Quark-lepton symmetric model at the LHC

We investigate the quark-lepton symmetric model of Foot and Lew in the context of the Large Hadron Collider (LHC). In this `bottom-up' extension to the Standard Model, quark-lepton symmetry is achieved by introducing a gauged `leptonic colour' symmetry which is spontaneously broken above the electroweak scale. If this breaking occurs at the TeV scale, then we expect new physics to be discovered at the LHC. We examine three areas of interest: the Z$'$ heavy neutral gauge boson, charge $\pm1/2$ exotic leptons, and a colour triplet scalar diquark. We find that the LHC has already explored and/or will explore new parameter space for these particles over the course of its lifetime.Comment: 24 pages, 6 figure

Phenomenology of a very light scalar (100 MeV <mh<<m_h< 10 GeV) mixing with the SM Higgs

In this paper we investigate the phenomenology of a very light scalar, $h$, with mass 100 MeV $<m_h<$ 10 GeV, mixing with the SM Higgs. As a benchmark model we take the real singlet scalar extension of the SM. We point out apparently unresolved uncertainties in the branching ratios and lifetime of $h$ in a crucial region of parameter space for LHC phenomenology. Bounds from LEP, meson decays and fixed target experiments are reviewed. We also examine prospects at the LHC. For $m_h \lesssim m_B$ the dominant production mechanism is via meson decay; our main result is the calculation of the differential $p_T$ spectrum of $h$ scalars originating from B mesons and the subsequent prediction of up to thousands of moderate (triggerable) $p_T$ displaced dimuons possibly hiding in the existing dataset at ATLAS/CMS or at LHCb. We also demonstrate that the subdominant $Vh$ production channel has the best sensitivity for $m_h \gtrsim m_B$ and that future bounds in this region could conceivably compete with those of LEP.Comment: 13 pages, 9 figure

Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) we give a general formula for the entanglement entropy associated to an arbitrary $(m|n-m)$ partition of a generic $n$-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod $k$) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod $k$). For $G = SU(2)_k$, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a "W-like" entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have "GHZ-like" entanglement (i.e., tracing out one torus does lead to a separable state).Comment: 37 pages, 19 figure

Noncooperatively Optimized Tolerance: Decentralized Strategic Optimization in Complex Systems

We introduce noncooperatively optimized tolerance (NOT), a generalization of highly optimized tolerance (HOT) that involves strategic (game theoretic) interactions between parties in a complex system. We illustrate our model in the forest fire (percolation) framework. As the number of players increases, our model retains features of HOT, such as robustness, high yield combined with high density, and self-dissimilar landscapes, but also develops features of self-organized criticality (SOC) when the number of players is large enough. For example, the forest landscape becomes increasingly homogeneous and protection from adverse events (lightning strikes) becomes less closely correlated with the spatial distribution of these events. While HOT is a special case of our model, the resemblance to SOC is only partial; for example, the distribution of cascades, while becoming increasingly heavy-tailed as the number of players increases, also deviates more significantly from a power law in this regime. Surprisingly, the system retains considerable robustness even as it becomes fractured, due in part to emergent cooperation between neighboring players. At the same time, increasing homogeneity promotes resilience against changes in the lightning distribution, giving rise to intermediate regimes where the system is robust to a particular distribution of adverse events, yet not very fragile to changes

The interpretive approach to religious education : challenging Thompson's interpretation

In a recent book chapter, Matthew Thompson makes some criticisms of my work, including the interpretive approach to religious education and the research and activity of Warwick Religions and Education Research Unit. Against the background of a discussion of religious education in the public sphere, my response challenges Thompson’s account, commenting on his own position in relation to dialogical approaches to religious education. The article rehearses my long held view that the ideal form of religious education in fully state funded schools of a liberal democracy should be ‘secular’ but not ‘secularist’; there should be no implication of an axiomatic secular humanist interpretation of religions

Improving California brush ranges /

C37