cdms-ii - CDMS Experiment - University of California, Berkeley

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2 CHAPTER 1. INTRODUCTION Though the Higgs mechanism is appealing from the standpoint of preserving the gauge symmetry, it has a few problems 1 . One of the problems is the Gauge Hierarchy problem. If we consider first order quantum corrections to the Higgs self energy, we find that the fermion Yukawa couplings lead to diagrams like those shown in Fig. 1.1. The contribution of such loops to the Higgs mass diverges quadratically ∆µ 2 ∼ λ 2 fΛ 2 (1.2) where λ f is the Yukawa coupling of the fermion f and Λ corresponds to the cutoff from which new physics must enter. In the Standard Model, the radiative corrections are dominated by loops with the top quark, the W bosons, and the Higgs itself. Natural values for Λ would be M GUT or M P lanck . The problem with the quadratic divergence is that Electro-Weak symmetry breaking gives 〈φ〉 = √ µ 2 λ ∼ 200 GeV which is only possible if extreme fine tuning cancels the corrections of order M 2 P lanck from Eqn. 1.8. One might think that this problem would extend to the gauge bosons as well since they also receive corrections from diagrams similar to Fig. 1.1. However, in the case of the gauge bosons, they are protected by gauge invariance and diagrams cancel leaving only a logarithmic divergence. The removal of quadratic divergences for the gauge bosons by a symmetry presents an idea as to how the Gauge Hierarchy problem may be resolved. 1.1.2 The Problem of Dark Matter The second indicator of physics beyond the Standard Model is the mounting evidence for non-baryonic dark matter for which the Standard Model has no explanation. For reviews of this evidence, the reader is referred to [1, 2, 3]. In this section, I will briefly summarize two sets of observations that are especially relevant to CDMS II. 1 One problem, that we will not discuss, is that neither the Higgs nor any other fundamental scalar has been observed.
ç 1.1. HINTS OF PHYSICS BEYOND THE STANDARD MODEL 3 f h ç Figure 1.1: Fermion loop correction to the Higgs self energy. There are also corrections from loops with the gauge bosons and the Higgs itself. In the Standard Model, the t, W , and h loops give the largest contributions. Galactic Dark Matter The first set of observations deal with dark matter in spiral galaxies. It is possible to estimate the spatial mass distribution in a spiral galaxy by measuring the rotational velocity for objects that would be subject to the galaxy’s gravity. Specifically, we can determine the rotational veolocity of clouds of neutral hydrogen by measuring the Doppler shift of the fine structure line. If the majority of the mass of a galaxy is in the form of luminous matter, Keplerian mechanics predicts that the rotational velocity for objects far from the luminous part of a spiral galaxy should decrease as 1/ √ r. However, the measured rotation curves plateau instead of falling off indicating that there is substantial mass where there is no significant luminous matter. Fig. 1.2 shows the rotation curve of a typical spiral galaxy and Fig. 1.3 shows that this profile is characteristic of many spiral galaxies. The rotation curves suggest that the majority of the mass in a spiral galaxy is actually
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