QCD Observables Research Articles

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024

Renormalons and power corrections in pseudo- and quasi-GPDs

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and pseudo-GPDs which are used in lattice calculations of generalized parton distributions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-GPDs on x variable for nonzero skewedness parameter ξ. The kinematic point x=±ξ turns out to be special. We find that the nonperturbative corrections to quasi-GPDs at this point are suppressed by the first power of the hard scale only. These contributions come from soft momenta and have nothing to do with the known UV renormalon in the Wilson line. We also show that power corrections can be strongly suppressed by the normalization procedure. Published by the American Physical Society 2024

Hadron-level NLO predictions for QCD observables in photo-production at the Electron-Ion Collider

We present the first next-to-leading order accurate hadron-level predictions for inclusive QCD and jet observables in photo-production for electron-proton beams at the upcoming electron-ion collider. Our predictions show large K factors of about 60% and a dominating real correction. Published by the American Physical Society 2024

The Interrelated Roles of Correlations in the Nuclear Equation of State and in Response Functions: Application to a Chiral Confining Theory

We study the role of short-range correlations, as well as pion and rho loops governing long-range RPA correlations, in nuclear matter properties and response functions. We use an adapted formulation of the Brueckner G-matrix approach to generate a pair correlation function satisfying the Beg–Agassi–Gal theorem, providing a natural cutoff to the loop integrals. We present results for the case of a relativistic chiral theory, including the effects of quark confinement and of the chirally broken vacuum in a version where parameters are directly connected to QCD observables or constrained by well-established hadron phenomenology. This provides a unified and coherent view of the nuclear matter equation of state and the effect of correlations on neutrino–nucleus scattering.

Analytic Computation of three-point energy correlator in QCD

The energy correlator measures the energy deposited in multiple detectors as a function of the angles among them. In this paper, an analytic formula is given for the three-point energy correlator with full angle dependence at leading order in electron-positron annihilation. This is the first analytic computation of trijet event shape observables in QCD, which provides valuable data for phenomenological studies. The result is computed with direct integration, where appropriate parameterizations of both phase space and kinematic space are adopted to simplify the calculation. With full shape dependence, our result provides the expansions in various kinematic regions such as equilateral, triple collinear and squeezed limits, which benefit studies on both factorization and large logarithm resummation.

Complementarity of experimental and lattice QCD data on pion parton distributions

We extract pion parton distribution functions (PDFs) in a Monte Carlo global QCD analysis of experimental data together with reduced Ioffe time pseudo-distributions and matrix elements of current-current correlators generated from lattice QCD. By including both experimental and lattice QCD data, our analysis rigorously quantifies both the uncertainties of the pion PDFs and systematic effects intrinsic to the lattice QCD observables. The reduced Ioffe time pseudo-distributions significantly decrease the uncertainties on the PDFs, while the current-current correlators are limited by the systematic effects associated with the lattice. Consistent with recent phenomenological determinations, the behavior of the valence quark distribution of the pion at large momentum fraction is found to be $\ensuremath{\sim}(1\ensuremath{-}x{)}^{{\ensuremath{\beta}}_{\mathrm{eff}}}$ with ${\ensuremath{\beta}}_{\mathrm{eff}}\ensuremath{\approx}1.0--1.2$.

Higher-order non-global logarithms from jet calculus

Non-global QCD observables are characterised by a sensitivity to the full angular distribution of soft radiation emitted coherently in hard scattering processes. This complexity poses a challenge to their all-order resummation, that was formulated at the leading-logarithmic order about two decades ago. In this article we present a solution to the long-standing problem of their resummation beyond this order, and carry out the first complete next-to-leading logarithmic calculation for non-global observables. This is achieved by solving numerically the recently derived set of non-linear differential equations which describe the evolution of soft radiation in the planar, large-Nc limit. As a case study we address the calculation of the transverse energy distribution in the interjet rapidity region in e+e−→ dijet production. The calculation is performed by means of an algorithm that we formulate in the language of jet-calculus generating functionals, which also makes the resummation technique applicable to more general non-global problems, such as those that arise in hadronic collisions. We find that NLL corrections are substantial and their inclusion leads to a significant reduction of the perturbative scale uncertainties for these observables. The computer code used in the calculations is made publicly available.

Multicanonical reweighting for the QCD topological susceptibility

We introduce a reweighting technique which allows for a continuous sampling of temperatures in a single simulation and employ it to compute the temperature dependence of the QCD topological susceptibility at high temperatures. The method determines the ratio of susceptibility between any two temperatures within the explored temperature range. We find that the results from the method agree with our previous determination and that it is competitive with but not better than existing methods of determining the temperature derivative of the susceptibility. The method may also be useful in exploring the temperature dependence of other thermodynamical observables in QCD in a continuous way.

QCD sum rules with spectral densities solved in inverse problems

We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are solved with the operator-product-expansion input on the quark side by treating sum rules as an inverse problem. This new formalism does not involve the continuum threshold, does not require the Borel transformation and stability analysis, and can be extended to extract properties of excited states. Taking the two-current correlator as an example, we demonstrate that the series of $\rho$ resonances can emerge in our formalism, and the decay constants $f_{\rho(770)} (f_{\rho(1450)},f_{\rho(1700)},f_{\rho(1900)})\approx$ 0.22 (0.19, 0.14, 0.14) GeV for the masses $m_{\rho(770)} (m_{\rho(1450)},m_{\rho(1700)},m_{\rho(1900)})\approx$ 0.78 (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width $\Gamma_{\rho(770)}\approx 0.17$ GeV can be obtained by substituting a Breit-Wigner parametrization for the $\rho(770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $\rho$ resonances. Handling the conventional sum rules with the duality assumption as an inverse problem, we find that the multiple pole sum rules widely adopted in the literature do not describe the $\rho$ excitations reasonably. The precision of our theoretical outcomes can be improved systematically by including higher-order and higher-power corrections on the quark side. Broad applications of this formalism to abundant low energy QCD observables are expected.

Deep learning and AdS/QCD

We propose a deep learning method to build an AdS/QCD model from the data of hadron spectra. A major problem of generic AdS/QCD models is that a large ambiguity is allowed for the bulk gravity metric with which QCD observables are holographically calculated. We adopt the experimentally measured spectra of $\rho$ and $a_2$ mesons as training data, and perform a supervised machine learning which determines concretely a bulk metric and a dilaton profile of an AdS/QCD model. Our deep learning (DL) architecture is based on the AdS/DL correspondence (arXiv:1802.08313) where the deep neural network is identified with the emergent bulk spacetime.

Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

We identify a property of renormalizable SU(N)/U(1) gauge theories, the intrinsic Conformality ($iCF$), which 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: the PMC$_\infty$. 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 (Principle of Maximum Conformality). We introduce a new method to identify conformal and $\beta$-terms which can be applied either to numerical or to theoretical calculations. We illustrate the PMC$_\infty$ for the thrust and C-parameter distributions in $e^+ e^-$ annihilation and then we show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC$_\infty$ can significantly improve the precision of pQCD predictions; its implementation in multi-loop analysis also simplifies the calculation of higher orders corrections in a general renormalizable gauge theory.

Comparing optimized renormalization schemes for QCD observables

Based on the renormalization group summation method of McKeon ${\it et\; al.}$, it is shown that the renormalization group equation, while related to the radiatively mass scale $\mu$, would perform a summation over QCD perturbative terms. Employing the full QCD $\beta$-function within this summation, all logarithmic corrections can be presented as log-independent contributions. In another step of this approach, the renormalization scheme dependence of QCD observables, characterized by Stevenson, is required to be examined. In this regard, two choices of renormalization scheme would be exposed. In one of them, the QCD observable is expressed in terms of two powers of running coupling constant. In the other one, the perturbative series expansion is written as an infinite series in terms of the two-loop running coupling represented by the Lambert $W$-function. In both cases, the QCD observable involves parameters which are renormalization scheme invariant and a coupling constant which is independent of the renormalization scale. We then consider the approach of complete renormalization group improvement (CORGI). In this approach, using the self consistency principle, it is possible to reconstruct the conventional perturbative series in terms of scheme invariant quantities and the coupling constant as a function of Lambert $W$-function. One of the key differences between CORGI and the renormalization group summation method of McKeon ${\it et\; al.}$ is that the later treats renormalization scale and scheme independently while the former would encounter both dependencies together. In continuation, numerical results of the two approaches are compared for $R_{e^+e^-}$ ratio and the Higgs decay width to gluon-gluon.

Renormalon-based resummation for QCD observables

A method of evaluation of spacelike QCD observables D(Q2) is presented, motivated by the renormalon structure of these quantities.

Anisotropic string tensions and inversely magnetic catalyzed deconfinement from a dynamical AdS/QCD model

We extend previous work on dynamical AdS/QCD models by introducing an extra ingredient under the form of a background magnetic field, this to gain insight into the influence such field can have on crucial QCD observables. Therefore, we construct a closed form analytic solution to an Einstein-Maxwell-dilaton system with a magnetic field. We specifically focus on the deconfinement transition, reporting inverse magnetic catalysis, and on the string tension, reporting a weaker/stronger confinement along/perpendicular to the magnetic field. The latter, being of importance to potential modelling of heavy quarkonia, is in qualitative agreement with lattice findings.

Nonsinglet polarized nucleon structure function in infrared-safe QCD

The polarized nucleon structure function in the nonsinglet case is investigated here by a new insight rather than conventional perturbative QCD (pQCD). For this purpose we note that the solution of the evolution equations in moment space involves noninteger powers of the coupling constant. Therefore it is possible to employ a new approach which is called fractional analytical perturbation theory Consequently, it is possible to remove the Landau singularities of the renormalized coupling, i.e., at the scales $Q \sim \Lambda$, using this approach. This provides an opportunity to continue the desired calculations toward small values of energy scales even less than the $\Lambda$ scale. To modify the analytical perturbation theory, a newer approach is introduced, called 2$\delta$anQCD, in which the spectral function of the holomorphic coupling is parameterized in the low-energy region by two delta functions. This model gives us more reliable results for the considered QCD observables, even in the deep infrared region. We calculate the nonsinglet part of the polarized nucleon structure function, using the 2$\delta$anQCD model, and compare it with the result from the underlying pQCD where both are in a new defined scheme, called the Lambert scheme. For this purpose we employ the anQCD package in the \textit{Mathematica} environment to establish the analytic (holomorphic) coupling constant. The results at various energy scales are also compared with the available experimental data, and it turns out that there is a good consistency between them. The results show that the obtained nucleon structure function at small energy scales has smoother behavior when using the 2$\delta$anQCD model than the underlying pQCD. In fact the coupling constant in analytic QCD behaves moderately and it makes the result approach the available data in a better way.

One-loop angularity distributions with recoil using Soft-Collinear Effective Theory

Angularities are event shapes whose sensitivity to the splitting angle of a collinear emission is controlled by a continuous parameter b, with −1 < b < ∞. When measured with respect to the thrust axis, this class of QCD observables includes thrust (b = 1) and jet broadening (b = 0), the former being insensitive to the recoil of soft against collinear radiation, while the latter being maximally sensitive to it. Presently available analytic results for angularity distributions with b ≠ 0 can be applied only close to the thrust limit since recoil effects have so far been neglected. As a first step to establish a comprehensive theoretical framework based on Soft-Collinear Effective Theory valid for all recoil-sensitive angularities, we compute for the first time angularity distributions at one-loop order in αs for all values of b taking into account recoil effects. In the differential cross section, these amount to novel sub-leading singular contributions and/or power corrections, where the former are characterized by fractional powers of the angularity and contribute appreciably close to the peak region, also for b ≳ 0.5. Our calculations are checked against various limits known in the literature and agree with the numerical output of the Event2 generator.

Principle of maximum conformality and complete renormalization group improvement approaches to optimize QCD observables: Similarity, differences, and preference

The principle of maximum conformality (PMC) in perturbative QCD predicts energy scales which are independent of the renormalization scheme and choice of the renormalization scale. In this approach the observable can be divided to the conformal and nonconformal sectors. Nonconformal dependence terms are absorbed into the running coupling constant. By absorbing these terms at any desired order, a unique scale can be obtained at that order, and the final result for the observable is independent of the initial choice of renormalization scale and also the employed scheme. This feature is in accordance with the invariant property of renormalization group. On the other side, we consider another approach which is called the complete renormalization group improvement (CORGI) to optimize the perturbative series of QCD observables. In this approach, using the self-consistency principle, all perturbative terms can be reconstructed such that they are expressed in terms of the quantities which do not depend on the renormalization scale. Each reconstructed term in this approach involves a resummation of infinite terms at a specified order. Therefore the conventional perturbative series of QCD observables appear in terms of scheme-invariant quantities. This approach is then expected to get more reliable results with respect to what we obtain in conventional perturbation theory. Considering these two approaches, we are looking to find the differences and similarities and the probable relation which might exist between them. Since the PMC approach is founded on more strong theoretical bases, the comparison between these two approaches will reveal the priority which naturally should be assigned to the PMC approach. We examine some QCD observables like the R-ratio for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation, ${R}_{\ensuremath{\tau}}$ for $\ensuremath{\tau}$ decay, and Higgs decay width to $b\overline{b}$ and gluon-gluon, and we compare the results for these observable in two approaches. For QCD observables in which there are experimental data, the results we obtain from both CORGI and PMC approaches are in good agrement with the experimental data. In other cases, the results from theses two approaches are near to each other; however, they are a little different from the results of the conventional perturbation theory.

Renormalon-motivated evaluation of QCD observables

A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization scale independent only at the one-loop level, and a large-$\beta_0$-type renormalon motivated ansatz is made for the Borel transform of this quantity. This leads to a `dressed' Borel transform of the considered observable ${\cal D}(Q^2)$. From there, a Neubert-type distribution is obtained for the observable. The described method is then applied to the massless Adler function and the related decay ratio of the $\tau$ lepton semihadronic decays. Comparisons are then made with an evaluation method at higher truncated orders, developed in our earlier works, which is a renormalization scale invariant extension of the diagonal Pad\'e approximants.

Soft-Collinear Effects in Threshold and Joint Resummation

Large perturbative corrections, which appear in perturbative expressions for many QCD observables, either at small \(Q_T\) or at partonic threshold, can be organized by way of all order resummation. Joint resummation allows simultaneous resummation of threshold and recoil effects and its impact has been assessed upto leading log, next-to-leading log (NLL) and in some cases up to NNLL accuracy. We discuss another class of terms, called soft-collinear effects, which give rise to corrections of the form \(\frac{\ln ^jN}{N}\) and their impact on the joint resummed calculations of prompt photon production cross section.

Soft thermal contributions to 3-loop gauge coupling

We analyze 3-loop contributions to the gauge coupling felt by ultrasoft (“magnetostatic”) modes in hot Yang-Mills theory. So-called soft/hard terms, originating from dimension-six operators within the soft effective theory, are shown to cancel 1097/1098 of the IR divergence found in a recent determination of the hard 3-loop contribution to the soft gauge coupling. The remaining 1/1098 originates from ultrasoft/hard contributions, induced by dimension-six operators in the ultrasoft effective theory. Soft 3-loop contributions are likewise computed, and are found to be IR divergent, rendering the ultrasoft gauge coupling non-perturbative at relative order mathcal{O}left({alpha}_{mathrm{s}}^{3/2}right) . We elaborate on the implications of these findings for effective theory studies of physical observables in thermal QCD.