The photon angular momentum contrroversy: Resolution of a conflict between laser optics and particle physics

The claim some years ago, contrary to all textbooks, that the angular momentum of a photon (and gluon) can be split in a gauge-invariant way into an orbital and spin term, sparked a major controversy in the Particle Physics community. A further cause of upset was the realization that the gluon polarization in a nucleon, a supposedly physically meaningful quantity, corresponds only to the gauge-variant gluon spin derived from Noether's theorem, evaluated in a particular gauge. On the contrary, Laser Physicists have, for decades, been happily measuring physical quantities which correspond to orbital and spin angular momentum evaluated in a particular gauge. This paper reconciles the two points of view.Comment: 6 pages, no figure

Some Remarks on Methods of QCD Analysis of Polarized DIS Data

The results on polarized parton densities (PDFs) obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and dynamic 1/Q^2 corrections to spin structure function g_1, is demonstrated. It is pointed out that the precise data in the preasymptotic region require a more careful matching of the QCD predictions to the data in this region in order to determine the polarized PDFs correctly.Comment: 14 pages, 8 figure

A New Study of the Polarized Parton Densities in the Nucleon

We present a new next-to-leading order QCD analysis of the world data on inclusive polarized deep inelastic lepton-nucleon scattering adding to the old set of data the final SMC results, the HERMES proton and very recent SLAC/E155 deuteron data. We find an excellent fit to the data and present results for the polarized parton densities in different factorization schemes. These results are in a good agreement with what follows from the theory. We have also found that the main effect of the newly incorporated data is a better determination of the polarized gluon density.Comment: 9 pages, latex, 5 ps figures Presented at the 7th International Workshop on Deep Inelastic Scattering and QCD, Zeuthen, Germany, April 19-23, 199

Parton intrinsic motion: suppression of the Collins mechanism for transverse single spin asymmetries in p(transv. polarised) p --> pion + X

We consider a general formalism to compute inclusive polarised and unpolarised cross sections within pQCD and the factorisation scheme, taking into account parton intrinsic motion in distribution and fragmentation functions, as well as in the elementary dynamics. Surprisingly, the intrinsic partonic motion, with all the correct azimuthal angular dependences, produces a strong suppression of the transverse single spin asymmetry arising from the Collins mechanism. As a consequence, and in contradiction with earlier claims, the Collins mechanism is unable to explain the large asymmetries found in p(transv. polarised) p --> pion + X at moderate to large Feynman x_F. The Sivers effect is not suppressed.Comment: LaTeX, 21+1 pages, 1 ps figur

Partition regularity with congruence conditions

An infinite integer matrix A is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector x such that Ax is monochromatic. Given an image partition regular matrix A, can we also insist that each variable x_i is a multiple of some given d_i? This is a question of Hindman, Leader and Strauss. Our aim in this short note is to show that the answer is negative. As an application, we disprove a conjectured equivalence between the two main forms of partition regularity, namely image partition regularity and kernel partition regularity.Comment: 5 page

The angular momentum controversy: What's it all about and does it matter?

The general question, crucial to an understanding of the internal structure of the nucleon, of how to split the total angular momentum of a photon or gluon into spin and orbital contributions is one of the most important and interesting challenges faced by gauge theories like Quantum Electrodynamics and Quantum Chromodynamics. This is particularly challenging since all QED textbooks state that such an splitting cannot be done for a photon (and a fortiori for a gluon) in a gauge-invariant way, yet experimentalists around the world are engaged in measuring what they believe is the gluon spin! This question has been a subject of intense debate and controversy, ever since, in 2008, it was claimed that such a gauge-invariant split was, in fact, possible. We explain in what sense this claim is true and how it turns out that one of the main problems is that such a decomposition is not unique and therefore raises the question of what is the most natural or physical choice. The essential requirement of measurability does not solve the ambiguities and leads us to the conclusion that the choice of a particular decomposition is essentially a matter of taste and convenience. In this review, we provide a pedagogical introduction to the question of angular momentum decomposition in a gauge theory, present the main relevant decompositions and discuss in detail several aspects of the controversies regarding the question of gauge invariance, frame dependence, uniqueness and measurability. We stress the physical implications of the recent developments and collect into a separate section all the sum rules and relations which we think experimentally relevant. We hope that such a review will make the matter amenable to a broader community and will help to clarify the present situation.Comment: 96 pages, 11 figures, 5 tables, review prepared for Physics Report

Parton distribution functions of proton in a light-front quark-diquark model

We present the parton distribution functions (PDFs) for un- polarised, longitudinally polarized and transversely polarized quarks in a proton using the light-front quark diquark model. We also present the scale evolution of PDFs and calculate axial charge and tecsor charge for $u$ and $d$ quarks at a scale of experimental findings.Comment: XXII DAE-BRNS High Energy Physics Symposium, December 12-16, 2016, University of Delhi, India; 4 pages, 1 figur

The Ext algebra and a new generalisation of D-Koszul algebras

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gr\"obner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.Comment: New title; minor changes; 25 page