piN elastic scattering first version (D1232) + bug fix

One bug fix included.

piN elastic scattering first version (D1232)

This release contains the initial implementation of pion-nucleon elastic scattering total and differential cross-section, including only the s-channel $\Delta(1232)$ contribution. It's kept for comparison with the future more complete and more complicated versions.

version in agreement with Deniz' new code

This version was used for comparison with Deniz' new, fairly automatic code. We reached an agreement for the s- and u-channel contribution of N(1440) and N(1520) to pion photoproduction, including interferences.

We found a bug in the spin-3/2 -> nucleon+gamma vertex (incoming/outgoing resonances can't be distinguished based on the sign of energy, not even at low energies where antibaryons are excluded - in fact, distinguishing baryons and antibaryons even makes no sense in the case of spacelike momenta, which occurs e.g. in u-channel diagrams). A similar bug may still exist in the 3/2-3/2-pion vertex.

version with full agreement with Deniz' code for pion photoproduction

After finding several errors, we got to an agreement with Deniz in pion photoproduction, which includes:

• Born contributions (with and without form factors)
• D1232, N1440, and probably all spin-1/2 and 3/2 resonance s-channel contributions
  - with only "Dyson" term in resonance width parametrization and no form-factor in RNpi vertex
  - with the Moniz parametrization + the corresponding form factor
  (Dyson term is approximated according to Gyuri's summary of width parametrizations)

Born form factors are implemented according to my draft "3reac", using the code created for pi+n->dilepton. I implemented the old version according to my 2012 PRC paper too. (The results do not agree.)

Initial release

Initial release of the code calculating the process piN->Ne+e-. Based on the code used for the publication arXiv:2012.07546. Changes made after finishing the publication:

• including rho width parametrization used by Bonn-Gatchina
• include piN_Npipi to calculate the pion pair production process
• restructuring into two libraries (FeynTools, ELModel) plus executables
• start using Visual Studio Code and cmake