the sign and size of the polarised gluon DF; and the origin of the proton spin. In all cases where sound analyses of data are available, SCI predictions are semiquantitatively in agreement with the results. Those mismatches which exist are typically attributable to the momentum-independence of the underlying interaction. Judiciously interpreted, the SCI delivers a sound and insightful explanation of proton structure as expressed in DFs.

Numerical implementation of evolution equations for twist-3 collinear PDFs

Twist-3 collinear parton distribution functions (PDFs) are matrix elements of quark-gluon-quark or three-gluons light-cone operators. They depend on three momentum fraction variables, which are restricted to a hexagon region, and the evolution kernels are defined via two-dimensional convolution in these variables. We present the numerical realisation of the twist-3 evolution equations at leading order in the strong coupling for all kinds of twist-3 PDF (quark, gluon, chiral-even/odd, etc). We provide two independent codes (in C and Fortran) that have been extensively cross-checked, and are ready-to-use. We supplement the paper with a review of known properties of twist-3 PDFs.

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum Pz ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

Peristaltic transport with multiple solutions of heat and mass transfer using modified Buongiorno nanofluid model over tapered channel with long wave‐length at small Reynolds number

AbstractThis research paper aims to investigate the peristaltic transport of a nanofluid (NF) in a tapered asymmetric channel. Initially, the governing equations for the balance of mass, momentum, temperature, and volume fraction for the NF using Reiner–Philippoff (RP) based NF are formulated. Subsequently, these equations are employed to analyze long wavelength and small Reynolds number scenarios. The numerical results for various flow features are thoroughly examined and discussed. Dual solutions have been examined for some factors. So, stability assessment is implemented to find stable solution. Novelty of the existing is to investigate the peristaltic motion of Buongiorno's NF model and its stability which has not investigated in the previous literatures. It has been demonstrated that modifying the RPF parameter leads to a transition in the fluid's velocity, changing it from a dilatant liquid to a Newtonian fluid and from Newtonian to pseudoplastic. The findings indicate that the temperature curves rise as Brownian motion and thermophoretic factors increase, while they decrease as the Prandtl number increases. Furthermore, a concise mathematical and graphical analysis is carried out to examine the impact of each key parameter on the flow characteristics.

Next-to-eikonal corrections to dijet production in Deep Inelastic Scattering in the dilute limit of the Color Glass Condensate

We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at next-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region.

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s=13 TeV

A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at s=13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb−1 collected in 2016–2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta (pTγ&gt;100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass (mγγ&gt;350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters |ζ1|&lt;0.073 TeV−4 and |ζ2|&lt;0.15 TeV−4, using an effective field theory. Additionally, upper limits are placed on the production of axionlike particles with coupling strength to photons f−1 that varies from 0.03 TeV−1 to 1 TeV−1 over the mass range from 500 to 2000 GeV. © 2024 CERN, for the CMS and TOTEMs Collaboration 2024 CERN