Emerging phenomenology of 〈Amin2〉

Abstract

We discuss phenomenology of the vacuum condensate (A a µ ) 2 min in pure gauge theories, where A a µ is the gauge potential. Both Abelian and non-Abelian cases are considered. In case of the compact U (1) the non-perturbative part of the condensate (A a µ ) 2 min is saturated by monopoles. In the non-Abelian case, a two-component picture for the condensate is presented according to which finite values of order Λ 2 QCD are associated both with large and short distances. We obtain a lower bound on the (A a µ ) 2 min by considering its change at the phase transition. Numerically, it produces an estimate similar to other measurements. Possible physical manifestations of the condensate are discussed.

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

“…(6) the lattice result g 2 A 2 = 2.76 GeV 2 of Ref. [8], a value compatible with the bound resulting from the discussions of Gubarev et al [9,10] on the physical meaning of A 2 and its possible importance for confinement. As for the contributions O i (1/Q 2 ) (i = A, G) in Eq.…”

“…(3) below] which the running coupling has in the Landau-gauge DS studies [20,28,29,30,31] and the ideas on the possible relevance of the A 2 gluon condensate [2,3,4,5,8,9,10,11,12,13,14]. In the present paper, we give a simplified and more intuitive derivation thereof as follows.…”

“…After it turned out more recently that the Landau-gauge value of A 2 corresponds to a more general gauge-invariant quantity, it attracted a lot of theoretical attention [8,9,10,11,12,13,14,15,16,17,18], to quote just several of many papers offering evidence that A 2 condensate may be important for the nonperturbative regime of Yang-Mills theories. In Ref.…”

Description of gluon propagation in the presence of anA2condensate

“…[29]. The authors of that work define the Landau gauge gluon propagator as 11) and γ = −13/22. (We do not ascribe any particular significance to Eq.…”

“…(There is a suggestion that such a condensate may be related to the presence of instantons in the vacuum [4].) The importance of that condensate raises the question of gauge invariance and there are now a large number of papers that address that and related issues [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. We will not attempt to review that large body of literature, but will consider how the presence of an < A a µ A µ a > condensate modifies the gluon propagator and the vacuum polarization function in QCD.…”