# P1: Precision hadron physics: (g-2)μ and αem(M2Z)

### Research areas

• Lattice gauge theory

### Goals

Project P1 aims for a clarification of the presently seen discrepancy between the Standard Model (SM) prediction of $$(g-2)_\mu$$ and its direct measurement. The main highlights are:

Measurements of the hadronic cross section in $$e^+e^-$$ annihilation via the ISR method at the BESIII experiment will be continued in the second funding period. We will refine the accuracy of the important hadronic channel $$e^+e^- \to π^+π^-$$and will measure in addition the low energy as well as the high energy regions. Furthermore, additional final states will be measured.  Recently, a dedicated energy scan has been carried out between 2 GeV and 4.6 GeV.  This data taking was proposed by Mainz researchers. The data will be analyzed, and the $$R_{\rm incl}$$ ratio will be extracted with the goal to reduce the uncertainty to 3 %, which is a factor of 2 improvement over the best measurements so far.
Earlier than originally foreseen,  the ISR analyses carried out by Mainz researchers prompted several important spin-off studies in the fields of light quark spectroscopy as well as charmonium spectroscopy. There is a perfect synergy between the cross section measurements and hadron spectroscopy as the data sets, the experimental tools, and the Monte Carlo programs are identical. We will continue investigations of this kind and will also perform a dedicated scan around the $$\chi_{c1}$$ resonance (quantum numbers $$J^{PC}=1^{++}$$ with the goal to discover this resonance in the annihilation reaction $$e^+e^- \to \chi_{c1}$$, which is possible via a two-photon box diagram. This would be the first time a production of a non-vector resonance would be seen in $$e^+e^-$$ annihilation. The data taking for this scan was proposed by Mainz researchers and approved by the BESIII collaboration.
A recent search for the dark photon at A1/MAMI was able to set stringent limits for the existence of this hypothetical particle. Since the mass region below 50 MeV/c$$^2$$ is not accessible at MAMI a new multi-purpose spectrometer, MAGIX, will be developed and used to search for dark photons in this mass region. MAGIX will operate as the internal target setup at the new MESA accelerator. Within project P1 we will develop a GEM-based focal plane detector for MAGIX.
The calculation of the leading hadronic vacuum polarization contribution to the muonic $$(g−2)$$ on gauge ensembles with dynamical up, down and strange quarks is currently in progress. We employ the time-momentum representation, which not only can be used consistently with our choice of boundary condition, but also offers advantages for the calculation of quark-disconnected contributions. In addition, we use a new method, proposed by Meyer, for the determination of the disconnected piece, which makes use of a Lorentz-covariant integral representation. We have added a gauge ensemble at the physical pion mass, which greatly reduces the overall systematic error of our previous determination due to the chiral extrapolation. In order to better constrain the long-distance contributions in the spatially summed vector correlator, we have performed a dedicated study of the spectroscopy in the vector channel including two-pion states. This effort shares the same technology as our spectroscopy studies for project S3, namely the determination of the energies of multi-particle states on a torus using the Lüscher formalism. Our preliminary results indicate a somewhat larger estimate for the hadronic vacuum polarization contribution compared to our earlier two-flavour study and also relative to the result obtained using dispersion theory.
We pursue several complementary activities to constrain the hadronic light-by-light scattering contribution. Lattice calculations of the forward scattering amplitude can be compared with dispersive sum rules via the optical theorem. We have shown that phenomenological models for the hadronic cross sections provide a good description of the lattice data, which provides a stringent test of model estimates for the light-by-light scattering contribution to $$(g-2)_\mu$$. Lattice calculations of the transition form factor for $$\pi^0\to\gamma^\ast\gamma^\ast$$ are in progress, using ensembles including a dynamical strange quark, thus improving on our earlier calculation in two-flavour QCD. We have also started to compute the hadronic light-by-light scattering contribution to $$(g-2)$$ directly, by combining a semi-analytical calculation of the QED kernel in infinite volume with lattice calculations of the relevant four-point correlation function.