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Register a new userNaturalness Sum Rules and Their Collider Tests
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We present the most general sum rules reflecting the cancellation of ultraviolet divergences in the Higgs potential in weakly-coupled, natural extensions of the Standard Model. There is a separate sum rule for the cancellation of the quadratic and logarithmic divergences, and their forms depend on whether the divergences are canceled by same-spin or opposite-spin partners. These sum rules can be applied to mass eigenstates and conveniently used for direct collider tests of naturalness. We study in detail the feasibility of testing these sum rules in the top sector at a future $100TeV$ proton collider within two benchmark models, the Little Higgs (LH) and the Maximally Symmetric Composite Higgs (MSCH). We show how the two ingredients of the sum rules, the top partner masses and their Yukawa couplings to the Higgs, can be measured with sufficient accuracy to provide a highly non-trivial quantitative test of the sum rules. In particular, we study observables sensitive to the sign of the top partner Yukawa, which is crucial for verifying the sum rules but is notoriously difficult to measure. We demonstrate that in the benchmark models under study, a statistically significant discrimination between the two possible signs of each Yukawa will be feasible with a 30 ab$^{-1}$ data set at $100TeV$.
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The notion of stringy naturalness-- that an observable O_2 is more natural than O_1 if more (phenomenologically acceptable) vacua solutions lead to O_2 rather than O_1-- is examined within the context of the Standard Model (SM) and various SUSY extensions: CMSSM/mSUGRA, high-scale SUSY and radiatively-driven natural SUSY (RNS). Rather general arguments from string theory suggest a (possibly mild) statistical draw towards vacua with large soft SUSY breaking terms. These vacua must be tempered by an anthropic veto of non-standard vacua or vacua with too large a value of the weak scale m(weak). We argue that the SM, the CMSSM and the various high-scale SUSY models are all expected to be relatively rare occurances within the string theory landscape of vacua. In contrast, models with TeV-scale soft terms but with m(weak)~100 GeV and consequent light higgsinos (SUSY with radiatively-driven naturalness) should be much more common on the landscape. These latter models have a statistical preference for m_h~ 125 GeV and strongly interacting sparticles beyond current LHC reach. Thus, while conventional naturalness favors sparticles close to the weak scale, stringy naturalness favors sparticles so heavy that electroweak symmetry is barely broken and one is living dangerously close to vacua with charge-or-color breaking minima, no electroweak breaking or pocket universe weak scale values too far from our measured value. Expectations for how landscape SUSY would manifest itself at collider and dark matter search experiments are then modified compared to usual notions.
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.
Correlations between light neutrino observables are arguably the strongest predictions of lepton avour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a nonzero value of the lightest neutrino mass and to distinct predictions for the e ective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modi cation of the predictions derived from neutrino mass sum rules. We show that, in most cases, the predictions are fairly stable: while small quantitative changes can appear, they are generally rather mild. We therefore establish the predictivity of neutrino mass sum rules on a level far more general than previously known.
We re-analyse the prospects of discovering supersymmetry at the LHC, in order to re-express coverage in terms of a fine-tuning parameter and to extend the analysis to scalar masses (m_0) above 2 TeV. We use minimal supergravity (mSUGRA) unification assumptions for the SUSY breaking parameters. The discovery reach at high m_0 is of renewed interest because this region has recently been found to have a focus point, leading to relatively low fine-tuning, and because it remains uncertain how much of the region can be ruled out due to lack of radiative electroweak symmetry breaking. The best fine tuning reach is found in a mono-leptonic channel, where for mu>0, A_0=0 and tan beta=10 (within the focus point region), and a top mass of 174 GeV, all points in mSUGRA with m_0 < 4000 GeV, with a fine tuning measure up to 210 (500) are covered by the search, where the definition of fine-tuning excludes (includes) the contribution from the top Yukawa coupling. Even for arbitrarily high m_0, mSUGRA can be discovered through gaugino events, provided the gaugino mass parameter M_1/2 < 460 GeV. In this region, the mono-leptonic channel still provides the best reach.
We review the calculations of form factors and coupling constants in vertices with charm mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to heavy ion collisions and to B decays. We then present an introduction to the method of QCD sum rules and describe how to work with the three-point function. We give special attention to the procedure employed to extrapolate results obtained in the deep euclidean region to the poles of the particles, located in the time-like region. We present a table of ready-to-use parametrizations of all the form factors, which are relevant for the processes mentioned in the introduction. We discuss the uncertainties in our results. We also give the coupling constants and compare them with estimates obtained with other methods. Finally we apply our results to the calculation of the cross section of the reaction $J/psi + pi rightarrow D + bar{D^*}$.
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