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Register a new userKroll-Lee-Zumino quantum field theory of pionic interactions: rho-meson propagator at two-loop level and electromagnetic pion form factor
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The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pionic strong interactions is used to compute the rho-meson propagator at the two-loop level.
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The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next to leading (one loop) order in perturbation theory. Due to renormalizability, this determination involves no free parameters. The result is $<r^2_pi>_s = 0.40 {fm}^2$. This value gives for $bar{ell}_4$, the low energy constant of chiral perturbation theory, $bar{ell}_4 = 3.4$, and $F_pi/F = 1.05$, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $rhopipi$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) NNLO contribution.
The electromagnetic form factor of the pion in the space-like region, and at finite temperature, $F_{pi}(Q^{2},T)$, is obtained from a QCD Finite Energy Sum Rule. The form factor decreases with increasing T, and vanishes at some critical temperature, where the pion radius diverges. This divergence may be interpreted as a signal for quark deconfinement.
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J. P. B. C. de Melo
, R^omulo Moreira Moita
, Kazuo Tsushiman (Laboratorio de Fisica Teorica e Computacional
2016
The pion electromagnetic form factor is calculated at lower and higher momentum transfer in order to explore constituent quark models and the differences among those models. In particular, the light-front constituent quark model is utilized here to calculate the pion electromagnetic form factor at lower and higher energies. The matrix elements of the electromagnetic current, are calculated with both plus and minus components of the electromagnetic current in the light-front. Further, the electromagnetic form factor is compared with other models in the literature and experimental data.
A novel method is employed to compute the pion electromagnetic form factor, F_pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pions valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.
A renormalizable non-Abelian theory of strong interactions of pions, mediated by rho-mesons, is formulated at tree- and at one-loop level in perturbation theory. Hadron masses are generated through spontaneous symmetry breaking using the Higgs mechanism. Quantization and gauge fixing is achieved using the generalized class of $R_xi$ gauges. As an application of this theory, pion-pion scattering lengths are obtained at tree-level in good agreement with data.
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