Constraints on models for the Higgs boson with exotic spin and parity in VH→Vbbˉ\boldsymbol{VH\rightarrow Vb\bar{b}} final states

We present constraints on models containing non-standard model values for the spin $J$ and parity $P$ of the Higgs boson, $H$, in up to 9.7~fb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s} =$ 1.96~TeV collected with the D0 detector at the Fermilab Tevatron Collider. These are the first studies of Higgs boson $J^{P}$ with fermions in the final state. In the $ZH\rightarrow \ell\ell b\bar{b}$, $WH\rightarrow \ell\nu b\bar{b}$, and $ZH\rightarrow \nu\nu b\bar{b}$ final states, we compare the standard model (SM) Higgs boson prediction, $J^{P}=0^{+}$, with two alternative hypotheses, $J^{P}=0^{-}$ and $J^{P}=2^{+}$. We use a likelihood ratio to quantify the degree to which our data are incompatible with non-SM $J^{P}$ predictions for a range of possible production rates. Assuming that the production rate in the signal models considered is equal to the SM prediction, we reject the $J^{P}=0^{-}$ and $J^{P}=2^{+}$ hypotheses at the 97.6$\%$ CL and at the 99.0$\%$ CL, respectively. The expected exclusion sensitivity for a $J^{P}=0^{-}$ ($J^{P}=2^{+}$) state is at the 99.86$\%$ (99.94$\%$) CL. Under the hypothesis that our data is the result of a combination of the SM-like Higgs boson and either a $J^{P}=0^{-}$ or a $J^{P}=2^{+}$ signal, we exclude a $J^{P}=0^{-}$ fraction above 0.80 and a $J^{P}=2^{+}$ fraction above 0.67 at the 95$\%$ CL. The expected exclusion covers $J^{P}=0^{-}$ ($J^{P}=2^{+}$) fractions above 0.54 (0.47).Comment: 13 Figures, 3 Tables, 19 pages. Accepted by Phys. Rev. Let

Parity Mixed Doublets in A = 36 Nuclei

The $\gamma$-circular polarizations ($P_{\gamma}$) and asymmetries ($A_{\gamma}$) of the parity forbidden M1 + E2 $\gamma$-decays: $^{36}Cl^{\ast} (J^{\pi} = 2^{-}; T = 1; E_{x} = 1.95$ MeV) $\rightarrow$ $^{36}Cl (J^{\pi} = 2^{+}; T = 1; g.s.)$ and $^{36}Ar^{\ast} (J^{\pi} = 2^{-}; T = 0; E_{x} = 4.97$ MeV) $\rightarrow$ $^{36}Ar^{\ast} (J^{\pi} = 2^{+}; T = 0; E_{x} = 1.97$ MeV) are investigated theoretically. We use the recently proposed Warburton-Becker-Brown shell-model interaction. For the weak forces we discuss comparatively different weak interaction models based on different assumptions for evaluating the weak meson-hadron coupling constants. The results determine a range of $P_{\gamma}$ values from which we find the most probable values: $P_{\gamma}$ = $1.1 \cdot 10^{-4}$ for $^{36}Cl$ and $P_{\gamma}$ = $3.5 \cdot 10^{-4}$ for $^{36}Ar$.Comment: RevTeX, 17 pages; to appear in Phys. Rev.

Natural solution to the naturalness problem -- Universe does fine-tuning

We propose a new mechanism to solve the fine-tuning problem. We start from a multi-local action $S=\sum_{i}c_{i}S_{i}+\sum_{i,j}c_{i,j}S_{i}S_{j}+\sum_{i,j,k}c_{i,j,k}S_{i}S_{j}S_{k}+\cdots$, where $S_{i}$'s are ordinary local actions. Then, the partition function of this system is given by \begin{equation} Z=\int d\overrightarrow{\lambda} f(\overrightarrow{\lambda})\langle f|T\exp\left(-i\int_{0}^{+\infty}dt\hat{H}(\overrightarrow{\lambda};a_{cl}(t))\right)|i\rangle,\nonumber\end{equation} where $\overrightarrow{\lambda}$ represents the parameters of the system whose Hamiltonian is given by $\hat{H}(\overrightarrow{\lambda};a_{cl}(t))$, $a_{cl}(t)$ is the radius of the universe determined by the Friedman equation, and $f(\overrightarrow{\lambda})$, which is determined by $S$, is a smooth function of $\overrightarrow{\lambda}$. If a value of $\overrightarrow{\lambda}$, $\overrightarrow{\lambda}_{0}$, dominates in the integral, we can interpret that the parameters are dynamically tuned to $\overrightarrow{\lambda}_{0}$. We show that indeed it happens in some realistic systems. In particular, we consider the strong CP problem, multiple point criticality principle and cosmological constant problem. It is interesting that these different phenomena can be explained by one mechanism.Comment: 21 pages, 4 figure

Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the s=1/2s = 1/2 kagome system ZnCu_3(OH)_6Cl_2

Motivated by recent nuclear magnetic resonance experiments on ZnCu$_3$(OH)$_6$Cl$_2$, we present an exact-diagonalization study of the combined effects of non-magnetic impurities and Dzyaloshinskii-Moriya (DM) interactions in the $s = 1/2$ kagome antiferromagnet. The local response to an applied field and correlation-matrix data reveal that the dimer freezing which occurs around each impurity for $D = 0$ persists at least up to $D/J\simeq 0.06$, where $J$ and $D$ denote respectively the exchange and DM interaction energies. The phase transition to the ($Q = 0$) semiclassical, 120$^\circ$ state favored at large $D$ takes place at $D/J\simeq 0.1$. However, the dimers next to the impurity sites remain strong up to values $D \sim J$, far above this critical point, and thus do not participate fully in the ordered state. We discuss the implications of our results for experiments on ZnCu$_3$(OH)$_6$Cl$_2$.Comment: 11 pages, submitted to PR

Z_2-gradings of Clifford algebras and multivector structures

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.Comment: 10 pages, LaTeX; v2 accepted for publication in J. Phys.

On the Star Class Group of a Pullback

For the domain $R$ arising from the construction $T, M,D$, we relate the star class groups of $R$ to those of $T$ and $D$. More precisely, let $T$ be an integral domain, $M$ a nonzero maximal ideal of $T$, $D$ a proper subring of $k:=T/M$, $\phi: T\to k$ the natural projection, and let $R={\phi}^{-1}(D)$. For each star operation $\ast$ on $R$, we define the star operation $\ast_\phi$ on $D$, i.e., the ``projection'' of $\ast$ under $\phi$, and the star operation ${(\ast)}_{_{T}}$ on $T$, i.e., the ``extension'' of $\ast$ to $T$. Then we show that, under a mild hypothesis on the group of units of $T$, if $\ast$ is a star operation of finite type, 0\to \Cl^{\ast_{\phi}}(D) \to \Cl^\ast(R) \to \Cl^{{(\ast)}_{_{T}}}(T)\to 0 is split exact. In particular, when $\ast = t_{R}$, we deduce that the sequence 0\to \Cl^{t_{D}}(D) {\to} \Cl^{t_{R}}(R) {\to}\Cl^{(t_{R})_{_{T}}}(T) \to 0 is split exact. The relation between ${(t_{R})_{_{T}}}$ and $t_{T}$ (and between \Cl^{(t_{R})_{_{T}}}(T) and \Cl^{t_{T}}(T)) is also investigated.Comment: J. Algebra (to appear