Positivity bounds on gluon TMDs for hadrons of spin ≤\le 1

We consider the transverse momentum dependent gluon distribution functions (called gluon TMDs) by studying the light-front gluon-gluon correlator, extending the results for unpolarized and vector polarized targets to also include tensor polarized targets -- the latter type of polarization is relevant for targets of spin $\ge1$. The light-front correlator includes process-dependent gauge links to guarantee color gauge invariance. As from the experimental side the gluon TMDs are largely unknown, we present positivity bounds for combinations of leading-twist gluon distributions that may be used to estimate their maximal contribution to observables. Since the gluonic content of hadrons is particularly relevant in the small-$x$ kinematic region, we also study these bounds in the small-$x$ limit for the dipole-type gauge link structure using matrix elements of a single Wilson loop.Comment: 10 page

Renormalization group invariants in supersymmetric theories: one- and two-loop results

We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to the more constrained pMSSM and dMSSM, leading to even more invariants. Extending our search to the two-loop level we find that the number of invariants is considerably reduced

Directed flow from C-odd gluon correlations at small xx

It is shown that odd harmonic azimuthal correlations, including the directed flow $v_1$, in forward two-particle production in peripheral proton-nucleus ($pA$) collisions can arise simply from the radial nuclear profile of a large nucleus. This requires consideration of the C-odd part of the gluonic generalized transverse momentum dependent (GTMD) correlator of nucleons in the nucleus. The gluonic GTMD correlator is the Fourier transform of an off-forward hadronic matrix element containing gluonic field strength tensors that are connected by gauge links. It is parametrized in terms of various gluon GTMD distribution functions (GTMDs). We show (in a gauge invariant way) that for the relevant dipole-type gauge link structure in the small-$x$ limit the GTMD correlator reduces to a generalized Wilson loop correlator. The Wilson loop correlator is parametrized in terms of a single function, implying that in the region of small $x$ there is only one independent dipole-type GTMD, which can have a C-odd part. We show that the odderon Wigner distribution, which is related to this C-odd dipole GTMD by a Fourier transform, generates odd harmonics in the two-particle azimuthal correlations in peripheral $pA$ collisions. We calculate the first odd harmonic $v_1$ for forward production within the color glass condensate framework in the limit of a large number of colors. We find that nonzero odd harmonics are present without breaking the rotational symmetry of the nucleus, arising just from its inhomogeneity in the radial direction. Using a CGC model with a cubic action, we illustrate that percent level $v_1$ can arise from this C-odd mechanism. In contrast, we show that only even harmonics arise in diffractive dijet production in ultra-peripheral $pA$ collisions where this gluon dipole GTMD also appears.Comment: 23 pages, 3 figures. v2: References added; Added plot for A=63 in Fig.3 and a discussion on the A dependence. Version accepted for publication in JHE

Theoretical restrictions on the parameters of the indirect addilog system revisited

The correct parameter restrictions- less restrictive than commonly thought-of the indirect addilog system (IAS) are derived. Under correct restrictions, the IAS is superior to the linear expenditure system in computable general equilibrium models with data scarcity.CGE-modelling;indirect addilog system;parameter restriction