Interplay of New Physics effects in (g − 2)ℓ and h → ℓ+ℓ− — lessons from SMEFT

We explore the interplay of New Physics (NP) effects in (g− 2)ℓ and h→ℓ+ℓ− within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and SU(2)L gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimental sensitivity to different representative benchmark scenarios. We also consider two simple UV completions, a Two Higgs Doublet Model and a single scalar LeptoQuark extension of the SM, and show how tree level matching to SMEFT followed by the one-loop RG evolution down to the electroweak scale can reproduce with high accuracy the (g−2)ℓ and h→ℓ+ℓ− contributions obtained by the complete one- and even two-loop calculations in the full models.

On the B-discrete spectrum

In this paper, we introduce the B-discrete spectrum of an unbounded closed operator and we prove that a closed operator has a purely B-discrete spectrum if and only if it has a meromorphic resolvent. After that, we study the stability of the B-discrete spectrum under several type of perturbations and we establish that two closed invertible linear operators having quasisimilar totally paranormal inverses have equal spectra and B-discrete spectra.

A general version of Neubauer’s lemma and closed range almost closed operators

In this paper, almost closed subspaces and almost closed linear operators are described in a Hilbert space. We show Neubauer’s lemma and we give necessary and sufficient conditions for an almost closed operator to be with closed range and we exhibit sufficient conditions under which it is either closed or closable.

Ordered Structures of Constructing Operators for Generalized Riesz Systems

A sequence {φn} in a Hilbert space H with inner product <·,·> is called a generalized Riesz system if there exist an ONB e={en} in H and a densely defined closed operator T in H with densely defined inverse such that {en}⊂D(T)∩D((T-1)⁎) and Ten=φn, n=0,1,⋯, and (e,T) is called a constructing pair for {φn} and T is called a constructing operator for {φn}. The main purpose of this paper is to investigate under what conditions the ordered set Cφ of all constructing operators for a generalized Riesz system {φn} has maximal elements, minimal elements, the largest element, and the smallest element in order to find constructing operators fitting to each of the physical applications.

Essential Spectra

In this chapter, various essential spectra are studied. For a closed operator in a Banach space, a number of different sets have been used for the essential spectrum, the sets being identical for a self-adjoint operator in a Hilbert space. As well as the essential spectra, the changes that occur when the operator is perturbed are discussed. Constant-coefficient differential operators are studied in detail.

Brownian representations of cylindrical continuous local martingales

In this paper, we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular, we consider the class of cylindrical martingales with closed operator-generated covariations. We also prove that for every cylindrical continuous local martingale [Formula: see text] there exists a time change [Formula: see text] such that [Formula: see text] is Brownian representable.

Operator ideal of s-type operators using weighted mean sequence space

We introduce a different class of s-type operators by using the generalized weighted mean sequence space c0 (u, v), then it is shown that this new class of operators is a quasi-Banach operator ideal. Moreover, their injectivity and surjectivity are investigated according to sort of s-number. Finally, we proof that it is a closed operator ideal under some conditions.