The two ∇ 6 R 4 type invariants and their higher order generalisation

We show that there are two distinct classes of ∇ 6 R 4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F 2 ∇ 4 R 4 that generalises to 1/8 BPS protected F 2 k ∇ 4 R 4 couplings. We work out the supersymmetry constraints on the corresponding threshold functions, and argue that the functions in the second class satisfy to homogeneous differential equations for arbitrary k ≥ 1, such that the corresponding exact threshold functions in type II string theory should be proportional to Eisenstein series, which we identify. This analysis explains in particular that the exact ∇ 6 R 4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory

Constraints on t -channel leptoquark exchange from LHC contact interaction searches

The t -channel exchange of a first generation leptoquark could contribute to the cross section for qq¯→e+e- . The leptoquark is off-shell, so this process can be sensitive to leptoquarks beyond the mass reach of pair production searches at the LHC (currently mLQ>830  GeV). We attempt to analytically translate ATLAS bounds on (q¯γμq)(e¯γμe) contact interactions to the various scalar leptoquarks, we but encounter two difficulties: the leptoquark momentum is not negligible, and the leptoquarks do not induce the contact interaction studied by ATLAS, so the interference with the standard model is different. If bounds were quoted on the functional dependence of the cross section on s^ , rather than on particular contact interaction models, these difficulties could be circumvented. We use the results of such a “form factor” fit to CMS plots to obtain bounds on the various leptoquarks’ quark–lepton coupling of order λ2≲(mLQ/3 TeV) 2

Possible explanation of excess events in the search for jets, missing transverse momentum and a Z boson in pp collisions

We study to which extent SUSY extensions of the Standard Model can describe the excess of events of 3.0 standard deviations observed by ATLAS in the on- Z signal region, respecting constraints by CMS on similar signal channels as well as constraints from searches for jets and ETmiss . GMSB-like scenarios are typically in conflict with these constraints, and do not reproduce well the shape of the ETmiss distribution of the data. An alternative scenario with two massive neutralinos can improve fits to the total number of events as well as to the HT and ETmiss distributions. Such a scenario can be realised within the NMSSM

Minimal unitary representations from supersymmetry

We compute the supersymmetry constraints on the R 4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R 4 term in the corresponding invariants. The second-order derivative of this function restricted to the Joseph ideal vanishes in dimension lower than six. These results are extended to the ∇ 4 R 4 and the ∇ 6 R 4 corrections, based on the harmonic superspace construction of these invariants in the linearised approximation. We discuss the solutions of these differential equations and analysis the consequences on the non-perturbative type II low energy string theory effective action

Interior potential of a toroidal shell from pole values

We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $\Psi(R,Z)$ of a shell with a circular section at the pole of toroidal coordinates is first established. It depends on the mass of the shell, its main radius and axis-ratio $e$ (i.e. core-to-main radius ratio), and involves the product of the complete elliptic integrals of the first and second kinds. Next, we show that successive partial derivatives $\partial^{n +m} \Psi/\partial_{R^n} \partial_{Z^m}$ are also accessible by analytical means at that singular point, thereby enabling the expansion of the interior potential as a bivariate series. Then, we have generated approximations at orders $0$, $1$, $2$ and $3$, corresponding to increasing accuracy. Numerical experiments confirm the great reliability of the approach, in particular for small-to-moderate axis ratios ($e^2 \lesssim 0.1$ typically). In contrast with the ellipsoidal case (Newton's theorem), the potential is not uniform inside the shell cavity as a consequence of the curvature. We explain how to construct the interior potential of toroidal shells with a thick edge (i.e. tubes), and how a core stratification can be accounted for. This is a new step towards the full description of the gravitating potential and forces of tori and rings. Applications also concern electrically-charged systems, and thus go beyond the context of gravitation.Comment: Accepted for publication in MNRA

Phase transition in tensor models

Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a 1/ N expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in 1/ N (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field

Spin–orbit correlations in the nucleon

We investigate the correlations between the quark spin and orbital angular momentum inside the nucleon. Similarly to the Ji relation, we show that these correlations can be expressed in terms of specific moments of measurable parton distributions. This provides a whole new piece of information about the partonic structure of the nucleon

Moment analysis of hadronic vacuum polarization

I suggest a new approach to the determination of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon aμHVP in lattice QCD. It is based on properties of the Mellin transform of the hadronic spectral function and their relation to the HVP self-energy in the Euclidean. I show how aμHVP is very well approximated by a few moments associated to this Mellin transform and how these moments can be evaluated in lattice QCD, providing thus a series of tests when compared with the corresponding determinations using experimental data

Local logarithmic correlators as limits of Coulomb gas integrals

We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro conformal blocks. Although the Coulomb Gas formalism forces a diagonal coupling between the chiral and anti-chiral sectors of the Conformal Field Theory (CFT), we present new results for the multi-screening integrals which are potentially interesting for applications to critical statistical systems described by Logarithmic CFTs. In particular our findings extend and complement previous results, derived with Coulomb Gas methods, at <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math> and <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>−</mo><mn>2</mn></math>

Brane polarization is no cure for tachyons

Anti-M2 and anti-D3 branes placed in regions with charges dissolved in fluxes have a tachyon in their near-horizon region, which causes these branes to repel each other. If the branes are on the Coulomb branch this tachyon gives rise to a runaway behavior, but when the branes are polarized into five-branes this tachyon only appears to lower the energy of the polarized branes, without affecting its stability. We analyze brane polarization in the presence of a brane-brane-repelling tachyon and show that when the branes are polarized along the direction of the tachyon the polarized shell is unstable. This implies that tachyons cannot be cured by brane polarization and indicates that, at least in a certain regime of parameters, anti-D3 branes polarized into NS5 branes at the bottom of the Klebanov-Strassler solution have an instability