We use heavy baryon chiral perturbation theory to evaluate the two-photon exchange corrections to the low-energy elastic lepton-proton scattering at next-to-leading order accuracy, i.e., O(α, M −1 ), including a non-zero lepton mass. We consider the elastic proton intermediate state in the two-photon exchange invoking soft photon approximation. The infrared singular contributions are projected out using dimensional regularization. The resulting infrared singularity-free two-photon exchange contribution is in good numerical agreement with existing predictions based on standard diagrammatic soft photon approximation evaluations.

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First, we discuss the conditions under which the non-relativistic and relativistic types of the Breit–Wigner energy distributions are obtained. Then, upon insisting on the correct normalization of the energy distribution, we introduce a Flatté-like relativistic distribution -denominated as Sill distribution- that (i) contains left-threshold effects, (ii) is properly normalized for any decay width, (iii) can be obtained as an appropriate limit in which the decay width is a constant, (iv) is easily generalized to the multi-channel case (v) as well as to a convoluted form in case of a decay chain and - last but not least - (vi) is simple to deal with. We compare the Sill distribution to spectral functions derived within specific QFT models and show that it fairs well in concrete examples that involve a fit to experimental data for the $$\rho $$ ρ , $$a_1(1260)$$ a 1 ( 1260 ) , and $$K^*(982)$$ K ∗ ( 982 ) mesons as well as the $$\varDelta (1232)$$ Δ ( 1232 ) baryon. We also present a study of the $$f_2(1270)$$ f 2 ( 1270 ) which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the $$a_0(980)$$ a 0 ( 980 ) -$$a_0(1450)$$ a 0 ( 1450 ) and the $$K_0^*(700)$$ K 0 ∗ ( 700 ) -$$K_0^*(1430)$$ K 0 ∗ ( 1430 ) resonances as examples.

We study the decays of the J PC = 1 −+ hybrid nonet using a Lagrangian invariant under the flavor symmetry, parity reversal, and charge conjugation. We use the available experimental data, the lattice predictions, and the flavor constraints to evaluate the coupling strengths of the π 1 (1600) to various two-body mesonic states. Using these coupling constants, we estimate the partial widths of the two-body decays of the hybrid pion, kaon and the isoscalars. We find that the hybrid kaon can be nearly as broad as the π 1 (1600). Quite remarkably, we find also that the light isoscalar must be significantly narrow while the width of the heavy isoscalar can be matched to the recently observed η 1 (1855).

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We have investigated the effect of the finite size of the constituent quarks on singlet and triplet nucleon-nucleon potentials, obtained in the framework of the SU (2) nonrelativistic quark model using the resonating group method in the Born-Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one gluon exchange potential (OGEP), and instanton induced interaction (III). The effects of the smearing of the contact interactions and the variation of the constituent mass of the quarks are discussed.