1. 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

2. 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

3. 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

4. Two quantum annihilation process
e+(p+) + e-(p-)  (q1) + (q2) 2 1 + 1 2

5. 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)

6. Enhance contributions come from collinear regions
A lot of photons emission inside narrow cones (with opening angle 20 << 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

7. 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

8. 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

9. 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%

10. 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 

11. 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