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MC generator for the process e + e - with RC pro mille accuracy. G.Fedotovich, A.Sibidanov Budker Institute of Nuclear Physics Novosibirsk, Russia. LNF, Frascati 11 April 2008. Outline. Motivation
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MC generator for the process e+e- with RC pro mille accuracy G.Fedotovich, A.Sibidanov Budker Institute of Nuclear Physics Novosibirsk, Russia LNF, Frascati 11 April 2008
Outline • Motivation • SF approach – to describe photon jet radiation in collinear region – include enhance contributions • Stability cross section vs two inner parameters • Comparison with cross section produced by MCG with one photon radiation • 5. Conclusion
Motivation • Pure QED process. Cross section of the process e+e- is big enough to use for luminosity measurement • Alternative method to better understand and correctly estimate systematic error in luminosity • Cross section contains radiative corrections connected with ISR only • Feynman graph for this process does not contain effects of VP. Contrary to Bhabha and cross sections. •This cross section is even with respect to polar angle 90° Powerful instrument to study acceptance systematic
Two quantum annihilation process e+(p+) + e-(p-) (q1) + (q2) 2 1 + 1 2
Cross section with tree photons in FS e+(p+) + e-(p-) (q1) + (q2) + (q3) Well known expression, M.V.Terentjev: Two final photons are detected with their polar angles with respect to initial beam directions much more than 1/ (= E/me)
Enhance contributions come from collinear regions A lot of photons emission inside narrow cones (with opening angle 20 << 1) along initial electrons & positrons described by SF approach. But! Where x = E/E, E – separate parameter between S & H L = ln(s/m²) is a large logarithm (for s ~ 1 GeV², L 15) The terms proportional to (L-1) are taken into account in all order of in SF approach. Residuary term is a compensator
Shifted Born cross section Initial electrons and positrons loose energy by radiation photon jets e+(z1p+) + e-(z2p-) (q1) + (q2) + n(jets) When z1 and z2 are equal 1 this cross section transforms to
Total cross section • This cross section consist of three different parts: • Photon jet radiation in collinear region. • Two compensators – which represent the residuary contribution comes from collinear region with one photon emission • The last term represent HPh emission out of narrow cones • The sum two last terms does not depend on and 0
Cross section stability vs inner parameters When changes on three order of magnitude cross section variations are inside corridor 0.05% When 0 changes on two order of magnitude cross section variations are inside corridor 0.05%
Comparison of the cross sections produced by MCGPJ and MCG with one photon radiation CMD-2 cut Relative cross sections diff.in % for VEPP2000 energy region Relative cross sections diff.in % vs acollinearity angle
Conclusion 1.MC generator for the process e+e- annihilation into two photons is constructed 2. This process has enough big cross section to use for Luminosity monitoring like LAB events 3. The event of this process has a simple signature in detector 4. Very important advantage – no VP effects in first order of 5. This cross section is even with respect to polar angle 90°. Powerful instrument to study acceptance systematic
