Gluon TMD studies at EIC

A high-energy Electron-Ion Collider (EIC) would offer a most promising tool to study in detail the transverse momentum distributions of gluons inside hadrons. This applies to unpolarized as well as linearly polarized gluons inside unpolarized protons, and to left-right asymmetric distributions of gluons inside transversely polarized protons, the so-called gluon Sivers effect. The inherent process dependence of these distributions can be studied by comparing to similar, but often complementary observables at LHC.Comment: 6 pages, no figures, contribution to the proceedings of the 6th International conference on Physics Opportunities at an ElecTron-Ion Collider (POETIC VI), \'Ecole Polytechnique, Palaiseau, France, September 7-11, 201

Gluon TMDs in quarkonium production

Quarkonium production offers good possibilities to study gluon TMDs. In this proceedings contribution this topic is explored for the linearly polarized gluons inside unpolarized hadrons and unpolarized gluons inside transversely polarized hadrons. It is argued that $\chi_{b0/2}$ and $\eta_b$ production at LHC are best to study the effects of linearly polarized gluons in hadronic collisions, by means of angular independent ratios of ratios of cross sections. This can be directly compared to $\cos 2\phi$ asymmetries in heavy quark pair and dijet production in DIS at a future high-energy Electron-Ion Collider (EIC), which probe the same TMDs. In the small-$x$ limit this corresponds to the Weizs\"acker-Williams (WW) gluon distributions, which should show a change in behavior for transverse momenta around the saturation scale. Together with investigations of the dipole (DP) gluon distributions, this can provide valuable information about the polarization of the Color Glass Condensate if sufficiently small $x$ are reached. Quarkonia can also be useful in the study of single transverse spin asymmetries. For transversely polarized hadrons the gluon distribution can be asymmetric, which is referred to as the Sivers effect. It leads to single spin asymmetries in for instance $J/\psi$ (pair) production at AFTER@LHC, which probe the WW or $f$-type gluon Sivers TMD. It allows for a test of a sign-change relation w.r.t. the gluon Sivers TMD probed at an EIC in open heavy quark pair production. Single spin asymmetries in backward inclusive $C$-odd quarkonium production, such as $J/\psi$ production, may offer probes of the DP or $d$-type gluon Sivers TMD at small $x$-values in the polarized proton, which in that limit corresponds to a correlator of a single Wilson loop, describing the spin-dependent odderon.Comment: 9 pages, no figures, contribution to the proceedings of the ECT* Workshop: New Observables in Quarkonium Production (Quarkonium2016), Trento, Italy, 28 February - 4 March 201

Overview of Spin Physics at EIC

The possibilities to measure spin effects at a high-energy Electron-Ion Collider (EIC) are reviewed from a theory point of view. Various types of spin distributions and promising observables are discussed.Comment: 9 pages; based on an invited talk at the 23rd International Spin Physics Symposium (SPIN2018), 10-14 September, 2018, Ferrara, Ital

Fine-tuning and the doublet-triplet splitting problem in the minimal SU(5)SU(5) GUT

In this paper we analyse the doublet-triplet splitting problem in the minimal non-super-symmetric $SU(5)$ GUT. We take into account the full symmetry breaking pattern with both high scale $SU(5)$ breaking and electroweak symmetry breaking. Our analysis shows that the only phenomenologically acceptable model has three vevs, with a strong hierarchy determined by the minimization conditions. The amount of fine-tuning in the model is then numerically evaluated by looking at the effect of variation of input parameters on both the minimization conditions and the bosonic masses. Regarding the vevs as output parameters, a large amount of fine-tuning is required in this scenario, which is an expression of the doublet-triplet splitting problem. We show that this problem is more general, since a model with coupled scalar sectors will in general never realise a hierarchy in vevs. To avoid these problems we advocate imposing the desired hierarchy in vevs as part of the theory. We argue for this viewpoint because the $SU(5)$ breaking and electroweak symmetry breaking need to be adjusted to each other anyway and cannot be regarded as independent mechanisms. We suggest that not only the symmetry breaking pattern needs to be imposed, but also the scales at which the breakings happen. We show quantitatively that the generic theory with hierarchy imposed does not require any fine-tuning of the free parameters which can all be natural and perturbative as desired.Comment: 14 pages, 3 figure

Opportunities for spin physics at EIC

This is a brief overview of the spin physics opportunities at a high energy, high luminosity, polarized Electron-Ion Collider (EIC). It covers measurements of electroweak polarized structure functions, quark and gluon PDFs, TMDs, GPDs and GTMDs. Exploiting the many possible final states allows to probe various spin effects. Open and bound heavy quark production can be used to probe gluon TMDs, but also color-octet NRQCD long distance matrix elements. Spin-dependent fragmentation functions can be used too, but are also interesting in themselves. Especially for studies of the small-$x$ and the high-$Q^2$ spin structure the EIC will be essential.Comment: 6 pages, contribution to the Proceedings of the XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2019, 8-12 April, 2019, Torino, Ital

Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths

In recent years, probabilistic analysis of highly dependable Markovian systems has received considerable attention. Such systems typically consist of several component types, subject to failures, with spare components for replacement while repair is taking place. System failure occurs when all (spare) components of one or several types have failed. In this work we try to estimate the probability of system failure before some fixed time bound $\tau$ via stochastic simulation. Obviously, in a highly dependable system, system failure is a rare event, so we apply importance sampling (IS) techniques, based on knowledge of the behaviour of the system and the way the rare event occurs. In our talk we discern several interesting ways in which the rare event can occur, each of which has its own way of affecting the efficiency of an importance sampling technique

Theoretical aspects of transversity observables

Theoretical aspects of transversity observables are reviewed. The main focus is on two leading twist transversity single spin asymmetries, one arising from the Collins effect and one from the interference fragmentation functions. Electron-positron annihilation experiments which are required to obtain these fragmentation functions are discussed, as well as the issues of factorization, evolution and Sudakov factors for the relevant observables. These theoretical considerations pinpoint the most realistic scenarios towards measurements of transversity.Comment: 4 pages, uses espcrc2.sty, Talk presented at the "International Workshop on the Spin Structure of the Proton and Polarized Collider Physics", ECT*, Trento, Italy, July 23-28, 200

GTMD model predictions for exclusive coherent diffractive J/ψJ/\psi production

We extend a previous GTMD model to improve the description of the HERA data on diffractive dijet production, and include exclusive coherent diffractive $J/\psi$ production data. We find that within our gluon GTMD model context and assumptions, there is considerable tension between the data for these two types of processes concerning the $t$ dependence. Photo- and electroproduction data for protons and nuclei from EIC and UPC data from LHC and RHIC can help to establish whether a common GTMD description is possible, as one would expect, and to facilitate studies of such data we provide predictions for the various experiments. We point out explicitly in which sense this goes beyond the description in terms of GPDs.Comment: 15 pages, 19 figures; new references added and some modifications of the tex