# P2: Accomplishments of the second funding period

The progress made in the conceptual design of the experiment including all the research and development work has been summarized in a conceptual design report and will be published as an invited review paper in EPJ A. It has been accepted for publication and can be found under The P2 Experiment - A future high-precision measurement of the electroweak mixing angle at low momentum transfer, D. Becker et al., accepted for publication in Eur. Phys. J. A, arXiv:1802.04759.

• Subproject A: Accelerator concept
The accelerator concept for the Mainz energy-recovering superconducting accelerator MESA has been further developed and the realization of parts (like the electron source) has progressed. MESA is a major infrastructure initiative within the old PRISMA cluster of excellence and the new, continued PRISMA+ cluster of excellence. The necessary R&D as well as invest funds have been primarily funded by PRISMA. In 2015, an extension building of the MESA underground areas in the framework of the German “Forschungsbau”-program evaluated by the German science council was granted: the so-called ”Centrum für Fundamentale Physik, CFP”. This new building, in conjunction with the already existing halls, allows for an optimal arrangement of accelerator and the experiments. The civil construction will be completed in spring 2021. The accelerator design is fixed and all components will be delivered ahead of the availability of the building. The delay caused by the civil construction gives us ample opportunity to test the components beforehand which will be an advantage concerning rapid installation and commissioning. In particular the most demanding components, the SRF-cryo modules, have both been delivered in 2018 and are tested in the HIM experimental hall, which has been prepared for the 2 K operation of superconducting cavities. A liquid Helium supply and a sub-atmospheric compressor system operating between 16 and 1100 mbar is installed.
• Subproject B: Extraction of the weak charge of the proton
In order to predict the achievable precision in the measurement of the weak mixing angle, error propagation calculations were performed using Monte Carlo methods. It turned out that using almost the full MESA energy of $$E=145$$ MeV and a polar scattering angle range of $$25^o \leq \theta\ 45^o$$ provides the best results. The achievable precision is $$\Delta\sin^2\theta_W=3.7\cdot10^{-4}$$ which corresponds to a 0.16 % measurement based on 10,000 h measurement time. Other systematic error stemming from aluminum target window etc. have been included.
• Subproject C: Experimental set-up: solenoid spectrometer and detector
Experiment design
The full Monte Carlo simulation using GEANT4 has been furthermore improved with respect to the geometry of the experiment. Interactions of scattered particles with the shielding and the response of the detectors to the impact of particles. A superconducting solenoid magnet with an inner diameter of about 2.4 m and a maximum field strength of 0.8 T will be used. Currently, CAD drawings are being developed for the mechanical design. A cooperation with Silviu Covrig from Jefferson Lab has been further strengthened for a the design of a 60 cm long liquid hydrogen target.
Detector development
The concept of a P2 detector is based on single modules that consist of fused silica bars together with photomultiplier tubes. In the final design, 82 wedge-shaped modules that consist of the material Spectrosil-2000 from Heraeus, each with a length of 65 cm, will be used. Numerous beam tests at MAMI were performed, testing the response of the detectors both to electrons and photons at different energies in the X1 beam line and the A2 tagger facility. Simultaneously, the GEANT 4 simulations were further developed that provide the detector response for a wide range of impact scattering angles and impact energies for different particles. The beam tests allowed for a thorough validation of the GEANT4 detector response. The full detector response for electrons as well as for background photons down to energies of 10 MeV has been validated with beam tests and implemented in the GEANT4 Monte Carlo simulations.
Experiment electronics
A low noise, high resolution ADC will be used to digitize the signals from the PMT tubes of the fused silica bars. These ADCs are developed jointly for the P2 experiment and the MOLLER experiment at Jefferson Lab. A cooperation with Michael Gericke from the University of Manitoba has been strengthened. A prototype which was used for the QWeak experiment was tested in a test beam the MAMI facility.
• Subproject D: Suppression of false asymmetries
Testing helicity correlated beam parameters and monitors at MAMI for P2
We have carried out several beamtimes in our dedicated beam line at the 180 MeV stage of MAMI to measure the characteristics of electronics components for the MESA beam monitors and stabilization systems. Tests with polarized beam with helicity switching rates up to 1 kHz have been performed, measuring beam position, angle and intensity, correlated with the beam helicity. An FPGA-based fully digital feedback system was successfully employed for the stabilization of beam position and angle. It showed better performance than achieved with analog systems at MAMI for the A4 parity violation experiment. From the acquired data we have estimated the systematic uncertainties for the P2 experiment due to uncertainties in helicity correlations of beam parameters. The solenoid tests have not yet taken place as all other components of this complex test setup had to be implemented and tested first, but is still an option for future tests.
• Subproject E: Strategy for polarization measurements
The Double Scattering Polarimeter (DSP)
This polarimeter employs double elastic (Mott-)scattering to measure the effective analyzing power of a polarimeter. The polarimeter is installed in a separate laboratory which also presently houses the source foreseen for MESA. Recently an additional Wien filter has been built and was integrated in the beamline between source and polarimeter. By changing between unpolarized and polarized beams and by using the Wien filter to provide different spin orientations, double scattering measurements can be carried out in five different ways. First measurements with the setup have have been done and the study of the systematic effects have progressed.
R&D for Hydro-Møller at MESA
We have decided that it is necessary to have an in house fabrication of the 0.3 K atomic trap, since a long term reliable operation of the complex technology requires permanent on-site competences. The conceptual design of the cryostat has been completed and the distribution of tasks between outside vendors and our own machine shop has been defined. Most parts have passed the design phase and have been produced. The remaining parts have been produced too and the heat exchanger components have been made and the remaining parts have become available. The refrigerator will be tested in stages.
• Subproject F: Theory
Photonic higher-order corrections do not contribute to the weak charge of the proton; however, the emission of unobserved photons will lead to a shift of the effective $$Q^2$$, thereby affecting the extraction of the weak charge from the measured polarization asymmetry. Our investigations have shown that these kinematic effects are relevant, leading to a correction of the asymmetry in the order of several percent which depends strongly on the energy and scattering angle. Higher-order corrections are expected to be much smaller. First- and second-order QED radiative corrections, i.e. including radiation of up to two photons and including one- and two-loop corrections are implemented in a Monte Carlo event generator. Numerical results for unpolarized scattering have been studied in detail. The program has been interfaced to the detector simulation software and can be used for detector studies. This will allow us to keep QED radiative effects affecting the data analysis under full control.
A novel class of radiative corrections with an exchange of two photons and parity violation in the hadronic system has been studied.These corrections had previously not received much attention. They can be considered as a shift of the axial part of the $$\gamma Z$$-box correction. We could show that the effect can contribute with a small shift to the proton weak charge, $$\delta Q_W^p = (-0.17 \pm 0.25) \times 10^{-3}$$, i.e. well inside the one permille precision goal of the MESA measurement.
on currently available data was used to obtain a new prediction for the vector part of the dispersive $$\gamma Z$$-box correction, $${\rm Re}☐^V_{\gamma Z} (E = 0.155 {\rm GeV}) = (1.1 \pm 0.2) \times 10^{-3}$$. This confirms that the precision of measurements of the weak mixing angle at MESA will not be limited by this kind of theory uncertainty.
A tracking detector is necessary to determine the average momentum transfer $$Q^2$$ of the scattered electrons detected by the integrating detectors. Due to the high rates and low momenta of electrons, the tracker will be based on fast, thin, high-voltage monolithic active pixel sensors (HV-MAPS). We have developed a four plane tracker geometry based on the requirements of track finding and momentum reconstruction. Currently a detailed mechanical design including a gaseous helium cooling system is being worked out and simulated, mechanical prototyping has started. The HV-MAPS sensor is being developed in close collaboration with the Mu3e experiment. Recently, the first large area (2 by 1cm$$^2$$) sensor has been received from the foundry and is under test. Its predecessor, the MuPix7 chip, demonstrated all essential capabilities on a small chip. Conceptual design and component selection and evaluation for the tracker data acquisition has started.