In the 1990s, very low experimental values for lifetime ratio $\tau (\Lambda_b)/\tau(B_d)$ triggered a considerable amount of doubt in applicability heavy quark expansion (HQE), which is based on assumption quark-hadron duality (QHD) inclusive total decay rates. However, these turned out to be result purely problems, and current HFLAV average reads (\Lambda_b)/\tau(B_d) = 0.969(6)$. this work, ...

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with polynomial (Laurent polynomial) reciprocity laws and the space of cusp (modular) forms. In this article we introduce Hecke operators on the space of weighted Dedekind...

Let $G/K$ be a simply connected compact irreducible symmetric space of real rank one. For each $K$-type $\tau$ we compare the notions $\tau$-representation equivalence with $\tau$-isospectrality. We exhibit infinitely many $K$-types so that, for arbitrary discrete subgroups $\Gamma$ and $\Gamma'$ $G$, if multiplicities $\lambda$ in spectra Laplace operators acting on sections induced $\tau$-vec...

We consider the integrated correlators associated with four-point correlation functions $\langle \mathcal{O}_2\mathcal{O}_2\mathcal{O}^{(i)}_p \mathcal{O}^{(j)}_p \rangle$ in four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) $SU(N)$ gauge group, where $\mathcal{O}^{(i)}_p$ is a superconformal primary charge (or dimension) $p$ and superscript $i$ represents possible degener...

In this paper, we prove that the generalized Brézin–Gross– Witten tau-function is a hypergeometric solution of BKP hierarchy with simple weight generating function. We claim it describes spin version strictly monotone Hurwitz numbers. A family tau-functions hierarchy, corresponding to rational functions, investigated. particular, cut-and-join operators are constructed, and explicit description ...

Electroweak interactions assign a central role to the gauge group $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$, which is either realized linearly (SMEFT) or nonlinearly (e.g., HEFT) in effective theory obtained when new physics above electroweak scale integrated out. Although discovery of Higgs boson has made SMEFT default assumption, nonlinear realization remains possible. The two...

Abstract. Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on Rn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second o...