Improving the precision of strong interaction at low and high energies

Abstract

A fundamental goal of elementary particle physics is to understand the structure and behavior of strongly interacting matter in terms of its fundamental constituents and to search for physics beyond the Standard Model (SM). Precision studies are essential for discovering new physics, both at low and high energies. This thesis focuses on precision in Quantum Chromodynamics (QCD) at low and high energies.

We study:

The electromagnetic form factor of the pion,

The weak form factors of K 3 decays,

The precise determination of the strong coupling constant ( s) from hadronic decays.

The pion electromagnetic form factor is central to QCD, crucial for understanding chiral symmetry breaking, and provides sensitive tests of chiral perturbation theory (ChPT). K 3 decays, where a kaon decays to a pion, a charged lepton, and a neutrino, yield the most precise determination of the CKM matrix element Vus. Hadronic decays provide the most precise determination of the strong coupling constant s, which is of fundamental importance.

Chapter Summaries Chapter 1

Reviews scattering experiments and introduces form factors.

Defines spacelike and timelike momentum transfer.

Discusses pion electromagnetic form factors, K 3 form factors, and issues in extracting s from hadronic decays.

Introduces the formalism of improved fixed-order perturbation theory (FOPT).

Chapter 2

Presents a general formalism for deriving bounds on weak and electromagnetic form factors using perturbative QCD correlators, analyticity, and unitarity.

Provides solutions to the Meiman problem and integral equations incorporating phase and modulus information along the unitarity cut.

Chapter 3

Studies constraints on expansion parameters (c and d) of the pion electromagnetic form factor using spacelike and timelike data.

Results provide checks on determinations of c and on prior work involving the muon (g - 2).

Chapter 4

Derives bounds on scalar radius and curvature parameters of the scalar K form factor using analyticity, dispersion relations, and values at the Callan-Treiman points.

Results show strong correlations between parameters and sensitivity to higher-loop corrections.

Chapter 5

Investigates scalar K form factor at low energies using unitarity bounds with phase and modulus information.

Provides stringent constraints on slope and curvature parameters and predicts narrow ranges for higher-order ChPT corrections.

Chapter 6

Explores vector and scalar K form factors using analyticity and unitarity in a model-independent framework.

Derives constraints on parameterizations valid in semileptonic ranges and predicts domains where zeros of form factors are excluded.

Chapter 7

Revisits extraction of s(M ) from hadronic decays.

Compares fixed-order perturbation theory (FOPT) and contour-improved perturbation theory (CIPT).

Proposes an improved FOPT with explicit renormalization group summation.

Obtains s(M ) = 0.338 ± 0.010 in the MS scheme.

Chapter 8

Presents future directions and summarizes the thesis.