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

Abstract

In this paper, we reanalyze the I = 0 scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous Hölder-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances σ and f0(980), we obtain a prediction for light quark mass mq(2 GeV) = 1 2 (mu(2 GeV) + m d (2 GeV)) = 4.7 +0.8 −0.7 MeV, which is consistent with the PDG (Particle Data Group) value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of σ and f0(980) at 2 GeV, which are approximately 0.64 − 0.83 GeV and 0.40 − 0.48 GeV respectively.

Vector and scalar mesons’ mixing from QCD sum rules

“…The result (4.7) suggests that f 0 (500) and f 0 (1710) are respectively good candidates for mixed states of glueballs withqq andss components. The f 0 (980) may also couple toqq, but its coupling should be much weaker than the f 0 (500) [70]. There is excellent agreement between theqq mass prediction (4.7) and that of Ref.…”

“…where we have used masses of u, d and s quarks at the energy scale µ 0 =2 GeV [1], which corresponds to the energy scale at which decay constants were derived in [70](since m q f q and m s f s are energy scale independent), i.e., m q = (m u + m d ) /2 = 3.5 MeV, m s = 96 MeV. (4.9)…”

Determination of the up/down-quark mass within QCD sum rules in the scalar channel

“…In the complex energy plane, the isoscalar scalar resonance poles for the f 0 (500), f 0 (980), f 0 (1370) are found, whose contributions are coherently included in the spectrum functions, together with two-meson continuum effects from the chiral effective field theory. The prescription of the unitarized chiral spectrum functions improves the Breit-Wigner description of the broad scalar σ resonance [19]. Furthermore, there is no free parameter in our spectrum functions, since they can be predicted from the scattering observables [23][24][25].…”

“…The golden cases to determine the m d + m u and m d − m u would be the divergence of the isovector axial-vector current and the divergence of isovector vector current, respectively [13,17]. Alternatively the isoscalar scalar channel can be also used to calculate the m d + m u [14,18,19]. In this situation, on the phenomenological side one needs the isoscalar scalar spectral functions, which can contain the contributions from the scalar resonances f 0 (500)(σ ), f 0 (980), f 0 (1370) and other heavier ones.…”

$$\bar{B}_s \rightarrow f_0(980)$$ form factors and the width effect from light-cone sum rules

“…For the scalar isoscalar pion form factor Γ π defined withnn source current, the N -subtracted omnés representation gives a good description for the data up to k 2 = 1.5 2 GeV 2 with considering the generalized Watson theorem of the ππ → ππ phase[78][79][80][81][82][83].…”