Higgs and supersymmetry

Global frequentist fits to the CMSSM and NUHM1 using the MasterCode framework predicted M _h ?119 GeV in fits incorporating the (g?2) _μ constraint and ?126 GeV without it. Recent results by ATLAS and CMS could be compatible with a Standard Model-like Higgs boson around M _h ?125 GeV. We use the previous MasterCode analysis to calculate the likelihood for a measurement of any nominal Higgs mass within the range of 115 to 130 GeV. Assuming a Higgs mass measurement at M _h ?125 GeV, we display updated global likelihood contours in the (m ₀,m _1/2) and other parameter planes of the CMSSM and NUHM1, and present updated likelihood functions for $m_{\tilde{g}}, m_{\tilde{q}_{R}}We perform a determination of the strong coupling constant using the latest ATLAS inclusive jet cross section data, from proton?Cproton collisions at $\sqrt{s}=7~\mathrm{TeV}$ , and their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the different data inputs are studied and compared. The theoretical prediction is obtained using NLO QCD, and it also includes non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600?GeV, the running of the strong coupling being also tested in this range. Good agreement is observed when comparing our result with the world average at the Z-boson scale, as well as with the most recent results from the Tevatron.     

Fractional supersymmetry as a superposition of ordinary supersymmetry

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.     

Unconstrained supersymmetry

This is a first step towards better superfield formulations of supersymmetric field theories. The simple Wess-Zumino model (including renormalizable interactions) is formulated in terms of an unconstrained, scalar superfield, obeying a wave equation that includes the square of the super Klein-Gordon operator. This wave equation is derived from an action principle, by unconstrained variation of the superfield. The physical content of the theory is the same as for the original formulation by Wess and Zumino, and the Feynman rules are identical to those of Grisaru, Roek and Siegel. Next, super electrodynamics, including minimal interactions with a scalar matter multiplet, is given a similar treatment. There is no need, in this case, to include higher derivatives in the Lagrangian. The matter field is an unconstrained, scalar superfield, and the gauge fields are also contained in an unconstrained, scalar superfield. The scattering matrix coincides with that of the conventional form of super electrodynamics with Wess-Zumino matter fields. Supersymmetric spinorial currents are found by simple and direct application of the Noetherian method, in superfield language. Conservation laws of the formD _a J ^a =0 (resp.D _a J ^ab =0) are derived from gauge invariance (resp. supersymmetry). Extension to super Yang-Mills theories is straightforward.On leave of absence from Universidad Complutense, Madrid. Permanent address: Department of Theoretical Physics, Universidad Complutense, 28040 Madrid, Spain.     

Low-energy supersymmetry

We discuss the problem of constructing a model in which supersymmetry is unbroken down to low energies. It is suggested that the scalar partners of quarks and leptons may get their masses through radiative corrections and that the breaking of the weak interactions also occurs through radiative corrections. A toy model is constructed which illustrates these ideas.     

Dimensional regularization and supersymmetry

A detailed numerical integration of the Oppenheimer-Volkoff equations for isothermal partially degenerate neutral lepton configurations shows that the mass distribution of the dark halo around the giant elliptical galaxy M87, as revealed by X-ray observations, can be very naturally accounted for, in detail, by an atmosphere of (10–50 eV) neutrinos.     

Fermion flows and supersymmetry

Even fermionic stochastic flows are shown to be closely related to the mathematics of supersymmetry.     

Secret supersymmetry

We present new non-linear realizations of the N = 1 supergravity algebra. They allow us to build interesting realistic models of the four forces of nature. These models are different from all previous ones in that particles do not appear in (broken) supersymmetric multiplets.These new non-linear realizations also permit us to construct the effective low-energy lagrangian of an arbitrary supergravity theory in which supersymmetry is spontaneously broken. We are thus able to analyze what are the model-independent low-energy effects of supergravity. We find that the number of Higgs fields and the way they couple to quark and lepton matter is a feature which distinguishes supersymmetric theories from non-supersymmetric ones.     

Non-minimal and non-universal supersymmetry

I motivate and discuss non-minimal and non-universal models of supersymmetry and supergravity consistent with string unification at 10¹⁰ GeV.     

Dimensional regularization and supersymmetry

We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories.     

Vacuum stability and supersymmetry

Radiative effects are shown to cause breakdown of the semiclassical ground state in a massless theory of fermions and spinless bosons when the coupling of fermions to bosons is larger than the boson self-coupling. Supersymmetry forms the boundary, in coupling constant space, separating theories with and without stable semiclassical vacua.     

Strong gravity and supersymmetry

We construct a supersymmetric theory for a strong f- plus a weak g-graviton, together with their accompanying massive gravitinos, by gauging the graded OSp(2, 2, 1) × OSp(2, 2, 1) structure. The mixing term between f- and g-fields, which makes the strong graviton massive, can be introduced through a spontaneous symmetry-breaking mechanism implemented in this paper by constructing a non-linear realization of the symmetry group.     

Non-commutative geometry and supersymmetry

A direct correspondence between supersymmetric models and a recently proposed field theory based on non-commutative geometry is established.     

Measuring supersymmetry

If new physics is found at the LHC (and the ILC) the reconstruction of the underlying theory should not be biased by assumptions about high-scale models. For the mapping of many measurements onto high-dimensional parameter spaces we introduce SFitter with its new weighted Markov chain technique. SFitter constructs an exclusive likelihood map, determines the best-fitting parameter point and produces a ranked list of the most likely parameter points. Using the example of the TeV-scale supersymmetric Lagrangian we show how a high-dimensional likelihood map will generally include degeneracies and strong correlations. SFitter allows us to study such model-parameter spaces employing Bayesian as well as frequentist constructions. We illustrate in detail how it should be possible to analyze high-dimensional new-physics parameter spaces like the TeV-scale MSSM at the LHC. A combination of LHC and ILC measurements might well be able to completely cover highly complex TeV-scale parameter spaces.     

Hidden supersymmetry

Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles. Supersymmetry is broken at the macroscopic scale of the observable particles by a discrete symmetry but remains exact at the scale of the fundamental particle and is thus hidden. This provides a link between theories at very high energies and the observed particle physics. Supersymmetric particles are confined in usual matter.