1. Cross section of the process
e+e-+-o with FSR
G.V.Fedotovich, E.A.Kuraev, A.L.Sibidanov,
Budker Institute of nuclear physics
Novosibirsk, Russia ,
Frascati,Italy

2. OUTLINE
٭ What we can expect at VEPP-2000
٭ Motivation to have theoretical accuracy of the cross sections with RC better than 0.2%
٭ SF approach – to take into account photon jets radiation in collinear region (for ISR)
٭ Cross section of the process e+e-+-o() with FSR
٭ Conclusion

3. Physics at VEPP-2000 ’, ’’, ’, ’ and so on
٭ Precise measurement of Xsect.(~0.2 – 0.3% for +- and ~0.5% for +-o and ~1% for 4 channel)
٭ Study of the cross section with multihadrons in FS: e+e-  2h, 3h, 4h …, h= ,K,
٭ Study of the excited states of the vector mesons:
’, ’’, ’, ’ and so on
٭ Study of nucleon-antinucleon pair production –
nucleon electromagnetic form-factors,
search for NNbar resonance near threshold
٭ Study of the processes with ISR
٭ Two photon physics

4. R(s) measurements at low s
Babar/Belle (ISR) R
VEPP-2000
KEDR(3-5%, ~15%)
KLOE (ISR)
BES
VEPP-2M
At VEPP-2M the cross-sections of each final state
were measured exclusively and the same we will plan
to do at VEPP-2000

5. Lay-out of VEPP-2000 CMD-3 SND beam current – 200 mA
revolution time – ns
beam current – mA
beam length – cm
energy spread – MeV
circumference – m
beta function in IP x= z =4.3 cm
L = 1032 cm-2s-1 at 2E=2.0 GeV
L = 1031 cm-2s-1 at 2E=1.0 GeV
CMD-3
SND

6. 3D view CMD-3 detector ٭Z-chamber, LXe calorim.
and eight CsI octants,TOF, MR system are inside detector and cosmic tested
٭Super conductive solenoids of VEPP-2000 are located in touch to DC flanges – problem with magnetic field uniformity inside DC volume
٭Map of magnetic field was measured in real conditions
٭SC solenoid inside detect. m.f. ~ 1.35 T achieved
(project m.f. ~ 1.5 T)
٭DC is inserted now. Prelim.ampl. and digitizing electronic is ready totally

7. systematic uncertainty for hadronic cross sections
How the “dress” cross sections are measured
Main factors giving dominant contributions to
systematic uncertainty for hadronic cross sections
All modes except 2:
٭ Integrated luminosity Lee is measured using large angle Bhabha scattering events
٭ Efficiency ee is calculated via MC + corrections for detector imperfections. Phase space & some dynamic models are treated to estimate the systematic error
٭ RC ee is taken into accounts effects of ISR only. Theoretical accuracy of xsections ~0.5% we can expect
٭ VP effects are included in cross section properties and excluded from RC (dress xsection is measured)

8. BARE cross sections are required to evaluate
hadronic contribution to the value a
But Bare cross section is recalculated through Dress.To provide Bare cross section accuracy at the level 0.5% (or better) we MUST:
1. Include Coulomb interaction of charged pions in FS:
2. Extract VP effects from virtual photon propagator
3. Add to Bare cross section one photon radiation in FS
where ~1

9. 3 event in CMD-2 detector
Two tracks in DC and two clusters in CsI calorimeter which
do not belong to tracks
R- plane
Plane with beam axis

10. Specific selection criteria used in CMD-2 for the process e-e+ 
Kinematics cuts (some examples):
Accolinearity angle between two tracks in R- plane:
|| 1- 2|-| > 0.25 radian to eliminate collinear events
2. Average momentum of two charged pions should be inside gap:
0.35 < (P1+P2)/2Ebeam < 0.8 to put down collinear events
3. Invariant mass of two charged pions Мinv < 1.66 Ebeam - this condition also suppress collinear events
4. To provide good reconstruction efficiency in DC only the part of the acceptance was used: 0.85 < 1,2 <  radian for polar angles
5. EMC is needed to put down cosmic background and to eliminate events e+e- e+e- ,  ,   which
have very similar signature in detector (in one plane).
6. Angle between missing momentum direction of the two
charged pions and two photon directions is grater than
0.1 radian

11. Selection criteria used in CMD-2 for the process e-e+ 
Dependence of the mass squared of two charged particles
as a function of the acollinearity angle in R- plane
|| 1- 2|-| > 0.25 rad.

12. Cross-section with ISR (one photon is radiated by e+e-)
where c = cos(), c0 = cos(0) and Kf = ²/3 – 1/2
٭ First term describes one photon radiation inside narrow cones
٭ Second term describes one hard photon radiation out of
narrow cones (wide polar angles)
٭ Last term represents Soft and Virtual parts of the cross section
٭ Total cr.sect. does not depend on auxiliary parameters , 0

13. virtual and soft photon radiation in FS
Cross-section with
virtual and soft photon radiation in FS

14. Master formula for the process e+e-+-0 + n with ISR & FSR
x = /E - photon energy fraction in relative units

15. Shift Born cross section for the process e+e-+-0

16. Cross section stability e+e-+-0 + n vs auxiliary parameter 0.

17. Cross section stability e+e-+-0 + n vs auxiliary parameter E

18. RC for the process e+e-+-0 +  with one photon radiation in FS
Cross section dependence vs auxiliary parameter delta
(separate soft and hard photons)

19. RC for the process e+e-+-0 +  with one photon radiation in FS
(inside VEPP-2000 energy range)

20. Conclusion
1. For the first time RC with FSR was calculated (E.Kuraev). MCGPJ for the process e+e-  +-0 with ISR and FSR is constructed.
2. Theoretical accuracy is estimated as 0.2% (or better)
3. MCGPJ simulates photon jets in collinear regions and one hard photon out of narrow cones. The same approach as we used for others channels
4. Very important – geometrical efficiency must be determined with RC
5. Coulomb interaction in FS very similar to that as we have for two pion channel
6. “Bare” cross section can be determined now with accuracy better than 0.2% (for (g-2)/2 calculation)

21. “Dress and BARE” cross sections are required for different applications-
“DRESS” cross section dependence on energy is determined by strong interactions. Then VP effects in photon propagator MUST be attached to the vertex of the hadrons production  0
------ + e- - e+
“DRESS” cross section ALSO contains correction due to photon radiation in FS in order to provide the systematical accuracy better than 0.5%  0
------ e- +  e+ -
Coulomb interaction of pions (electro- magnetic corrections ) MUST be excluded from “DRESS” cross section. They are taken into account in radiative corrections  0 
------ e- +

22. hard photon radiation in FS
Cross-section with
hard photon radiation in FS

23. Back slides