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Brodsky, Stanley J.

Publications and source records attributed to Brodsky, Stanley J..

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

QCD Running Coupling in the Nonperturbative and Near-Perturbative Regimes

We use analytic continuation to extend the gauge-gravity duality nonperturbative description of the strong force coupling into the transition, near-perturbative, regime where perturbative effects become important. By excluding the unphysical region in coupling space from the flow of singularities in the complex plane, we derive a specific relation between the scales relevant at large and short distances; this relation is uniquely fixed by requiring maximal analyticity. The unified effective coupling model gives an accurate description of the data in the nonperturbative and the near-perturbative regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Nature's Strongest Force

The strongest force in the universe is called, aptly, the strong force. We never get to witness its fearsome power because it works only across subatomic distances, where it binds quarks together inside protons and neutrons and joins those nucleons into atomic nuclei. Of the four basic forces of nature, the strong force is by far the most potent—it’s 100 trillion trillion trillion times stronger than the force of gravity. Additionally, it’s also the most mysterious.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

50 Years of quantum chromodynamics

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μ r and thus determining the correct values of the QCD running coupling α s (μ r ) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μ r $\in$ [Q/2, 2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist’s choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the N c → 0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC ∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e + e - annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC ∞ applied to the thrust distribution investigating both the QCD conformal window and the QED N c → 0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC ∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC ∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities R e+e- , R$_Τ$ and Γ (H→$b\bar{b}$) up to the four-loop accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

QCD running couplings and effective charges

Here we discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2) $ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $\alpha_s$} at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $\alpha_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $\alpha_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $\alpha_s$. We conclude by highlighting how the nonperturbative knowledge of $\alpha_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Extending the predictive power of perturbative QCD using the principle of maximum conformality and the Bayesian analysis

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: R e+e– and R τ , which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Elimination of QCD Renormalization Scale and Scheme Ambiguities

The setting of the renormalization scale (μ r ) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer Q in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in e + e – annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of μ r are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Detailed comparison of renormalization scale-setting procedures based on the principle of maximum conformality

The 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 ∞ ). 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 $Γ(H→b\bar{b}$) 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Artificial dynamical effects in quantum field theory

In Newtonian mechanics, studying a system in a non-Galilean reference frame can lead to inertial pseudoforces appearing, such as the centrifugal force that seems to arise in dynamics analysed in a rotating frame. Likewise, artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework that violates Poincaré invariance. Here, we highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. By contrast, the treatment of the same problem using light-front quantization is free from spurious pseudoeffects because Poincaré invariance is effectively preserved for all practical intents and purposes. We illustrate these statements using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

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) ℓp→ℓ'p'X includes a diffractive deep inelastic (DDIS) contribution ℓp→ℓ'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 ' ~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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

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

In this study, we calculate the $t\bar{t}$ pQCD production cross-section at the NNLO and determine the top-quark pole mass from recent measurements at the LHC at the center-of-mass energy $\sqrt{S}=13$ TeV to a high precision by applying the principle of maximum conformality (PMC). The PMC provides a systematic method that rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal $\beta$ 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 prediction of PMC calculations that the magnitudes 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 agrees 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

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 γ + η c production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e + + e – → γ + 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 renormalization scale-and-scheme independent prediction, σ | NNLO,PMC ≃ 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 Padé approximation approach, we predict σ | NNNLO,PMC+Pade ≃ 18.99 fb, which is consistent with the recent BELLE measurement ${\sigma}^{\mathrm{obs}}={16.58}_{-9.93}^{+10.51}$ fb at $\sqrt{s}$ ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

QCD hidden-color hexadiquark in the 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 [ud] diquarks in a strongly bound 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 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. Overall, 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Comparing light-front quantization with instant-time quantization

Here in this paper we compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the restriction to equal times that makes the commutation (or anticommutation) relations appear to be so different. While our results are valid for both bosons and fermions, for fermions there are subtleties associated with tip of the light cone contributions that need to be taken care of. At the level of Feynman diagrams we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional light-front Feynman diagrams reproduce the widely used three-dimensional light-front on-shell Hamiltonian Fock space formulation in which the light-front energy and light-front momentum are on shell. Moreover, we show that the contributions of pole terms in non-vacuum instant-time and non-vacuum light-front Feynman diagrams are equal. However, because of circle at infinity contributions we show that this equivalence of pole terms fails for four-dimensional light-front vacuum tadpole diagrams. Then, and precisely because of these circle at infinity contributions, we show that light-front vacuum tadpole diagrams are not only nonzero, they quite remarkably are actually equal to the pure pole term instant-time vacuum tadpole diagrams. Light-front vacuum diagrams are not correctly describable by the on-shell Hamiltonian formalism, and thus not by the closely related infinite momentum frame prescription either. Thus for the light-front vacuum sector we must use the off-shell Feynman formalism as it contains information that is not accessible in the on-shell Hamiltonian Fock space approach. We show that light-front quantization is intrinsically nonlocal, and that for fermions this nonlocality is present in Ward identities. One can project fermion spinors into so-called good and bad components, and both of these components contribute in Ward identities. Central to our analysis is that the transformation from instant-time coordinates and fields to light-front coordinates and fields is a unitary, spacetime-dependent translation. Consequently, not only are instant-time quantization and light-front quantization equivalent, because of general coordinate invariance they are unitarily equivalent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

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 $\mu^c_M=-0.00127(38)_{\rm stat}(5)_{\rm sys}$, 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗