A classical model of the gluon bag. Exact solutions of Yang-Mills equations with a singularity on the sphere

The bag and the string: Are they opposed?

“…It is well known [26] that the tunneling through an infinitely high potential barrier of the form λ(x − x 0 ) −2 with λ ≥ 3 4 is forbidden in one-dimensional quantum mechanics. One can easily check that this condition is fulfilled by expression (22). Therefore, the boundary of the bag sets up an impenetrable quantum-mechanical barrier to every colored object.…”

“…The boundary of the bag keeps colored objects in the bag from escaping, and hence such objects are permanently trapped in it. Furthermore, external colored objects are unable to penetrate into the bag because the leading singularity of expression (22) is a second-order pole. It is well known [26] that the tunneling through an infinitely high potential barrier of the form λ(x − x 0 ) −2 with λ ≥ 3 4 is forbidden in one-dimensional quantum mechanics.…”

“…The effective potential (22) with the parameters m = 0.34 GeV, ε = 1 GeV, α s = 0.73, σ = 0.14 GeV 2 is shown in Fig. 2.…”

“…(13)- (17) to give U (r; ε) = 1 2 κ(κ + 1) (22) Let us compare (22) and (19). The terms in the first line of (22) closely resembles the respective terms involved in (19), except for changing the overall factor of the Cornell potential. However, the terms of the second line dramatically change the situation.…”

“…[6] where successes and drawbacks of the MIT bag model [3], the SLAC bag model [4], and the soliton bag model [5] are considered at length. Of special interest to our discussion are solutions of the classical Yang-Mills equations that were argued to have a direct bearing on the bag [22,23]. A solution of this kind is singular on a sphere of radius r 0 , and hence is interpreted as a Yang-Mills black hole with the color "event horizon" at r = r 0 .…”