scholarly journals Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Gustavo O. Heymans ◽  
Marcus Benghi Pinto
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
State Of The Art ◽  
Critical Coupling ◽  
Scalar Theory ◽  
Perturbative Series ◽  
Supercritical Region ◽  
Mass Gap ◽  
Perturbative Result ◽  
Symmetric Phase

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

scholarly journals PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

2014 ◽  
Vol 35 ◽  
pp. 1460442
Author(s):  
DIOGO BOITO
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Systematic Study ◽  
Higher Order ◽  
Perturbative Expansion ◽  
Main Stream ◽  
Spectral Functions ◽  
Perturbative Series ◽  
Fixed Order ◽  
Adler Function

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of αs. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

scholarly journals WEAK QUENCHED DISORDER AND CRITICALITY: RESUMMATION OF ASYMPTOTIC(?) SERIES

2002 ◽  
Vol 16 (27) ◽  
pp. 4027-4079 ◽  
Author(s):  
YU. HOLOVATCH ◽  
V. BLAVATS'KA ◽  
M. DUDKA ◽  
C. VON FERBER ◽  
R. FOLK ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
Asymptotic Series ◽  
Analytical Description ◽  
Quenched Disorder ◽  
Site Disorder ◽  
Disordered Models ◽  
Random Site ◽  
Theoretical Results ◽  
Theory Series

In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of the available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.

scholarly journals On the perturbative expansion of exact bi-local correlators in JT gravity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Luca Griguolo ◽  
Jacopo Papalini ◽  
Domenico Seminara
Keyword(s):  
Exact Result ◽  
Bernoulli Polynomials ◽  
Exact Expression ◽  
Zero Temperature ◽  
Leading Order ◽  
Positive Weight ◽  
Perturbative Series ◽  
Compact Expression ◽  
Semiclassical Expansion ◽  
Perturbative Result

Abstract We study the perturbative series associated to bi-local correlators in Jackiw-Teitelboim (JT) gravity, for positive weight λ of the matter CFT operators. Starting from the known exact expression, derived by CFT and gauge theoretical methods, we reproduce the Schwarzian semiclassical expansion beyond leading order. The computation is done for arbitrary temperature and finite boundary distances, in the case of disk and trumpet topologies. A formula presenting the perturbative result (for λ ∈ ℕ/2) at any given order in terms of generalized Apostol-Bernoulli polynomials is also obtained. The limit of zero temperature is then considered, obtaining a compact expression that allows to discuss the asymptotic behaviour of the perturbative series. Finally we highlight the possibility to express the exact result as particular combinations of Mordell integrals.

ON THE LOW-ENERGY SPECTRUM OF SPONTANEOUSLY BROKEN Φ4THEORIES

2011 ◽  
Vol 26 (08) ◽  
pp. 531-542 ◽  
Author(s):  
M. CONSOLI
Keyword(s):  
Perturbation Theory ◽  
Energy Spectrum ◽  
Energy Gap ◽  
Low Energy ◽  
Order Perturbation ◽  
Analytic Calculation ◽  
Leading Order ◽  
Standard Interpretation ◽  
Ising Limit ◽  
Symmetric Phase

The low-energy spectrum of a one-component, spontaneously broken Φ4theory is generally believed to have the same simple massive form [Formula: see text] as in the symmetric phase where 〈Φ〉 = 0. However, in lattice simulations of the 4D Ising limit of the theory, the two-point connected correlator and the connected scalar propagator show deviations from a standard massive behavior that do not exist in the symmetric phase. As a support for this observed discrepancy, we present a variational, analytic calculation of the energy spectrum E1(p) in the broken phase. This analytic result, while providing the trend [Formula: see text] at large |p|, gives an energy gap E1(0)< mh, even when approaching the infinite-cutoff limit Λ→∞ with that infinitesimal coupling λ ~ 1/ ln Λ suggested by the standard interpretation of "triviality" within leading-order perturbation theory. We also compare with other approaches and discuss the more general implications of the result.

scholarly journals A (gravitational) toy story

2017 ◽  
Vol 26 (09) ◽  
pp. 1750096
Author(s):  
W. Barreto ◽  
H. P. de Oliveira ◽  
B. Rodriguez-Mueller
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Critical Exponent ◽  
Critical Behavior ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Hole Formation ◽  
Black Hole Formation ◽  
Mass Gap

Frequently in Physics, insights and conclusions can be drawn from simple, idealized models. The discovery of critical behavior in the gravitational collapse of a massless scalar field leads to the simulation of binary black holes, from its coalescence to merging and ringdown. We refined a toy model to explore black hole formation as these events unfold to revisit the instability of a gravitational kink. We confirmed a conjecture related to a mass gap for critical behavior at the threshold of black hole formation. We find a critical exponent twice the standard value. Surprisingly, this larger critical exponent is also present in the multiple critical behavior for the black hole formation from a massless scalar field in asymptotically anti-de Sitter spacetimes. What is the meaning of this mass gap? Does it have physical relevance?

scholarly journals Regularized perturbative series for the ionization potential of atomic ions

2017 ◽  
Vol 95 (2) ◽  
pp. 184-189 ◽  
Author(s):  
Gabriel Gil ◽  
Augusto González
Keyword(s):  
Perturbation Theory ◽  
Ionization Potential ◽  
Relativistic Effects ◽  
Covalent Radius ◽  
Energy Curve ◽  
Perturbative Series ◽  
Atomic Ions ◽  
Nist Database ◽  
Expansion Coefficients ◽  
The One

We study N-electron atoms with nuclear charge Z. It is well known that, in the cationic (Z > N) large-Z region, the atom behaves as a weakly interacting system. The anionic (Z < N) regime, on the other hand, is characterized by an instability threshold at [Formula: see text], below which the atom spontaneously emits an electron. We construct a regularized perturbative series (RPS) for the ionization potential that is based on the behaviors for large Z and Z near Zc. The large-Z expansion coefficients are analytically computed from perturbation theory, whereas the slope of the energy curve at Z = N − 1 is computed from a kind of zero-range forces theory that uses as input the electron affinity and the covalent radius of the neutral atom with N − 1 electrons. Relativistic effects in the one-particle Hamiltonian are considered at the level of first-order perturbation theory. Our RPS formula is to be used to check the consistency of the ionization potential values for atomic ions contained in the NIST database.

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