# S1: Baryon form factors

### Research areas

• Lattice gauge theory

### Goals

Precision information on low-energy baryon structure comes both from electron scattering and atomic spectroscopy. Surprisingly, the extraction of the proton charge radius from muonic hydrogen Lamb shift is in strong contradiction, by around 5.6 standard deviations, with the values obtained from energy level shifts in electronic hydrogen or from electron-proton scattering. This ''proton radius puzzle" has triggered a large activity worldwide. Project S1 is a combined experimental and theoretical effort to advance the precision frontier on baryon form factors (FFs).

The highlights are:

1. Dispersion theory in electron scattering processes
The dilepton production process $$e^- p \to e^- p l^- l^+$$ will be investigated to access the subtraction function which is, at present, the leading hadronic uncertainty in the extraction of the proton radius from the muonic atom spectroscopy. To improve on the dispersive fits of two-photon exchange calculations both for spectroscopy and lepton scattering, a new global fit of nucleon structure functions will be performed, jointly with S2. We furthermore plan, jointly with P2, to improve radiative correction calculations for elastic electron scattering to achieve a precision goal of 0.1%.
2. Theory of timelike nucleon FFs
To interpret the new results from BABAR and BESIII for the timelike nucleon FFs up to around 10 GeV$$^2$$, we plan to use both dispersive and effective field theory techniques. In support of the experimental program, we will extend our study to the $$e^+ e^- \to \bar p n \pi^+$$ and $$e^+ e^- \to \bar p p \pi^0$$, both in the threshold region and in the resonance region to extract the timelike $$N \to \Delta(1232)$$ magnetic dipole FF.
3. Lattice QCD program
Calculations for the nucleon electromagnetic, axial, and strange FFs, in simulations with $$u$$, $$d$$, and $$s$$ quarks, will be improved using a lattice ensemble at the physical pion mass, employing techniques to control excited-state contamination, aiming at a 2% accuracy.
4. Spacelike electromagnetic form factor program at MAMI
New proton FF measurements will be performed with the cluster jet target, via the Rosenbluth technique and via the ISR technique with considerably reduced background. Data for the neutron FFs will be taken with the newly installed neutron polarimeter.
5. Baryon timelike form factor measurements at BESIII
We plan to measure the $$e^+e^- \rightarrow \bar{p} p \pi^0$$ process at BESIII with the aim to extract the timelike nucleon-$$\Delta(1232)$$ magnetic transition FF. Furthermore, the $$e^+e^- \rightarrow \bar{p} n \pi^+$$ and $$e^+e^- \rightarrow \bar{n} p \pi^-$$ processes with an associated soft-pion will be measured and their connection with the timelike nucleon axial FF explored.