Abstract
A set of four Finite Energy QCD sum rules are used to determine the magnetic field dependence of the sum of the up- and down-quark masses of QCD, $(m_u + m_d)$, the pion decay constant $f_\pi$, the pion mass $m_\pi$, the gluon condensate, $\langle 0| \alpha_s\, G^2|0\rangle$, and the squared energy threshold for the onset of perturbative QCD, $s_0$, related to the Polyakov loop of lattice QCD.
Highlights
The method of QCD sum rules (QCDSR) [1] is a wellestablished technique to obtain results in QCD analytically, complementing Lattice QCD simulations (LQCD)
Modern applications of QCDSR are based on a pioneer proposal relating QCD to hadronic physics in the complex squared-energy s-plane [5]
While the Wilson coefficients in the operator product expansion (OPE), Eq (5) can be computed in perturbative QCD (PQCD), the values of the vacuum condensates cannot be obtained analytically from first principles, as this would be tantamount to solving QCD analytically and exactly
Summary
The method of QCD sum rules (QCDSR) [1] is a wellestablished technique to obtain results in QCD analytically, complementing Lattice QCD simulations (LQCD). While the Wilson coefficients in the OPE, Eq (5) can be computed in PQCD, the values of the vacuum condensates cannot be obtained analytically from first principles, as this would be tantamount to solving QCD analytically and exactly These condensates can be determined from the QCDSR themselves, in terms of some input experimental information, e.g., spectral function data from eþe− annihilation into hadrons, or hadronic decays of the τ-lepton. The hadronic state, the a1ð1260Þ, with full width Γa1 1⁄4 250–600 MeV [18] can be safely neglected, as it lies above the threshold for PQCD, s0 ≃ 1 GeV2, and its width is quite large in comparison with the zero-width of the pion This situation would still prevail even if s0 grows somewhat in the presence of a magnetic field. The hadronic spectral function for the other two correlators, Π5ðq2Þ and ψ5ðq2Þ is given by
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
