Related papers: Renormalization of Singular Potentials and Power C…
We exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation. Among other things we use the formalism to develop a good analytic…
We consider nucleon-nucleon scattering using the formulation of chiral effective field theory which is claimed to be renormalization group invariant. The cornerstone of this framework is the existence of a well-defined infinite-cutoff limit…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
Nuclear effective field theory organizes the calculation of observables as a power series in terms of the ratio of soft and hard momentum scales. The rigorous implementation of this idea requires a mixture of perturbative and…
The study of the effective potential for non-renormalisable scalar SO(N) symmetric theories leads to recurrence relations for the coefficients of the leading logarithms. These relations can be transformed into generalised…
We develop the abstract framework for a proof-theoretic analysis of theories with scope beyond ordinal numbers, resulting in an analog of Ordinal Analysis aimed at the study of theorems of complexity $\Pi^1_2$. This is done by replacing the…
Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For…
We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at…
In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering…
We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT…
Effective field theories (EFTs) require regularization and renormalization to gain predictive power. While regularization is inconsequential from the point of view of the observable predictions of EFT -- in a renormalized theory we expect…
Finite-range regularised (FRR) chiral effective field theory is presented in the context of approximation schemes ubiquitous in modern lattice QCD calculations. Using FRR techniques, the power-counting regime (PCR) of chiral perturbation…
Ranking theories according to their strength is a recurring motif in mathematical logic. We introduce a new ranking of arbitrary (not necessarily recursively axiomatized) theories in terms of the encoding power of their $\beta$-models:…
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the…
We consider the renormalisation of a softly-broken supersymmetric theory with singlet fields and a superpotential with a linear term. We show that there exist exact beta-functions for both the linear term in the superpotential and the…
In this work we consider the renormalization of the chiral two-pion exchange potential with explicit delta-excitations for nucleon-nucleon scattering at next-to-leading (NLO) and next-to-next-to-leading order (N2LO). Due to the singular…
In an effort to understand the physical implications of the newly discovered non-trivial directions in scalar field theory, we compute lowest order scattering amplitudes, cross sections, and the 1-loop effective potential. To lowest order,…
We propose a new power counting for the effective field theory describing a near-threshold state with unstable constituents, such as the X(3872) meson. In this counting, the momenta of the heavy particles, the pion mass and the excitation…
We show that the direction of renormalization in effective field theory is constrained by fundamental principles in the infrared$\unicode{x2014}$unitarity, analyticity, and Lorentz invariance. Our theorem, in the spirit of the $a$-theorem…
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the $B_0$ parameter…