P2: Milestones second funding period

P2 magnetic spectrometer

  • Design, construction, installation and commissioning of the magnetic support, scattering chamber and other components.
  • Full Monte Carlo simulation of magnetic spectrometer and integrating detector set-up including radiative corrections.
  • Installation of the integrating read-out electronics.

Development of highest-precision polarimetry

  • Calibration of the double scattering polarimeter.
  • Consistency checks at the 0.5 % level.
  • Commissioning of the Hydro-Møller 8 T solenoid with 0.3 K supra-fluid Helium film.

Tracking system for determination of the momentum transfer Q2 with the P2 magnetic spectrometer

  • Development of a track finding and fitting algorithm optimized for the P2 tracker.
  • Optimization for fast reconstruction of millions of tracks per second.
  • Preparation of the average Q2 measurement using simulated data including a first estimation of systematic errors.

Theoretical work necessary for the interpretation of the measurements

  • Calculation of dominating two-loop and two-photon corrections for the parity-violating asymmetry.
  • Complete Monte Carlo simulation program providing photonic corrections at the required precision.
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P2: Project-related publications from the first funding period

Publications in international refereed journals and books

  1. Measurement of parity violation in electron-quark scattering
    D. Wang et al., (The Jefferson Lab PVDIS Collaboration), MITP/14-030, Nature 506 (2014) 67.
  2. High-voltage pixel detectors in commercial CMOS technologies for ATLAS, CLIC and Mu3e experiments
    I. Peric, P. Fischer, C. Kreidl, H.H. Nguyen, H. Augustin, N. Berger, M. Kiehn and A.K. Perrevoort et al., Nucl.Instrum.Meth. A731 (2013) 131.
  3. New measurements of the transverse beam asymmetry for elastic electron scattering from selected nuclei
    S. Abrahamyan, et al., Phys.Rev.Lett. 109 (2012), 192501


  1. P2 - The weak charge of the proton
    D. Becker, K. Gerz, S. Baunack, K. Kumar and F.E. Maas, AIP Conf.Proc. 1563 (2013) 78.
  2. P2 - The weak charge of the proton 
    D. Becker, K. Gerz, S. Baunack, K. Kumar and F.E. Maas, PoS Bormio 2013 (2013) 024.
  3. Measurement of the axial and the strangeness magnetic form factor of the proton with a P2 backward angle setup
    S. Baunack, D. Becker, K. Gerz, K. Kumar and F.E. Maas, AIP Conf.Proc. 1563 (2013) 73.
  4. Measurement of the weak charge of the carbon-12 nucleus within the P2 experiment in Mainz
    K. Gerz, D. Becker, S. Baunack, K. Kumar and F.E. Maas, AIP Conf.Proc. 1563 (2013) 86.
  5. Measurement of the isovector axial form factor at Q\(^2\) = 0.23 (GeV/c)\(^2\)
    D. Balaguer Ríos, S. Baunack, B. Glaser, F.E. Maas and Y. Imai, AIP Conf.Proc. 1563 (2013) 204.
  6. The polarimetry chain for the P2 experiment
    K. Aulenbacher, I. Alexander and V. Tioukine, Nuovo Cim. C035N04, (2012) 186.
  7. Polarimetry at MAMI
    V. Tioukine and K. Aulenbacher, AIP Conf.Proc. 1563, (2013) 276.
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P2: Accomplishments of the first funding period

  • 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.
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P2: The weak charge of the proton

Research areas

  • Experimental particle and hadron physics
  • Theoretical particle and hadron physics
  • Accelerator physics

Project leaders


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.

Scale dependence of the weak mixing angle, \(\sin^2 \theta_W(\mu)\) compared with existing and forthcoming measurements (Jens Erler, Rodolfo Ferro-Hernández, JHEP 1803 (2018) 196)

The momentum transfer at P2 is lower by many orders of magnitude (\(Q^2 \approx\) 0.05 (GeV/c)\(^2\)) as compared with high-energy experiments. Thus the information obtained in the P2 experiment is complementary to the LEP -- and upcoming LHC -- measurements. P2 is closely connected to the subprojects S1 and P1 since electromagnetic form factors and quantum corrections involving the hadronic structure will be needed in the analysis of the P2 measurement. There is, in addition, a very close connection with the parity violation experiment planned within subproject N. The experiment will be performed at the upcoming MESA accelerator which is funded within the Mainz cluster of excellence PRISMA\(^+\) and will be installed in the new research building (Forschungsbau nach GG §93b). The proposed measurements are also complementary to the future experimental program foreseen at JLab (MOLLER experiment), which aims for a similar precision in a determination of \(\sin^2 \theta_W\). Compared to the goal of the Qweak experiment at JLab, which has recently published the result of their full statistics data, we aim for a factor 3.5 improved precision.

A conceptual design report of the P2 experiment has been
published in Eur. Phys. J. A (2018) 54: 208.

The major highlights for the third funding period are:

  1. 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.
  2. Realisation of high precision polarimetry for electron beams.
  3. Calculation of electroweak radiative corrections and nuclear form factor effects for the measurement of the weak charge of the proton.
  4. Commissioning of the P2 spectrometer, including the MESA control systems for parity violating electron scattering.
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