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Radiative Corrections in Direct Scan Experiments at e+e- Colliders

This article discusses the use of MC generators with radiative corrections in direct scan experiments at e+e- colliders, focusing on various processes for luminosity measurement. It also explores the potential improvements and future possibilities in this field.

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Radiative Corrections in Direct Scan Experiments at e+e- Colliders

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  1. MC generatorswith radiative corrections used in direct scan experiments at e+e- colliders G.Fedotovich, E.Kuraev and A.Sibidanov Budker Institute of Nuclear Physics Novosibirsk Phipsi09, Beijing IHEP, 16 October

  2. OUTLINE • Motivation to have several processes for luminosity • measurement.New generation electron-positron colliders with • high luminosity (BES-III, VEPP-2000, DAFNE) •  MC generators photon jets (MCGPJ) for the process ee  • ee+ n and comparison with BHWIDE and BABAYAGA codes •  MCGPJ for the processes ee  + n and comparison • with KKMC and BhabhaYaga@NLO codes •  MC generators for the processes ee   + n •  What we have and what we can expect in the nearest future • ee   + n, KK + n, 3 + n (ISR & FSR) • ee KLKS + n, 0 + n,  + n (ISR) • ee  4 + n,0 +n,5 + n, KK + n, KK + n (ISR only) •  Conclusion

  3. VEPP-2000 begins to operate for experiments  New accelerator features – round beams must provide high luminosity (around , ,  mesons at least 10 times bigger)  Upgrade two detectors was done (CMD-3 & SND) – new possibilities for charged and neutral particles identification  We plan to put down the main systematic errors for hadronic cross section measurement to the level 0.3% (60ppm0.3% = 0.2ppm. New (g-2) experiment at FNAL will deliver 0.14ppm) Accuracy of luminosity measurement is a crucial point to reach final precision 0.3% for hadronic cross sections  Independent processes e+e- annihilation into e+e-, +-,  necessary to use for luminosity determination – crosscheck possibility to study and estimate systematic MC generators for these processes with RC of pro mille accuracy are extremely needed

  4. Bhabha process ee  ee main channel generally used for luminosity measurement Advantages Disadvantages It is pure QED process ISR + FSR + Interference complicated matrix element Cross section is big enough Detection efficiency strongly depends on polar angle Events have a simple Feynman graphs contain VP signature in detector Total energy deposition Asymmetrical XS behaviour in calorimeter vs polar angle – problems with acceptance determination How to improve theoretical precision of XS calculation with RC for this process

  5. Cross section construction e- photon jets radiation along momenta of particles inside narrow cones e+ e- VP effects by leptons and hadrons must be included to each amplitude Matrix element for one photon radiation at large angle out of narrow cones ( > 0,  > ) enough to provide systematic error less than 0.2% (no enhanced contribution inside these regions) Enhanced contributions proportional to / Ln(sm2e) and coming from collinear regions are taking into account by means of SF approach e+ 2 + + 2 + + 2 + Three part of the cross section

  6. Bhabha cross section ee  e e (dependence on inner parameters) XS dependence vs inner parameter XS dependence vs inner parameter0 In both cases XS deviations are inside corridor ±0.1% Relative XS difference for MCGPJ code & BHWIDE vs acollin. polar angle Relative XS difference MCGPJ code & “Berends” vs acollinearity polar angle All enhance contributions increase cross section on 0.25% only

  7. ee  ee cross section vs energy CMD-2 selection criteria for collinear events were applied  < 0.25 rad,  < 0.15 rad, 1 < final <  - 1 Comparison with BHWIDE code Comparison with BabaYaga @NLO - precision 0.1% Relative XS difference does not exceed 0.2% Relative XS difference does not exceed 0.2% Vacuum polarization effects were removed in both codes

  8. Crucial point is how to estimate theoretical precision MCGPJ with RC Indirect arguments are: It was found out that relative XS difference with “Berends” code is less than 0.2% for “soft” selection criteria Comparison with BHWIDE code (0.5%) and BABAYAGA (0.1%) confirms very good agreement between XS, while different theoretical approaches were treated. Radiation two and more photons in collinear regions increases XS for amount 0.2% only. Therefore theoretical systematic accuracy XS with RC certainly is better than 0.2% for “soft” selection criteria. May be better In order to believe to 0.2% precision the experimental proofs are needed ! We plan to do it with CMD-3

  9. Cross section ee   It is pure QED process, but cross section in ten times smaller than Bhabha. Nevertheless it is enough for high luminisity collid. Cross section slowly depends on polar angle and it is even with respect to angle 90°. Powerful instrument to study acceptance systematic Cross section contains RC with photon jets radiation along initial particles only. FSR with one hard photon is enough Alternative method to better understand and correctly estimate systematic error for luminosity. Problems with muons ID at high energies This process goes through one annihilation channel – direct way to extract VP (required for many applications) Double ratio can serve as a power tool experimentally to check precision of theoretical calculation It was done with CMD-2 data and for this ratio we obtained:–1.7% ± 1.4%st ± 0.7%syst.With CMD-3 we plan to improveaccuracy for this ratio and to achieve:x% ± 0.4%st ± 0.3%syst

  10. Cross section construction ee   2  2  +  2   Elastic part + ~90% One photon radiation out of narrow cones + ~5% Relative contribution of FSR to cross section ~0.3% 0.3% Photon jet radiation inside narrow cones -enhanced contributions It was elucidated by M.Voloshin that all enhanced contrib.  to ² increase cross section not more than 0.02% & they quickly fall down vs energy Main conclusion:It is enough to take into account only first order RC to provide systematic error of the cross section with FSR less than0.1% Cross section precision with RC  0.2 % is expected for MCGPJ Experimental proves are needed

  11. Comparison MCGPJ code with KKMC & BabaYaga Vacuum polarization effects switch off in both generators Relative cross section difference with respect to KKMC code Relative cross section difference with respect to BabaYaga@NLO code preliminary  0.17 % CMD-2 selection criteria were applied for collinear events

  12. What we have checked with CMD-2 E = 195 MeV double ratio Average deviation for double ratio is: –1.7%±1.4%st±0.7%syst Practically it was the first direct study theoretical precision of XS with RC at ~1% level

  13. What can we check with CMD-3 2E = 520 MeV 2E = 520 MeV ee E+,MeV e+e- +- +-   E-,MeV 2D-plot for p+ vs p- 2D-plot for E+ vs E- Energy gap - both sep.meth. overlap. Events separation based on momentum measurement in DC & energy deposition in calorimeter With CMD-3 we will be able to improve both as statistical & as systematic accuracy in 3 and 2 times respectively: x% ± 0.4%stat ± 0.3%syst Better understand & estimate systematic due to PID procedure

  14. Process e+e-  + n() Alternative process to measure luminosity Main features – we will be able to detect photon point conversion inside LXe calorim. Simple signature in detector: no tracks in DC & two collinear clusters in calorimeters with identical energy Spatial resolution  1 mm with cosmic rays was achieved CMD-3

  15. MC generator for the process e+e-  + n() with RC pro mille accuracy • Pure QED process. Cross section is big enough to use for luminosity measurement • Alternative method to better understand and correctly estimate systematic error for luminosity • Cross section contains radiative corrections connected with ISR • Feynman graphs for this process do 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 1 2 + 1 2 How to improve the accuracy? SF approach – to describe photon jet radiation in collinear region to include the most enhanced contributions

  16. Simulation results (MCGPJ) In both cases the cross sections deviations are inside corridor ±0.1% stability vs inner parameter  stability vs inner parameter 0 Comparison with Berends code (first order corrections) XS difference vs beam energy XS difference vs acollin. angle 

  17. Cross sections with neutral particles in FS ee  KLKS+n, 0+n, +n, 0+n Initial state radiation only. Photon jets along electrons and positrons without angular distribution “Boosted” cross sections are for these modes. MCGPJ code is not ready while, but it can be done quickly Theoretical cross section accuracy with RC is estimated to be at 0.2% and may be smaller Cross sections with charged particles in FS: ee 3+n,4+n,5+n, KK+n, KK+n, KK+n MCGPJ code with ISR & FSR is done only for 3 channel. All corrections   aretaken into account (FSR contributes 0.3%) There are no analytical expressions for some Born cross sections.Butconstant matrix element is not a bad approximation for smooth cross sections FSR effects will contribute not more than 0.5%. As a result cross section accuracy with ISR only can be estimated as 1%

  18. Conclusions Three alternative processes ee  ee + n ,  + n,  +n must be used for luminosity measurement to better estimate & understand experimental & theoret. system. accuracy For Bhabha process BHWIDE code, MCGPJ & new version BABAYAGA code are available now and theyhave theoretical precision 0.5%, 0.2% & 0.1% respectively For the process ee   + n there are three codes KKMC & MCGPJ & BabaYaga@NLO now. Theoretical systematic accuracy for these codes are 0.1%, 0.2% and 0.1% respectively Deviation of muon cross section from QED prediction is about –1.7% ± 1.4% ± 0.7%. At CMD-3 we expect to have ± 0.4%st. ± 0.3%syst. Unique way to control theoretical precision For the process ee   +n only MCGPJ is available while. Theoretical systematic uncertainty is about 0.1% (or better)

  19. Conclusions Good agreement is observed for total cross sections produced by MCGPJ generator, BHWIDE, KKMC & BABAYAGA We plan to include NLO corrections to MCGPJ (0.1%) MCGPJ code for processes KLKS+n,0+n, +n, 0+nwith neutral particles in FS is in progress now. “Boosted” cross sections are calculated (E.A.Kuraev et. all, Dubna) Born cross sections are required for the channels with charged particles in FS: 4+n,5+n, KK+n, KK+n, KK+n. Without FSR the cross sections accuracy will be around 1-2% MCGPJ covers a lot of processes. Simulation efficien. more than ten times better with respect to currently exist MC generators. Code structure allows one easy to add new processand so on… We must overcome many problems in order to reach the hadronic cross sections accuracy with CMD-3 at VEPP-2000 as 0.3%, if stars on the sky will be favourable for us

  20. Relative cross section difference vs invariant mass of muon pair (BabaYaga@NLO – MCGPJ) 2E = 3.5 GeV 2E = 1 GeV (/)aver=0.02±0.09% (/)aver=0.2±0.07% CMD-2 cut,  0.25 rad Main part of statistic concentrates at first point (soft ph.rad.) In real condition the acollinearity cut  is chosen as large as possible to illuminate angle resolution of the tracker, because the shape of tails for angle resolution of tracker is difficult to control during long time run. Typical resolution for polar angle is inside band 5  50 mrad

  21. ee   (K+K-) cross section calculation 2  + 2   +  2 +  “Dress” cross section Photon jets radiation along initial particlesinside narrow cones 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 evidence are needed to believe this approach

  22. What is R(s) required in dispersion relations? “removing” of VP “including” of FSR 2 “bare” cross section bare(e+e- hadrons) = dress(e+e- hadrons)|1 - (s)|² [1 + (/)(s)] • 1. Cross sections with radiation of one photon in final state are calculated • for the processes: e+e-  , +-. • It is required for all hadrons channels. • 3. For R(s) calculation VP effects should be removed from all hadrons • cross sections.

  23. Total cross sectione+e-  + n()consists of three different parts: Photon jet radiation in collinear region described by SF approach Two compensators – which represent the residuary contribution comes from collinear region with one photon emission The last term represents HPh emission out of narrow cones The sum of two last terms does not depend on  and 0 Shifted Born cross section represents cross section in Lab.S when initial electrons and positrons loose some part of energy radiating photon jets in collinear region

  24. Total cross sectione+e-  + n() consists of three different parts: Photon jet radiation in collinear region described by SF approach Two compensators – which represent the residuary contribution comes from collinear region with one photon emission The last term represents HPh emission out of narrow cones The sum of two last terms does not depend on  and 0 Shifted Born cross section represents cross section in Lab.S when initial electrons and positrons loose some part of energy radiating photon jets in collinear region

  25. E = 300 MeV ee   Events distribution vs p- preliminary

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