Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

Abstract

General solution of RG equations in the framework of background perturbation theory is written down in the large Nc limit. A simplified (model) approximation to the general solution is suggested which allows to write β(α) and α(β) to any loop order. The resulting αB(Q 2 ) coincides asymptotically at large |Q 2 | with standard (free) αs, saturates at small Q 2 ≥ 0 and has poles at time-like Q 2 in agreement with analytic properties of physical amplitudes in the large Nc limit.

Restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

“…(3.4) that the only effect of M B is to moderate the IR behavior of the perturbative potential, whereby the Landau ghost pole and IR renormalons disappear, while the short distance behavior, as well as the Casimir scaling property, stay intact [11].…”

The pole heavy-quark masses in the Hamiltonian approach

“…[8]) α crit = 0.60 was used, but in analytical perturbation theory [17] the large value α crit = 4π/β 0 ∼ = 1.4 appeared. In the background perturbation theory (BPT) which will be used here, α crit is smaller and fully defined by Λ QCD [16,18]. For the definition of α static (r) it is better to start with the vector coupling in momentum space:…”

Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism

“…Replacing in (22) the sum over n by the integral and renormalizing the integral in the same way as in (19) one obtains…”

“…The corresponding extrapolation was done in [21,22] where it was shown, that equidistant mass squared spectra of hadrons allow to replace all logs by Euler ψ-functions, and thus obtain for finite Q 2 < 0 simple poles in Minkovskian region, while for large Q 2 > 0 in Euclidean region one has standard logarithmic terms. The whole scheme works nicely for both β(α s ) and α s and agrees well both with lattice and phenomenology [21,22].…”