The Weak Interactions

We present the phenomenology of the weak interactions in a historical perspective, from Fermi’s four-fermion theory to the V−A current×current interaction. The experiments of C.S. Wu, which established parity violation, and M. Goldhaber, which measured the neutrino helicity, are described. We study in turn the leptonic, semi-leptonic and non-leptonic weak interactions. We introduce the concept of the conserved vector current and the partially conserved axial current and show that the latter is the result of spontaneously broken chiral symmetry with the pion the corresponding pseudo-Goldstone boson. We study Gell–Mann’s current algebra and derive the Adler–Weisberger relation. Strangeness changing weak interactions and the Cabibbo theory are described. We present a phenomenological analysis of CP-violation in the neutral kaon system and we end with the intermediate vector boson hypothesis.

Conserved vector current in QCD-like theories and the gradient flow

We present analytical results for the Euclidean 2-point correlator of the flavor- singlet vector current evolved by the gradient flow at next-to-leading order $$ \left(\mathcal{O}\left({g}^2\right)\right) $$ O g 2 in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormalizes as usual. We explicitly derive the asymptotic solution of the Callan-Symanzik equation for the connected 2-point correlators of these evolved currents in the limit of small gradient-flow time $$ \sqrt{t} $$ t , at fixed separation |x − y|. Incidentally, this computation determines the leading coefficient of the small-time expansion (STE) for the evolved currents in terms of their local nonevolved counterpart. Our computation also implies that, in the evolved case, conservation of the vector current, hence transversality of the corresponding 2-point correlator, is no longer related to the nonrenormalization, in contrast to the nonevolved case. Indeed, for small flow time the evolved vector current is conserved up to $$ \mathcal{O} $$ O (t) softly violating effects, despite its t-dependent nonvanishing anomalous dimension.

Chapter 11 Physics of Soft Pions and the Lightest Scalars at BES-III

The following sections are included: Partially Conserved Vector Current (PCAC) and Soft Pions Beyond the Breit–Wigner Description of a Broad Resonance Final State Interaction Theorem and Omnés Solution On the Nature of the Lightest Scalar Resonances