We consider how, for quasi-degenerate neutrinos with tri-bi-maximal mixing at a high-energy scale, the mixing angles are affected by radiative running from high to low-energy scales in a supersymmetric theory. The limits on the high-energy scale that
follow from consistency with the observed mixing are determined. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing.
We further develop the constrained mass variable techniques to determine the mass scale of invisible particles pair-produced at hadron colliders. We introduce the constrained mass variable M_3C which provides an event-by-event lower bound and upper b
ound to the mass scale given the two mass differences between the lightest three new particle states. This variable is most appropriate for short symmetric cascade decays involving two-body decays and on-shell intermediate states which end in standard-model particles and two dark-matter particles. An important feature of the constrained mass variables is that they do not rely simply on the position of the end point but use the additional information contained in events which lie far from the end point. To demonstrate our method we study the supersymmetric model SPS 1a. We select cuts to study events with two Neutralino_2 each of which decays to Neutralino_1, and two opposite-sign same-flavor (OSSF) charged leptons through an intermediate on-shell slepton. We find that with 300 fb^-1 of integrated luminosity the invisible-particle mass can be measured to M=96.4 +/- 2.4 GeV. Combining fits to the shape of the M_3C constrained mass variable distribution with the max m_ll edge fixes the mass differences to +/- 0.2 GeV.
We develop techniques to determine the mass scale of invisible particles pair-produced at hadron colliders. We employ the constrained mass variable m_2C, which provides an event-by-event lower-bound to the mass scale given a mass difference. We compl
ement this variable with a new variable m_2C,UB which provides an additional upper bound to the mass scale, and demonstrate its utility with a realistic case study of a supersymmetry model. These variables together effectively quantify the `kink in the function Max m_T2 which has been proposed as a mass-determination technique for collider-produced dark matter. An important advantage of the m_2C method is that it does not rely simply on the position at the endpoint, but it uses the additional information contained in events which lie far from the endpoint. We found the mass by comparing the HERWIG generated m_2C distribution to ideal distributions for different masses. We find that for the case studied, with 100 fb^-1 of integrated luminosity (about 400 signal events), the invisible particles mass can be measured to a precision of 4.1 GeV. We conclude that this techniques precision and accuracy is as good as, if not better than, the best known techniques for invisible-particle mass-determination at hadron colliders.
We propose an improved method for hadron-collider mass determination of new states that decay to a massive, long-lived state like the LSP in the MSSM. We focus on pair produced new states which undergo three-body decay to a pair of visible particles
and the new invisible long-lived state. Our approach is to construct a kinematic quantity which enforces all known physical constraints on the system. The distribution of this quantity calculated for the observed events has an endpoint that determines the mass of the new states. However we find it much more efficient to determine the masses by fitting to the entire distribution and not just the end point. We consider the application of the method at the LHC for various models and demonstrate that the method can determine the masses within about 6 GeV using only 250 events. This implies the method is viable even for relatively rare processes at the LHC such as neutralino pair production.
Grand Unified Theories predict relationships between the GUT-scale quark and lepton masses. Using new data in the context of the MSSM, we update the values and uncertainties of the masses and mixing angles for the three generations at the GUT scale.
We also update fits to hierarchical patterns in the GUT-scale Yukawa matrices. The new data shows not all the classic GUT-scale mass relationships remain in quantitative agreement at small to moderate tan beta. However, at large tan beta, these discrepancies can be eliminated by finite, tan beta-enhanced, radiative, threshold corrections if the gluino mass has the opposite sign to the wino mass.
We compare m_T2 with m_CT; both are kinematic variables designed to find relationships between masses of pair-produced new states with symmetric decay chains. We find that for massless visible particles m_CT equals m_T2 in a particular limit. We iden
tify advantages and disadvantages to the use of each variable. Toveys paper on m_CT also introduced a powerful concept of extracting mass information from an analysis at intermediate stages of a symmetric decay chain. We suggest that m_T2 is a better tool for performing this analysis than m_CT due to m_T2s better properties under initial state radiation.
