Properties of effective massive Yang-Mills theory in the limit of vanishing vector boson mass (original) (raw)

The strong couplings of massive Yang-Mills theory

Journal of High Energy Physics, 2022

We study the massive Yang-Mills theory in which the mass term is added by hand. The standard perturbative approach suggests that the massless limit of this theory is not smooth. We confirm that this issue is related to the existence of additional degrees of freedom, which are absent in the massless theory. Nevertheless, we show that the longitudinal modes become strongly coupled at the Vainshtein scale, which coincides with the scale of the unitarity violation. Beyond this scale, they decouple from the remaining degrees of freedom, and the massless theory is restored up to small corrections. From here, it follows that the apparent discontinuity in the massless limit is only an artefact of the perturbation theory. The massless limit of massive Yang-Mills theory is smooth, as originally proposed in [21].

vs. pole masses of gauge bosons II: two-loop electroweak fermion corrections

Nuclear Physics B, 2003

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represent a gauge invariant subclass of diagrams. All calculations were performed in the linear R ξ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters sin 2 θ W and the mass ratio m 2 Z /m 2 H . We also present the corresponding on-shell mass counter-terms for the massive gauge bosons, which will be needed for the calculation of observables at two-loops in the on-shell renormalization scheme.

One loop fermion contribution to the effective potential for constant SU(2) Yang-Mills fields

1999

We obtain a series expansion for the one loop fermion contribution to the effective potential for constant A^a_\mu fields in SU(2) theory with a massive fermionic doublet. The series converges for bounded electric fields in terms of the magnetic fields and the gauge potentials. One finds that spontaneous fermion pair creation may be absent for arbitrary strong pure electric fields, with an appropriate choice of the classical currents.

WIS/06/04-FEB-DPP The Effective Potential of the N = 0 ∗ Yang-Mills Theory

2004

We study the N = 4 SYM theory with SU(N) gauge group in the large N limit, deformed by giving equal mass to the four adjoint fermions. With this modification, a potential is dynamically generated for the six scalars in the theory, φ i. We show that the resulting theory is stable (perturbatively in the ’t Hooft coupling), and that there are some indications that 〈φ 〉 = 0 is the vacuum of the theory. Using the AdS/CFT correspondence, we compare the results to the corresponding supergravity computation, i.e. brane probing a deformed AdS5 × S 5 background, and we find qualitative agreement. 1

Generalization of Yang-Mills Theory

2005

In the present paper we shall extend the gauge principle so that it will enlarge the original algebra of the Abelian gauge transformations found earlier in our studies of tensionless strings to the non-Abelian case. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The invariant Lagrangian does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant. The extended gauge theory has the same index of divergences of its Feynman diagrams as the Yang-Mills theory does and most probably will be renormalizable. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup of an enlarged family of particles with higher spins. I analyze the masses o...

An effective action for Yang-Mills field strengths

Nuclear Physics B, 1990

We investigate the gauge-invariant semi-classical effective action for the field strength tensor of Yang-Mills theories and emphasize that renormalization introduces a physical scale in this formulation. The stationary points of the renormalized action are partially classified by a topological number, and imply a non-vanishing (G 2). For SU(2) all homogeneous vacuum solutions are explicitly constructed, for SU(3) numerical results are presented. The SU(2) and SU(3) ground states are found to differ qualitatively. An effective fermion theory is extracted which in the low-momentum regime reduces to a particular four-point interaction, but resembles gluon exchange at high momentum transfers.

One-loop renormalization of the Yang-Mills theory with BRST-invariant mass term

Divergent part of the one-loop effective action for the Yang-Mills theory in a special gauge containing forth degrees of ghost fields and allowing addition of BRST-invariant mass term is calculated by the generalized t'Hooft-Veltman technique. The result is BRST-invariant and defines running mass, coupling constant and parameter of the gauge.

The Effective Potential of the N = 0* Yang-Mills Theory

Journal of High Energy Physics, 2004

We study the N = 4 SYM theory with SU(N ) gauge group in the large N limit, deformed by giving equal mass to the four adjoint fermions. With this modification, a potential is dynamically generated for the six scalars in the theory, φ i . We show that the resulting theory is stable (perturbatively in the 't Hooft coupling), and that there are some indications that φ = 0 is the vacuum of the theory. Using the AdS/CFT correspondence, we compare the results to the corresponding supergravity computation, i.e. brane probing a deformed AdS 5 × S 5 background, and we find qualitative agreement.

QCD Theory of the Hadrons and Filling the Yang–Mills Mass Gap

Symmetry, 2020

The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang-Mills gauge theory dynamics, unlike their counterparts in Maxwell's U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang-Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang-Mills dynamics are inverted and their fermions inserted into these Yang-Mills monopoles to create a system, this system in its unperturbed state contains exactly three fermions due to the monopole rank-3 and its three additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the three fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang-Mills mass gap.