February 2000. // Revised april 2007This short note summarizes how in practice one applies radiative corrections to the measured cross sections d^5σ (ep\ to epγ) for DA-1 and DA-2 data of VCS-E93050 (polarizabilities). It does not intend to explain what radiative corrections are. For this I refer to specialized litterature (see References)

Fonvieille, H.

HAL Clermont Université

VCS-E93050 Polarizability data at Q2 =1and2GeV 2.P racticaluseofradiativecorrectionstomeasuredcrosssectionsd5σ(ep to epγ)H. FonvieilleTo cite this version:H. Fonvieille. VCS-E93050 Polarizability data at Q2 =1and2GeV 2.P racticaluseofradiativecorrectionstomeasuredcrosssectionsd5σ (ep to epγ).2001, pp.1-4. <in2p3-00674846>HAL Id: in2p3-00674846http://hal.in2p3.fr/in2p3-00674846Submitted on 28 Feb 2012HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.H.FonvieilleLPC-Clermont-FdFebruary 2000. // Revised april 2007.VCS-E93050Polarizability data at Q2 = 1 and 2 GeV2.Practical use of radiative correctionsto measured cross sections d5σ (ep→ epγ)This short note summarizes how in practice one applies radiative corrections to themeasured cross sections d5σ(ep → epγ) for DA-1 and DA-2 data of VCS-E93050(polarizabilities). It does not intend to explain what radiative corrections are. Forthis I refer to specialized litterature (see References).1 Where to find the informationsRadiative corrections to Virtual Compton Scattering have been studied [1], [2] andoutlined [3] in several Thesis works. The latest dedicated reference on the subjectis ref. [4].I have taken all basic informations from the thesis of Dominique Marchand and JulieRoche on VCS-MAMI. It is worth pointing out that the correction factor presentedin this memo applies only when Luc Van Hoorebeke’s simulation code VCSSIM [5]is used to compute the solid angle. This is because Luc’s code already incorporatesa well-defined part of the radiative corrections to Virtual Compton Scattering.12 Some terminology2.1 Real radiative correctionsVCSSIM includes all radiative effects that are sensitive to experimental cuts. Itincludes internal and external bremsstrahlung, so we don’t have to bother withthem. Extra-terms that need to be considered are:1) a term due to real photon emission which is independent of experimental cuts(see [3] p.104). It is called Tanal (see [2] p.118).2) a term introduced by continuity to elastic scattering, and still to be confirmedtheoretically [6]. I name it δcont here. I guess it corresponds to the term (δ1 + δ(0)2 )in ref. [4] (Table 1).2.2 Virtual radiative correctionsThey are independent of experimental cuts. This term is called δV (see [2] p.118).3 Practical use of radiative corrections for VCSOnce we have a measured value d5σmeasured, we have to compute:d5σcorr = d5σmeasured × Frad , where Frad = exp(−δV − Tanal − δcont).Frad is the global radiative correction factor not taken into account in VCSSIM.Table below gives the values for DA-1 and DA-2 settings of E93050. Kinematicpoints are taken from [2] p.118.Numerical values differ slightly from [2] because they have been updated by Nicoled’Hose [6]. The correction factor Frad depends mostly on Q2, and only very slightlyon variables like q′cm or cos θγγcm.The (systematic) error bar on this correction factor is estimated to be ±2 % [6],[4], i.e. inducing a ±2 % relative error on the cross section. This error is reportedin the last line of the table.Conclusion: in practice for E93050 data analysis, the cross section after applica-tion of Frad will be about 7 % lower than the measured cross section obtained withVCSSIM.2JLab-E93050 kinematicsKinematics close to DA-1 : close to DA-2 :E=4.0 GeV, E’=3.33 GeV E=4.4 GeV, E’=3.24 GeVθe = 15.7◦ θe = 21.5◦Q2 = 1 GeV2 Q2 = 2 GeV2Tanal +26.7 % +29.2 %δcont -1.3 % -1.5 %δV -18.3 % -20.3 %Frad ( +93.1 ± 2.0 ) % ( +92.9 ± 2.0 ) %Addendum 2007:Values of radiative corrections for the first VCS experiment at MAMI.MAMI VCS kinematicsKinematics qcm=0.6 GeV/c, ǫ = 0.61, q′cm = 111 MeV/cE=0.843 GeV, E’=0.528 GeV, θe = 53.14◦Q2 = 0.356 GeV2Tanal +22.0 %δcont -1.2 % (*)δV -15.6 %Frad ( +94.9 ± 2.0 ) %(*) = the value of (δ1 + δ(0)2 ) averaged over the two MAMI kinematics of Table 1in ref. [4].Thanks to Luc Van Hoorebeke and Nicole d’Hose for their remarks.References[1] D. Lhuillier, The`se Univ. Caen, DAPNIA-SPhN-97-01T (1997).[2] D. Marchand, The`se Univ. Blaise Pascal, DAPNIA-SPhN-98-04T (1998).3[3] J. Roche, The`se Univ. Blaise Pascal, DAPNIA-SPhN-98-06T (1998).[4] M. Vanderhaeghen et al., preprint hep-ph/0001100 (2000). Phys.Rev.C 62(2000) 025501.[5] L. Van Hoorebeke, VCSSIM Manual. Now published in: P.Janssens et al, Nucl.Instr. Meth. A566 (2006) 675-686.[6] N. d’Hose, private communication.4

VCS-E93050 Polarizability data at Q^2= 1 and 2 GeV^2. Practical use of radiative corrections to measured cross sections d5σ (ep \ to epγ)

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