M1: Accomplishments of first funding period 

  • Sum rule studies of γγ processes and light-by-light scattering
    We derived two new exact super-convergence relations, which relate the forward light-by-light scattering to energy weighted integrals of the γγ-fusion cross sections, see Ref.1. They complement the known super-convergence relation based on the extension of the GDH sum rule to the light-light system. All of the new relations were verified exactly in perturbation theory at leading order in scalar and spinor QED, and proof to all orders in perturbation theory was given within the context of the Φ4 quantum field theory, see Ref. 2. We then applied the super-convergence relations to the γγ-production of mesons, and showed quantitatively that they lead to relations between the γγ-transition form factors for (pseudo-)scalar, axial-vector and tensor mesons.
  • Hadronic light-by-light (HLbL) contributions to (g-2)µ: Evaluation of axial-vector, scalar, and tensor meson pole contributions
    We provided an improved estimate for the HLbL correction to the muon’s anomalous magnetic moment aµ ≡ (g-2)µ/2, by considering single meson contributions beyond the leading pseudo-scalar mesons. Based on available experimental input as well as constraints from light-by-light scattering sum rules, we provided new estimates for the effects of axial-vector, scalar, and tensor mesons to aµ, see Ref. 7.
  • Phenomenological studies of η and η′ transition form factors (FFs) using rational approximants
    The η and η′ transition form factors were analyzed in the space-like region in a model-independent way through the use of rational approximants (Refs. 3, 4, 5). The slope and curvature parameters of the form factors as well as their values at zero and infinity were extracted from experimental data. These results allow improved extractions of the mixing parameters of the η−η′ system as well as improve on the pseudoscalar-exchange contributions to the HLbL contribution to aµ (Ref. 10).
  • HLbL contributions to aµ: development of a dispersion relation framework
    We started with the development of a new general dispersive formalism for evaluating the HLbL scattering contribution to the anomalous magnetic moment of the muon. In the suggested approach, this correction is related to the imaginary part of the muon’s electromagnetic vertex function. The latter may be directly related to measurable hadronic processes by means of unitarity and analyticity. As a test of the new formalism, we applied it to evaluate a 2-loop scalar three-point function (Ref. 13), as well as to evaluate the meson pole exchange contribution to aµ (Ref. 15). In both cases, an exact agreement was found with the direct two-loop calculation.
  • Measurement of the spacelike π0 transition FF at BES-III
    At BESIII a γγ program has been successfully launched by Mainz researchers. Before, no such analyses were carried out by the collaboration. We developed a single-tag analysis technique, which allows to access the spacelike transition FF of mesons over a wide Q2 range. For the first funding period of the CRC, the transition FFs of pseudoscalar mesons are in the focus of interest. The measurement of the π0 transition FF is especially important as the pion exchange plays a dominant role in the hadronic light-by-light (HLbL) contribution. We currently analyze a data sample of 2.9 fb−1 taken at a cms energy of 3.77 GeV. By exploiting the single-tag technique, the transition FF between 0.3 GeV2 and 3.1 GeV2 is accessible. The BESIII measurement will yield a significanly improved FF in that energy range compared to existing data from CLEO and CELLO. The BESIII measurement is complementary to relatively recent data from BABAR and BELLE above 4 GeV2 and covers the most relevant energy range in view of the HLbL motivation. The analysis is in a very advanced stage, some systematic studies are however still ongoing. We are very confident that a publication within the first half of 2015 will be possible.
  • Measurement of the spacelike η and η′ transition FFs at BESIII
    Also in the case of the spacelike η and η′ transition FFs, the single tag technique is employed. For both analyses, the π+π-γγ final states is investigated with η → π+π-π0, η′ → π+π-η and the subsequent decay of η → γγ. Preliminary results are foreseen for the end of the first funding period. Similar to the π0 FF, the world’s best measurements below 3 GeV2 will be achieved.
  • Measurement of the spacelike γγ → π+π- process at BESIII
    Although originally foreseen for the second funding period, we already started the analysis of the charged two-pion channed in the single-tag mode. The main reason for this is the fact that the channel came out to be of special importance for the HLbL motivation, but has never been measured before by any experiment so-far. It was shown that a special effort has to be devoted to the background suppression of γγ → µ+µ- events as well as other QED background channels. We expect preliminary results to come out within the course of 2015, while the final publication might be expected at the beginning of the second funding period.
  • Measurement of the timelike η transition FF in the Dalitz decay η → e+eγ with Crystal Ball/TAPS
    A high-accuracy measurement of the Dalitz decay η → e+e-γ (Ref. 6) was achieved with one order of magnitude greater statistics compared to our previous publication. This was achieved by analyzing a new data sample and by using more sophisticated analysis tools. Our new result is currently the most precise determination of the transition FF from η → e+e-γ decays and yields the world’s best measurement of the timelike transition FF of the η meson at low q2, where q2 is the invariant mass of the e+e- pair. Above the di-muon mass the results are comparable in statistics to measurements at CERN, where the decay to a photon and muon pairs has been analyzed. The FFs are found to be in good agreement in that q2 range.
  • Preparation of the timelike η′ transition FF measurement at Crystal Ball/TAPS
    For the measurement of η′ decays the end-point tagging spectrometer was installed in the beamline. To improve data taking rates upgrades of the DAQ- and trigger systems were successfully performed, leading to a three times higher η′ production rate than in 2012. It is planned to take in total 10 weeks of data for studying η′ decays. This would mean a six times higher η′ sample compared to 2012. The first 4 weeks were already taken in summer 2014 and analyses are ongoing. A conservative estimate based on the first 4 weeks of data gives roughly 600 analyzed η′ Dalitz decays from 10 weeks of data taking.
  • Access to timelike transition FFs through the processes e+e- → ηγ and e+e- → η'γ at BES-III
    We are currenly analyzing the production of η and η′ mesons in conjuction with a photon exploiting recent BES-III data in the so-called XYZ region at a cms energy of 4.3 GeV with an integrated luminosity of 5.1 fb−1. Cross sections for the reactions e+e- → ηγ and e+e- → η′γ are determined using the decay modes η → π+π-π0 and η′ → π+π-η and subsequent decays of π0, η to two photons. From these cross sections timelike transition FFs for η and η′ are extracted at momentum transfers around q2 = 18.5 GeV2. The statistical precision of the extracted timelike transition FFs is comparable to BABAR results in the timelike region at q2 = 112 GeV2 (Phys. Rev. D 74, 012002) as well as to BABAR measurements in the spacelike region for Q2 = 10 ... 30 GeV2 (Phys. Rev. D 84, 052001). Studies of systematic uncertainties are currently performed and analysis results will be prepared for internal review within the BES-III collaboration.
  • Data driven approaches to constrain the hadronic contribution to aµ
    We organized three workshops to discuss strategies for improvements of the accuracy of the hadronic contributions to aµ. One workshop was held at the ECT* in Trento (see Ref. 11 for mini-proceedings), and two workshops were held in Mainz (see Ref. 14 for mini-proceedings). Each of the meetings had about 40 participants, and brought together the leading researchers working in this field, both in theory and experiment. As a result of the lively discussions at these meetings, it was agreed to prepare a whitepapertowards a data driven approach to constrain the hadronic contribution to aµ. This will update and extend a previous whitepaper, which was prepared for the US Particle Physics ”Snowmass” Self Study in 2013 (Ref. 12).