Related papers: The trace anomaly and the parton model
We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective…
We review the latest information that is available about the parton distributions of the proton, paying particular attention to the determination of the gluon. We briefly describe the various processes that have been advocated to be a…
Anomaly detection and localization are widely used in industrial manufacturing for its efficiency and effectiveness. Anomalies are rare and hard to collect and supervised models easily over-fit to these seen anomalies with a handful of…
The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…
The chiral anomaly can be considered as an object defined either on the space of gauge potentials or on the orbit space. We will discuss the relation between the two descriptions. We will also relate to the cohomology of the group of gauge…
Anomaly detection methods are widely used but often rely on ad hoc rules or strong assumptions, and they often focus on tail events, missing ``inlier'' anomalies that occur in low-density gaps between modes. We propose a unified framework…
We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their relationship to the uncertainties in…
It is a well-known fact that the first and last non-trivial coefficients of the characteristic polynomial of a linear operator are respectively its trace and its determinant. This work shows how to compute recursively all the coefficients…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
We present a complete study of the one graviton-two neutral gauge bosons vertex at 1-loop level in the electroweak theory. This vertex provides the leading contribution to the interaction between the Standard Model and gravity, mediated by…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
The goal of this study was to test the equality of two covariance matrices by using modified Pillai's trace statistics under a high-dimensional framework, i.e., the dimension and sample sizes go to infinity proportionally. In this paper, we…
Let $A$ be an $m\times m$ positive semidefinite block matrix with each block being $n$-square. We write $\mathrm{tr}_1$ and $\mathrm{tr}_2$ for the first and second partial trace, respectively. In this paper, we prove the following…
We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of…
Phenomenological implications of the anomalous baryon current in the Standard Model are discussed, in particular neutrino-photon interactions at finite baryon density. A pedagogical derivation of the baryon current anomaly is given.
I discuss the issue of uncertainties in parton distributions and in the physical quantities which are determined in terms of them. While there has been significant progress on the uncertainties associated with errors on experimental data,…
We develop a framework for the reconstruction of the non-forward kernels which govern the evolution of twist-two distribution amplitudes and off-forward parton distributions beyond leading order. It is based on the knowledge of the special…
We construct a new example of the high derivative four-dimensional conformal operator. This operator acts on fermions, and its contribution to the trace anomaly has opposite sign, as compared to conventional scalars, spinors and vectors.…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D…