The ρ(1S, 2S), ψ(1S, 2S), Υ(1S, 2S) and ψ t (1S, 2S) Mesons in a Double Pole QCD Sum Rule

Abstract

We use the method of double pole QCD sum rule which is basically a fit with two exponentials of the correlation function, where we can extract the masses and decay constants of mesons as a function of the Borel mass. We apply this method to study the mesons: ρ(1S, 2S), ψ(1S, 2S), Υ(1S, 2S) and ψt(1S, 2S). We also present predictions for the toponiuns masses ψt(1S, 2S) of m(1S) = 357 GeV and m(2S) = 374 GeV.

Double Pole Method in QCD Sum Rules for Vector Mesons

“…where α s is the strong coupling constant, m q is the light quark mass, α s π G 2 is the gluon condensate, qq hi is the quark condensate and s min 0 ¼ 4 m 2 q . Following [19], for the ρ meson we use the parameters: α s ¼ 0:5, m q ¼ 6:4 AE 1:25 ðÞ MeV, qq hi ¼À 0:24 AE 0:01…”

“…In this work, we made a little revision about the QCD Sum rules method and presented a new method for calculation of the hadronic parameters like mass and decay constant [19] as function of the Borel mass.…”

“…Note that the same procedure can be done for Eqs. (19) and ( 24) for decoupling of the m 2 mass. So, for the m 2 mass we have:…”

Reanalysis of the X(3915) , X(4500) and X(4700) with QCD sum rules

“…[27], M. S. Maior de Sousa and R. Rodrigues da Silva study the masses and decay constants of the ρ(1S, 2S), ψ(1S, 2S), Υ(1S, 2S) using Eqs. (48-49), and observe that the ground state masses are (much) smaller than the experimental values.…”

“…In Ref. [26], we apply this approach to study the Z c (3900) and Z(4430) as the 1S and 2S axialvector hidden-charm tetraquark states, respectively, and use the energy scale formula µ = M 2 X/Y /Z − (2M c ) 2 to overcome the shortcoming [27], and reproduce the experimental values of the masses M Zc(3900) and M Z(4430) . In Ref.…”