G.V.Fedotovich

Budker Institute of Nuclear Physics Novosibirsk

MC generators with radiative corrections used in direct e+e- scan experiments

Outline1. MC generators for the processes ee ee(n) Comparison with BHWIDE and BABAYAGA codes

2. MC generators for the processes ee (n), (n) Comparison with KKMC codes 3. MC generators for the processes ee (n),

KK(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

applications

6. Another approach to calculate ahad.LO

7. Conclusion

Luminosity measurement

L=Nee

vis(ee ee)

Main sources of systematic errors in previous experiments wereQuality 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)

Bhabha scattering events are preferable for normalize purpose to calculate cross sections with collinear events in FS

L=Nxx

vis(ee xx)

vis(ee xx) = ------ Nxx

Nee

vis(ee ee)

Cross section construction: include all corrections and enhanced contributions

Vacuum polarization effects by leptons and hadrons should be inserted to each amplitude

Enhanced contributions proportional to [(/Ln(sm2

e)]n ~[1/30]n, n=1,2,..coming from collinear regions are taking into account by means of SF formalism (E.Kuraev, V.Fadin)

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 regions)

Σ +

2

+

2

+

+

4

+2

Σ

How to improve the accuracy of cr. sect. calculation for the process ee ee

Yyyyyyyyyyyyyy photon jets

in collinear regions

Bhabha cross section ee 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%

ee ee cross section vs energy

Difference between cross sections calculated by MCGPJ code, BHWIDE and BabaYaga is inside corridor 0.1%

Comparison with BHWIDE code, 0.5%(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

Comparison with BabaYagacode, 0.1% (new version)

ee ee cross section

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.

CMD-2 cut

CMD-2 cut

ee ee cross section

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.

Comparison with experimental distributions

ee ee 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 !!!

Contribution of vacuum polarization to Bhabha crosssection as a function of energy, %

ee ee cross section

,

ee ee 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

ee ee cross section

Relative cross sections difference as a function of cut applied to transverse momentum of both particles.

CMD-2 cut

ee ee 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 !

Vacuum polarization effects by leptons and hadrons are inserted to each diagram.

Only one hard photon radiation out of narrow cone.

One hard photon for FSR + interference terms.

Photon jets radiation along initial particles.

+

2

+

2

+

2

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 can serve as apowerful tool for it

ee cross section calculation (ten times smaller than Bhabha cross section)

~90%

~5%

~0.3%

Cross section accuracy with RC 0.2 % is expected for MCGPJ.

Second and so on…photonsradiation inside narrow cones -enhanced contributions

)//()/( eeeeNN

ee cross section

Relative contribution of FSR to cross section with ONLY one hard photon emission, %. CMD-2 selection criteria were used.

BUT,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.

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%.

0.17 %

Difference with KKMC code with FSR, %

Difference with KKMC code without FSR, %

0.06 %

Vacuum polarization effects switch off in both generators

MCGPJ code comparison with KKMC (0.1%) (S.Jadach, B.F.L.Ward, Z.Was)

ee cross section

Number of selected muon pairsto electrons ones divided on the ratio of theoretical cross sections. Average deviation is: –1.7% ± 1.4%st ± 0.7%syst.

For low energies CMD-2 momentum resolution is enough to separates e,,

It is practically the first direct exami-nation of the theoretical accuracy of the cross section with RC at ~1% level

CMD-2 data

ee (K+K-) cross section calculation

2|F |

2 E, MeV

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 tocalculate RC. Clear evidences are needed to believe this approach

+

+

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2

2

2

2Photon jets radiation along initial

particles inside narrow cones “Dress” cross section

ee cross sectionComparison 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

ee cross section (low energies)

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 wellBad ² if we used MC generator with radiation of one photon

E = 185 MeV E = 185 MeV

Two collinear tracks in DCOne cluster in calorimeter(not associated with tracks)No signal in outer muon range systemNo signal in endcap BGO calorim. - reject 0 events

Cross section ratio ISR + FSR/ISR vs energyDigit upper every curve – threshold of the photon energy to detectEnergy interval 2*360 2*390 MeVis preferable

The process ee with FSR is a unique tool to answer on question – can we tread a pion like a point object

Selection events with FSR Two dimensional plot for xx events

Variables on axis: vertical - W = p/E, horizontal - M²

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).

experiment (CMD-2)simulation

Spectrum of events with FSR as a function of the emitted photon energy

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

Histogram – simulation (MCGPJ), bar points – CMD-2 data

average div. ~ (2.1 ± 2.3)%

Processes with neutral particles in FS (only initial state radiation are considered: ee (n), KLKS(n), 0(n), (n), ’(n), 0(n)

Cross section accuracy with RC is estimated to be at ~0.2% Very important channel ee : 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%

Relative cr. sect. difference (jet/jet vs energy

Relative cr. sect. difference(jet/jet vs angle , rad

CMD-2 cut

What is R(s) required? Definition of R(s) depends on the application

Bare(s)=Dress(s)|1-P(s)|²[1+(/)(s)]fCI(s)

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% ANDcross sections with radiation of one photon in final state should be obtained.

Today it is done for the processes: e+e- ee , , 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.

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:

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

Special experiment - it is necessary to measure cross sections of the THREE QED PROCESSES ONLY: 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 RCEffects of FSR and CI must be included into RC

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

dxmx

xxahad )

1()1( 2

21

0

.

2|)(1|

exp

sBorn

Contribution to aµ

Time-like region Space-like region

Red lines – resonance contributions x < 0.7 analytical approximation

Cross section of all three QED processes can be measured in one direct scan experiment.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.

Conclusions

• MC generators to simulate different processes were done : ee ee, BHWIDE (0.5%), MCGPJ (0.2%?!) and BabaYaga (0.1%)

• ee , -, KKMC (0.1%), MCGPJ (0.2%?!)

• ee 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 • ee , 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%.

Conclusions

• 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

Conclusions• 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 (0² 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!!!