Naturalness and Supersymmetry

Supersymmetry solves the gauge hierarchy problem of the Standard Model if the masses of supersymmetric partners of the SM particles are close to the weak scale. In this thesis, we argue that the supersymmetric Standard Model, while avoiding the fine tuning in electroweak symmetry breaking, requires unnaturalness/fine tuning in some (other) sector of the theory. For example, Baryon and Lepton number violating operators are allowed which lead to proton decay and flavor changing neutral currents. We study some of the constraints from the latter in this thesis. We have to impose an R-parity for the theory to be both natural and viable. In the absence of flavor symmetries, the supersymmetry breaking masses for the squarks and sleptons lead to too large flavor changing neutral currents. We show that two of the solutions to this problem, gauge mediation of supersymmetry breaking and making the scalars of the first two generations heavier than a few TeV, reintroduce fine tuning in electroweak symmetry breaking. We also construct a model of low energy gauge mediation with a non-minimal messenger sector which improves the fine tuning and also generates required Higgs mass terms. We show that this model can be derived from a Grand Unified Theory despite the non-minimal spectrum.Comment: LaTeX, 154 pages, figures. Ph.D. thesis (UC Berkeley, May 1998

Using Energy Peaks to Measure New Particle Masses

We discussed in arXiv:1209.0772 that the laboratory frame distribution of the energy of a massless particle from a two-body decay at a hadron collider has a peak whose location is identical to the value of this daughter's (fixed) energy in the rest frame of the corresponding mother particle. For that result to hold we assumed that the mother is unpolarized and has a generic boost distribution in the laboratory frame. In this work we discuss how this observation can be applied for determination of masses of new particles, without requiring a full reconstruction of their decay chains or information about the rest of the event. We focus on a two-step cascade decay of a massive particle that has one invisible particle in the final state: C -> Bb -> Aab, where C, B and A are new particles of which A is invisible and a, b are visible particles. Combining the measurements of the peaks of energy distributions of a and b with that of the edge in their invariant mass distribution, we demonstrate that it is in principle possible to determine separately all three masses of the new particles, in particular, without using any measurement of missing transverse momentum. Furthermore, we show how the use of the peaks in an inclusive energy distribution is generically less affected by combinatorial issues as compared to other mass measurement strategies. For some simplified, yet interesting, scenarios we find that these combinatorial issues are absent altogether. As an example of this general strategy, we study SUSY models where gluino decays to an invisible lightest neutralino via an on-shell bottom squark. Taking into account the dominant backgrounds, we show how the mass of the bottom squark, the gluino and (for some class of spectra) that of the neutralino can be determined using this technique.Comment: 42 pages, 11 figure

Top Compositeness and Precision Unification

The evolution of Standard Model gauge couplings is studied in a non-supersymmetric scenario in which the hierarchy problem is resolved by Higgs compositeness above the weak scale. It is argued that massiveness of the top quark combined with precision tests of the bottom quark imply that the right-handed top must also be composite. If, further, the Standard Model gauge symmetry is embedded into a simple subgroup of the unbroken composite-sector flavor symmetry, then precision coupling unification is shown to occur at~10^{15} GeV, to a degree comparable to supersymmetric unification.Comment: v2: few extra comments added; slightly shorter version published in PR

Probing the Randall-Sundrum geometric origin of flavor with lepton flavor violation

The ``anarchic'' Randall-Sundrum model of flavor is a low energy solution to both the electroweak hierarchy and flavor problems. Such models have a warped, compact extra dimension with the standard model fermions and gauge bosons living in the bulk, and the Higgs living on or near the TeV brane. In this paper we consider bounds on these models set by lepton flavor violation constraints. We find that loop-induced decays of the form l->l'+gamma are ultraviolet sensitive and uncalculable when the Higgs field is localized on a four-dimensional brane; this drawback does not occur when the Higgs field propagates in the full five-dimensional space-time. We find constraints at the few TeV level throughout the natural range of parameters, arising from muon-electron conversion in the presence of nuclei, rare muon decays, and rare tau decays. A "tension" exists between loop-induced dipole decays such as mu->e+gamma and tree-level processes such as muon-electron conversion; they have opposite dependences on the five-dimensional Yukawa couplings, making it difficult to decouple flavor-violating effects. We emphasize the importance of the future experiments MEG and PRIME. These experiments will definitively test the Randall-Sundrum geometric origin of hierarchies in the lepton sector at the TeV-scale.Comment: 27 pgs, 15 figs; v2: numerical bug in tau decays fixe

Composite Higgs-Mediated FCNC

We discuss how, in the presence of higher-dimensional operators, the Standard Model (SM) fermion masses can be misaligned in flavor space with the Yukawa couplings to the Higgs boson, even with only one Higgs doublet. Such misalignment results in flavor-violating couplings to the Higgs and hence flavor-changing neutral current (FCNC) processes from tree-level Higgs exchange. We perform a model-independent analysis of such an effect. Specializing to the framework of a composite Higgs with partially composite SM gauge and fermion fields, we show that the constraints on the compositeness scale implied by epsilon_K can be generically as strong as those from the exchange of heavy spin-1 resonances if the Higgs is light and strongly coupled to the new states. In the special and well motivated case of a composite pseudo-Goldstone Higgs, we find that the shift symmetry acting on the Higgs forces an alignment of the fermion mass terms with their Yukawa couplings at leading order in the fermions' degree of compositeness, thus implying much milder bounds. As a consequence of the flavor-violating Higgs couplings, we estimate BR(t -> c h) ~ 10^{-4} and BR(h -> tc) ~ 5 x 10^{-3} both for a pseudo-Goldstone (if t_R is fully composite) and for a generic composite Higgs. By virtue of the AdS/CFT correspondence, our results directly apply to 5-dimensional Randall-Sundrum compactifications.Comment: 14 pages; v2: important change in the model-independent analysis of section 2, a comment added in the conclusions on how our results are modified by relaxing the assumptions of linear couplings and flavor anarchy. A few typos corrected, two references added. All conclusions unchanged. Version published in PR

Mass Measurement Using Energy Spectra in Three-body Decays

In previous works we have demonstrated how the energy distribution of massless decay products in two body decays can be used to measure the mass of decaying particles. In this work we show how such results can be generalized to the case of multi-body decays. The key ideas that allow us to deal with multi-body final states are an extension of our previous results to the case of massive decay products and the factorization of the multi-body phase space. The mass measurement strategy that we propose is distinct from alternative methods because it does not require an accurate reconstruction of the entire event, as it does not involve, for instance, the missing transverse momentum, but rather requires measuring only the visible decay products of the decay of interest. To demonstrate the general strategy, we study a supersymmetric model wherein pair-produced gluinos each decay to a stable neutralino and a bottom quark-antiquark pair via an off-shell bottom squark. The combinatorial background stemming from the indistinguishable visible final states on both decay sides can be treated by an "event mixing" technique, the performance of which is discussed in detail. Taking into account dominant backgrounds, we are able to show that the mass of the gluino and, in favorable cases, that of the neutralino can be determined by this mass measurement strategy.Comment: 42 pages, 12 figures, Journal-submitted versio

A simple, yet subtle "invariance" of two-body decay kinematics

We study the two-body decay of a mother particle into a massless daughter. We further assume that the mother particle is unpolarized and has a generic boost distribution in the laboratory frame. In this case, we show analytically that the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the (fixed) energy of that particle in the rest frame of the corresponding mother particle. Given its simplicity and "invariance" under variations of the boost distribution of the mother particle, our finding should be useful for the determination of masses of mother particles. In particular, we anticipate that such a procedure will then not require a full reconstruction of this two-body decay chain (or for that matter, information about the rest of the event). With this eventual goal in mind, we make a proposal for extracting the peak position by fitting the data to a well-motivated analytic function describing the shape of such energy distribution. This fitting function is then tested on the theoretical prediction for top quark pair production and its decay and it is found to be quite successful in this regard. As a proof of principle of the usefulness of our observation, we apply it for measuring the mass of the top quark at the LHC, using simulated data and including experimental effects.Comment: 5 pages, 2 figures, discussions and references adde