Chiral Symmetry and Electromagnetic Probes

This is the summary of my talk, given at the 2nd RHIC II science workshop in the electromagnetic-probes-working group. I shortly summarize some of the fundamental physical questions, related to chiral symmetry, which can possibly be addressed by measurement of electromagnetic probes. 1 QCD and Chiral Symmetry Due to the asymptotic freedom of QCD [Mut87], i.e., the fact that the renormalized running coupling becomes large at small scattering-momentum transfers, we cannot describe the observed color-neutral bound states of quark-antiquark pairs (mesons) or three quarks (baryons), utilizing the usual methods of perturbation theory. To make contact with hadronic observables [DGH92, RW00], one uses the chiral symmetry of QCD in the light-quark sector, i.e., for uand d(to less accuracy also s-) quarks to formulate effective hadronic models like the σ model. Chiral symmetry is the transformation of the quark fields with an SU(2)V × SU(2)A [or SU(3)V × SU(3)A] flavor rotation: ψ → exp[−i(~ αV + γ5~ αA)~ T ]ψ, (1) where ~ T are the 3 (8) generators of SU(2) [SU(3)] in flavor space. This is a symmetry of the QCD Lagrangian LQCD = − 1 4 F μν a F a μν + ψ̄( / D − M̂)ψ (2) in the limit of vanishing quark masses M̂ → 0. Here, F μν a are the (non-Abelian) field-strength tensors of the 8 gluons, Dμ = ∂μ+igA a μλ /2 the covariant derivative [λ Gell-Mann matrices, the 8 generators of (color) SU(3)c], and M̂ the mass matrix of the quarks (acting in flavor space). In the limit M̂ → 0 (the “chiral limit”), the Noether currents, ~jV (x) = ψ̄ ~ Tγ ψ, ~jA(x) = ψ̄ ~ Tγ5γ ψ, (3) ∗e-mail: [email protected]