Testing a non-perturbative mechanism for elementary fermion mass generation: numerical results

Based on a recent proposal according to which elementary particle masses could be generated by a non-perturbative dynamical phenomenon, alternative to the Higgs mechanism, we carry out lattice simulations of a model where a non-abelian strongly interacting fermion doublet is also coupled to a doublet of complex scalar fields via a Yukawa and an “irrelevant" Wilson-like term. In this pioneering study we use naive fermions and work in the quenched approximation. We present preliminary numerical results both in the Wigner and in the Nambu-Goldstone phase, focusing on the observables relevant to check the occurrence of the conjectured dynamical fermion mass generation effect in the continuum limit of the critical theory in its spontaneously broken phase.

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CHIRALLY EXTENDED QUANTUM CHROMODYNAMICS

International Journal of Modern Physics C ◽

10.1142/s0129183195000599 ◽

1995 ◽

Vol 06 (05) ◽

pp. 725-742 ◽

Cited By ~ 4

Author(s):

RICHARD C. BROWER ◽

YUE SHEN ◽

CHUNG-I TAN

Keyword(s):

Quantum Chromodynamics ◽

Quark Mass ◽

Continuum Limit ◽

Chiral Limit ◽

Scalar Fields ◽

Weak Coupling Limit ◽

Slowing Down ◽

Large N ◽

Chiral Invariance ◽

The Continuum

We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As examples of such universality, we present the large N solutions of two prototype models for XQCD, in which the mass of the spurious pion and sigma resonance go to infinity with the cut-off. Even if the universality conjecture turns out to be false, we believe that XQCD will still be useful as a low energy effective action for QCD phenomenology on the lattice. Numerical simulations are recommended to further investigate the possible benefits of XQCD in extracting QCD predictions.

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Lattice regularisation and entanglement structure of the Gross-Neveu model

Journal of High Energy Physics ◽

10.1007/jhep07(2021)207 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Gertian Roose ◽

Nick Bultinck ◽

Laurens Vanderstraeten ◽

Frank Verstraete ◽

Karel Van Acoleyen ◽

...

Keyword(s):

Field Theory ◽

Continuum Limit ◽

Matrix Product ◽

Transition Line ◽

Mass Generation ◽

Mass Gap ◽

Matrix Product State ◽

Linear Representations ◽

The Continuum ◽

Gross Neveu Model

Abstract We construct a Hamiltonian lattice regularisation of the N-flavour Gross-Neveu model that manifestly respects the full O(2N) symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorems. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large N limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for N = 2, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of O(4), corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

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THE CHIRAL U(1) SYMMETRY IN LATTICE QCD WITH WILSON FERMIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x95001108 ◽

1995 ◽

Vol 10 (15) ◽

pp. 2269-2290 ◽

Cited By ~ 3

Author(s):

CARLO UNGARELLI

Keyword(s):

Lattice Qcd ◽

Chiral Symmetry ◽

Continuum Limit ◽

Axial Current ◽

Numerical Results ◽

Ward Identities ◽

Definition Of ◽

The Continuum ◽

Wilson Fermions

The properties of singlet flavor chiral symmetry of lattice QCD with Wilson fermions are analyzed. We show that a suitable U(1) axial current can be defined, satisfying, in the continuum limit, the Adler-Bell-Jackiw anomaly. Moreover, the renormalization properties of composite operators which appear in U(1) chiral Ward identities are discussed. Finally, starting from the renormalized Ward identities for the axial U(1) current, we analyze a definition of topological susceptibility suitable for nonperturbative studies and discuss preliminary numerical results.

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The Higgs boson: A major discovery and a problem

From Random Walks to Random Matrices ◽

10.1093/oso/9780198787754.003.0012 ◽

2019 ◽

pp. 195-208

Author(s):

Jean Zinn-Justin

Keyword(s):

Higgs Boson ◽

Particle Physics ◽

Gauge Theories ◽

Higgs Mechanism ◽

Higgs Model ◽

Fermion Mass ◽

Simplified Models ◽

Mass Generation ◽

Abelian Gauge ◽

The Standard Model

Chapter 12 describes the main steps in the construction of the electroweak component of the Standard Model of particle physics. The classical Abelian Landau–Ginzburg–Higgs mechanism is recalled, first introduced in the macroscopic description of a superconductor in a magnetic field. It is based on a combination of spontaneous symmetry breaking and gauge invariance. It can be generalized to non–Abelian gauge theories, quantized and renormalized. The recent discovery of the predicted Higgs boson has been the last confirmation of the validity of the model. Some aspects of the Higgs model and its renormalization group (RG) properties are illustrated by simplified models, a self–interacting Higgs model with the triviality issue, and the Gross–Neveu–Yukawa model with discrete chiral symmetry, which illustrates spontaneous fermion mass generation and possible RG flows.

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Is the Higgs mechanism of fermion mass generation a fact? A Yukawa-less first-two-generation model

Physics Letters B ◽

10.1016/j.physletb.2016.02.059 ◽

2016 ◽

Vol 755 ◽

pp. 504-508 ◽

Cited By ~ 19

Author(s):

Diptimoy Ghosh ◽

Rick Sandeepan Gupta ◽

Gilad Perez

Keyword(s):

Higgs Mechanism ◽

Fermion Mass ◽

Generation Model ◽

Mass Generation

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Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

EPJ Web of Conferences ◽

10.1051/epjconf/201817508009 ◽

2018 ◽

Vol 175 ◽

pp. 08009 ◽

Cited By ~ 2

Author(s):

Stefano Capitani ◽

Giulia Maria de Divitiis ◽

Petros Dimopoulos ◽

Roberto Frezzotti ◽

Marco Garofalo ◽

...

Keyword(s):

Mass Term ◽

Fermion Mass ◽

Mass Generation ◽

Complex Scalar ◽

Abelian Gauge ◽

Twisted Mass ◽

Chiral Transformation ◽

Complex Scalar Field ◽

Stringent Test ◽

Field Theoretical Model

In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.

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Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization

Physical Review D ◽

10.1103/physrevd.104.054514 ◽

2021 ◽

Vol 104 (5) ◽

Author(s):

Riccardo Fantoni ◽

John R. Klauder

Keyword(s):

Monte Carlo ◽

Continuum Limit ◽

Scalar Fields ◽

Point Function ◽

Real Scalar ◽

Monte Carlo Evaluation ◽

The Continuum

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Instability and Collapse in Discrete Wave Equations

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2005-0011 ◽

2005 ◽

Vol 5 (3) ◽

pp. 223-241

Author(s):

A. Carpio ◽

G. Duro

Keyword(s):

Continuum Limit ◽

Wave Equations ◽

Numerical Solutions ◽

Blow Up ◽

Theoretical Predictions ◽

Initial States ◽

The Impact ◽

The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

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