scholarly journals Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

2018 ◽  
Vol 175 ◽  
pp. 08024 ◽  
Author(s):  
Andrew Gasbarro
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Pion Mass ◽  
Effective Field ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Lattice Data ◽  
Conformal Window ◽  
Quark Masses ◽  
Low Energies

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Alejandro Ayala ◽  
José Luis Hernández ◽  
L. A. Hernández ◽  
Ricardo L. S. Farias ◽  
R. Zamora
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Strong Field ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Field Case

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

CHIRAL SYMMETRY RESTORATION IN THE LINEAR SIGMA MODEL

1992 ◽  
Vol 03 (05) ◽  
pp. 993-1009 ◽  
Author(s):  
H. MEYER-ORTMANNS ◽  
H.-J. PIRNER ◽  
A. PATKÓS
Keyword(s):  
Chiral Symmetry ◽  
Sigma Model ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Gradual Change ◽  
Chiral Symmetry Restoration ◽  
Meson Octet ◽  
First Order Transition ◽  
Experimental Values

We report on results about the mass sensitivity of chiral symmetry restoration in the linear sigma model. For masses of the pseudoscalar meson octet which are close to the experimental values, we observed only a gradual change in the order parameters, when the temperature was changed. To estimate the size of the first order transition region around the chiral limit, we have varied the mass input for the tree level parametrization in several ways. The point with realistic meson masses turned out to lie well inside the crossover region.

THE HEART OF FACTORIZATION

2014 ◽  
Vol 25 ◽  
pp. 1460014
Author(s):  
MATTHEW D. SCHWARTZ
Keyword(s):  
Effective Field Theory ◽  
Recent Progress ◽  
Gauge Theories ◽  
Effective Field ◽  
Effective Theory ◽  
Tree Level ◽  
Soft Collinear Effective Theory ◽  
Factorization Formula ◽  
The Many ◽  
Traditional Approaches

Factorization is at the heart of nearly any calculation in pertubative QCD. It follows from the universal behavior of gauge theories in soft and collinear limits. This talk gives a summary of recent progress on producing a more transparent understanding of factorization and connecting traditional approaches to those of Soft-Collinear Effective Theory. The main result is the formulation and proof, at tree-level, of a factorization formula in QCD. The proof exploits the many advantages of spinor helicity methods, but does not use any effective field theory tricks. Once the factorization formula is proven, the transition to an effective theory description is effortless.

THE DEPENDENCE OF THE NUCLEON MASS ON THE PION MASS IN THE EXTENDED QUARK SIGMA MODEL

2010 ◽  
Vol 19 (10) ◽  
pp. 2051-2062 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Sigma Model ◽  
Pion Mass ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Nucleon Mass ◽  
Field Equations ◽  
Analytic Expressions ◽  
The Mean

The dependence of the nucleon mass on the pion mass is studied in the framework of the extended quark sigma model. We apply the modified quark sigma model to analyze the pion–nucleon sigma term. Analytic expressions are derived using the Feynman–Hellman theorem. The field equations are solved in the mean-field approximation. The results are compared with the CP-PACS group and the cloudy bag model. The results indicate that the extended linear sigma model provides good agreement compared to other models in the mean-field approximation.

scholarly journals Degeneracy Patterns of Chiral Companions at Finite Temperature

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1400
Author(s):  
Juan M. Torres-Rincon
Keyword(s):  
Chiral Symmetry ◽  
Nuclear Physics ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Smooth Transition ◽  
Linear Sigma Model ◽  
Spontaneous Breaking ◽  
Low Energies ◽  
Effective Theories ◽  
Chiral Partner

Chiral symmetry represents a fundamental concept lying at the core of particle and nuclear physics. Its spontaneous breaking in vacuum can be exploited to distinguish chiral hadronic partners, whose masses differ. In fact, the features of this breaking serve as guiding principles for the construction of effective approaches of QCD at low energies, e.g., the chiral perturbation theory, the linear sigma model, the (Polyakov)–Nambu–Jona-Lasinio model, etc. At high temperatures/densities chiral symmetry can be restored bringing the chiral partners to be nearly degenerated in mass. At vanishing baryochemical potential, such restoration follows a smooth transition, and the chiral companions reach this degeneration above the transition temperature. In this work I review how different realizations of chiral partner degeneracy arise in different effective theories/models of QCD. I distinguish the cases where the chiral states are either fundamental degrees of freedom or (dynamically-generated) composed states. In particular, I discuss the intriguing case in which chiral symmetry restoration involves more than two chiral partners, recently addressed in the literature.

scholarly journals Kinematic numerators from the worldsheet: cubic trees from labelled trees

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Song He ◽  
Linghui Hou ◽  
Jintian Tian ◽  
Yong Zhang
Keyword(s):  
Sigma Model ◽  
Building Blocks ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Natural Class ◽  
Yang Mills ◽  
Tree Expansion ◽  
Labelled Trees ◽  
Logarithmic Functions ◽  
Special Case

Abstract In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with kinematic numerators automatically satisfying Jacobi-identities, once any half-integrand on the worldsheet is reduced to logarithmic functions. We review a natural class of worldsheet functions called “Cayley functions”, which are in one-to-one correspondence with labelled trees, and natural expansions of known half-integrands onto them with coefficients that are particularly compact building blocks of kinematic numerators. We present a general formula expressing kinematic numerators of all cubic trees as linear combinations of coefficients of labelled trees, which satisfy Jacobi identities by construction and include the usual combinations in terms of master numerators as a special case. Our results provide an efficient algorithm, which is implemented in a Mathematica package, for computing all tree amplitudes in theories including non-linear sigma model, special Galileon, Yang-Mills-scalar, Einstein-Yang-Mills and Dirac-Born-Infeld.

scholarly journals Chiral Perturbation Theory at NNNLO

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1262
Author(s):  
Nils Hermansson-Truedsson
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Chiral Perturbation Theory ◽  
Pion Mass ◽  
Effective Field ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Effective Lagrangian ◽  
Low Energies

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum p2, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.

Sign in / Sign up

Export Citation Format

Share Document