A new ep → epγ experiment is foreseen at MAMI in order to study the Q2 - dependence of the structure functions PLL − PT T /ǫ and PLT and the generalized polarizabilities αE(Q2 ) and βM(Q2 ) of the proton.Predviđamo novo mjerenje ep → epγ u MAMI radi proučavanja Q2 -ovisnosti strukturnih funkcija PLL − PT T /ǫ i PLT te poopćenih polarizabilnosti αE(Q2 ) i βM(Q2 ) protona

Fonvieille (for the MAMI-A1 Collaboration), H.

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Printed ISSN 1330–0016Online ISSN 1333–9133CD ISSN 1333–8390CODEN FIZBE7THE NEXT VIRTUAL COMPTON SCATTERING EXPERIMENT AT MAMIH. FONVIEILLEfor the MAMI-A1 CollaborationClermont-Université, Université Blaise Pascal, CNRS-IN2P3,Laboratoire de Physique Corpusculaire, BP 10448, F-63000 Clermont-Ferrand, FranceReceived 28 December 2010; Accepted 19 October 2011Online 26 January 2012A new ep → epγ experiment is foreseen at MAMI in order to study the Q2-dependence of the structure functions PLL − PTT /ǫ and PLT and the generalizedpolarizabilities αE(Q2) and βM (Q2) of the proton.PACS numbers: 13.60.Fz UDC 539.171Keywords: ep → epγ scattering, structure functions PLL − PTT /ǫ and PLT , generalizedpolarizabilities, Q2-dependence1. IntroductionLow-energy virtual Compton scattering (VCS) γ∗p → γp allows to access thegeneralized polarizabilities (GPs) of the proton. The GPs are fundamental quanti-ties characterizing the electromagnetic structure of a nucleon that is deformed byan applied EM field. A series of dedicated VCS experiments have been performed[1 – 4] via the photon electroproduction reaction ep → epγ. After a little more thana decade of measurements, a picture emerges for the electric and magnetic GPs,αE(Q2) and βM (Q2), as a function of the four-momentum transfer Q2 or the dis-tance scale. When confronted to theoretical models (for a review see Refs. [5, 6]),these observables show a non-trivial Q2-behavior, which calls for further investiga-tion. This is the goal of the next VCS experiment at MAMI [7].2. Photon electroproduction and VCS analysis techniquesVCS on the proton is performed by exclusive photon electroproduction ep →epγ. The amplitude for this process is the coherent sum of the Bethe-Heitler, BornFIZIKA B (Zagreb) 20 (2011) 2, 173–178 173fonvieille et al.: the next virtual compton scattering experiment at mamiand non-Born contributions. The Bethe-Heitler and Born amplitudes are known anddepend only on the elastic form factors GpE , GpM . The sum of these two amplitudesis noted (BH+Born). The non-Born amplitude is the unknown part, parametrizedat low energy by the GPs.There are two techniques which allow to extract information on the GPs from aVCS experiment: the LEX (low-energy expansion) [8 – 11] and dispersion relations(DR) [12, 13]. In the LEX approach, the cross section is developed as an expansionin q′cm, the CM momentum of the outgoing photon. The first term is the BH+Borncross section, while the second term depends on two structure functions, PLL −PTT /ǫ and PLT which contain the electric and magnetic GPs. These structurefunctions are fitted from the experimental cross section. In the DR approach, thecross section is calculated including all orders in q′cm; it has some free parametersrelated to the unconstrained part of the electric and magnetic GPs. By adjustingthese parameters on experimental data, one has access to the structure functionsPLL − PTT /ǫ and PLT and the electric and magnetic GPs.3. World data on VCS unpolarized observablesThe various measurements have been made from lowQ2 (0.06 GeV2 at Bates [3])up to 0.9 and 1.8 GeV2 at JLab [4]. The MAMI data [1, 2] were up to now concen-trated at Q2 = 0.33 GeV2.Figure 1 shows our present knowledge of the structure functions PLL − PTT /ǫand PLT . The filled squares and filled circles are obtained according to LEX andDR analyses, respectively. The data agree rather well with the HBChPT calculation(solid curve) at order p3 [14], in the low-Q2 region where the theory is applicable.The dashed curve is an example of DR calculation, assuming one single dipole shapefor the unconstrained part of the GPs. Here the free parameters of the model havebeen adjusted on the Jlab data. Up to a small term containing the spin-flip GPs,these structure functions are proportional to αE and βM , therefore they give analmost direct image of the electric and magnetic GPs.Two main conclusions can be drawn from the figure.• First, regarding PLL − PTT /ǫ, or as well αE , it is not possible to accountfor all data points with a simple shape (e.g. a ∼ dipole for αE in the DRmodel). The comparison of the experimental data with the dashed curve issuggestive of a possible “structure” in the region of Q2 ∼ 0.3 GeV2, for whichphysical interpretations are open. It could be due to the contribution of somespecific resonances in the polarizabilities, or to the meson cloud surroundingthe nucleon. A recent work [15] has advised a new parametrization of theelectric GP to account for the whole data set; induced polarizations in thenucleon are then calculated using the light-front formalism.• Second, the behavior of PLT , or as well βM , is rather poorly known exper-imentally; values are small and they are measured with large relative error174 FIZIKA B (Zagreb) 20 (2011) 2, 173–178fonvieille et al.: the next virtual compton scattering experiment at mamibars. The extremum predicted at low Q2, originating from a cancellation oflarge paramagnetic and diamagnetic contributions, would need to be betteridentified.The above statements have been the guidelines for designing a new VCS exper-iment at MAMI.0204060800 0.25 0.5 0.75 1 1.25 1.5 1.75 2DR        (if one dipole)example Λα = 0.7 GeVChPT o(p3)(ε = 0.645)PLL-PTT/ε (GeV-2)RCSBatesMAMIJLab JLab-20-15-10-500 0.25 0.5 0.75 1 1.25 1.5 1.75 2DR        (if one dipole)example Λβ = 0.63 GeVQ2 (GeV 2)PLT   (GeV-2)RCSBatesMAMIJLab JLabLEX analysisdirect DR fit PROPOSED POINTS (LEX)Fig. 1. Existing measurements [1 – 4] of the VCS structure functions PLL − PTT /ǫ(top) and PLT (bottom). The inner (resp. outer) error bar is statistical (resp.total). Curves show calculations from HBChPT [14] and dispersion relations [12]with some fixed value of the free parameters (Λα, Λβ). The open triangles showthe projected points of the experiment foreseen at MAMI.FIZIKA B (Zagreb) 20 (2011) 2, 173–178 175fonvieille et al.: the next virtual compton scattering experiment at mami4. The proposed experimentMore data are needed to improve our knowledge of the electric and magneticGPs. We propose to further explore their Q2-dependence by performing high-precision measurements of the unpolarized ep → epγ cross section at three newvalues of Q2 = 0.1, 0.2 and 0.5 GeV2. For more details we refer the reader toRef. [7].The strategy is to work at the highest q′cm orW below the pion threshold and thehighest value of the virtual photon polarization ǫ. Angular bins will be chosen in away that allows both LEX and DR extractions of the observables. The kinematicalsettings will also make use of the OOP capability of the A1 equipment (spectrometerB) and the beam energy of MAMI-C. The experiment requires a careful studyof systematics, which are often the dominant error. Precise measurements of theproton form factors GpE , GpM at low Q2 [16] will improve the determination of theVCS observables. Indeed the GP effect is always determined by a deviation tothe Bethe-Heitler+Born cross section, which depends intrinsically on these formfactors.5. ConclusionIn summary, the GPs are new observables of the nucleon, sensitive in an originalway to the pion cloud and the nucleon resonance spectrum. The electric and mag-netic GPs can be measured more extensively and more precisely at low Q2 usingthe knowledge acquired from previous experiments. The exploration of their non-trivial Q2-dependence will help building a consistent picture of these fundamentalobservables. MAMI with its A1 equipment provides unique conditions in the worldto perform this experiment successfully.References[1] J. Roche et al., Phys. Rev. Lett. 85 (2000) 708.[2] P. Janssens et al., Eur. Phys. J. A 37 (2008) 1.[3] P. Bourgeois et al., Phys. Rev. Lett. 97 (2006) 212001.[4] G. Laveissière et al., Phys. Rev. Lett. 93 (2004) 122001.[5] C. E. Hyde-Wright and K. de Jager, Ann. Rev. Nucl. Part. Sci. 54 (2004) 217.[6] N. d’Hose, Eur. Phys. J. A 28 (2006) 117.[7] H. Merkel and H. Fonvieille, spokespersons, MAMI Proposal A1/1-09 (2009).[8] P. A. M. Guichon, G. Q. Liu and A. W. Thomas, Nucl. Phys. A 591 (1995) 606.[9] P. A. M. Guichon and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 41 (1998) 125.[10] D. Drechsel, G. Knochlein, A. Y. Korchin, A. Metz and S. Scherer, Phys. Rev. C 57(1998) 941.176 FIZIKA B (Zagreb) 20 (2011) 2, 173–178fonvieille et al.: the next virtual compton scattering experiment at mami[11] D. Drechsel, G. Knochlein, A. Y. Korchin, A. Metz and S. Scherer, Phys. Rev. C 58(1998) 1751.[12] B. Pasquini, M. Gorchtein, D. Drechsel, A. Metz and M. Vanderhaeghen, Eur. Phys.J. A 11 (2001) 185.[13] D. Drechsel, B. Pasquini and M. Vanderhaeghen, Phys. Rept. 378 (2003) 99.[14] T. R. Hemmert, B. R. Holstein, G. Knochlein and D. Drechsel, Phys. Rev. D 62 (2000)014013.[15] M. Gorchtein, C. Lorce, B. Pasquini and M. Vanderhaeghen, Phys. Rev. Lett. 104(2010) 112001.[16] J. C. Bernauer et al., Phys. Rev. Lett. 105 (2010) 242001.FIZIKA B (Zagreb) 20 (2011) 2, 173–178 177fonvieille et al.: the next virtual compton scattering experiment at mamiSLJEDEĆE MJERENJE VIRTUALNOG COMPTONOVOG RASPRŠENJA UMAMIPredvid–amo novo mjerenje ep → epγ u MAMI radi proučavanja Q2-ovisnostistrukturnih funkcija PLL − PTT /ǫ i PLT te poopćenih polarizabilnosti αE(Q2) iβM (Q2) protona.178 FIZIKA B (Zagreb) 20 (2011) 2, 173–178

Sljedeće mjerenje virtualnog Comptonovog raspršenja u MAMI

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