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Program A02-2	Study of charge symmetry breaking from the precise and accurate measurement of the nn scattering length using virtual photons
Principal Investigator	ISHIKAWA, Takatsugu (Tohoku University)

Abstract: Charge symmetry is a consequence of isospin invariance, and observables are basically unaffected by changing protons (ps) into neutrons (ns) and ns into ps. Recently, the masses of nuclei including a Λ baryon suggest that Λp and Λn interactions are different, and charged symmetry breaking is proposed [1]. Since a direct measurement of nn scattering is impossible, the nn scattering length has been determined indirectly. In this research, we plan to determine the nn scattering length precisely and accurately using the γ^*d → π⁺nn reaction with a virtual photon γ^* produced from electron scattering. The planned experiment will be performed at the Mainz MAMI facility in Germany, which has three extremly high energy-resolution magnetic spectrometers, and high energy-resolution electron beam. To compare the deduced nn scattering length to the pp scattering length, we quantitatively discuss charge symmetry breaking, and try to give a clue to the origin of the breaking.

Charge symmetry is a consequence of isospin invariance, and observables are basically unaffected by changing protons (ps) into neutrons (ns) and ns into ps. This symmetry corresponds to invariance under changing u quarks (us) into d quarks (ds) and ds to us. Thus, charge symmetry breaking comes from a difference of masses between the u and d quarks and from that of electromagnetic interaction. Recently, the masses of nuclei including a Λ baryon suggest that Λp and Λn interactions are different, and charged symmetry breaking is proposed . How about NN interaction? It seems the nn interaction is more attractive than the pp interaction. The scattering length a, which is one of the most fundamental parameter to describe the interaction, is a_pp = –17.3±0.4 fm for pp scattering (after removing the electromagnetic-interaction (EM) effect) and a_nn = –18.6±0.4 fm for nn scattering [2]. The effect from the ud mass difference is considered to be ∼0.3 fm [3], the discrepancy cannot be explained at present. In the a_pp determination, the uncertainty from statistics is very small, and major uncertainty comes from the EM-effect correction. On the other hand, the major uncertainty seems from statistics because no EM effect is involved in the first order.
   The a_nn value has been more-or-less precisely determined through the nn interaction in the final state of some reaction. There is a possibility that a_nn is not accurate. So far, the two kind of reactions were used to determine a_nn,

  π^–d → nnγ, and
  nd → nnp.

The systematic uncertainty for the production amplitude in the π^–d → nnγ reaction affects the accuracy of the deduced a_nn. The nd → nnp reaction have more than two nucleons in the final state. The systematic uncertainty for the many-body problem affects the accuracy of a_nn.
   To extract the nn → nn scattering effect, it is important to minimize the nn relative momentum, and to minimize the final-state interaction from other particles. In this research, we plan to determine a_nn using the γ^*d → π⁺nn reaction with a virtual photon beam γ^* generated from (e, e') scattering. The γ^*s with an energy around 200 MeV will be used, and momentum is measured for the forward-going π⁺ mesons.

Theoretical-calculated differential cross section d³σ/dM_nndΩ for the forward-going π⁺ mesons (0°) in the γ^*d → π⁺nn reaction at E_γ = 200 MeV. The M_nn stand for the nn invariant mass which is equivalent to the nn relative momentum, and measured π⁺ momentum. The values for the NN scattering length is a_pp = a_nn = –17.3 fm in the Nijmegen I and Reid93 potentials. A different value for a_nn = –18.9 fm has been adopted in the CD-Bonn potential. The shape of the π⁺ momentum distribution is affected by the value of a_nn. The production amplitude for this reaction is well known, and is described in the dynamically coupled-channel model to describe meson and baryon scattering [4]. To select a large π⁺n relative momentum condition, we can maximize the nn scattering effect in the shape of the differential cross section. Figure 1 shows the theoretical-calculated differential cross section d³σ/dM_nndΩ for the forward-going π⁺ mesons in the γd → π⁺nn reaction at E_γ = 200 MeV. Here, the Mnn stands for the nn invariant mass which is equivalent to the nn relative momentum, and measured π⁺ momentum. A large value of a_nn gives a large d³σ/dM_nndΩ near M_nn = 2M_n where M_n denotes the neutron mass at rest. Precise and accurate determination of d³σ/dM_nndΩ near M_nn = 2M_n allow us to determine correct a_nn, and give an answer to a simple question ”Are the scattering lengths different between pp scattering and nn scattering? How about the difference?“

   We plan to perform an experiment to determine a_nn using the electron beam at the Mainz MAMI facility. The virtual photons (γ^*s) with an energy around 200 MeV are generated from electron scattering. The momentum distribution is measured for the π⁺ mesons which are produced in the γ^*d → π⁺nn reaction and is emitted at the same direction to γ^*s. As shown in Figure 1, the differential cross section should be precisely and accurately determined in a narrow range from 139.9 to 140.3 MeV/c to determine a_nn. In general, we cannot achieve the tagging-energy resolution for a real photon beam, and measured π⁺ momentum distribution is smeared. Using a virtual photon is the best solution to improve the energy resolution of the incident photon beam. The energy spread of the electron beam at the Mainz MAMI facility is ∼10^–6, and three magnetic spectrometers to measure the momentum of scattered electrons and emitted π⁺s has an momentum resolution of ∼10^–4. Thus, we can measure the nn invariant mass in the γ^*d → π⁺nn reaction with a mass resolution of higher than 0.1 MeV/c.
   Precisely and accurately determined a_nn is useful information to give a clue to the origin of charge symmetry breaking together with other information —a mass difference between the proton and neutron, mixing between ρ⁰ and Ω mesons, and so on. In addition, the improved a_nn significantly affects the NN potential used for calculations on the nuclear structure and reaction.

Members

Reference Materials

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• [2] E.S. Konobeevski, S. V. Zuyev, V. I. Kukulin, V. N. Pomerantsev, arXiv:1703.00519 (2017).
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