q-deformations of statistical mechanical systems and motives over finite fields

We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over the field with one element and to categorifications of Bost-Connes systems.Comment: 25 pages, LaTe

Tuning Co valence state in cobalt oxyhydrate superconductor by post reduction

We report a successful tuning of Co valence state in cobalt oxyhydrate superconductor via a facile post reduction using NaOH as reducing agent. The change in Co valence was precisely determined by measuring the volume of the released oxygen. The possible hydronium-incorporation was greatly suppressed in concentrated NaOH solution, making the absolute Co valence determinable. As a result, an updated superconducting phase diagram was obtained, which shows that the superconducting transition temperature increases monotonically with increasing Co valence in a narrow range from +3.58 to +3.65.Comment: 17 pages, 5 figures and 1 table. Chem. Mat. in pres

Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames

We study gravitational interaction of Higgs boson through the unique dimension-4 operator $\xi H^\dag H R$, with $H$ the Higgs doublet and $R$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $\xi$ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero $\xi$ coupling in both frames, and analyze the unitarity constraints. We study the $\xi$-induced weak boson scattering cross sections at O(1-30)TeV scales, and propose to probe the Higgs-gravity coupling via weak boson scattering experiments at the LHC(14TeV) and the next generation pp colliders (50-100TeV). We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data.Comment: 40pp, JCAP Final Version. Use jcappub.sty, only minor rewordings, references adde

Palladium-catalyzed carbon-hydrogen bond functionalization utilizing an exo-directing strategy

Transition metal catalyzed functionalization of carbon-hydrogen bonds (C−H bonds) has become an exponentially growing field. Particularly, Pd-catalyzed methods with various directing groups (DGs) have been developed for site selectivity. In addition, the use of an oxime as a DG proved to be an efficient and removable DG. However, alcohol-based directing strategies are still rare and underdeveloped. The research and development in this dissertation mainly focused on the utilization of masked alcohols as DGs for late stage diversification. With an exo-directing strategy, the syntheses of chemically differentiated vicinal diols and 2-hydroxyalkylphenol derivatives were achieved. Through a series of studies on cyclopalladation of methine groups, the first direct C−H activation complex was prepared and characterized. Additionally, a comprehensive introduction of TM-catalyzed alkylation of aromatic C−H bonds with simple olefins was illustrated.Chemistr

High pressure investigation of superconducting signatures in CeCu2_{2}Si2_{2} : ac- magnetic susceptibility and heat capacity, resistivity and thermopower

Taking advantage of a novel multiprobe setup we have measured, on a unique sample, the ac-magnetic susceptibility, the resistivity, the ac-specific heat and the thermopower of the superconductor heavy fermion CeCu$_{2}$Si$_{2}$ under pressure up to 5.1 GPa. At the superconducting transition temperature $T_c$, the Meissner signal corresponds to that expected for the sample volume and coincides with the specific heat jump and the resistive transition completion temperatures. Differing from previous observations, here the susceptibility measurements did not reveal any anomaly in the vicinity of the resistive transition onset

Gravitational Interaction of Higgs Boson and Weak Boson Scattering

With the LHC discovery of a 125 GeV Higgs-like boson, we study gravitational interaction of the Higgs boson via the unique dimension-4 operator involving Higgs doublet and scalar curvature, $\,\xi H^\dag H R\,$, with nonminimal coupling $\,\xi\,$. This Higgs portal term can be transformed away in Einstein frame and induces gauge-invariant effective interactions in the Higgs sector. We study the weak boson scattering in Einstein frame, and explicitly demonstrate the longitudinal-Goldstone boson equivalence theorem in the presence of $\,\xi\,$ coupling. With these, we derive unitarity bound on the Higgs gravitational coupling $\,\xi\,$ in Einstein frame, which is stronger than that inferred from the current LHC Higgs measurements. We further study $\xi$-dependent weak boson scattering cross sections at TeV scale, and propose a new LHC probe of the Higgs-gravity coupling $\,\xi\,$ via weak boson scattering experiments.Comment: 7pp, Phys.Rev.D Published Version. All results + conclusions un-changed. Only minor rewording to clarify the Importance of this wor