Given Order In Perturbation Theory Research Articles

FeynGrav 2.0

We present a new version of FeynGrav. The present version supports Feynman rules for matter with non-vanishing mass and SU(N) Yang-Mills model. We revisit the gauge fixing procedure for gravity and derive interaction rules valid for an arbitrary gauge fixing parameter. We provide a few simple examples of calculations to illustrate package usage. Program summaryProgram Title: FeynGravCPC Library link to program files:https://doi.org/10.17632/rwnrbbdkkv.1Developer's repository link:github.com/BorisNLatosh/FeynGravLicensing provisions: GPLv3Programming language: Wolfram Mathematica 10 and higherExternal routines/libraries: FeynCalc [1,2]Nature of problem: FeynGrav is a software package that simplifies calculations involving the Feynman rules for gravity. These rules are complex and consist of numerous terms, but FeynGrav makes it possible to work with a specific set of rules within the FeynCalc environment. The package includes interaction rules for regular matter with different spin values, as well as for the SU(N) Yang-Mills model in curved spacetime and general relativity. FeynGrav provides scripts to generate the relevant interaction rules and libraries of pre-generated expressions, making it a powerful tool for researchers in the field of theoretical physics.Solution method: I propose a framework that provides a straightforward way to obtain expressions for the corresponding Feynman rules by efficiently utilizing perturbative expansions. In particular, within the perturbative approach to quantum gravity, certain quantities admit finite perturbative expansions, while others have infinite perturbative expansions. I derive formulas that allow the generation of terms with infinite expansions for any given order of perturbation theory. In all actions describing gravitational interactions, all derivatives can be placed on terms with finite perturbative expansions via integration by parts. In this way, the proposed framework gives a simple algorithm for deriving Feynman rules.Additional comments including restrictions and unusual features: Scripts responsible for generating interaction rules are placed in the “Rules” folder. They can be used separately and only require FeynCalc to run. The “Libs” folder contains the “FeynGravLibrariesGenerator.wl” script and the libraries it generates. “FeynGrav.wl” is the main package file that imports data from the libraries and uses it to work with the interaction rules. The file “FeynGrav_Examples.nb” contains examples of calculations.

Rapidity evolution of the entanglement entropy in quarkonium: Parton and string duality

We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium in theories with nontrivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large ${N}_{c}$, the reduced density matrices that ``resum'' the leading rapidity logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov-like evolution equations. We study their entanglement entropy in a simplified $1+1$ toy model and in 3D QCD. The entanglement entropy in these cases, after resummation, is shown to saturate the Kolmogorov-Sinai bound of 1. Remarkably, in 3D QCD the essential growth rate of the entanglement entropy is found to vanish at large rapidities, a result of kinematical ``quenching'' in transverse space. The one-body reduction of the entangled density matrix obeys a Balitsky-Fadin-Kuraev-Lipatov evolution equation, which can be recast as an evolution in an emergent AdS space, at large impact parameter and large rapidity. This observation allows the extension of the perturbative wee parton evolution at low $x$, to a dual nonperturbative evolution of string bits in curved ${\mathrm{AdS}}_{5}$ space, with manifest entanglement entropy in the confining regime.

Galaxy bias from forward models: linear and second-order bias of IllustrisTNG galaxies

We use field-level forward models of galaxy clustering and the EFT likelihood formalism to study, for the first time for self-consistently simulated galaxies, the relations between the linear b_1 and second-order bias parameters b 2 and b K 2 . The forward models utilize all of the information available in the galaxy distribution up to a given order in perturbation theory, which allows us to infer these bias parameters with high signal-to-noise, even from relatively small volumes (L box = 205 Mpc/h). We consider galaxies from the simulations, and our main result is that the b 2(b 1) and b K 2 (b 1) relations obtained from gravity-only simulations for total mass selected objects are broadly preserved for simulated galaxies selected by stellar mass, star formation rate, color and black hole accretion rate. We also find good agreement between the bias relations of the simulated galaxies and a number of recent estimates for observed galaxy samples. The consistency under different galaxy selection criteria suggests that theoretical priors on these bias relations may be used to improve cosmological constraints based on observed galaxy samples. We do identify some small differences between the bias relations in the hydrodynamical and gravity-only simulations, which we show can be linked to the environmental dependence of the relation between galaxy properties and mass. We also show that the EFT likelihood recovers the value of σ8 to percent-level from various galaxy samples (including splits by color and star formation rate) and after marginalizing over 8 bias parameters. This demonstration using simulated galaxies adds to previous works based on halos as tracers, and strengthens further the potential of forward models to infer cosmology from galaxy data.

Two-loop evolution equation for the B -meson distribution amplitude

We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We argue that the evolution kernel to all orders in perturbation theory can be written as a logarithm of the generator of special conformal transformations times the cusp anomalous dimension, up to a scheme-dependent overall constant. Up to this constant term, the evolution kernel to a given order in perturbation theory can be obtained from the calculation of special conformal anomaly at one order less.

R–ratio of electron–positron annihilation into hadrons: higher–order π2–terms

High–energy behavior of R–ratio of electron–positron annihilation into hadrons is studied. In particular, it is argued that at any given order of perturbation theory the re–expansion of the R–ratio in the ultraviolet asymptotic can be reduced to the form of power series in the naive continuation of the strong running coupling into the timelike domain. The convergence range of the re–expanded R–ratio and the corresponding higher–order π2–terms are discussed.

Supersymmetry restoration in superstring perturbation theory

Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

Can infrared gravitons screenΛ?

It has been suggested that infrared gravitons in de Sitter space may lead to a secular screening of the effective cosmological constant. This seems to clash with the naive expectation that the curvature scalar should stay constant due to the Heisenberg equation of motion. Here, we show that the tadpole correction to the local expansion rate, which has been used in earlier analyses as an indicator of a decaying effective $\ensuremath{\Lambda}$, is not gauge invariant. On the other hand, we construct a gauge-invariant operator which measures the renormalized curvature scalar smeared over an arbitrary window function, and we find that there is no secular screening of this quantity (to any given order in perturbation theory).

Improved perturbation theory for improved lattice actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.

Finite temperature perturbation theory and large gauge invariance

We examine finite temperature perturbation theory for Chern-Simons theories, in the context of an analogue 0+1-dimensional model. In particular, we show how nonextensive terms arise in the perturbative finite temperature effective action, using both the real-time and imaginary-time formalisms. We illustrate how large gauge invariance is restored at all orders, despite being broken at any given order in perturbation theory. We discuss which aspects generalize to a perturbative analysis of finite temperature Chern-Simons terms in higher dimensions.

Limitations to dimensional reduction at high temperature

The claim that renormalizable four-dimensional field theories in the infinite-temperature limit undergo a reduction to effective three-dimensional ones is analyzed in perturbation theory. An essential ingredient is the finite-temperature renormalization group in the imaginary-time formalism. A precise criterion for the occurence of complete dimensional reduction is given. This is satisfied only in exceptional cases, and is violated e.g. by ϕ 4 and QCD. These theories dimensionally reduce only up to a given order in perturbation theory. Illustrative one-loop calculations are given on the basis of a novel summation technique. The perturbative structure of QED and QCD at high temperature is examined in detail. Ward identities as well as explicit computations are used to explain why QED dimensionally reduces to all orders, but QCD does not. In addition, a potential instability deriving from an anomalous diagram is identified and cured.

Renormalized Scattering Operator in Closed Form. I.φ3Model

We present a method of obtaining the results of renormalization which makes no explicit reference either to perturbation theory or to the removal of infinities, but instead is based directly on physical requirements. Applied to scalar ${\ensuremath{\varphi}}^{3}$ theory, the method yields a closed expression for the renormalized scattering operator $S$ in the Dyson form as an implicitly time-ordered exponential of an interaction Hamiltonian plus quasilocal counterterms. Except for the over-all phase of $S$, these counterterms are given as explicit functionals of the vacuum expectation value of the bilinear product of operator derivatives of $S$ with respect to the asymptotic in-field $a(x)$, which enables them to be calculated recursively to any given order of perturbation theory from lower orders. $S$ is calculated in a straightforward manner up to third order of perturbation theory, and the two-point function to fourth order, and all are shown to be finite, the infinities canceling automatically. The second- and third-order results are identical with those of conventional renormalized perturbation theory. No comparable calculation of the fourth-order result seems to be available.