Real and Virtual Compton Scattering: the nucleon polarisabilities

We give an overview of low-energy Compton scattering (gamma^(*) p --> gamma p) with a real or virtual incoming photon. These processes allow the investigation of one of the fundamental properties of the nucleon, i.e. how its internal structure deforms under an applied static electromagnetic field. Our knowledge of nucleon polarisabilities and their generalization to non-zero four-momentum transfer will be reviewed, including the presently ongoing experiments and future perspectives.Comment: 20 pages, 12 figures. Minireview/Proceedings of "Many-Body Structure of Strongly Interacting Systems", Mainz, Germany, Feb. 23-25 2011 . V2: typos corrected. version to appear in EPJ Special Topic

Monte Carlo simulation of virtual Compton scattering below pion threshold

This paper describes the Monte Carlo simulation developed specifically for the VCS experiments below pion threshold that have been performed at MAMI and JLab. This simulation generates events according to the (Bethe-Heitler + Born) cross section behaviour and takes into account all relevant resolution-deteriorating effects. It determines the `effective' solid angle for the various experimental settings which are used for the precise determination of photon electroproduction absolute cross section.Comment: 24 pages, 6 figures, to be published in Nuclear Instruments and Methods in Physics Research, A One author adde

A new measurement of the structure functions PLL−PTT/epsilonP_{LL}-P_{TT}/epsilon and PLTP_{LT} in virtual Compton scattering at Q2=Q^2= 0.33 (GeV/c)2^2

The cross section of the $ep \to e' p' \gamma$ reaction has been measured at $Q^2 = 0.33$ (GeV/c)$^2$. The experiment was performed using the electron beam of the MAMI accelerator and the standard detector setup of the A1 Collaboration. The cross section is analyzed using the low-energy theorem for virtual Compton scattering, yielding a new determination of the two structure functions P_LL}-P_{TT}/epsilon and $P_{LT}$ which are linear combinations of the generalized polarizabilities of the proton. We find somewhat larger values than in the previous investigation at the same $Q^2$. This difference, however, is purely due to our more refined analysis of the data. The results tend to confirm the non-trivial $Q^2$-evolution of the generalized polarizabilities and call for more measurements in the low-$Q^2$ region ($\le$ 1 (GeV/c)$^2$).Comment: 9 pages, 10 figures. EPJA version. slight revisions in the text and figure

Pion production in deeply virtual Compton scattering

Using a soft pion theorem based on chiral symmetry and a $\Delta(1232)$ resonance model we propose an estimate for the production cross section of low energy pions in the deeply virtual Compton scattering (DVCS) process. In particular, we express the $e p \to e \gamma \pi N$ processes in terms of generalized parton distributions. We provide estimates of the contamination of the $e p \to e \gamma p$ DVCS observables due to this associated pion production processes when the experimental data are not fully exclusive, for a set of kinematical conditions representative of present or planned experiments at JLab, HERMES and COMPASS.Comment: 50 pages, 22 figure

First Measurement of Chiral Dynamics in \pi^- \gamma -> \pi^- \pi^- \pi^+

The COMPASS collaboration at CERN has investigated the \pi^- \gamma -> \pi^- \pi^- \pi^+ reaction at center-of-momentum energy below five pion masses, sqrt(s) < 5 m(\pi), embedded in the Primakoff reaction of 190 GeV pions impinging on a lead target. Exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, t' < 0.001 (GeV/c)^2. Using partial-wave analysis techniques, the scattering intensity of Coulomb production described in terms of chiral dynamics and its dependence on the 3\pi-invariant mass m(3\pi) = sqrt(s) were extracted. The absolute cross section was determined in seven bins of $\sqrt{s}$ with an overall precision of 20%. At leading order, the result is found to be in good agreement with the prediction of chiral perturbation theory over the whole energy range investigated.Comment: 10 pages, 5 figure

Resonance Production and ππ\pi\pi S-wave in π−+p→π−π−π++precoil\pi^- + p \rightarrow \pi^- \pi^- \pi^+ + p_{recoil} at 190 GeV/c

The COMPASS collaboration has collected the currently largest data set on diffractively produced $\pi^-\pi^-\pi^+$ final states using a negative pion beam of 190 GeV/c momentum impinging on a stationary proton target. This data set allows for a systematic partial-wave analysis in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/c$^2$ , and in 11 bins of the reduced four-momentum transfer squared, $0.1 < t < 1.0$ (GeV/c)$^2$ . This two-dimensional analysis offers sensitivity to genuine one-step resonance production, i.e. the production of a state followed by its decay, as well as to more complex dynamical effects in nonresonant $3\pi$ production. In this paper, we present detailed studies on selected $3\pi$ partial waves with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{-+}$, $2^{++}$, and $4^{++}$. In these waves, we observe the well-known ground-state mesons as well as a new narrow axial-vector meson $a_1(1420)$ decaying into $f_0(980) \pi$. In addition, we present the results of a novel method to extract the amplitude of the $\pi^-\pi^+$ subsystem with $I^{G}J^{PC} = 0^+ 0^{++}$ in various partial waves from the $\pi^-\pi^-\pi^+$ data. Evidence is found for correlation of the $f_0(980)$ and $f_0(1500)$ appearing as intermediate $\pi^- \pi^+$ isobars in the decay of the known $\pi(1800)$ and $\pi_2(1880)$.Comment: 96 page

Measurement of the charged-pion polarisability

The COMPASS collaboration at CERN has investigated pion Compton scattering, $\pi^-\gamma\rightarrow \pi^-\gamma$, at centre-of-mass energy below 3.5 pion masses. The process is embedded in the reaction $\pi^-\mathrm{Ni}\rightarrow\pi^-\gamma\;\mathrm{Ni}$, which is initiated by 190\,GeV pions impinging on a nickel target. The exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, $Q^2<0.0015$\,(GeV/$c$)$^2$. From a sample of 63\,000 events the pion electric polarisability is determined to be $\alpha_\pi\ =\ (\,2.0\ \pm\ 0.6_{\mbox{\scriptsize stat}}\ \pm\ 0.7_{\mbox{\scriptsize syst}}\,) \times 10^{-4}\,\mbox{fm}^3$under the assumption$\alpha_\pi=-\beta_\pi$, which relates the electric and magnetic dipole polarisabilities. It is the most precise measurement of this fundamental low-energy parameter of strong interaction, that has been addressed since long by various methods with conflicting outcomes. While this result is in tension with previous dedicated measurements, it is found in agreement with the expectation from chiral perturbation theory. An additional measurement replacing pions by muons, for which the cross-section behavior is unambigiously known, was performed for an independent estimate of the systematic uncertainty.Comment: Published version: 9 pages, 3 figures, 1 tabl

Measurement of the Longitudinal Spin Transfer to Lambda and Anti-Lambda Hyperons in Polarised Muon DIS

The longitudinal polarisation transfer from muons to lambda and anti-lambda hyperons, D_LL, has been studied in deep inelastic scattering off an unpolarised isoscalar target at the COMPASS experiment at CERN. The spin transfers to lambda and anti-lambda produced in the current fragmentation region exhibit different behaviours as a function of x and xF . The measured x and xF dependences of D^lambda_LL are compatible with zero, while D^anti-lambda_LL tends to increase with xF, reaching values of 0.4 - 0.5. The resulting average values are D^lambda_LL = -0.012 +- 0.047 +- 0.024 and D^anti-lambda_LL = 0.249 +- 0.056 +- 0.049. These results are discussed in the frame of recent model calculations.Comment: 13 pages, 7 figure

Virtual Compton Scattering and the Generalized Polarizabilities of the Proton at Q^2=0.92 and 1.76 GeV^2

Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P_LL-P_TT/epsilon and P_LT, and the electric and magnetic generalized polarizabilities (GPs) alpha_E(Q^2) and beta_M(Q^2) at values of the four-momentum transfer squared Q^2= 0.92 and 1.76 GeV^2. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q^2-range, and point to their non-trivial behavior.Comment: version 2: modified according to PRC Editor's and Referee's recommendations. Archival paper for the E93-050 experiment at JLab Hall A. 28 pages, 23 figures, 5 cross-section tables. To be submitted to Phys.Rev.