Search results for "normalization"

Massive Spin One and Renormalizable Gauges

2015

For many decades of the last century, physicists were struggling to define consistent (renormalizable and unitarity preserving) models for spin-one massive particles (Proca fields). As we know, this was beautifully achieved by Weinberg, Salam and Glashow in 1967 when they proposed an electroweak unified theory which we now call the Standard Model. The electroweak symmetry breaking mechanism, among other things, generates mass terms for the W and Z bosons, while preserving renormalizability and unitarity. The longitudinal degrees of freedom of the massive spin-one particles are given by the Goldostone bosons. Choosing one gauge or another might seem just a matter of convenience and in most c…

Renormalization aspects of chaotic strings

2014

Chaotic strings are a class of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. In this paper we introduce different types and models for chaotic strings, where 2B-strings with finite length are considered in detail. We demonstrate possibilities to extract renormalized quantities, which are expected to describe essential properties of the string.

Renormalization-scheme ambiguity and perturbation theory near a fixed point

1984

We consider the perturbative calculation of critical exponents in massless, renormalizable theories having a nontrivial fixed point. In conventional perturbation theory, all results depend on the arbitrary renormalization scheme used. We show how to resolve this problem, following the "principle of minimal sensitivity" approach. At least three orders of perturbation theory are required for quantitative results. We give scheme-independent criteria for determining the presence or absence of a fixed point in $n\mathrm{th}$ order, and discuss the conditions under which perturbative results might be reliable. As illustrations we discuss QED with many flavors, and ${({\ensuremath{\varphi}}^{4})}_…

Wilsonʼs momentum shell renormalization group from Fourier Monte Carlo simulations

2011

Abstract Previous attempts to accurately compute critical exponents from Wilsonʼs momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model , we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants ( u 0 , r 0 ) for different values of the momentum shell thickness parameter b by simulation using our recently developed Fourier Monte Carlo algorithm. We report strong anomalies in the b-dependence of the fixed point couplings and the resulting exponents y τ and ω in the vicinity of a shell parameter b ⁎ 1 characte…

DIFFERENTIAL RENORMALIZATION AND EPSTEIN–GLASER RENORMALIZATION

2001

Chiral structure of the Roper resonance using complex-mass scheme

2010

The pole mass and the width of the Roper resonance are calculated as functions of the pion mass in the framework of low-energy effective field theory of the strong interactions. We implement a systematic power-counting procedure by applying the complex-mass scheme.

Scaling violation in the infinite-momentum frame

1978

The theory of scaling violation is studied in asymptotically free gauge theories formulated in the infinite-momentum frame. The transition probabilities occurring in the equation governing the q/sup 2/ dependence of the parton distributions are calculated directly. The equivalence of this formalism for the longitudinal parton distributions with the usual one based on the operator-product expansion is demonstrated. The assets of our method are calculational simplicity and reference to physical intuition.

Neutrino-deuteron scattering: Uncertainty quantification and new L1,A constraints

2020

We study neutral- and charged-current (anti)neutrino-induced dissociation of the deuteron at energies from threshold up to 150 MeV by employing potentials, as well as one- and two-body currents, derived in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$). We provide uncertainty estimates from $\ensuremath{\chi}\mathrm{EFT}$ truncations of the electroweak current, dependences on the $\ensuremath{\chi}\mathrm{EFT}$ cutoff, and variations in the pool of fit data used to fix the low-energy constants of $\ensuremath{\chi}\mathrm{EFT}$. At 100 MeV of incident (anti)neutrino energy, these uncertainties amount to about 2--3% and are smaller than the sensitivity of the cross sections …

The classical statistical mechanics of Frenkel-Kontorova models

1995

The scaling properties of the free energy, specific heat, and mean spacing are calculated for classical Frenkel-Kontorova models at low temperature, in three regimes: near the integrable limit, the anti-integrable limit, and the sliding-pinned transition (“transition by breaking of analyticity”). In particular, the renormalization scheme given in previous work for ground states of Frenkel-Kontorova models is extended to nonzero-temperature Gibbs states, and the hierarchical melting phenomenon of Vallet, Schilling, and Aubry is put on a rigorous footing.

Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background

2021

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization metho…