Abstract. The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit. The s-wave and p-wave numerical results are presented for the case of Yukawa interactions. An approximate analytic expression is also found for the Sommerfeld factor of Yukawa interactions with arbitrary partial waves, which is exact in the Coulomb limit. It is demonstrated that this result is accurate to within 10% for some common scenarios. The non s-wave Sommerfeld effect is determined to be significant, and can allow higher partial waves to dominate cross sections.

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 Delta<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 $\tan\beta$ 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.Comment: 27 pages, 6 Figures; Eqs.(15)-(18) and (A.2)-(A.5) simplified; figures 1-3 update

We consider current precision electroweak data, Z ′ searches and dark matter constraints and analyse their implications for an extension of the SM that includes an extra U (1)

In the framework of the Constrained Minimal Supersymmetric Standard Model (CMSSM) we evaluate the electroweak fine tuning measure that provides a quantitative test of supersymmetry as a solution to the hierarchy problem. Taking account of current experimental constraints we compute the fine tuning at two-loop order and determine the limits on the CMSSM parameter space and the measurements at the LHC most relevant in covering it. Without imposing the LEPII bound on the Higgs mass, it is shown that the fine tuning computed at two-loop has a minimum ∆ = 8.8 corresponding to a Higgs mass m h = 114 ± 2 GeV. Adding the constraint that the SUSY dark matter relic density should be within present bounds we find ∆ = 15 corresponding to m h = 114.7 ± 2 GeV and this rises to ∆ = 17.8 (m h = 115.9±2 GeV) for SUSY dark matter abundance within 3σ of the WMAP constraint. We extend the analysis to include the contribution of dark matter fine tuning. In this case the overall fine tuning and Higgs mass are only marginally larger for the case SUSY dark matter is subdominant and rises to ∆ = 28.7 (m h = 116.98 ± 2 GeV) for the case of SUSY dark matter saturates the WMAP bound. For a Higgs mass above these values, fine tuning rises exponentially fast. The CMSSM spectrum that corresponds to minimal fine tuning is computed and provides a benchmark for future searches. It is characterised by heavy squarks and sleptons and light neutralinos, charginos and gluinos.

Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m h ) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (∆) of the electroweak scale, and dark matter consistency. As a result, the Higgs mass is predicted to be just above the LEP2 bound, m h = 115.9 ± 2 GeV, corresponding to a minimal ∆ = 17.8, value obtained from consistency with electroweak and WMAP (3σ) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for m h above LEP2 bound), ∆ grows ≈ exponentially on either side of the above value of m h , which stresses the relevance of this prediction. A value m h > 121 (126) GeV cannot be accommodated within the CMSSM unless one accepts a fine-tuning cost worse than ∆ > 100 (1000), respectively. We review how the above prediction for m h and ∆ changes under the addition of new physics beyond the MSSM Higgs sector, parametrized by effective operators of dimensions d=5 and d=6. For d=5 operators, one can obtain values m h ≤ 130 GeV for ∆ < 10. The size of the supersymmetric correction that each individual operator of d=6 brings to the value of m h for points with ∆ < 100 (< 200), is found to be small, of few ≤ 4 GeV (≤ 6 GeV) respectively, for M = 8 TeV where M is the scale of new physics. This value decreases (increases) by approximately 1 GeV for a 1 TeV increase (decrease) of the scale M . The relation of these results to the Atlas/CMS supersymmetry exclusion limits is presented together with their impact for the CMSSM regions of lowest fine-tuning. †