Given a von Neumann algebra M denote by S(M) and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M, τ) (resp. S0(M, τ)) be the algebra of all τ -measurable (resp. τ -compact) operators from S(M). We give a complete description of all derivations on the above algebras of operators in the ca...

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...

Charged-lepton flavor-violating processes are unobservable in the standard model, but they are predicted to be enhanced in several extensions to the standard model, including supersymmetry and models with leptoquarks or compositeness. We present a search for such processes in a sample of 99x10(6)Upsilon(2S) decays and 117x10(6)Upsilon(3S) decays collected with the BABAR detector. We place upper...

Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...