# Theory

# The EIC Theory Working Group

We solicit overarching questions/topics from the EIC community for discussions involving both theorists and experimentalists. Please submit questions for the EIC User Group's Theoretical Physics Working Group using this google form. Any input is welcome, thank you for your help!

Alessandro Bacchetta (Pavia), Wim Cosyn (FIU), Felix Ringer (ODU/JLab), Anna Stasto (Penn State)

# Topics and open questions

In the following, we summarize different topics and open questions that have recently been discussed in the community.

## QED Radiative Corrections

Different approaches have been proposed in the literature. For example, there are parton showers based on the work by Akhundov et al. and Mo et al.,which have been used to account for QED effects on the experimental side. Numerical results can be found in the work by Badelek et al. Recently, an alternative approach was proposed by Liu et al. Here radiative corrections are accounted for on the theory side. There have been several recent workshops at CFNS, Duke, and Trento. Recently, the EIC Theory Working Group hosted a meeting on QED radiative corrections: Indico.

## Polarized Bethe-Heitler process

Understanding the elastic polarized Bethe-Heitler e + p→ e + p +γ scattering process is important to monitor the EIC luminosity, with the photon emitted at very forward angles. A calculation of the relevant cross section was performed by Afanasev et al. . New numerical computations are needed for the EIC.

A first meeting was organized: Indico.

Conclusions after the first meeting:

- A calculation of the photon flux from the doubly polarized contribution at tree level does not seem to be readily available as it is for the unpolarized part (classic original Bethe-Heitler paper)
- Bethe Heitler calculations are available from DVCS papers, but neglet electron mass (Belitsky, Mueller, Kirchner) or numerical accuracy needs to be checked for the formalism based on four vector contractions (Kreisten, Liuti et al.).
- After the tree level result, we will need to look at one loop corrections. Those corrections were sizeable in some single spin asymmetry calculations.
- Required precision for EIC luminosity measurement is 1%.

Papers mentioned during the meeting

- Haas, Makarenko, "Precision calculation of processes used for luminosity measurement at the ZEUS experiment" : One loop calculations for HERA (but unpolarized)
- Afanasev, Akushevich, Merenkov, "Model independent radiative corrections in processes of polarized electron nucleon elastic scattering": Calculation of photon emission for elastic polarized ep scattering.
- Kriesten, Liuti et al. "Extraction of generalized parton distribution observables from deeply virtual electron proton scattering experiments": Contains polarized BH expressed with four-vector contractions, no masses neglected. Potential issue that might need checks was raised by H. Spiesberger about numerical stability at very forward photon angles.
- Belitsky, Mueller, Kirchner, "Theory of DVCS on the nucleon": polarized BH expressions but with electron mass neglected (which cannot be neglected for the small angle photons).

## Diffractive minima in eA scattering

The measurement of diffractive minima in eA scattering will be an important measurement at the future EIC. There are quantitative questions about the location of the minima and whether they can be washed out to some degree in eA collisions.

The question was if it the white paper plot reflects reality, or if it reflects more the low energy elastic eA curves.

We received input from Jose Manuel Udias (Complutense Madrid) on this:
"With eA scattering the smearing (distortion) of the diffraction minima is mostly due to Coulomb interaction, particularly relevant for heavy nuclei and low energies of the electrons. For light nuclei and moderate electron energies (say larger than 300 MeV), the experimental cross-sections do show a nice diffraction pattern, very similar to the 'plain' theoretical calculations. This Columb distortion in eA reactions is due to the interaction of the probe with the nucleus, before and after the exchange of the virtual boson. In the case that you comment, if the probe that produces the vector boson does not 'see' the nucleus much, that is, if these are photons or light neutral particles, or the energy of said probe is high enough (say above 2 GeV), then what we call 'distorted wave approximation' is not needed, and the plane-wave diffraction patterns will survive to a large extent. The position of the minima, however, would depend on the nuclear distribution. A 'hard' ball would produce stronger dips that a Fermi distribution, but if you're using the 'standard' nuclear density distributions, with 2 or 3 parameters Fermi functions fit to elastic eA data, then again I would say this prediction is safe. Specially the position of the first or second minima is robust. I mean, if the effect you look is 3% in the position of the minima, then you're OK. But if you pretend to be able of 'identifying' deviations from the 'expected position of the minima' of the order of 0.1%, then all the assumptions should be carefully reviewed, and you better use the best nuclear density determination at hand."

## Studies of the crossing angle at the EIC

There have been several dedicated meetings in 2021. Different simulation tools are available, which are being explored further.

Technical Note "Accelerator and beam conditions critical for physics and detector simulations for the Electron-Ion Collider" which initiated the discussion.

First meeting (Indico): Different simulation tool implementations were presented.

Second Meeting (Indico): Formulation of kinematical variables as Lorentz invariants was presented and discussed.

## Broader Community Questions

These questions were posed to the WG and require organization of the community on a broader level

- The interpretation of the EIC data in terms of non-perturbative QCD objects (unpolarised PDFs, polarised PDFs, nuclear PDFs, (nuclear) fragmentation functions) requires an integrated analysis framework where all these objects and others (TMDs etc) can be simultaneously determined.

- How can lattice QCD assist the experiments on 3D tomography of the proton at EIC? Recent progress in lattice allows reliable calculation of the parton distribution functions for a moderate range of x, and has also shown promising potential to calculate the generalized parton distributions and transverse-momentum-dependent distributions. It would be nice to see how such results can be incorporated into the global analysis of the experimental data.

## Topics submitted to the WG

- Studies of small systems at EIC: paper, paper
- Threshold vector meson production, effect of young vector meson
- Are jets broadened or narrowed in e+A SIDIS (compared to e+p)? paper