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John C. Collins

Publications and source records attributed to John C. Collins.

At least 19 recordsLinked to original sources
arXiv2020

Sudakov Form Factors

The theory of the on-shell Sudakov form factor to all order of logarithms is explained.

hep-ph↗
arXiv2016

Axodraw Version 2

We present version two of the Latex graphical style file Axodraw. It has a number of new drawing primitives and many extra options, and it can now work with \program{pdflatex} to directly produce output in PDF file format (but with the aid of an auxiliary program).

cs.OH↗
arXiv2013

Neurally Implementable Semantic Networks

We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the meanings of all nodes and external events the node links with; (b) the systematic use of nodes that stand for categories or types, with separate nodes for instances of these types; (c) an implementation of relationships that does not use intrinsically typed links between nodes.

q-bio.NC↗
arXiv2012

Inability to find justification of a $k_T$-factorization formula by following chains of citations

Fundamental to much work in small-x QCD is a k_T-factorization formula. Normal expectations in theoretical physics are that when such a result is used, citations should be given to where the formula is justified. We demonstrate by examining the chains of citations back from current work that violations of this expectation are widespread, to the extent that following the citation chains, we do not find a proof or other justification of the formula. This shows a substantial deficit in the reproducibility of a phenomenologically important area of research. Since the published formulae differ in normalization, we test them by making a derivation in a simple model that obeys the assumptions that are stated in the literature to be the basis of k_T-factorization in the small-$x$ regime. We find that we disagree with two of the standard normalizations.

hep-ph↗
arXiv2012

The QCD Evolution of the Sivers Function

We extend the Collins-Soper-Sterman (CSS) formalism to apply it to the spin-dependence governed by the Sivers function. We use it to give a correct numerical QCD evolution of existing fixed-scale fits of the Sivers function. With the aid of approximations useful for the non-perturbative region, we present the results as parametrizations of a Gaussian form in transverse momentum space, rather than in the Fourier conjugate transverse coordinate space normally used in the CSS formalism. They are specifically valid at small transverse momentum. Since evolution has been applied, our results can be used to make predictions for Drell-Yan and semi-inclusive deep inelastic scattering at energies different from those where the original fits were made. Our evolved functions are of a form that they can be used in the same parton model factorization formulas as used in the original fits, but now with a predicted scale dependence in the fit parameters. We also present a method by which our evolved functions can be corrected to allow for twist-3 contributions at large parton transverse momentum.

hep-ph↗
arXiv2006

Renormalization of the Vector Current in QED

It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the MSbar-renormalized current by a definite finite renormalization. This happens in such a way that Gauss's law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.

hep-th↗
arXiv2005

Initial State Parton Showers Beyond Leading Order

We derive a new method for initial-state collinear showering in Monte-Carlo event generators which is based on the use of unintegrated parton correlation functions. Combined with a previously derived method for final-state showering, the method solves the problem of treating both the hard scattering and the evolution kernels to be used in arbitrarily non-leading order. Although we only treat collinear showering, so that further extensions are needed for QCD, we have discovered several new results: (1) It is better to generate exact parton kinematics in the hard scattering rather than with the subsequent parton showering, and similarly at each step of the showering. (2) Parton showering is then done conditionally on the exact energy-momentum of the initiating parton. (3) We obtain a factorization for structure functions in terms of parton correlation functions so that parton kinematics can be treated exactly from the beginning. (4) We obtain two factorization properties for parton correlation functions, one in terms of ordinary parton densities and one, suitable for event generation, in terms of parton correlation functions themselves.

hep-ph↗
arXiv2004

Universality of soft and collinear factors in hard-scattering factorization

Universality in QCD factorization of parton densities, fragmentation functions, and soft factors is endangered by the process dependence of the directions of Wilson lines in their definitions. We find a choice of directions that is consistent with factorization and that gives universality between e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the Drell-Yan process. Universality is only modified by a time-reversal transformation of the soft function and parton densities between Drell-Yan and the other processes, whose only effect is the known reversal of sign for T-odd parton densities like the Sivers function. The modifications of the definitions needed to remove rapidity divergences with light-like Wilson lines do not affect the results.

hep-ph↗
arXiv2003

What exactly is a parton density?

I give an account of the definitions of parton densities, both the conventional ones, integrated over parton transverse momentum, and unintegrated transverse-momentum-dependent densities. The aim is to get a precise and correct definition of a parton density as the target expectation value of a suitable quantum mechanical operator, so that a clear connection to non-perturbative QCD is provided. Starting from the intuitive ideas in the parton model that predate QCD, we will see how the simplest operator definitions suffer from divergences. Corrections to the definition are needed to eliminate the divergences. An improved definition of unintegrated parton densities is proposed.

hep-ph↗
arXiv2002

Parton Distribution Functions suitable for Monte-Carlo event generators

In the usual factorization theorems, which give predictions only for inclusive cross sections, there is considerable freedom in the choice of the scheme to define the parton distribution functions. These theorems do not directly apply to Monte-Carlo event generators, and more general factorization theorems which give predictions for fully exclusive cross sections are needed. It has been shown that appropriate parton distribution functions are uniquely defined by the showering algorithm. In this paper, we present results of calculations of the Monte-Carlo parton distribution functions in terms of the commonly used MSbar parton distribution functions. At small x the differences are large, which demonstrates the importance of using the correct parton distribution functions in an event generator rather than MSbar parton distribution functions. We present some simple approximations that enable an understanding of the sizes of the results to be obtained.

hep-ph↗
arXiv2002

Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering

Recently, Brodsky, Hwang and Schmidt have proposed a new mechanism that gives a transverse spin symmetry at leading twist in semi-inclusive deep-inelastic scattering. I show that the new mechanism is compatible with factorization and is due to an transverse-spin asymmetry in the k_T distribution of quarks in a hadron (the "Sivers asymmetry"). An earlier proof that the Sivers asymmetry vanishes because of time-reversal invariance is invalidated by the path-ordered exponential of the gluon field in the operator definition of parton densities. Instead, the time-reversal argument shows that the Sivers asymmetry is reversed in sign in hadron-induced hard processes (e.g., Drell-Yan), thereby violating naive universality of parton densities. Previous phenomenology with time-reversal-odd parton densities is therefore validated.

hep-ph↗
arXiv2001

On the Compatibility Between Physics and Intelligent Organisms

It has been commonly argued, on the basis of Goedel's theorem and related mathematical results, that true artificial intelligence cannot exist. Penrose has further deduced from the existence of human intelligence that fundamental changes in physical theories are needed. I provide an elementary demonstration that these deductions are mistaken.

physics.bio-ph↗
arXiv1999

Leptoproduction of Heavy Quarks II -- A Unified QCD Formulation of Charged and Neutral Current Processes from Fixed-target to Collider Energies

A unified QCD formulation of leptoproduction of massive quarks in charged current and neutral current processes is described. This involves adopting consistent factorization and renormalization schemes which encompass both vector-boson-gluon-fusion (flavor creation) and vector-boson-massive-quark-scattering (flavor excitation) production mechanisms. It provides a framework which is valid from the threshold for producing the massive quark (where gluon-fusion is dominant) to the very high energy regime when the typical energy scale μis much larger than the quark mass m_Q (where the quark-scattering should be prevalent). This approach effectively resums all large logarithms of the type (alpha_s(mu) log(mu^2/m_Q^2)^n which limit the validity of existing fixed-order calculations to the region mu ~ O(m_Q). We show that the (massive) quark-scattering contribution (after subtraction of overlaps) is important in most parts of the (x, Q) plane except near the threshold region. We demonstrate that the factorization scale dependence of the structure functions calculated in this approach is substantially less than those obtained in the fixed-order calculations, as one would expect from a more consistent formulation.

hep-ph↗