Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
Andre V. Giannini, Yasushi Nara
备注：
v4: The right panel of figure 5 now shows the leading order result in the Z->0 region, in agreement with Eqs. (52) - (54) (now written for an arbitrary number of colors, Nc). Matches the published version
The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-$x$ in the limit of large valence charge density, {\it i}.{\it e}., a large nucleus made of uncorrelated color charges. In this work, we explore the effects of the first non-trivial (even C-parity) non-Gaussian correction on the color charge density to the MV model ("quartic" term) in SU(2) and SU(3) color group in the non-perturbative regime. We compare our (numerical) non-perturbative results to (analytical) perturbative ones in the limit of small or large non-Gaussian fluctuations. The couplings in the non-Gaussian action, $\barμ$ for the quadratic and $κ_4$ for the quartic term, need to be renormalized in order to match the two-point function in the Gaussian theory. We investigate three different choices for the renormalization of these couplings: i) $κ_{4}$ is proportional to a power of $\barμ$; ii) $κ_4$ is kept constant and iii) $\barμ$ is kept constant. We find that the first two choices lead to a scenario where the small-$x$ action evolves towards a theory dominated by large non-Gaussian fluctuations, regardless of the system size, while the last one allows for controlling the deviations from the MV model.
We propose a new method to renormalize lattice operators. The method is based on the technique to compute the spectral sum appearing in the Shifman-Vainshtein-Zakharov QCD sum rule from lattice correlators. The application of this technique to the light quark system is useful for operator renormalization as well as for the test of perturbative QCD and OPE. We determine the renormalization constant of the vector current and discuss extensions to other current operators.
Correlators of heavy-light quark currents in HQET: Perturbative contribution up to 4 loops and beyond
Budker Institute of Nuclear Physics（布德克尔核物理研究所）；Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（杜布纳联合核研究所鲍戈留博夫理论物理实验室）
In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing $a$= 0.03 fm $\sim$ 0.12 fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtr…
In the present work we consider the influence on the heavy quark correlators due to the instanton background in the framework of instanton liquid model (ILM) of QCD vacuum by taking into account also the perturbative gluon effects. For a single heavy quark this leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. In the heavy quark-antiquark ($Q\bar{Q}$) sector we obtain the potential consisting the direct instanton induced part and the one-gluon exchange (OGE) perturbative part which is screened at large distances due t…
We introduce the concept of the nucleon energy correlators, a set of novel objects that encode the microscopic details of a nucleon, such as the parton angular distribution in a nucleon, the collinear splitting to all orders, as well as the internal transverse dynamics of the nucleon. The nucleon energy correlators complement the conventional nucleon/nucleus tomography, but without introducing the non-perturbative fragmentation functions or the jet clustering algorithms. We demonstrate how the nucleon energy correlators can be measured in the lepton-nucleon deep inelastic scattering. The predi…
Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler function and the scalar correlator are investigated, and models for Borel transforms of their perturbative series are constructed, which respect general constraints from the operator product expansion and the renormalisation group. As a novel ingredient, the QCD coupling is employed in the so-called $C$-scheme, which has certain advantages. For the Adler function, …
We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conform…
Energy Correlators in $V + X$ as a Benchmark Observable for Precision QCD
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；High Energy Physics Division, Argonne National Laboratory（阿贡国家实验室高能物理部）；Department of Physics, Yale University（耶鲁大学物理系）；Institute of Nuclear Physics（核物理研究所）；Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）
We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pse…
In quantum field theories at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Although data from lattice simulations can in principle be used to determine spectral function characteristics, existing methods rely on the extraction of these quantities from temporal correlators, which requires one to circumvent an ill-posed inverse problem. In these proceedings we report on a recent approach that instead utilises the non-perturbative constraints imposed by field locality to extract spectral function information directly from spatial c…
Constraints on Higher-Order Perturbative Corrections in $b\to u$ Semileptonic Decays from Residual Renormalization-Scale Dependence
约束的逐步减少的剩余重整化尺度的依赖性增加循环顺序的方法获得的边界未知的高阶微扰校正重整化群不变量。这种技术适用于包容性的半轻子过程$b\to u \barν_\ell\ell^-$（明确已知的两个循环的顺序），以获得上的三个和四个循环的微扰系数，是无法通过重整化群访问的界限。利用最小灵敏度原理，得到了微扰对$Γ(b\to u \barν_\ell\ell^-)$的贡献的估计，该估计包含了来自尚未确定的高阶QCD修正的理论不确定性.
We determine the non-perturbative corrections to the gauge coupling constant and the topological charge in the Yang Mills theory. The method makes no explicit use of instanton calculations but instead relies on boundary properties of the quantum partition function. The approach may offer important clues regarding the behavior of the coupling constant and the theta angle for other gauge theories like QCD and supersymmetric QCD.
The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the $π^{2}$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polar…
We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{\rm f} \geq 3$ degenerate heavy quarks at a low energy scale $μ_{\rm dec}$, together with a non-perturbative determination of the ratio $Λ/μ_{\rm dec}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{\rm f} = 3$ QCD, demonstrating that a precise value of the strong coupling $α_s$ can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume in…
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
