arXiv subjects

Stanley J. Brodsky

Publications and source records attributed to Stanley J. Brodsky.

At least 37 records · Page 2Linked to original sources

arXiv2023

Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality

The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC$_\infty$). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities $R_{e^+e^-}$, $R_τ$, and $Γ(H \to b \bar{b})$ up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling $α_s(Q)$ by the recursive use of the renormalization group equation, whose argument $Q$ represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

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arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

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arXiv2022

Heavy quark contribution to the electromagnetic properties of the nucleon

Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form factors, distribution amplitudes, structure functions, etc. We will extend this nonperturbative light-front QCD approach to study the heavy quark-antiquark contribution to the electromagnetic properties of nucleon. Our framework is based on a study of the eigenfunctions of the QCD light-front Hamiltonian, the frame-independent light-front wave functions (LFWFs) underlying hadron dynamics. We analyze the heavy quark content in the proton, induced either directly by the nonperturbative $|uud+Q\bar Q\rangle$ Fock state or by the $|uud+g\rangle$ Fock state, where the gluon splits into a heavy quark-antiquark pair. The specific form of these LFWFs are derived from LFHQCD. Using these LFWFs, we construct light-front representations for the heavy quark-antiquark asymmetry, the electromagnetic form factors of nucleons induced by heavy quarks, including their magnetic moments and radii.

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arXiv2022

Proceedings of the Low-$x$ 2021 International Workshop

The purpose of the Low-$x$ Workshop series is to stimulate discussions between experimentalists and theorists in diffractive hadronic physics, QCD dynamics at low $x$, parton saturation, and exciting problems in QCD at HERA, Tevatron, LHC, RHIC, and the future EIC. The central topics of the workshop, summarized in the current Proceedings, were: Diffraction in ep and e-ion collisions (including EIC physics); Diffraction and photon-exchange in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions; Spin Physics; Low-$x$ PDFs, forward physics, and hadronic final states. This Workshop has been the XXVIII edition in the series of the workshop.

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arXiv2022

Predictions for the Sivers Single-Spin Asymmetry from Holographic QCD

A new approach to nonperturbative QCD, holographic light-front QCD, provides a comprehensive model for hadron dynamics and spectroscopy, incorporating color confinement, a universal hadron mass scale, the prediction of a massless pion in the chiral limit, and connections between the spectroscopy of mesons, baryons and tetraquarks across the full hadron spectrum. In this article we present predictions for the Sivers asymmetry and related transverse momentum distributions for the proton based on the light-front wavefunctions of the baryon eigenstate predicted by holographic QCD.

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arXiv2022

Onset of color transparency in holographic light-front QCD

The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, $Q$. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, $e A \to e' πX$ for mesons produced at $Q^2 > 3 ~ {\rm GeV}^2$. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon $e\, {\rm C}\to e' p X$, where $X$ stands for the inclusive sum of all produced final states, fails to observe CT at $Q^2$ up to 14.2 GeV$^2$. In this paper, the onset of CT is determined by comparing the $Q^2$-dependence of the hadronic cross sections for the initial formation of a small color-singlet configuration using the generalized parton distributions from holographic light-front QCD. A critical dependence on the hadron's twist, $τ$, the number of hadron constituents, is found for the onset of CT, with no significant effects from the nuclear medium. This effect can explain the absence of proton CT in the present kinematic range of the JLab experiment. The proton is predicted to have a "two-stage" color transparency with the onset of CT differing for the spin-conserving (twist-3, $τ=3$) Dirac form factor with a higher onset in $Q^2$ for the spin-flip Pauli (twist-4) form factor. In contrast, the neutron is predicted to have a "one-stage" color transparency with the onset at higher $Q^2$ because of the dominance of its Pauli form factor. The model also predicts a strong dependence at low energies on the flavor of the quark current coupling to the hadron.

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arXiv2022

Towards a single scale-dependent Pomeron in holographic light-front QCD

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion which was derived in a previous article [Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,μ)$ to large $μ^2$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory $α_P(t, μ)$ not only depends on the momentum transfer squared $t$, but also on the physical scale $μ$ of the amplitude, such as the virtuality $Q^2$ of the interacting photon in inclusive diffractive electroproduction. This can explain not only the $Q^2$ evolution of the proton structure function $F_2(x,Q^2)$ at small $x$, but also the observed energy and $Q^2$ dependence of high energy diffractive processes involving virtual photons up to LHC energies.

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arXiv2021

Novel Corrections to the Momentum Sum Rule for Nuclear Structure Functions

We address novel features of deep inelastic lepton scattering on nuclei at small Bjorken variable $x_{Bj}$. In this regime the lepton-nuclear cross section involves the interference between the standard lepton-quark scattering amplitude for the deep inelastic scattering (DIS) process on a single nucleon and a two-step process where diffractive scattering on a first nucleon combines with the amplitude for DIS on a second nucleon. The phases associated with the $t$-channel exchanges to the diffractive amplitude can produce either a destructive or constructive quantum-mechanical interference of the one-step and two-step amplitudes. This provides a mechanism regulating the respective amounts of shadowing suppression and anti-shadowing enhancement at low $x_{Bj}$. Furthermore, the standard leading-twist operator product and handbag diagram analyses of the forward virtual Compton amplitude on the nucleus are inapplicable, barring a conventional probabilistic interpretation. A main observable consequence is the impossibility of extracting momentum and spin sum rules from nuclear structure functions. We present numerical predictions supporting this picture and test them against DIS neutrino-nucleus and charged-lepton-nucleus scattering data.

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arXiv2021

Supersymmetric and Other Novel Features of Hadron Physics from Light-Front Holography

I survey recent developments in hadron physics which follow from the application of superconformal quantum mechanics and light-front holography. This includes new insights into the physics of color confinement, chiral symmetry, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. I also will discuss some novel features of QCD -- such as color transparency, hidden color, and asymmetric intrinsic heavy-quark phenomena. The elimination of renormalization scale ambiguities and the modification of QCD sum rules due to diffractive phenomena are also briefly reviewed.

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arXiv2021

The Diffractive Contribution to Deep Inelastic Lepton-Proton Scattering: Implications for QCD Momentum Sum Rules and Parton Distributions

The cross section for deep inelastic lepton-proton scattering (DIS) $\ell p \to \ell' X$ includes a diffractive deep inelastic (DDIS) contribution $\ell p \to \ell' p' X$, in which the proton remains intact with a large longitudinal momentum fraction $x_F$ greater than 0.9 and small transverse momentum. The DDIS events, which can be identified with Pomeron exchange in the $t$-channel, account for approximately $10\%$ of all of the DIS events. Thus, when one measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS events as a contribution to the DIS cross section, whether or not the final-state proton $p'$ is detected. In such events, the missing momentum fraction $x_{p'} \sim 0.9$ carried by the final-state proton $p'$ in the DDIS events could be misidentified with the light-front momentum fraction carried by sea quarks or gluons in the protons' Fock structure. As we shall show in this article, the underlying QCD Pomeron-exchange amplitude which produces the DDIS events does not obey the operator product expansion nor satisfy momentum sum rules. Thus we conclude that the quark and gluon distributions measured in DIS experiments will be misidentified, unless the measurements explicitly exclude the DDIS events and that a correct determination of the parton distribution functions (PDFs) derived from the DIS data requires the explicit subtraction of the DDIS contribution from the full DIS cross section.

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arXiv2021

Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC

In this paper, we calculate the $t\bar{t}$ pQCD production cross-section at NNLO and determine the top-quark pole mass from recent measurements at the LHC at $\sqrt{S}=13$ TeV center-of-mass energy to high precision by applying the Principle of Maximum Conformality (PMC). The PMC provides a systematic method which rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling constant. The PMC predictions satisfy the requirements of renormalization group invariance, including renormalization scheme independence, and the PMC scales accurately reflect the virtuality of the underlying production subprocesses. By using the PMC, an improved prediction for the $t\bar{t}$ production cross-section is obtained without scale ambiguities, which in turn provides a precise value for the top-quark pole mass. Moreover, the predictive power of PMC calculations that the magnitude of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production. The resulting determination of the top-quark pole mass $m_t^{\rm pole}=172.5\pm1.4$ GeV from the LHC measurement at $\sqrt{S}=13$ TeV is in agreement with the current world average cited by the Particle Data Group (PDG). The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at $\sqrt{S}=13$ TeV with previous LHC measurements at lower CM energies.

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arXiv2021

Gluon matter distribution in the proton and pion from extended holographic light-front QCD

The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effective QCD scales.

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arXiv2021

Longitudinal dynamics and chiral symmetry breaking in holographic light-front QCD

The breaking of chiral symmetry in holographic light-front QCD is encoded in its longitudinal dynamics with its chiral limit protected by the superconformal algebraic structure which governs its transverse dynamics. The scale in the longitudinal light-front Hamiltonian determines the confinement strength in this direction: It is also responsible for most of the light meson ground state mass consistent with the Gell-Mann-Oakes-Renner constraint. Longitudinal confinement and the breaking of chiral symmetry are found to be different manifestations of the same underlying dynamics as found in 't Hooft large $N_C$ QCD(1 + 1) model.

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arXiv2021

PMC$_\infty$: Infinite-Order Scale-Setting method using the Principle of Maximum Conformality and preserving the Intrinsic Conformality

We show results for Thrust and C-parameter in $e^+ e^-$ annihilation to 3 jets obtained using the recently developed new method for eliminating the scale ambiguity and the scheme dependence in pQCD namely the Infinite-Order Scale-Setting method using the Principle of Maximum Conformality (PMC$_\infty$). This method preserves an important underlying property of gauge theories: intrinsic Conformality (iCF). It leads to a remarkably efficient method to eliminate the conventional renormalization scale ambiguity at any order in pQCD. A comparison with Conventional Scale Setting method (CSS) is also shown.

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arXiv2020

Scale-Fixed Predictions for $γ+ η_c$ production in electron-positron collisions at NNLO in perturbative QCD

In the paper, we present QCD predictions for $η_{c} + γ$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\toγ+η_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling $α_s(Q^2)$. The renormalization group equation then sets the value of $α_s$ for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a scale-and-scheme independent prediction, $σ|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large $K$ factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the $\rm Pad\acute{e}$ approximation approach, we predict $σ|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $σ^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution.

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arXiv2020

QCD Hidden-Color Hexa-diquark in the Central Core of Nuclei

Hidden-color configurations are a key prediction of QCD with important physical consequences. In this work we examine a QCD color-singlet configuration in nuclei formed by combining six scalar $[u d]$ diquarks in a strongly bound $\rm SU(3)_C$ channel. The resulting hexadiquark state is a charge-2, spin-0, baryon number-4, isospin-0, color-singlet state. It contributes to alpha clustering in light nuclei and to the additional binding energy not saturated by ordinary nuclear forces in \he as well as the alpha-nuclei sequence of interest for nuclear astrophysics. We show that the strongly bound combination of six scalar isospin-0 $[ud]$ diquarks within the nuclear wave function - relative to free nucleons - provides a natural explanation of the EMC effect measured by the CLAS collaboration's comparison of nuclear parton distribution function ratios for a large range of nuclei. These experiments confirmed that the EMC effect; i.e., the distortion of quark distributions within nuclei, is dominantly identified with the dynamics of neutron-proton (``isophobic'') short-range correlations within the nuclear wave function rather than proton-proton or neutron-neutron correlations.

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arXiv2020

Constraints on charm-anticharm asymmetry in the nucleon from lattice QCD

We present the first lattice QCD calculation of the charm quark contribution to the nucleon electromagnetic form factors $G^c_{E,M}(Q^2)$ in the momentum transfer range $0\leq Q^2 \leq 1.4$ $\rm GeV^2$. The quark mass dependence, finite lattice spacing and volume corrections are taken into account simultaneously based on the calculation on three gauge ensembles including one at the physical pion mass. The nonzero value of the charm magnetic moment $μ^c_M=-0.00127(38)_{\rm stat}(5)_{\rm sys}$, as well as the Pauli form factor, reflects a nontrivial role of the charm sea in the nucleon spin structure. The nonzero $G^c_{E}(Q^2)$ indicates the existence of a nonvanishing asymmetric charm-anticharm sea in the nucleon. Performing a nonperturbative analysis based on holographic QCD and the generalized Veneziano model, we study the constraints on the $[c(x)-\bar{c}(x)]$ distribution from the lattice QCD results presented here. Our results provide complementary information and motivation for more detailed studies of physical observables that are sensitive to intrinsic charm and for future global analyses of parton distributions including asymmetric charm-anticharm distribution.

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arXiv2020

Renormalization Scale Setting for Heavy Quark Pair Production in $e^+e^-$ Annihilation near the Threshold Region

Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.

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