Subproject A: Accelerator concept
The Mainz energy-recovering superconducting accelerator MESA had been proposed within the PRISMA cluster of excellence. This funding application has been granted in 2012. The accelerator design for MESA is in its ﬁnal stage. The main components, the SRF-cryo modules, will be ordered in 2014 and delivered in 2016. Start of commisioning is forseen for 2017, the full energy of 150 MeV will be available in 2018, continuous operation for experiments will be available in 2019.

Subproject B: Extraction of the weak charge of the proton
The impact of all possible sources of uncertainty on the achievable precision in the measurement of the weak mixing angle is determined by MC based variations of all these quantities. The algorithm has been further developed and includes now energy loss in the target, the speciﬁc detector design and the detector response. Different detector setups are tested now to ﬁnd the optimal conﬁguration. Currently, the achievable precision is determined to be \(\Delta{\sin}^2\theta_W = 3.2·10^{-4}\) which corresponds to a 0.13 % measurement.

Subproject C: Experimental set-up: solenoid spectrometer and detector Experiment design
A full Monte Carlo simulation using GEANT4 has been implemented that includes processes in the target and tracks the particles on their way into the detector volume. It could be shown that a detector setup based on a toroid as well as one based on a solenoid magnetic ﬁeld is feasible and will yield a sufﬁcient separation of elastically scattered signal electrons from background. Various detector conﬁgurations with different magnetic ﬁeld strengths and collimators are tested now with the precision algorithm to ﬁnd an optimal design. Detector development
The concept of a P2 detector is based on single modules that consist of fused silica bars together with photomultiplier tubes. Several fused silica bars of two different qualities and with different geometries were and tested using the MAMI electron beam. The inﬂuence of different polishing techniques and wrapping materials on the photon yield were investigated. Additionally, different light guides were tested. Two types of photomultiplier tubes were tested. GEANT4 based MC simulations were implemented in order to understand the results of the beam tests. It turned out that the light yield is sufﬁcient to reach the desired precision in the measurement of the weak mixing angle. A further beam test is scheduled for December. The goal is to ﬁnd out the optimum balance between photon yield and material costs. Experiment electronics
Two different topics were adressed so far: A prototype of a new PMT base was developed which allows to change remotely the signal gain by about two orders of magnitude. This feature is necessary later in the experiment where there are two operating modes: A high current mode for data taking (integrating mode) and a low current mode for particle tracking (single events). Most recently, an ADC which was used in the QWeak experiment arrived in Mainz to start investigations on a low noise, high resolution ADC.

Subproject D: Suppression of false asymmetries Testing helicity correlated beam parameters and monitors at MAMI for P2
We have demonstrated that the helicity switch frequency for P2 (> 1kHz) can be achieved with nigligble impact on the measuremnt efﬁciency of P2. A helicity correlation measurement system for beam halo, based on optical diagnostics has been setup. Furthermore, a dedicated beam line setup at the 180 MeV stage of MAMI serves as a test bed to improve beam pickups, feedback, and stabilization systems. In particular there is the possibility to observe effects of the very strong longitudinal magnetic ﬁeld of the Hydro Møller solenoid. An FPGA-based fully didgital system for the stabilisation systems is under development including fast dipole magnets for fast beam steering. A ﬁrst beam test using the 180 MeV MAMI beam for the test of ﬁrst components is scheduled for spring 2015.

Subproject E: Strategy for polarization measurements The Double Scattering Polarimeter
This polarimeter employs double elastic scattering to measure the effective analyzing power of a polarimeter. The method has been adapted for the source at MESA. In spring 2014 ﬁrst successful double scattering experiments were performed. A sufﬁcient statistical accuracy has been demostrated. We will build in an additional Wien ﬁlter during the remaining period. This will enable us to perform systematic cross checks with the goal to state the polarimeter accuracy. 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. Design and technolgical R&D for the atomic trap has progressed considerably, in particular concerning the fabrications of the several heat exchangers. A ﬁrst test of the 1 K precooling stage will take place in this funding period.

Subproject F: Theory MITP workshop
A workshop at the MITP brought together experts who discussed topics related to Low-Energy Precision Physics and a number of recommendations for future research have been formulated. A scheme was developped for analysing experimental data and quoting results in a way that comparisons between different experiments is feasible. Two groups have reported about ﬁrst estimates of the 2-loop effects. Corresponding calculations still have to be completed and veriﬁed. Auxiliary measurements needed to reduce form factor uncertainties have been identiﬁed. In addition, investigations for a potential PV experiment with \(C^{12}\) have started. Theory uncertainties from \(\gamma Z\) box graphs
The state-of-the-art of the calculation of theory uncertainties due to \(\gamma Z\) box graph contributions to the parity-violating asymmtry has been reviewed and open questions are formulated. The analysis was made for the QWEAK experiment at Jefferson Lab, but is relevant also for the P2 project. Coulomb distortions in polarized electron nucleus scattering
A framework to calculate Coulomb distortions in the scattering of polarized electrons off heavy nuclei with charge \(Z_e\) has been derived in a master’s thesis. First numerical estimates show Z-dependent effects which are stronger than expected and may be relevant for the polarimetry. QED radiative effects
An existing Monte Carlo program, previously used for the analysis of DIS data at HERA, has been modiﬁed for applications at low-energy elastic scattering. It will allow us to evaluate kinematic effects due to bremsstrahlung.

The main objective of project P2 is the extraction of a precise value of the weak mixing angle, \(\sin^2 \theta_W\), from a measurement of the parity violating (PV) asymmetry in elastic electron proton scattering, with an accuracy comparable to that of the existing LEP measurements of \( \Delta \sin^2 \theta_W = 0.00037\) corresponding to a 0.16% relative uncertainty.

Design and construction of an integrating spectrometer for the measurement of the parity violating asymmetry in elastic electron-proton scattering based on integrating readout of quartz Cherenkov detectors, including a tracking system for the measurement of the average momentum transfer \(Q^2\)based on thin silicon pixel detectors, see the figure on the right.

Realisation of high precision polarimetry for electron beams.

Calculation of electroweak radiative corrections and nuclear form factor effects for the measurement of the weak charge of the proton.

Commissioning of the P2 spectrometer, including the MESA control systems for parity violating electron scattering.