Discrete symmetries in higher dimensions

We consider the constraints imposed by causality on the transformations of time reversal ?, charge conjugationC, and parityP in higher dimensional space-time.     

Feynman's path integral

Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, letC be the space of pathsq:T?? → configuration space of the system, letC be the topological dual ofC; then Feynman's integral for a particle of massm in a potentialV can be written where $$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$ and wheredw is a pseudomeasure whose Fourier transform is defined by for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.     

A remark on a theorem of Powers and Sakai

Given an abelian locally compact groupG and aC*-algebra with unit,U, the set of those continuous representations ofG by automorphisms ofU which fulfill a spectrum condition is closed.     

Electroweak radiative corrections to single top production

Fortran subroutines to calculate helicity amplitudes with massive spin-3/2 particles, such as massive gravitinos, which couple to the standard model and supersymmetric particles via the supercurrent, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external gravitinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the gauge invariance of the helicity amplitudes.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

HiggsSignals: Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC

HiggsSignals is a Fortran90 computer code that allows to test the compatibility of Higgs sector predictions against Higgs rates and masses measured at the LHC or the Tevatron. Arbitrary models with any number of Higgs bosons can be investigated using a model-independent input scheme based on HiggsBounds. The test is based on the calculation of a $\chi ^2$ measure from the predictions and the measured Higgs rates and masses, with the ability of fully taking into account systematics and correlations for the signal rate predictions, luminosity and Higgs mass predictions. It features two complementary methods for the test. First, the peak-centered method, in which each observable is defined by a Higgs signal rate measured at a specific hypothetical Higgs mass, corresponding to a tentative Higgs signal. Second, the mass-centered method, where the test is evaluated by comparing the signal rate measurement to the theory prediction at the Higgs mass predicted by the model. The program allows for the simultaneous use of both methods, which is useful in testing models with multiple Higgs bosons. The code automatically combines the signal rates of multiple Higgs bosons if their signals cannot be resolved by the experimental analysis. We compare results obtained with HiggsSignals to official ATLAS and CMS results for various examples of Higgs property determinations and find very good agreement. A few examples of HiggsSignals applications are provided, going beyond the scenarios investigated by the LHC collaborations. For models with more than one Higgs boson we recommend to use HiggsSignals and HiggsBounds in parallel to exploit the full constraining power of Higgs search exclusion limits and the measurements of the signal seen at $m_H\approx 125.5$  GeV.     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

W^+W^-, WZ and ZZ production in the POWHEG-BOX-V2

We present an implementation of the vector boson pair production processes $ZZ$ , $W^+W^-$ and $WZ$ within the POWHEG-BOX-V2. This implementation, derived from the POWHEG BOX version, has several improvements over the old one, among which the inclusion of all decay modes of the vector bosons, the possibility to generate different decay modes in the same run, speed optimization and phase space improvements in the handling of interference and singly resonant contributions.     

Unitarity constraints for new physics induced by dim-6 operators

We compute the helicity amplitudes for bosonboson scattering at high energy due to the operatorsO _BΦ,O _WΦ andO _UB , and we derive the corresponding unitarity bounds. Thus, we provide relations between the couplings of these operators and the corresponding New Physics thresholds, where either unitarity is saturated or new degrees of freedom are excited. We compare the results with those previously obtained for the operatorsO _W andO _UW and we discuss their implications for direct and indirect tests at present and future colliders. The present treatment completes the study of the unitarity constraints for all blind bosonic operators.     

Irreducible multiplier corepresentations of the extended Poincaré group

The irreducible multiplier corepresentations of the extended Poincaré groupP are, for positive and zero mass, determined by generalized inducing from a generalized little group. This approach is compared with the previous one of Wigner. Form>0, and any spinj, a particular realization is noted which is manifestly covariant on all four components ofP. The choice of covering group forP is discussed, and reasons are given for preferring a group for whichS andT generate the quaternion group of order 8.     

HiggsBounds-4: improved tests of extended Higgs sectors against exclusion bounds from LEP,the Tevatron and the LHC

We describe the new developments in version 4 of the public computer code HiggsBounds. HiggsBounds is a tool to test models with arbitrary Higgs sectors, containing both neutral and charged Higgs bosons, against the published exclusion bounds from Higgs searches at the LEP, Tevatron and LHC experiments. From the model predictions for the Higgs masses, branching ratios, production cross sections and total decay widths—which are specified by the user in the input for the program—the code calculates the predicted signal rates for the search channels considered in the experimental data. The signal rates are compared to the expected and observed cross section limits from the Higgs searches to determine whether a point in the model parameter space is excluded at 95 % confidence level. In this paper we present a modification of the HiggsBounds main algorithm that extends the exclusion test in order to ensure that it provides useful results in the presence of one or more significant excesses in the data, corresponding to potential Higgs signals. We also describe a new method to test whether the limits from an experimental search performed under certain model assumptions can be applied to a different theoretical model. Further developments discussed here include a framework to take into account theoretical uncertainties on the Higgs mass predictions, and the possibility to obtain the $\chi ^2$ likelihood of Higgs exclusion limits from LEP. Extensions to the user subroutines from earlier versions of HiggsBounds are described. The new features are demonstrated by additional example programs.     

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4?2ε dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop ε-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.     

Antisymmetrization of a mean field calculation of the T-matrix

The usual definition of the prior (post) interactionV(V′) between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projectorA must be included in the definition of the transition operator, T≡V′A + V′A GV. We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate ofT. The theory is illustrated by a calculation of forwardα-α scattering, making use of self consistent symmetries.     

\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

Anticommutativity equation in topological quantum mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological correlators in this theory. We prove that the generating function ? for these correlators satisfies the anticommutativity equation (D?F)². We show that the commutativity equation [dB, dB]=0 can be considered as a special case of the anticommutativity equation.     

On the existence of Feigenbaum's fixed point

We give a proof of the existence of aC ², even solution of Feigenbaum's functional equation $$g{\text{(}}x) = - \lambda _0^{ - 1} g{\text{(}}g( - \lambda _0 x)),g{\text{(0) = 1,}}$$ whereg is a map of [?1, 1] into itself. It extends to a real analytic function over ?.     

Irreducible Lie algebra extensions of the Poincaré algebra

We use cohomology of Lie algebras to analyse the abelian extensions of the Poincaré algebraP. We study particularly the irreducible and truly irreducible extensions: some irreducibility criteria are proved and applied to obtain a classification of types of irreducible abelian extensions ofP. We give a characterization of the minimal essential extensions in terms of truly irreducible extensions.