Pion and Kaon Polarizabilities at CERN COMPASS

Objective: The electric (ᾱ) and magnetic (β̄) pion Compton polarizabilities characterize the pion’s deformation in the electromagnetic field of the γ during γπ Compton scattering. They depend on the rigidity of the pion’s internal structure as a composite particle. The polarizabilities deduced by Antipov et al. in their low statistics Primakoff experiment (∼ 7000 events) were ᾱπ = −β̄π = 6.8 ± 1.4 ± 1.2, in units of 10−43 cm3. This value, ignoring the large error bars, is about three times larger than the chiral perturbation theory (χPT) prediction. Taking into account the very high beam intensity, fast data acquisition, high acceptance and good resolution of the CERN COMPASS experiment, one can expect from COMPASS statistics a factor 6000 higher, a data sample that includes many tests to control systematic errors, and a significantly reduced total measurement uncertainty for ᾱπ , of order 0.4. Methodology: CERN COMPASS studies of pion-photon interactions, to achieve a unique Primakoff physics program centered on pion polarizability studies. We use 100-200 GeV pion beams and a virtual photon target, and magnetic spectrometers and calorimeters to measure the complete kinematics of pion-photon reactions. COMPASS was set up during 2000/01, including a successful Primakoff test run, and then began data taking with a muon beam for the proton spin physics component of its program. COMPASS will next run its spin physics program and Primakoff program preparations, followed by its pion beam physics program, including pion polarizability. For pion polarizability, γπ scattering will be measured via radiative pion scattering (pion Bremsstrahlung) in the nuclear Coulomb field: π + Z → π ′ + γ + Z. A virtual photon from the Coulomb field of the target nucleus is scattered from the pion and emerges as a real photon accompanying the pion at small forward angles in the laboratory frame, while the target nucleus (in the ground state) recoils with a small transverse momentum kick pt. The radiative pion scattering reaction is equivalent to γ + π → γ + π scattering for laboratory γ’s of order 1 GeV incident on a target π at rest. The pion polarizabilities are determined by their effect on the shape of the measured γπ Compton scattering angular distribution. Significance: The pion polarizabilities are key observables, and provide stringent tests of our understanding of chiral symmetry, its spontaneous breakdown, the role of explicit symmetry breaking in QCD, and consequently the very foundations of nuclear physics. The χPT effective Lagrangian, using data from radiative pion beta decay, predicts the pion electric and magnetic polarizabilities ᾱπ = -β̄π = 2.7 ± 0.4. New high precision pion polarizability measurements via radiative pion scattering data from COMPASS will provide important new tests of this QCD chiral dynamics prediction. 1together with: F. Balestra, R. Bertini, M.P. Bussa, M. Colantoni, O. Denisov, A. Dolgopolov, M. Faessler, A. Ferrero, L. Ferrero, J. Friedrich, V. Frolov, R. Garfagnini, N. Grasso, V. Kolossov, R. Kuhn, A. Maggiora,M.Maggiora, A. Manara, Y. Mikhailov, V. Obraztsov, A. Olchevski, D. Panzieri, S. Paul, G, Piragino, J. Pochodzalla, V. Poliakov, A. Sadovski, M. Sans, L. Schmitt, H. Siebert, A. Skachkova, T. Walcher, A. Zvyagin 1 Scientific Background: Pion polarizabilities will be measured at the CERN COMPASS experiment [1, 2, 3, 4, 5, 6, 7, 8], a new high priority approved spectrometer facility at CERN that uses muon and pion beams for studies of hadron structure and spectroscopy. The polarizabilities are obtained from measurements of the γπ → γπ gamma-pion Compton scattering. For the pion, chiral perturbation theory (χPT) leads to precision predictions for the polarizabilities [9, 10, 11, 12]. Precision measurements of polarizabilities therefore subject the χPT techniques of QCD to new and serious tests. The polarizability measurements described here are a part of the global COMPASS Primakoff program [2, 3, 4] to study pion and Kaon polarizabilities, chiral anomalies, and pionic and kaonic Hybrid mesons. The global COMPASS physics program was described Sept. 2002 at a CERN COMPASS Future workshop [13]. 1.1 Pion Polarizabilities via Primakoff Scattering For the pion polarizability, γπ scattering was measured (with large uncertainties) with 40 GeV pions [14] via radiative pion scattering (pion Bremsstrahlung) in the nuclear Coulomb field: π + Z → π ′ +γ + Z′. (1) In this measurement, the incident pion Compton scatters from a virtual photon in the Coulomb field of a nucleus of atomic number Z; and the final state γ and pion are detected in coincidence. The radiative pion scattering reaction is equivalent to γ + π− → γ + π− scattering for laboratory γ’s of order 1 GeV incident on a target π− at rest. It is an example of the well tested Primakoff formalism [15, 16] that relates processes involving real photon interactions to production cross sections involving the exchange of virtual photons. In the 40 GeV radiative pion scattering experiments, it was shown experimentally [14] and theoretically [17] that the Coulomb amplitude clearly dominates, and yields sharp peaks in t-distributions at very small squared four momentum transfers (t) to the target nucleus t ≤ 6× 10−4 (GeV/c)2. Backgrounds from strong processes were low, and are expected to be even lower at the higher energy (∼ 190 GeV) planned for the CERN COMPASS experiment. All polarizabilities in this paper are expressed in units of 10−43 cm3. The χPT 1-loop prediction [9, 10] for the pion polarizability is ᾱπ = − β̄π = 2.7± 0.4; with values ᾱπ = 2.4± 0.5; β̄π = −2.1± 0.5 at two-loop [10]. Holstein [9] showed that meson exchange via a pole diagram involving the a1(1260) resonance provides the main contribution (ᾱπ = 2.6) to the polarizability. Xiong, Shuryak, Brown (XSB) [18] assuming a1 dominance find ᾱπ = 1.8. Many other QCD based polarizability calculations, including lattice QCD [19], are also available, as described in different polarizability articles [2, 11, 20]. In this report, we emphasize comparisons with model independent chiral perturbation predictions. But we will of course compare the data to all theoretical predictions. For the kaon, the lowest order χPT prediction [2, 9, 21] is ᾱK− = 0.5 . The kaon polarizability measurements at COMPASS should complement those for pion polarizabilities for chiral symmetry tests away from the chiral limit. More extensive studies of kaon polarizabilities were given in Ref. [22, 23]. Until now, only an upper limit [24] at 90% confidence was measured (via energy shifts in heavy Z kaonic atoms) for the K−, with ᾱK ≤ 200. Kaon polarizability measurements have never been carried out. For the kaon polarizability, due to the lower beam intensity, the statistics will be roughly 50 times less than for the pion case. But COMPASS would still obtain the first ever Kaon polarizability measurement. 1.2 Pion Polarizabilities For the γ-π interaction at low energy, chiral perturbation theory (χPT) provides a rigorous way to make predictions; because it stems directly from QCD and relies only on the solid assumptions of