After a brief introduction to the sigma model in QCD, we discuss how the sigma model can be relevant in the Standard Model. It is shown to be useful in the analysis of weak processes, such as the study of ∆I = 1/2 rule, and in the analysis of the Higgs sector as well. The sigma model description is also shown to be quite useful in searching for the effects of New Physics via gauge boson self-in...

A class of Einstein–Weyl spaces associated to an integrable system of hydrodynamic type. Abstract HyperCR Einstein–Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydr...

We establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-fillings of moon polyominoes. Let M be a moon polyomino with n rows and m columns. Consider all the 01-fillings of M in which every row has at most one 1. We introduce four mixed statistics with respect to a bipartition of rows or columns of M. More precisely, let S ⊆ {1, 2, . . . , n} an...

This Letter reports the breaking of spherical symmetry in complete electromagnetic multipole expansion when its sources are distributed on toroidal surfaces, identifying specic geometrical and physical changes fromthe familiar case a surface. In fact, for toroids dened by concentric rings symmetric conical rings, boundary conditions at latter not compatible general with integer values orbital a...

We construct the set of theories which share the property that the tree-level threshold amplitudes nullify even if both initial and final states contain the same type of particles. The origin of this phenomenom lies in the fact that the reduced classical dynamics describes isochronic systems. supported by the Lódź University grant No. 269 supported by KBN grant No. 5 P03B 060 21 1 The problem o...

We describe a Hopf algebraic approach to the Grothendieck ring of representations of subgroups Hπ of the general linear group GL(n) which stabilize a tensor of Young symmetry {π}. It turns out that the representation ring of the subgroup can be described as a Hopf algebra twist, with a 2-cocycle derived from the Cauchy kernel 2-cocycle using plethysms. Due to Schur-Weyl duality we also need to ...

An alternative pattern of the chiral symmetry breaking, suggested recently, is investigated. It could be self-consistent provided that the chiral SU(Nf )×SU(Nf ) symmetry is broken spontaneously down to SU(Nf )× ZNf rather than to SU(Nf )V . The discrete axial ZNf then would play a custodial role preventing the quark bilinears from condensation. It is shown that this pattern of the chiral symme...

A new method to extract |V bc | is proposed based on a sum–rule for semilep-tonic decays of the B meson. The method relies on much weaker assumptions than previous approaches which are based on heavy–quark symmetry. This sum–rule only relies on the assumption that the virtual cc pair content of the B meson can be neglected. The extraction of the CKM matrix element also requires that the sum–rul...