A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

Abstract

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules * Qi-Nan Wang( ) 1 Zhu-Feng Zhang( ) 1,2;1) T. G. Steele 2 Hong-Ying Jin( ) 3 Zhuo-Ran Huang( ) 2,3

Constraint on the light quark mass mq from QCD sum rules in the I=0 scalar channel

“…1, we plot the allowed region for (τ , s 0 ) by the Hölder inequality for κ = 2.0 and κ = 3.0 respectively. From this figure, we find that the α s corrections to α s G 2 and m qq q extend the allowed region to a higher τ region and lower s 0 region as in the ρ channel [9], and the instanton contribution extends the allowed region further more. 4 In practice, we will divide R (theo) bym 2 q in order to remove the to-be-fitted parameter from the theoretical side, i.e., we estimate the standard deviation for R (theo) (τ j ,mq)/m 2 q .…”

“…Based on our previous study, κ = 2.8 is the favored result in the vector channel with a traditional ESC model [9]. Although the factorization violation effect may differ between channels, it is still reasonable to assume the value of κ is in the region of 2-3 in the scalar channel, too.…”

“…(2), we also have included the α s corrections to dimension-4 operators, which may play an important role in the determination of the QCD sum rule window from the Hölder inequality as in Ref. [9].…”

“…In this paper, we will use the same iterative procedure to determine the sum rule window from the Hölder inequality rigorously as in Ref. [9], i.e., by choosing the maximally allowed region [τ min , τ max ] of the Hölder inequality which is consistent with fitted s 0 , where τ min and τ max are respectively the lower bound and upper bound of the allowed τ region.…”

“…In this paper, we will reinvestigate the I = 0 scalar channel using the improved MonteCarlo based QCD sum rule methodology recently proposed in Ref. [9]. After introducing a two Breit-Wigner type resonances parametrization for the phenomenological spectral density normalized by the low-energy theorem, a MonteCarlo based analysis will be presented for the QCD sum rule master equation with the I = 0 scalar current in the rigorous Hölder-inequality-determined sum rule window.…”