A possible massive solution to the Dyson equation with small gauge coupling

1993 ◽  
Vol 302 (4) ◽  
pp. 442-446 ◽  
Author(s):  
Giuliano Preparata ◽  
She-Sheng Xue
Keyword(s):  
Gauge Coupling ◽  
Dyson Equation ◽  
Small Gauge ◽  
Massive Solution

scholarly journals QUARK SPECTRUM ABOVE THE CRITICAL TEMPERATURE FROM SCHWINGER–DYSON EQUATION

2007 ◽  
Vol 16 (07n08) ◽  
pp. 2282-2288
Author(s):  
MASAYASU HARADA ◽  
YUKIO NEMOTO ◽  
SHUNJI YOSHIMOTO
Keyword(s):  
Critical Temperature ◽  
Weak Coupling ◽  
Gauge Coupling ◽  
Dyson Equation ◽  
Coupling Region ◽  
Chiral Phase ◽  
Loop Approximation ◽  
Wide Range ◽  
Region Temperature ◽  
Two Peaks

We investigate a spectrum of a fermion, which we call a quark, above the critical temperature of the chiral phase transition in a gauge theory using the Schwinger–Dyson (SD) equation. The SD equation enables us to study the spectrum over a wide range of the gauge coupling. It is shown that the quark spectrum has two sharp peaks which correspond to the normal quasi-quark and the plasmino and is consistent with that obtained in the hard thermal loop approximation in the weak coupling region, while it has also two peaks but with smaller thermal masses and broader widths in the strong coupling region. Temperature-dependence of the quark spectrum is also discussed.

PHASE STRUCTURE OF QCD-LIKE GAUGE THEORIES PLUS FOUR-FERMION INTERACTIONS

1991 ◽  
Vol 06 (37) ◽  
pp. 3385-3396 ◽  
Author(s):  
KEI-ICHI KONDO ◽  
SUSUMU SHUTO ◽  
KOICHI YAMAWAKI
Keyword(s):  
Fixed Point ◽  
Phase Structure ◽  
Gauge Theories ◽  
Anomalous Dimension ◽  
Gauge Coupling ◽  
Continuum Theory ◽  
Dyson Equation ◽  
The Other ◽  
Logarithmic Corrections ◽  
Gauge Interaction

We investigate the phase structure of (QCD-like) gauged Nambu-Jona-Lasinio model (QCD-like gauge theories plus four-fermion interactions) based on the ladder Schwinger-Dyson equation with one-loop running gauge coupling. Through analytical and numerial studies, we establish two-fixed points structure, one with a large anomalous dimension γm ≃ 2 and the other with a small one γm ≃ 0. We further obtain the power critical exponents through the equation of state, which, as they stand, imply that the former fixed point is a Gaussian fixed point. We emphasize that logarithmic corrections due to the gauge interaction is crucial to obtaining an interacting continuum theory at this fixed point.

RECOVERY OF GAUGE INVARIANCE IN STRONG-COUPLING QED

1992 ◽  
Vol 07 (29) ◽  
pp. 7239-7262 ◽  
Author(s):  
KONDO KEI-ICHI
Keyword(s):  
Critical Point ◽  
Vertex Function ◽  
Mean Field ◽  
Mass Function ◽  
Dyson Equation ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Massive Solution ◽  
Bare Coupling Constant ◽  
Arbitrary Gauge

Under a novel ansatz for the vertex function, the Schwinger- Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff Λ, there exists a bifurcation point ec(Λ) of the bare coupling constant above which the trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects the Ward-Takahashi identity, the critical point ec(∞) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky’s scaling of the essential-singularity type and that the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.

scholarly journals Full phase diagram of a UV completed $$ \mathcal{N} $$ = 1 Yang-Mills-Chern-Simons matter theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Adar Sharon ◽  
Tal Sheaffer
Keyword(s):  
Phase Diagram ◽  
Fixed Points ◽  
Gauge Coupling ◽  
Simons Theory ◽  
Yang Mills ◽  
Matter Theory ◽  
Small Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study the large N phase diagram of an asymptotically free UV completion of $$ \mathcal{N} $$ N = 1 SU(N) super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling λ ≡ N/k, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large N techniques, as well as new phases that characterize the Yang-Mills theory. We also conjecture the form of the phase diagram for general values of λ and for finite N.

scholarly journals Complete leading-order standard model corrections to quantum leptogenesis

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Paul Frederik Depta ◽  
Andreas Halsch ◽  
Janine Hütig ◽  
Sebastian Mendizabal ◽  
Owe Philipsen
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
Thermal Bath ◽  
Leading Order ◽  
Boltzmann Equations ◽  
The Standard Model ◽  
Majorana Neutrinos ◽  
Infinite Loop ◽  
First Time ◽  
The Universe

Abstract Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by $$ \mathcal{O} $$ O (1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Electroweak SU(2)L × U(1)Y model with strong spontaneously fermion-mass-generating gauge dynamics

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Petr Beneš ◽  
Jiří Hošek ◽  
Adam Smetana
Keyword(s):  
Chiral Symmetry Breaking ◽  
Axial Vector ◽  
Higgs Sector ◽  
Dyson Equation ◽  
Mass Splitting ◽  
Fermion Mass ◽  
Goldstone Bosons ◽  
The Standard Model ◽  
Exploratory Stage ◽  
The Masses

Abstract Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor SU(3)f symmetry with scale Λ. Anomaly freedom requires addition of three νR. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies Σf(p2) has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) Σf(p2) = $$ {M}_{fR}^2/p $$ M fR 2 / p where three Majorana masses MfR of νfR are of order Λ. (2) Σf(p2) = $$ {m}_f^2/p $$ m f 2 / p where three Dirac masses mf = m(0)1 + m(3)λ3 + m(8)λ8 of SM fermions are exponentially suppressed w.r.t. Λ, and degenerate for all SM fermions in f. (1) MfR break SU(3)f symmetry completely; m(3), m(8) superimpose the tiny breaking to U(1) × U(1). All flavor gluons thus acquire self-consistently the masses ∼ Λ. (2) All mf break the electroweak SU(2)L × U(1)Y to U(1)em. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) three νR-composed Higgses χi with masses ∼ Λ. (2) Two new SM-fermion-composed Higgses h3, h8 with masses ∼ m(3), m(8), respectively. (3) The SM-like SM-fermion-composed Higgs h with mass ∼ m(0), the effective Fermi scale. Σf(p2)-dependent vertices in the electroweak Ward-Takahashi identities imply: the axial-vector ones give rise to the W and Z masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in f. At the present exploratory stage the splitting comes out unrealistic.

scholarly journals Searching for Z′ bosons at the P2 experiment

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
P. S. Bhupal Dev ◽  
Werner Rodejohann ◽  
Xun-Jie Xu ◽  
Yongchao Zhang
Keyword(s):  
Parity Violation ◽  
Z Bosons ◽  
Gauge Coupling ◽  
New Physics ◽  
Polarized Electrons ◽  
Mixing Angles ◽  
Charge Assignment ◽  
Wide Range ◽  
Discovery Potential ◽  
Left And Right

Abstract The P2 experiment aims at high-precision measurements of the parity-violating asymmetry in elastic electron-proton and electron-12C scatterings with longitudinally polarized electrons. We discuss here the sensitivity of P2 to new physics mediated by an additional neutral gauge boson Z′ of a new U(1)′ gauge symmetry. If the charge assignment of the U(1)′ is chiral, i.e., left- and right-handed fermions have different charges under U(1)′, additional parity-violation is induced directly. On the other hand, if the U(1)′ has a non-chiral charge assignment, additional parity-violation can be induced via mass or kinetic Z-Z′ mixing. By comparing the P2 sensitivity to existing constraints, we show that in both cases P2 has discovery potential over a wide range of Z′ mass. In particular, for chiral models, the P2 experiment can probe gauge couplings at the order of 10−5 when the Z′ boson is light, and heavy Z′ bosons up to 79 (90) TeV in the proton (12C) mode. For non-chiral models with mass mixing, the P2 experiment is sensitive to mass mixing angles smaller than roughly 10−4, depending on model details and gauge coupling magnitude.

scholarly journals Primordial monopoles and strings, inflation, and gravity waves

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Joydeep Chakrabortty ◽  
George Lazarides ◽  
Rinku Maji ◽  
Qaisar Shafi
Keyword(s):  
Symmetry Breaking ◽  
Gravity Waves ◽  
Cosmic Strings ◽  
Wave Spectrum ◽  
Gauge Coupling ◽  
String Tension ◽  
Magnetic Monopoles ◽  
Intermediate Scale ◽  
Tension Parameter ◽  
The Universe

Abstract We consider magnetic monopoles and strings that appear in non-supersymmetric SO(10) and E6 grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter Gμ spans the range 10−6− 10−30, where G is Newton’s constant and μ is the string tension. We show how intermediate scale monopoles with mass ∼ 1013− 1014 GeV and flux ≲ 2.8 × 10−16 cm−2s−1sr−1, and cosmic strings with Gμ ∼ 10−11− 10−10 survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio r lies between 0.06 and 0.003 depending on the details of the inflationary scenario.

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