Impact of the Delta (1232) resonance in neutral pion photoproduction in chiral perturbation theory.

Abstract

We present an ongoing project to assess the importance of D-waves and the ∆(1232) resonance for descriptions of neutral pion photoproduction in Heavy Baryon Chiral Perturbation Theory. This research has been motivated by data published by the A2 and CB-TAPS collaborations at MAMI [1]. This data has reached unprecedented levels of accuracy from threshold through to the ∆ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of E γ = 170 MeV, it is necessary to include other aspects, in particular the ∆(1232) as a degree of freedom [2] and possibly higher partial waves [3].

Pion photoproduction in chiral perturbation theory with explicit treatment of the $Δ(1232)$ resonance

“…The first calculation of pion photoproduction with explicit ∆ degrees of freedom was completed in HBχPT [56], focusing on the neutral production channel close to threshold, which showed only moderate effects of the explicit ∆ treatment. A subsequent HBχPT study [58] found a more distinct improvement of the description in the HB framework. In the covariant approach, first studies of neutral pion photoproduction were done in Refs.…”

Threshold pion electro- and photoproduction off nucleons in covariant chiral perturbation theory

“…[34,36]. The ∆ role in π 0 photoproduction has been also investigated in HBChPT showing a rather important contribution [40]. 2 The inclusion of ∆ requires a modification of the power-counting scheme, due to the emergence of a new small parameter, δ = m ∆ − m N ≈ 300 MeV, in the ∆ propagator for the scattering amplitudes.…”