arXiv subjects

Stanley J. Brodsky

Publications and source records attributed to Stanley J. Brodsky.

At least 19 recordsLinked to original sources

arXiv2026

Regge spectral generator and form factors from hard exclusive amplitudes in holographic QCD

We show that the infinite tower of hard exclusive amplitudes in holographic light-front QCD leads to a spectral generator $G(α,λ)$ which encodes the full Regge spectrum. The construction assumes a Poisson distribution of Fock-state components, where $λ$ represents the average parton multiplicity above the valence configuration. The resulting generator yields a Regge spectrum invariant under continuous $λ$-deformations. Its even- and odd-twist projections yield the meson and baryon form factors with a single value of $λ$, fixed by the pion charge radius, which in turn determines the full $Q^2$ dependence. The constituent counting rules for both sectors follow from the structure of the spectral generator, which also provides a compact analytic representation of parton distributions.

hep-ph↗

arXiv2026

Poincaré invariance and the Unruh effect

In quantum field theory, the vacuum is popularly considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a temperature that grows with the acceleration. This is the Unruh effect. However, it has been shown that vacuum complexity is an artifact, produced by treating quantum field theory in a manner that does not manifestly enforce causality. Choosing a quantization approach that patently enforces causality, the quantum field theory vacuum is barren, bereft even of virtual particles. We show that acceleration has no effect on a trivial vacuum; hence, there is no Unruh effect in such a treatment of quantum field theory. Since the standard calculations suggesting an Unruh effect are formally consistent, insofar as they have been completed, there must be a cancelling contribution that is omitted in the usual analyses. We argue that it is the dynamical action of conventional Lorentz transformations on the structure of an Unruh detector.

physics.gen-ph↗

arXiv2026

Novel analysis for the energy-energy correlation in electron-positron annihilation in the perturbative domain

The energy-energy correlation (EEC) in electron-positron annihilation plays a crucial role in precision tests of quantum chromodynamics (QCD) and measurements of the QCD coupling constant. In this paper, we provide a novel analysis for the EEC by using the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC scales are determined by resumming the non-conformal $β$-terms that govern the behavior of the QCD running coupling via the renormalization group equation, and reflect the virtuality of the propagating gluons in QCD. It is noteworthy that the resulting PMC scale varies dynamically with the EEC's angular distribution, reflecting the expected scale's physical behavior. Moreover, due to the reabsorption of all $β$-terms, including also those related to the divergent renormalon terms such as $n!β^n_0α^n_s$, in the pQCD series, the behavior of the QCD perturbative coefficient using PMC, differs entirely from that of the conventional coefficient. Consequently, the PMC predicted EEC distribution agrees well with the experimental data in the perturbative domain.

hep-ph↗

arXiv2025

Holographic light-front QCD

This brief review presents the key components of light-front holographic quantum chromodynamics (HLFQCD). Particular attention is given to the introduction of the QCD color confinement scale within the context of a graded superconformal algebra. A concise overview of applications is provided, including spectroscopy, form factors, parton distributions of hadrons, and the relationship between entanglement entropy and high-energy scattering. While many other recent applications of HLFQCD exist in the literature, they are not included in this short overview of our latest work.

hep-ph↗

arXiv2025

Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting

We present a new approach to determining the strong coupling $α_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $Λ_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust ($T$) and $C$-parameter ($C$) distributions in $e^+e^-$ annihilation at a single annihilation energy $\sqrt{s}=M_Z$ (i.e.\ at the $Z^0$ peak). This new method is based on the \emph{intrinsic conformality} (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e.\ the PMC$_\infty$), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. This new method is based on the scale-invariance of the iCF, which allows determination of $α_s(μ_0)$ at any scale $μ_0$, and on the Maximum Likelihood statistical approach. We propose a novel approach to determining the best-fitting range by considering all possible intervals over the entire range of bins available in the perturbative region and selecting that which returns the most-likely-lowest $χ^2_{\rm min}$. This new method is designed to eliminate the errors that arise due to selection of the bin-interval and that have been neglected in previous analyses. In particular, using data for thrust and $C$-parameter at the $Z^0$ peak from ALEPH, OPAL, DELPHI and L3 experiments, we obtain the average value: $α_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $α_s(M_Z)$ is consistent with the world average...

hep-ph↗

arXiv2025

Self-consistent analysis for the $η_c\rightarrow γγ$ process

The next-to-next-to-leading-order (NNLO) pQCD predictions for both the decay width and the transition form factor in the $η_c\rightarrow γγ$ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the $η_c\rightarrow γγ$ process by applying the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme and scale ambiguities. The PMC renormalization scales are determined by absorbing the non-conformal $β$ terms which govern the behavior of the QCD running coupling via the Renormalization Group Equation. We obtain the PMC scale $Q_\star=4.49\,m_c$ for the $η_c\rightarrow γγ$ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated NNNLO and higher-order terms. The resulting value for $Γ_{η_c\rightarrow γγ}$ is in agreement with the Particle Data Group's reported value of $Γ_{η_c\rightarrow γγ}=5.1\pm0.4$ keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to $η_c\rightarrow γγ$ puzzle and supports the applicability of NRQCD to charmonium processes.

hep-ph↗

arXiv2025

Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling $α_{\rm eff}$ in the nonperturbative and near-perturbative regimes~\cite{deTeramond:2024ikl} by imposing rigorous renormalization-group results from asymptotically free gauge theories at $Q^2 \to \infty$. The asymptotic boundary conditions modify the scaling properties of $α_{\rm eff}$ at large values of the momentum transfer $Q^2$, and lead to a scale-dependent confinement strength $κ(Q^2)$. This requires that both $κ(Q^2)$ and $α_{\rm eff}\left(Q^2, κ(Q^2)\right)$ remain holomorphic in the complex $Q^2$ plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in~\cite{deTeramond:2024ikl}. For color $SU(3)$, a precise connection is found between the scaling exponent of $κ(Q^2)$ in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling at all scales, up to the highest available data.

hep-ph↗

arXiv2025

Advances for QCD and the Standard Model: Color-Confining Light-Front Holography and the Principle of Maximum Conformality

I review how the application of superconformal quantum mechanics and light-front holography leads to new insights into the physics of color confinement, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. Spontaneous chiral symmetry breaking is automatically fulfilled by supersymmetric Light-Front QCD. The light-front holographic approach (HLFQCD) also predicts the behavior of the QCD running coupling and other observables from the nonperturbative color-confining domain to the perturbative domain. One can determine the QCD running coupling to high precision from the data of just a single experiment over the entire perturbative regime by using the Principle of Maximum Conformality (PMC). The 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 Standard Model predictions, consistent with the principles of the renormalization group. I also briefly review a novel feature of hadronic physics predicted by QCD: intrinsic heavy quarks.

hep-ph↗

arXiv2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization scheme and scale ambiguities. We demonstrate that the PMC predictions satisfy all of the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann--Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially-divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

hep-ph↗

arXiv2025

Quantum Chromodynamics Resolution of the ATOMKI Anomaly in ${\rm {^4He}}$ Nuclear Transitions

Observations of anomalous angular correlations in electron-positron pairs produced from excited states of $^{4}$He, $^{8}$Be and $^{12}$C nuclei have been suggested as due to the creation and subsequent decay of a new light particle of mass $\sim$17 MeV. In this work, we investigate the possibility that the source of the observed signals is a set of new excitation channels created by the 12-quark hidden-color Fock state within the ${\rm {^4He}}$ nuclear wavefunction dubbed the ``hexadiquark.'' We calculate the invariant $e^+e^-$ mass spectrum for the electromagnetic transition from a new excitation of $^{4}$He, estimating its differential and total decay width. We find that we can fit the shape of the anomalous signal with the QCD Fock state at excitation energy $\rm E^{*} = 17.9 \pm 1$ MeV and a Gaussian form factor for the electromagnetic decay. We address the physical issues with the fit parameters using properties of the hexadiquark state, in particular the three weakly repulsive $\rm 6_C$ interactions of $\rm SU(3)_C$ between diquark pairs. Experimental tests of our model are described in detail. In light of this work, we emphasize the need for independent experimental confirmation or refutation of the ATOMKI results as well as dedicated experiments to search for the proposed new excitations of ${\rm ^4He}$ and other $α$-cluster nuclei.

hep-ph↗

arXiv2024

Color symmetry and confinement as an underlying superconformal structure in holographic QCD

Dedicated to the memory of our colleague, Harald Fritzsch, who, together with Murray Gell-Mann, introduced the color quantum number as the exact symmetry responsible for the strong interaction, thus establishing quantum chromodynamics (QCD) as a fundamental non-Abelian gauge theory. A basic understanding of hadron properties, however, such as confinement and the emergence of a mass scale, from first principles QCD has remained elusive: Hadronic characteristics are not explicit properties of the QCD Lagrangian and perturbative QCD, so successful in the large transverse momentum domain, is not applicable at large distances. In this article, we shall examine how this daunting obstacle is overcome in holographic QCD with the introduction of a superconformal symmetry in anti de Sitter (AdS) space which is responsible for confinement and the introduction of a mass scale within the superconformal group. When mapped to light-front coordinates in physical spacetime, this approach incorporates supersymmetric relations between the Regge trajectories of meson, baryon and tetraquark states which can be visualized in terms of specific $SU(3)_C$ color representations of quarks. We will also briefly discuss here the implications of holographic models for QCD color transparency in view of the present experimental interest. Based on the invited contribution to the book dedicated to the memory of Harald Fritzsch.

hep-ph↗

arXiv2024

The strong 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.

hep-ph↗

arXiv2024

Entropy from entangled parton states and high-energy scattering behavior

The relation between the gluon density in a hadron and entanglement entropy can shed a new light on the high energy scattering behavior of hadrons. Using the holographic light-front QCD framework the growth above the classical geometric cross section is directly related to the increase of the internal quantum entropy from the entangled parton distribution in hadrons. A rather consistent picture emerges from the scale dependence of the Pomeron from the QCD evolution of the gluon distribution function $g(x, μ)$, the rising of the integrated cross section in photoproduction of vector mesons, the deep inelastic scattering (DIS) experiments at HERA, hadron multiplicity and quantum entropy. We also point out a possible analogy between parton entanglement entropy and the black-hole entropy of Bekenstein and Hawking.

hep-ph↗

arXiv2023

High precision tests of QCD without scale or scheme ambiguities

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 $α_s(μ_R^2)$ 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 $N_C\to 0$ 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. [full abstract is in the paper].

hep-ph↗

arXiv2023

Elimination of QCD Renormalization Scale and Scheme Ambiguities

We present results for the thrust distribution in the electron positron annihilation to the three jet process at NNLO in the perturbative conformal window of QCD, as a function of the number of flavors $N_f$. Given the existence of an infrared interacting fixed point in this region, we can compare the Conventional Scale Setting (CSS) and the Principle of Maximum Conformality (PMC$_\infty$) methods along the entire renormalization group flow from the highest energies to zero energy. We then consider also the QED thrust, obtained as the limit $N_c \rightarrow 0$ of the number of colors and we show analogous comparison. QED in the low energy regime develops an infrared non-interacting fixed point. Using these quantum field theory limits as theoretical laboratories, we arrive at interesting results showing new features of the PMC$_\infty$.

hep-ph↗

arXiv2023

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.

hep-ph↗

arXiv2023

Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and 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.

hep-ph↗

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.

hep-ph↗