Confinement in QCD and generic Yang-Mills theories with matter representations

Frasca, Marco; Ghoshal, Anish; Groote, S.

doi:10.48550/arxiv.2202.14023

Cited by 4 publications

(7 citation statements)

References 49 publications

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“…Moreover, the non-local theory leads to interesting implications for the proton decay and Grand Unified Theories [52], as well as in braneworld models [53]. In addition, non-perturbative strongly coupled regimes, exact β functions and conditions of confinement in higher-derivative nonlocal theories are being actively investigated [54][55][56][57][58][59]. The results obtained so far shows that the effect of the non-locality in the strong coupling limits is to dilute any mass gap (that may be present in the theory) in the UV regime the system generates.…”

Section: Introductionmentioning

confidence: 99%

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Re-normalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

Chatterjee¹,

Frasca²,

Ghoshal³

et al. 2023

Preprint

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We derive a Nambu-Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories providing a set of Dyson-Schwinger equations in differential form. In the local case, we obtain closed form solutions in the simplest case of the scalar field and extended it to the Yang-Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang-Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we contend ourselves to have the non-locality mass sufficiently large compared to the mass scale arising from the integration of the Dyson-Schwinger equations. Such a choice grants good agreement, in the proper limit, with the spectrum of the local theory. We derive the gap equation for the fermions in the theory that gives some indication of quark confinement also in the non-local NJL case. This result is really important, as it seems to point to the fact the confinement (and breaking of scale invariance) could be an ubiquitous effect in nature that removes some degrees of freedom in a theory in order to favour others.

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Section: Introductionmentioning

confidence: 99%

“…V we derive the gap equation for the fermion in the theory and show that an identical argument as given in Refs. [58,59] can be applied here, giving some indication of quark confinement also in the non-local case. Sec.…”

Section: Introductionmentioning

confidence: 99%

Re-normalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

Chatterjee¹,

Frasca²,

Ghoshal³

et al. 2023

Preprint

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show abstract

“…[44,[51][52][53] for Large Hadron Collider (LHC) phenomenology, astrophysical implications, dimensional transmutation and dark matter and other phenomenology and proton decays in Grand Unified Theories (GUT) in this higher-derivative framework). For such higher-derivative Higgs theory the non-perturbative strongly-coupled regimes and exact β-functions, and conditions of confinement, have been actively investigated very recently by some of the authors [54][55][56][57][58]. 2 In order to study the non-perturbative regimes in Higgs theories, local and non-local, we revert to utilising exact solutions to the Higgs theory, as found in terms of Jacobi elliptical functions, following Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[63,64,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82]. Recently some of the authors studied this in context to non-perturbative hadronic contribution to muon (g-2) μ magnetic moment estimation [65], to prove confinement in QCD [58,66], non-perturbative false vacuum decay [83] and to study mass gap and confinement in string-inspired infinitederivative and Lee-Wick theories [54][55][56]. The main technique we will rely on is originally devised by Bender, Milton, Savage and the method for Dyson-Schwinger equations as shown in [84] that is widely used in the aforementioned studies.…”

Section: Introductionmentioning

confidence: 99%

Quintessence dark energy from strongly-coupled higgs mass gap: local and non-local higher-derivative non-perturbative scenarios

Frasca¹,

Ghoshal

Koshelev

2022

Eur. Phys. J. C

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We entertain the possibility that dark energy arises from the Higgs field of quintessence type in the non-perturbative regimes. For this purpose we utilize a set of exact solutions of Higgs field theory recently devised, in terms of Jacobi elliptical function for a massless quartic scalar field, that satisfy a massive dispersion relation. In certain regions of the parameter space, determined by the quartic coupling value, we show that such solutions have the property to give the correct behavior for the equation of state of the dark energy depending on the initial $$\theta $$ θ value of periodicity of the Jacobi elliptical function solution. It is seen that on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field, when conformal invariance is restored, the equation of state for the dark energy becomes manifest. Further we investigate scenarios within standard field theory framework and also extending to higher-derivative theories, namely infinite-derivative theory, motivated from p-adic string field theory, and Lee–Wick theories and in all cases, we find suitable choices of the parameter space leads to dark energy behavior of the Higgs field, which we compare.

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“…[59,60,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. Recently some of the authors studied this in context to non-perturbative hadronic contribution to muon (g-2) µ magnetic moment estimation [61], to prove confinement in QCD [58,62], non-perturbative false vacuum decay [79] and to study mass gap and confinement in string-inspired infinite-derivative and Lee-Wick theories [53][54][55]. The main technique we will rely on is originally devised by Bender, Milton, Savage and the method for Dyson-Schwinger equations as shown in [56] that is widely used in the aforementioned studies.…”

Section: Introductionmentioning

confidence: 99%

Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios

Frasca¹,

Ghoshal²,

Koshelev³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We entertain the possibility that dark energy arises from the Higgs field of quintessence type in the non-perturbative regimes. For this purpose we utilize a set of exact solutions of Higgs field theory recently devised, in terms of Jacobi elliptical function for a massless quartic scalar field, that satisfy a massive dispersion relation. In certain regions of the parameter space, determined by the quartic coupling value, we show that such solutions have the property to give the correct behavior for the equation of state of the dark energy depending on the initial θ value of periodicity of the Jacobi elliptical function solution. It is seen that on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field, when conformal invariance is restored, the equation of state for the dark energy becomes manifest. Further we investigate scenarios within standard field theory framework and also extending to higher-derivative theories, namely infinite-derivative theory, motivated from p-adic string field theory, and Lee-Wick theories and in all cases, we find suitable choices of the parameter space leads to dark energy behavior of the Higgs field, which we compare.

show abstract

Confinement in QCD and generic Yang-Mills theories with matter representations

Cited by 4 publications

References 49 publications

Re-normalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

Re-normalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance

Quintessence dark energy from strongly-coupled higgs mass gap: local and non-local higher-derivative non-perturbative scenarios

Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios

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