Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages

Implementing Unitarity in Perturbation Theory

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint UU^\dagger=\1 is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.Comment: to appear in Phys. Rev.

Discrete symmetries and models of flavor mixing

Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, {\it ad hoc} prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In this connection the quark-lepton complementarity could be a viable alternative to TBM. Observational consequences of the symmetries and future experimental tests of their existence are discussed.Comment: 14 pages, 5 figures. Talk given at the Symposium "DISCRETE 2010", 6 - 11 December 2010, La Sapienza, Rome, Ital

Unconditional Continuous Variable Dense Coding

We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We conclude that the requirements for a strong demonstration are not as stringent as previously thought and are within the reach of present technology

Clustering of childhood leukaemia in Hong Kong: association with the childhood peak and common acute lymphoblastic leukaemia and with population mixing.

Incidence data of childhood leukaemia (CL) in Hong Kong (1984-90) have been analysed for evidence of variation between small areas. All cases (n=261) were classified by morphological cell type, with the majority (n=205) being acute lymphoblastic leukaemia (ALL), and haematological review has permitted immunophenotypic classification for 73% of these. The data have been examined for evidence of spatial clustering within small census areas (TPUs) and for association with population mixing, with attention focused on those subgroups (especially the childhood peak of ALL--taken here to be diagnoses in children from 24 months up to the seventh birthday--and common ALL) which, it has been hypothesized, may be caused by unusual patterns of exposure and response to common infections. For the whole of Hong Kong, there was evidence of spatial clustering of ALL at ages 0-4 years (P = 0.09) and in the childhood peak (P<0.05). When these analyses were restricted to TPUs where extreme population mixing may have occurred, overall incidence was elevated and significant evidence of clustering was found for ALL (P<0.007) at these ages and for the common ALL in the childhood peak (P = 0.032). Replication of the analyses for subsets of leukaemia that were not dominated by the childhood peak of ALL found no evidence of clustering. This is the first investigation of an association between population mixing and childhood leukaemia in Asia and the first to include clustering and to consider particular subsets. The results are supportive of the 'infectious' aetiology hypothesis for subsets of childhood leukaemia, specifically common ALL in the childhood peak

Unitarity Bounds and the Cuspy Halo Problem

Conventional Cold Dark Matter cosmological models predict small scale structures, such as cuspy halos, which are in apparent conflict with observations. Several alternative scenarios based on modifying fundamental properties of the dark matter have been proposed. We show that general principles of quantum mechanics, in particular unitarity, imply interesting constraints on two proposals: collisional dark matter proposed by Spergel & Steinhardt, and strongly annihilating dark matter proposed by Kaplinghat, Knox & Turner. Efficient scattering required in both implies m < 12 GeV and m < 25 GeV respectively. The same arguments show that the strong annihilation in the second scenario implies the presence of significant elastic scattering, particularly for large enough masses. Recently, a variant of the collisional scenario has been advocated to satisfy simultaneously constraints from dwarf galaxies to clusters, with a cross section that scales inversely with velocity. We show that this scenario likely involves super-elastic processes, and the associated kinetic energy change must be taken into account when making predictions. Exceptions and implications for experimental searches are discussed.Comment: 4 pages, references adde

Vortex lines in the three-dimensional XY model with random phase shifts

The stability of the ordered phase of the three-dimensional XY-model with random phase shifts is studied by considering the roughening of a single stretched vortex line due to the disorder. It is shown that the vortex line may be described by a directed polymer Hamiltonian with an effective random potential that is long range correlated. A Flory argument estimates the roughness exponent to $\zeta=3/4$ and the energy fluctuation exponent to $\omega=1/2$, thus fulfilling the scaling relation $\omega=2\zeta-1$. The Schwartz-Edwards method as well as a numerical integration of the corresponding Burger's equation confirm this result. Since $\zeta<1$ the ordered phase of the original XY-model is stable.Comment: 8 pages RevTeX, 3 eps-figures include

Leptons in Holographic Composite Higgs Models with Non-Abelian Discrete Symmetries

We study leptons in holographic composite Higgs models, namely in models possibly admitting a weakly coupled description in terms of five-dimensional (5D) theories. We introduce two scenarios leading to Majorana or Dirac neutrinos, based on the non-abelian discrete group $S_4\times \Z_3$ which is responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino masses is naturally explained and normal/inverted mass ordering can be accommodated. We analyze two specific 5D gauge-Higgs unification models in warped space as concrete examples of our framework. Both models pass the current bounds on Lepton Flavour Violation (LFV) processes. We pay special attention to the effect of so called boundary kinetic terms that are the dominant source of LFV. The model with Majorana neutrinos is compatible with a Kaluza-Klein vector mass scale $m_{KK}\gtrsim 3.5$ TeV, which is roughly the lowest scale allowed by electroweak considerations. The model with Dirac neutrinos, although not considerably constrained by LFV processes and data on lepton mixing, suffers from a too large deviation of the neutrino coupling to the $Z$ boson from its Standard Model value, pushing $m_{KK}\gtrsim 10$ TeV.Comment: 37 pages, 4 figures; v2: Note added in light of recent T2K and MINOS results, figures updated with new limit from MEG, references added, various minor improvements, matches JHEP published versio

Towards Minimal S4 Lepton Flavor Model

We study lepton flavor models with the $S_4$ flavor symmetry. We construct simple models with smaller numbers of flavon fields and free parameters, such that we have predictions among lepton masses and mixing angles. The model with a $S_4$ triplet flavon is not realistic, but we can construct realistic models with two triplet flavons, or one triplet and one doublet flavons.Comment: 18 pages, 4 figures, references are adde

A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4

We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4xU(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings.Comment: 19 page