Coupling of ttˉt\bar t and γγ\gamma\gamma with a strongly interacting Electroweak Symmetry Breaking Sector

We report the coupling of an external $\gamma\gamma$ or $t\bar t$ state to a strongly interacting EWSBS satisfying unitarity. We exploit perturbation theory for those coupling of the external state, whereas the EWSBS is taken as strongly interacting. We use a modified version of the IAM unitarization procedure to model such a strongly interacting regime. The matrix elements $V_LV_L\to V_LV_L$, $V_LV_L\leftrightarrow hh$, $hh\to hh$, $V_LV_L\leftrightarrow\{\gamma\gamma,t\bar t\}$, and $hh\leftrightarrow\{\gamma\gamma,t\bar t\}$ are all computed to NLO in perturbation theory with the Nonlinear Effective Field Theory of the EWSBS, within the Equivalence Theorem. This allows us to describe resonances of the electroweak sector that may be found at the LHC and their effect on other channels such as $\gamma\gamma$ or $t\bar t$ where they may be discovered.Comment: 9 pages, 3 figures. Contributions to the Procs. of the XIIth Quark Confinement and the Hadron Spectrum, Thessaloniki, Greece, August 201

Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder

We prove that the addition of an arbitrarily small random perturbation of a suitable type to a quantum spin system rounds a first order phase transition in the conjugate order parameter in d <= 2 dimensions, or in systems with continuous symmetry in d <= 4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon, which for classical systems was proven by Aizenman and Wehr.Comment: Four pages, RevTex. Minor correction

Approximate closed-form formulas for the zeros of the Bessel Polynomials

We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of k and n is obtained. It is shown that the resulting complex number x(k,n)+i y(k,n) is O(1/n^2)-convergent to z_k for fixed kComment: 9 pages, 2 figure

Surveying the quantum group symmetries of integrable open spin chains

Using anisotropic R-matrices associated with affine Lie algebras $\hat g$ (specifically, $A_{2n}^{(2)}, A_{2n-1}^{(2)}, B_n^{(1)}, C_n^{(1)}, D_n^{(1)}$) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of $\hat g$. We show that these transfer matrices also have a duality symmetry (for the cases $C_n^{(1)}$ and $D_n^{(1)}$) and additional $Z_2$ symmetries that map complex representations to their conjugates (for the cases $A_{2n-1}^{(2)}, B_n^{(1)}, D_n^{(1)}$). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.Comment: 48 page