scholarly journals The ChPT: top-down and bottom-up

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Karol Kampf
Keyword(s):  
Sigma Model ◽  
Formal Structure ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Matrix Methods ◽  
Bottom Up ◽  
Higher Derivative ◽  
External Sources ◽  
Intrinsic Parity ◽  
Single Trace

Abstract In this work, higher-derivative corrections of the non-linear sigma model of both even and odd intrinsic-parity sectors are systematically studied, focusing on ordered amplitudes of flavor scalars in massless limit. It should correspond to a theory known as chiral perturbation theory (ChPT) without external sources and with only single-trace operators. We briefly overview its formal development and apply new S-matrix methods to its amplitude constructions. The bottom-up analysis of the tree-level amplitudes of different orders and multiplicities focuses on the formal structure of general ChPT. Possible theoretical simplifications based on the Kleiss-Kuijf and Bern-Carrasco-Johansson relations are presented. Finally, in the same context, the comparison with the so-called Z-function, which is connected with string theory, is also discussed.

scholarly journals Extended DBI and its generalizations from graded soft theorems

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Karol Kampf ◽  
Jiří Novotný ◽  
Petr Vaško
Keyword(s):  
Sigma Model ◽  
Power Counting ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Bottom Up ◽  
Slight Generalization ◽  
S Matrix ◽  
New Type ◽  
Mixed Power ◽  
Special Case

Abstract We analyze a theory known as extended DBI, which interpolates between DBI and the U(N) × U(N)/U(N) non-linear sigma model and represents a nontrivial example of theories with mixed power counting. We discuss symmetries of the action and their geometrical origin; the special case of SU(2) extended DBI theory is treated in great detail. The revealed symmetries lead to a new type of graded soft theorem that allows us to prove on-shell constructibility of the tree-level S-matrix. It turns out that the on-shell constructibility of the full extended DBI remains valid, even if its DBI sub-theory is modified in such a way to preserve its own on-shell constructibility. We thus propose a slight generalization of the DBI sub-theory, which we call 2-scale DBI theory. Gluing it back to the rest of the extended DBI theory gives a new set of on-shell reconstructible theories — the 2-scale extended DBI theory and its descendants. The uniqueness of the parent theory is confirmed by the bottom-up approach that uses on-shell amplitude methods exclusively.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

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.

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 Multi-spin soft bootstrap and scalar-vector Galileon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Karol Kampf ◽  
Jiří Novotný ◽  
Filip Přeučil ◽  
Jaroslav Trnka
Keyword(s):  
Effective Field Theories ◽  
Sigma Model ◽  
Bootstrap Method ◽  
Effective Field ◽  
Power Counting ◽  
Field Theories ◽  
Linear Sigma Model ◽  
Higher Derivative ◽  
Soft Limit ◽  
General Power

Abstract We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.

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 PION-NUCLEON SCATTERING WITHIN A GAUGED LINEAR SIGMA MODEL WITH PARITY-DOUBLED NUCLEONS

2007 ◽  
Vol 16 (07n08) ◽  
pp. 2388-2393 ◽  
Author(s):  
SUSANNA WILMS ◽  
FRANCESCO GIACOSA ◽  
DIRK H. RISCHKE
Keyword(s):  
Sigma Model ◽  
Chiral Condensate ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Model Parameters ◽  
Nucleon Scattering ◽  
Pion Nucleon ◽  
Scattering Lengths ◽  
Chiral Partner ◽  
Gauged Linear Sigma Model

We compute pion-nucleon scattering at tree-level within a gauged linear sigma model which contains the nucleon and its chiral partner. Such an investigation in principle allows to make definite predictions as to whether the main contribution to the nucleon mass comes from the chiral condensate or from the mixing with its chiral partner. We find that there seems to be no set of model parameters that allows for a simultaneous description of all experimentally measured scattering lengths and range parameters. This indicates the need to improve the dynamical ingredients of the model.

scholarly journals Expansions of tree amplitudes for Einstein–Maxwell and other theories

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Kang Zhou ◽  
Shi-Qian Hu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Recent Work ◽  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Quantum Field ◽  
Yang Mills

Abstract The expansions of tree-level scattering amplitudes for one theory into amplitudes for another theory, which have been studied in recent work, exhibit hidden connections between different theories that are invisible in the traditional Lagrangian formulism of quantum field theory. In this paper, the general expansion of tree Einstein–Maxwell amplitudes into the Kleiss–Kuijf basis of tree Yang–Mills amplitudes has been derived by applying a method based on differential operators. The obtained coefficients are shared by the expansion of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes and the expansion of tree special Yang–Mills scalar amplitudes into tree BS amplitudes, as well the expansion of tree Dirac–Born–Infeld amplitudes into tree non-linear sigma model amplitudes.

scholarly journals Standard Model Effective Potential from Trace Anomalies

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Renata Jora
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Effective Potential ◽  
Sigma Model ◽  
Low Energy ◽  
Boson Mass ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Higgs Boson Mass ◽  
Quantum Level

By analogy with the low energy QCD effective linear sigma model, we construct a standard model effective potential based entirely on the requirement that the tree level and quantum level trace anomalies must be satisfied. We discuss a particular realization of this potential in connection with the Higgs boson mass and Higgs boson effective couplings to two photons and two gluons. We find that this kind of potential may describe well the known phenomenology of the Higgs boson.

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