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MC generators with radiative corrections
used in direct e+e- scan experiments
Budker Institute of Nuclear Physics
1. MC generators for the processes ee  ee(n)
Comparison with BHWIDE and BABAYAGA codes
2. MC generators for the processes ee  (n), (n)
Comparison with KKMC codes
3. MC generators for the processes ee  (n), KK(n)
Contribution to the cross section coming from FSR effects
Comparison with Berends (one hard photon emission)
4. MC generator for the processes : , KLKS(n), 0(n),
(n), 0(n) without FS
5. “Dressed” and “bare” cross sections for different
6. Another approach to calculate ahad.LO
7. Conclusion
Luminosity measurement
Bhabha scattering events are preferable for normalize purpose
to calculate cross sections with collinear events in FS
vis(ee  ee)
vis(ee  xx)
vis(ee  xx) = ------
vis(ee  ee)
Main sources of systematic errors in previous experiments
Quality of events separation Nee , Nxx
typical value 0.4 %- 5%
Accuracy of beam energy measurement
typical value 0.3% - 1%
Events detection reconstruction efficiencies
typical value 0.2% - 2%
Systematic error of RC calculation
typical value 0.3% - 1%
Very soon accuracy of RC calculation with systematic error less
than 0.1% will be required for future forthcoming experiments
(for example CMD-3 experiments at VEPP-2000)
How to improve the accuracy of cr. sect.
calculation for the process ee  ee
Cross section construction: include all 
corrections and enhanced contributions
Vacuum polarization effects by leptons
and hadrons should be inserted to each
Enhanced contributions proportional to
[(/Ln(sm2e)]n ~[1/30]n, n=1,2,..coming
from collinear regions are taking into
account by means of SF formalism
(E.Kuraev, V.Fadin)
yyyyyyy photon jets
in collinear
One photon radiation at large angle out of
narrow cones ( > 0, E > E ) – enough to
provide systematic error about 0.1% (no
enhanced contributions inside these
Bhabha cross section ee  e e
as a function of inner parameters
Cross section dependence
vs inner parameter .
Cross section dependence
vs inner parameter 0.
In both cases the cross sections deviations are inside
corridor ±0.1%
ee  ee cross section vs energy
Comparison with BHWIDE
code, 0.5%
Comparison with BabaYaga
code, 0.1% (new version)
(S.Jadach, W.Placzek, B.F.L.Ward)
CMD-2 selection criteria for collinear events were applied:
 < 0.25 rad,  <0.15 rad, 1.1 < final < -1.1
Difference between cross sections calculated by MCGPJ code,
BHWIDE and BabaYaga is inside corridor 0.1%
ee  ee cross section
CMD-2 cut
CMD-2 cut
Relative cross sections difference for
MCGPJ code and BHWIDE vs
acollinearity polar angle.
Relative cross sections difference
for MCGPJ code and “Berends”
vs acollinearity polar angle.
ee  ee cross section
Comparison with experimental distributions
Events number vs acollinearity
polar angle . Solid line –
simulation (MCGPJ),
histogram – CMD-2 data. All
data upper 1040 MeV are
collected on this plot.
Events number vs acollinearity
azimuthal angle . Solid line –
simulation (MCGPJ), histogram –
CMD-2 data. All data upper 1040
MeV are collected on this plot.
ee  ee cross section
Relative contribution of photon jets with respect to
cross section with radiation of one hard photon, %
Radiation two and more photons (enhanced contributions coming
from collinear regions) contributes to cross section about
0.25% only !!!
ee  ee cross section
Contribution of vacuum polarization to Bhabha cross
section as a function of energy, %
, 
ee  ee cross section
Two dimensional plot of simulated events – energy of one photon vs another.
Left – MCGPJ code, right – “Berends”.
About 0.5% events have total energy E1+ E2 < 600 MeV .
Cross section strongly depends on the cut for transverse momentum p
ee  ee cross section
CMD-2 cut
Relative cross sections difference as a function of cut
applied to transverse momentum of both particles.
ee  ee cross section
Crucial point is how to estimate theoretical accuracy
of this approach.
To quantify the systematic error independent comparison was performed
with generator based on “Berends”, where first order  corrections are
treated exactly. It was found that the relative cross sections difference is
less than 0.2% for  about of 0.25 rad.
Comparison with BGWIDE code (0.5%) and BABAYAGA (0.1%)
demonstrates very good agreement between different distributions.
Conclusion: radiation two and more photons in collinear regions
contributes to cross section for amount 0.2% only. Since the accuracy
of this contribution is known with error better than 100% therefore
theoretical systematic accuracy of the cross section with RC certainly is
better than 0.2% for “soft” selection criteria.
In order to believe to 0.2% accuracy the different
experimental proofs are needed !
ee   cross section calculation
(ten times smaller than Bhabha cross section)
BUT this cross section is very important to perform cross check of the
theoretical accuracy of the cross sections with RC.
For example double ratio of ( N  / N ee ) /(   /  ee ) can serve as a
powerful tool for it
Vacuum polarization effects by leptons
 2
and hadrons are inserted to each diagram.
Only one hard photon radiation out of
narrow cone.
One hard photon for FSR + interference
 2
Second and so on…photons
radiation inside narrow cones enhanced contributions
Photon jets radiation along initial
Cross section accuracy with RC  0.2 % is expected
for MCGPJ.
ee   cross section
as it was elucidated by Smith and
Voloshin that all parametrically
enhanced contributions proportional
to ² increase cross section close to
threshold region only at the level
0.02% and these contributions fall
down with energy.
Relative contribution of FSR to
cross section with ONLY one hard
photon emission, %. CMD-2
selection criteria were used.
Main conclusion was done:
It is enough to take into account only
first order radiative corrections O()
to provide cross section systematic
error with FSR better than 0.1%.
MCGPJ code comparison with KKMC (0.1%)
(S.Jadach, B.F.L.Ward, Z.Was)
Vacuum polarization effects switch off in both generators
Difference with KKMC code
with FSR, %
  0.17 %
Difference with KKMC code
without FSR, %
  0.06 %
ee   cross section
CMD-2 data
For low energies CMD-2 momentum
resolution is enough to separates e,,
It is practically the first direct examination of the theoretical accuracy of
the cross section with RC at ~1% level
Number of selected muon pairs
to electrons ones divided on the
ratio of theoretical cross sections.
Average deviation is: –1.7% ±
1.4%st ± 0.7%syst.
ee   (K+K-) cross section
|F |
2  E, M eV
  jets radiation along initial
inside narrow cones
“Dress” cross section
Vacuum polarization effects by leptons and hadrons are included
in shape of resonance and removed from RC:“dressed” cross section
Pions were treated as point like objects and scalar QED was applied to
calculate RC. Clear evidences are needed to believe this approach
ee   cross section
Comparison with “Berends” code taking into account ONLY one
hard photon radiation. Practically all previous experiments
used it!!!
Deviations around -meson
amount to ± 1% and for
energies upper -meson the
difference rapidly increase
Relative cross section difference
vs acollinearity polar angle .
Beam energy 450 MeV
ee   cross section
(low energies)
E = 185 MeV
E = 185 MeV
CMD-2 spatial resolution is enough to separate e// events for low energy
Momentum and angle resolutions, decays on flight and interaction with
detector matter were smeared with simulated events kinematics parameters
Enveloping curve describes three peaks and long “tails” very well
Bad ² if we used MC generator with radiation of one photon
The process ee   with FSR is a unique tool to answer on
question – can we tread a pion like a point object
Two collinear tracks in DC
One cluster in calorimeter
(not associated with tracks)
No signal in outer muon
range system
No signal in endcap BGO calorim.
- reject 0 events
Cross section ratio ISR + FSR/ISR
vs energy
Digit upper every curve – threshold
of the photon energy to detect
Energy interval 2*360  2*390 MeV
is preferable
Selection  events with FSR
Two dimensional plot for xx events
Variables on axis: vertical - W = p/E, horizontal - M²
experiment (CMD-2)
Density population  events is clear seen inside region W < 0.4
and 1000 < M² < 40000 MeV².
Analysis is based on the integrated luminosity 1.2 pb-1 collected
at 8 energy points (left slope of the  meson).
Spectrum of  events with FSR as a function
of the emitted photon energy
Histogram – simulation (MCGPJ), bar points – CMD-2 data
average div. ~ (2.1 ± 2.3)%
About 3000  events with ph. en. > 50 MeV were selected for analysis
Inscriptions inside zone point the relative part of  events with FSR
The main conclusion is: For photons with energies up to pion’s mass we
can tread the pion as a pointlike object and scalar QED can be applied
Processes with neutral particles in FS
(only initial state radiation are considered: ee  (n),
KLKS(n), 0(n), (n), ’(n), 0(n)
Cross section accuracy with RC is estimated to be at ~0.2%
Very important channel ee  : Large cross section (2.5 times) –
independent way to measure luminosity, clean QED process and
no Feynman’s graphs with vacuum polarization effects.
aver. diff. ~0.25%
CMD-2 cut
Relative cr. sect. difference
(jet/jet vs energy
Relative cr. sect. difference
(jet/jet vs angle , rad
What is R(s) required?
Definition of R(s) depends on the application
Hadron spectroscopy (used to get meson’s mass, width, …): vacuum polariz.
effects is the part of the “Dress” cross-section. Final state radiation (FSR) and
Coulomb interaction (CI) are not and must be removed (they are in RC).
“Bare” cross-section used in R: vice versa – FSR and CI are the part of the
cross-section, VP is not and must be removed from all hadr. cross sections:
In order to keep systematic error of the “bare” cross section at the same level as
“dress” has VP effects should be calculated with syst. accuracy better than 0.1%
cross sections with radiation of one photon in final state should be obtained.
Today it is done for the processes: e+e-  ee , , K+K- , +-,   .
Indeed at the current systematic accuracy it is enough to do only for two
channels: e+e-   and K+K-  - give dominant contributions to aµ.
Factors determining systematic
accuracy RC calculation
Unaccounted corrections more higher orders:
1. Weak interactions contribute to cross sections later than 0.1% at
energies 2E < 3 GeV and we can omitted in our approach.
2. NLO corrections which proportional to ²ln(s/m²) ~ 10-4
fortunately small with respect to 0.1% level.
3. The uncertainty of about 0.1% is related to experimental systematic
errors for hadronic cross sections . For example, 1% error changes
“bare” cross sections at scale 0.03%.
4. Fourth source uncertainty due to theoretical models which are used
to describe hadronic cross sections energy dependence.
5. In paper Smith and Voloshin was done very important for us
conclusion: For FSR (except electrons) the combine effect of all
parametrically enhanced O(²) corrections is limited by 2•10-4
and it is beyond the accuracy 0.1%  0.2%.
Considering the uncertainty sours as independent total systematic
error of the cross sections with RC better than 0.2% MUST BE!!!
Another way of aµ calculation
had .
 (1  x ) (  1  x m  ) dx
Special experiment - it is necessary to measure cross sections of the
e+e-  , for luminosity measurement (no VP effects, accuracy < 0.1%)
BUT special calorimeter is required to detects photons (CMD-3)
e+e-  +- direct cross section measurement
to extract product |1 + (s)|² (accuracy < 0.1%)
VP effects must be removed from RC
Effects of FSR and CI must be included into RC
 exp
 Born
| 1   ( s ) |
e+e-  e+e- to extract the value (-q²) in spacelike region (accuracy <0.1%)
SCAN EXPERIMENT: Luminosity ~ 1032 cm-2 s-1 , ~ 100 energy points
with number of muon events 108 /per year (statistical accuracy about 0.1%
in every point)
Cross section has practically isotropic distribution vs polar angle
Contribution to aµ
Time-like region
Red lines – resonance contributions
Space-like region
x < 0.7 analytical approximation
Cross section of all three QED processes can be measured in one direct scan
Accuracy of RC calculation will not contribute to final systematic error (-q²)
We hope to achieve experimental systematic error 0.5% about with CMD-3 at
VEPP-2000. Of course, if stars on the sky will in favour for us.
• MC generators to simulate different processes were done :
ee  ee, BHWIDE (0.5%), MCGPJ (0.2%?!) and BabaYaga (0.1%)
• ee  , -, KKMC (0.1%), MCGPJ (0.2%?!)
• ee   and K+K-, MCGPJ (0.2%?!) that is all unfortunately
We can state now that pions can tread as point like object
(at 1% accuracy) and sQED applied to describe FSR
• ee  , KlKs, 0, , ’, 0, MCGPJ (0.2%?!) that is all
unfortunately. Neutral particles in final state – ISR is taking into
account only
• Good agreement between CMD-2 data and distributions for , 
produced by MCGPJ code is observed. Total statistic for Bhabha
scattering events is collected (2E > 1040 MeV)
• Muon cross section – deviation from QED prediction is about
–1.7% ± 1.4% ± 0.7%.
• Common description of three “peaks” for e// events at low energies
is impossible without photon jets (bad ²)
• “Dressed” cross sections for dynamic studies, “bare” cross sections for
dispersion relations
• New experiments are needed extremely to cross check the theoretical
accuracy of the cross sections with RC. Forthcoming CMD-3 results
can solve some problems
• Very interesting to see KLOE result for double ratio
(N/Nee)/(/ee) around -meson energy region (direct scan).
KLOE has statistic more than 100 times exceeds CMD-2!!!
• Very interesting to see KLOE result for the same double ratio in a
broad energy region to find out the syst. accuracy of the ISR approach
• Necessary study and develope another approach to estimate hadronic
contribution to aµ using data in spacelike region
• Rough theoretical estimation of the main systematic errors:
1. Weak interactions contribute less than 0.1% for 2E < 3 GeV
2. Next leading order RC proportional to ²Ln(s/m²) ~ 10-4 are
fortunately small with respect to 0.1%.
3. Soft or virtual photon emission simultaneously with one hard photon
emission and so on. If we assume that coefficient before these terms will
be of order of ten nevertheless their contribution can not exceed 0.1%.
4. Fourth source of uncertainty is due to vacuum polarization effects and
currently they are calculated with systematic error later than 0.1%.
5. Next source of uncertainty is mainly driven by collinear approximation
approach – several terms proportional to )0² and (0² were
omitted. Indeed photons inside jet have angular distribution. Numerical
estimations show that a contribution of these factors is about of 0.1%.
6. It is enough to take into account only first order radiative corrections
O() to provide cross section systematic error with FSR better than 0.1%.
(B.Smith and M.Voloshin)
Considering the uncertainties sources as independent the total
systematic error of the cr. sect. with RC smaller than 0.2% we
must expect!!!
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