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Explore detailed analysis of the process e+e-→γγ with remarkable precision, focusing on photon jet radiation in collinear region and related compensators. Discover the significance of this process for luminosity measurement and systematic error estimation, alongside comparisons with other methods for cross section calculations.
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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
