Dumitru Ghilencea

Fine tuning as an indication of physics beyond the MSSM

Abstract We investigate the amount of fine tuning of the electroweak scale in the presence of new physics beyond the MSSM, parametrized by higher dimensional operators. We show that these significantly reduce the MSSM fine tuning to Δ 10 for a Higgs mass between the LEPII bound and 130 GeV, and a corresponding scale M * of new physics as high as 30 to 65 times the higgsino mass. If the fine-tuning criterion is indeed of physical relevance, the findings indicate the presence of new physics in the form of new states of mass of O ( M * ) that generated the effective operators in the first instance. At small tan β these states can be a gauge singlet or a SU ( 2 ) triplet. We derive analytical results for the EW scale fine-tuning for the MSSM with higher dimensional operators, including the quantum corrections which are also applicable to the pure MSSM case in the limit the coefficients of the higher dimension operators vanish. A general expression for the fine-tuning is also obtained for an arbitrary two-Higgs doublet potential.

Supersymmetric Models with Higher Dimensional Operators

Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. If the theory has no other higher dimensional operators, under additional assumptions for the analytical continuation Minkowski-Euclidean space, the theory can be renormalisable. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.

Electroweak and dark matter constraints on a Z′ in models with a hidden valley

Abstract We consider current precision electroweak data, Z ′ searches and dark matter constraints and analyse their implications for an extension of the Standard Model (SM) that includes an extra U ( 1 ) ′ massive gauge boson and a particular hidden sector (“hidden valley”) with a confining (QCD-like) gauge group. The constraints on the Z ′ with arbitrary Z – Z ′ kinetic mixing coming from direct searches and precision tests of the Standard Model are analysed and shown to lead to a lower limit of 800 GeV on its mass. Renormalisable interactions involving the Z ′ probe the physics of the hidden valley sector which contains a pseudoscalar dark matter candidate. We find that dark matter constraints place an upper bound on the mass of the Z ′ of O ( 10 ) TeV . A TeV mass scale is needed for the hidden valley states, and the Sommerfeld factor for p-wave dark matter annihilation is found significantly to suppress the allowed parameter space of the model.

MSSM with dimension-five operators (MSSM5)

Abstract We perform a general analysis of the R-parity conserving dimension-five operators that can be present beyond the Minimal Supersymmetric Standard Model. Not all these operators are actually independent. We present a method which employs spurion-dependent field redefinitions that removes this “redundancy” and establishes the minimal, irreducible set of these dimension-five operators. Their potential effects on the MSSM Higgs sector are discussed to show that the tree level bound m h ⩽ m Z cannot be easily lifted within the approximations used, and quantum corrections are still needed to satisfy the LEPII bound. An ansatz is provided for the structure of the remaining couplings in the irreducible set of D = 5 operators, which avoids phenomenological constraints from flavor changing neutral currents. The minimal set of operators brings new couplings in the effective Lagrangian, notably “wrong”-Higgs Yukawa couplings and contact fermion–fermion–scalar–scalar interactions, whose effects are expected to be larger than those generated in the MSSM at loop or even tree level. This has implications in particular for LHC searches for supersymmetry by direct squark production.

UNIFICATION AND EXTRA SPACE-TIME DIMENSIONS

Abstract We analyse the phenomenological implications of a particular class of supersymmetric models with additional space-time dimensions below the unification scale. Assuming the unification of the gauge couplings and using a two-loop calculation below the scale of the additional space-time dimensions, we show that the value of α 3 ( M z ) is further increased from the two-loop Minimal Supersymmetric Standard Model prediction. We consider whether decompactification threshold effects could bring α 3 ( M z ) into agreement with experiment and discuss how accurately the threshold effects must be known in this case.

Living with ghosts and their radiative corrections

The role of higher derivative operators in 4D effective field theories is discussed in both nonsupersymmetric and supersymmetric contexts. The approach, formulated in the Minkowski space-time, shows that theories with higher derivative operators do not always have an improved UV behaviour, due to subtleties related to the analytical continuation from the Minkowski to the Euclidean metric. This continuation is further affected at the dynamical level due to a field-dependence of the poles of the Green functions of the particle-like states, for curvatures of the potential of order unity in ghost mass units. The one-loop scalar potential in λφ 4 theory with a single higher derivative term is shown to have infinitely many counterterms, while for a very large mass of the ghost the usual 4D renormalisation is recovered. In the supersymmetric context of the O’Raifeartaigh model of spontaneous supersymmetry breaking with a higher derivative (supersymmetric) operator, it is found that quadratic divergences are present in the one-loop self-energy of the scalar field. They arise with a coefficient proportional to the amount of supersymmetry breaking and suppressed by the scale of the higher derivative operator. This is also true in the Wess-Zumino model with higher derivatives and explicit soft breaking of supersymmetry. In both models, the UV logarithmic behaviour is restored in the decoupling limit of the ghost.

Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds

We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional = 1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k2) and the effective gauge coupling geff(k2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of geff(k2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of geff(k2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.

THE EFFECT OF YUKAWA COUPLINGS ON UNIFICATION PREDICTIONS AND THE NON-PERTURBATIVE LIMIT

Abstract We investigate the effects of Yukawa couplings on the phenomenological predictions for a class of supersymmetric models which allows for the presence of complete SU (5) multiplets in addition to the minimal supersymmetric standard model spectrum. We develop a two-loop analytical approach to quantify the predictions for gauge unification including Yukawa couplings. The effects of the heavy thresholds of the model are also included. In some cases accurate predictions can be made for the unification scale, irrespective of the initial (unknown) Yukawa couplings, so long as perturbation theory remains valid. We also consider the limit of a large number of extra states and compute the predictions in a resummed perturbation series approach to show that the results are stable in this limit. Finally we consider the possibility of making predictions for the case the gauge and Yukawa couplings enter the non-perturbative domain below the unification scale and estimate the errors which affect these predictions.

Higher Dimensional Operators in the MSSM

The origin and the implications of higher dimensional effective operators in 4‐dimensional theories are discussed in non‐supersymmetric and supersymmetric cases. Particular attention is paid to the role of general, derivative‐dependent field redefinitions which one can employ to obtain a simpler form of the effective Lagrangian. An application is provided for the Minimal Supersymmetric Standard Model extended with dimension‐five R‐parity conserving operators, to identify the minimal irreducible set of such operators after supersymmetry breaking. Among the physical consequences of this set of operators are the presence of corrections to the MSSM Higgs sector and the generation of “wrong”‐Higgs Yukawa couplings and fermion‐fermion‐scalar‐scalar interactions. These couplings have implications for supersymmetry searches at the LHC.

String thresholds and renormalization group evolution

Abstract We consider the calculation of threshold effects due to Kaluza–Klein and winding modes in string theory. We show that for a large radius of compactification these effects may be approximated by an effective field theory applicable below the string cut-off scale. Using this formalism we show that the radiative contribution to gauge couplings involving only massive Kaluza–Klein and winding modes may be calculated to all orders in perturbation theory and determine the full two-loop contribution involving light modes and estimate the magnitude of the higher-order contributions. For the case of the weakly coupled heterotic string we also discuss how an improved calculation can be made incorporating the string theory threshold corrections which avoids the limitations of the effective field theory approach. Using this formalism we determine the implications for gauge coupling unification for one representative model including the effects of two-loop corrections above the compactification scale. Finally we discuss the prospects for gauge unification in Type I models with a low string scale and point out potential fine tuning problems in this case.