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G.Fedotovich Budker Institute of Nuclear Physics

Prospect of accuracy improvements of the hadronic cross sections measurements to the level 10 -3 : experimental and theoretical problems. G.Fedotovich Budker Institute of Nuclear Physics Novosibirsk, Russia. LNF, Frascati

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G.Fedotovich Budker Institute of Nuclear Physics

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  1. Prospect of accuracy improvements of the hadronic cross sections measurements to the level 10-3: experimental andtheoretical problems G.Fedotovich Budker Institute of Nuclear Physics Novosibirsk, Russia LNF, Frascati 7 - 10 April 2008

  2. Outline • Current status of the accuracy of the hadronic cross sections measurements. Inspection of the last generation experiments - CMD-2, SND & KLOE • 2. Main sources of systematic errors: • • Accelerator • • Detector • • Theory • 3. What can we expect in the nearest future • 4. Usage of space-like data to calculate VP operator (-q2) • 5. Conclusion

  3. Some features of CMD-2, SND and KLOE experiments • • Large data sample due to high integrated luminosity and large detectors acceptance (calorimeter covers about 0.94). Every detector collected several millions +- events • Multiple scan (up and down) of the same energy range to avoid possible systematic in energy determination: step (2E) = 10 MeV in the continuum and about 1 MeV near  and  peaks (CMD-2 and SND) • Absolute calibration of beam energy using the resonance depolarization method (better than 10-4)  negligible systematic error comes due to energy uncertainty (CMD-2 and SND) • Good space resolution resulting in perfect momentum resolution (p/p ~ 0.4%, KLOE)  powerful instrument for charged PID • Excellent energy resolution at a few percent level (E/E ~ 4%, SND & KLOE) leads to small background & helps to separate events

  4. Some features of CMD-2, SND and KLOE experiments • • Detection efficiencies and calorimeter response were studied • using “pure” experimental data rather than MC events (~2106  • and  meson decays have been used, CMD-2 & SND) • • Charged and neutral triggers for the same data sample – possibility to measure and monitor triggers efficiencies (CMD-2 & SND) • • Changing events selection criteria to check cross section stability. • All detectors carefully studied this item • Cross check possibility – unstable particles detected via different decay modes (º→2, e+e-; →2, +-0, 30) • • MC generators based on differential cross sections with precise RC • for the processes of e+e- annihilation were developed (CMD-2 & KLOE)

  5. How cross sections are measured to understand the main factors giving dominant contributions to systematic uncertainty for hadronic cross sections All modes except 2 2 mode • Efficiencyis calculated via Monte Carlo + corrections for detector imperfections • Integrated luminosity Lis measured using LAB events • RC  accounts for ISR effects only • VP effects are included in cross section properties • Ratio N(2)/N(ee) is measured directly  detection inefficien-cies are cancelled out in part • RC account for ISR and FSR effects • Events separation procedure & analysis don’t rely on simulation • Form factor is measured to better precision than L

  6. Luminosity measurement • Precision of luminosity measurement will be improved significantly due to better extraction of Bhabha events, increasing detection efficiency and more accurate calculation of the radiative corrections. • Alternative method to measure luminosity based on the process e+e-γ γ. In that case Feynman graph does not contain VP effects. Powerful instrument to understand systematic.

  7. R measurement at CMD-2, SND and KLOE (for √s<1GeV 2pi dominant channel)

  8. R measurement at CMD-3 (systematic errors review)

  9. Derivative d|F(E)|²/dE/|F(E)|²x E/E Energy determination (E/E = 10-3) Derivative jumps up and down inside corridor 1%. Near  and  mesons reach values 6%. Conservative upper estimation is 1% - energy region gives the main hadronic contribution to aµ = (g –2)/2 Very important task for machine physiciststo determine beam energy with relative accuracy E/E  10-4 or even better

  10. π/μ/e separation based on charged particle momentum CMD-2 260 MeV CMD-3 320 MeV • DC resolution will be 2.5 times better (already achieved) • Magnetic field will be increased 1.5 times (already achieved) • As a result π/μ/e separation based on momentum will be possibleup to 2*320 MeV - practically to the  peak Vertical axis – the number of standard deviations between average momentum of pions and muons

  11. π/μ/e separation based on energy deposition CМD-3 CMD-2 • Energy resolution of barrel part will be improved (8X0 15X0) • π/e separation will be considerably better • Part pions “looks” like muons will be suppress to the level 10% (was 25% at CMD-2). We can tryπ/μ separation based on energy deposition • Information of energy deposition in depth of calorimeter provides additional factor for π/µ separation π/μ/e разделение по энерговыделению без вычитания мюонов

  12. Fiducial volume • Z-chamber: In first approach we will have the same z-coordinate resolutionthe accuracy of the fiducial volume measurementwill not change. At polar angles  ~ 60° z≈ 0.7 mm & system. shift is smaller 0.1 mm. For LAB events it leads to acceptance uncertainty about 0.2% • LXe calorimeter: For normal incident particles ~ 90° z≈ 0.9mm. The acceptance will be determined with the same accuracy. The capability for cross check will be in hand. Very possible we improve the measurement accuracy of the detector acceptance by factor of 1.5 • We assume that fiducial volume will be determined at least with the same accuracy (or better) as we had at CMD-2 • 3. Huge statistics: Help to study systematic of z-coordinate determination in DC & to improve the accuracy of DC calibration procedure. Study in detail angular distributions of multi hadrons events to choose model for simulation

  13. Radiative corrections What we have currently and what we can expect in the nearest future - theoretical aspects. • For all three detectors MC generators with precise RC were developed. • Channel e+e-  e+e-: BHWIDE (LEP, 0.5%), MCGPJ (CMD-2, 0.2%) photon jet radiation in collinear region, BabaYaga (KLOE, 0.5  0.1%) used parton shower approach. We plan to include NLO corrections and increase the accuracy of our MCGPJ to 0.1% level (for all other channels too). This work is in progress with Dubna, E.Kuraev et.al. • Channel e+e-  +-,+-: KKMC used in LEP experiments adopted for low energies, 0.1%, BUT for VP effects smooth approximation was applied. Resulting systematic accuracy is not better than 1% (out of  &  energy region). MCGPJ (CMD-2, 0.2%). Quite possible that in our case systematic uncertainty is better than 0.1%. B.Smith, M.Voloshin: PL B 324 – all enhanced second order corrections contribute not more than 0.02% and quickly decrease with energy increase

  14. Radiative corrections • Channel e+e-   MCGPJ (CMD-2, 0.2%). This process has a big cross section. Very important channel for luminosity measurement – cross check possible. ISR only. Feynman graph does not contain VP effects. • Channel e+e-  +-, K+K-: MCGPJ (CMD-2, 0.2%). ISR & FSR are taken into account. Unfortunately there are no other MC generator with similar accuracy for comparison. Experimental and theoretical evidences are required to prove validity of sQED application for pions & kaons • Channels with neutral particles in FS: e+e-  KLKS, 0, , 0. ISR are taken into account. MCGPJ (CMD-2, 0.2% or better). Very possible that accuracy is better than 0.1% • VP effects currently are calculated with accuracy better than 0.05% (on  with 0.5% & on  - 0.15%) and do not contribute to final systematic error

  15. Trigger & reconstruction efficiencies •  Trigger efficiency close to 100%. Charged & neutral triggers for the same data sample – powerful instrument to monitor trigger stability and it’s real efficiency (CMD-2, KLOE & CMD-3) • Efficiency oftrack reconstruction in DC will be better than 98% with uncertainty <0.1% (CMD-3 & new SND) • Bremsstrahlung of electrons (positrons) on the wall of the machine vacuum chamber. At CMD-2 and SND we had correction about (0.5  0.05)% (s<1GeV). We (& SND) hope to have the same accuracy in experiments at VEPP-2000. • Optimization of selection criteria for collinear events: Polar angle – compromise for every detector, Threshold on transverse momentum of charged particles in DC, Choice of optimal acollinearity angle between tracks in DC Choice threshold on energy deposition in calorimeters and so on… • reconstruction – main source of systematic error for processes with in FS. LXe calorimeter will significantly push down this error

  16. Another way for aµ calculation • Special experiment is necessary to measure cross sections of ONLYTHREE PURE QED PROCESSES : e+e-  , for luminosity measurement (no VP effects, accuracy < 0.1%). BUT special calorim. is required to detect photon conversion point (LXe in CMD-3) •  e+e-  +- direct cross section measurement to extract |1 + (s)|² (accuracy < 0.1%). VP effects must be removed from RC. Effects of FSR and CI must be included into RC •  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 •  e+e-  e+e- process to extract (-q²) from t-channel in space-like region (accuracy <0.1%)

  17. Contribution to aµ Time-like region Space-like region t = -s(1-cos)/2 t  -0.04 GeV² x  0.75 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 for LAB better than 0.3% with CMD-3 at VEPP-2000.

  18. Analytical behavior of (q²) in space-like region This interval of q² variations corresponds to x changing from 0.01 to 0.99 Very ghostly chance to measure (q²) in this region with pro mille accuracy

  19. Conclusions • Despite decades of experiments, precise studies of e+e annihilation into hadrons at low energies are still interesting and can provide a lot of important information ● In a few years new precision data from CMD-3 and SND working at VEPP-2000 as well as with ISR at DAFNE and B–factories and BELLE are expected ● Progress is particularly expected for the channel e+e-→+-, where systematic uncertainty 0.3% or even better will be achieved ● MC generators were done : • ee  ee, BHWIDE (0.5%), MCGPJ (0.2%?!) and BabaYaga (0.1%) • ee  ,-, KKMC (0.1% adopted for low ener.), MCGPJ (0.2%) • ee   and K+K-, MCGPJ (0.2%?!) • Only ISR is taken into account for processes with neutral particles in final state: ee  , KlKs, 0,,’, 0, MCGPJ(0.2%) We can expect progress in theoretical improvement of the accuracy of RC calculation with pro mille accuracy

  20. ● Measurement of beam energy with relative accuracy better than 10-4 are extremely needed (resonance depolarization techniques only) ● To have enough statistic ~106 at every energy point (~100) machine with luminosity greater than 1032 cm-2s-1 in  meson energy region is required ● To illuminate possible systematic error in hadronic cross sections more accurate and independent measurements (CMD-3 & SND) are necessitated ● Efforts of theorists are required to build models to describe in detail energy dependence of cross sections with 4 & more pions in FS ● CMD-3 and SND will measure hadronic cross sections with accuracy close to pro mille. DAFNE HEPr can provide independent measurement of the hadronic cross sections - valuable information for cross check accuracy with CMD-3 & SND ● Luminosity and trigger efficiency must be measured in different channels at the same data sample to arrange cross check for better study of systematic ●Usage of space-like data can help in understanding of systematic in hadronic contribution to aµ (in far future, JLAB)

  21. CMD-3 • circumference– 24.4 m • revolution time – 82 nsec • beam current– 0.2 A • beam length – 3.3 cm • energy spread– 0.7 MeV • x=z =6.3 cm • L = 1032cm-2s-1at 2E=2.0 GeV • L = 1031cm-2s-1 2E=1.0 GeV VEPP-2000 SND Total integrated luminosity with all detectors on VEPP-2M ~ 70 pb-1

  22. Luminosity measurement Nee Nxx L= L= vis(ee  ee) vis(ee  xx) Bhabha scattering events are preferable for normalize purpose to calculate cross sections with collinear events in FS vis(ee  xx) = ----- vis(ee  ee) Main sources of systematic errors in previous experiments were 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)

  23. Dominant channele+e- → +- energy interval energy interval 390 – 520 MeV600 – 960 MeV Group aµ(), 10-10 aµ(), 10-10 Old 48.72 ± 1.45 ± 1.12 (1.83) 374.8 ± 4.1 ± 8.5 (9.4) CMD-2 46.17 ± 0.98 ± 0.32 (1.03) 377.1 ± 1.9 ± 2.7 (3.3) SND 47.80 ± 1.73 ± 0.69 (1.86) 376.8 ± 1.3 ± 4.7 (4.8) CMD-2/SND 46.55 ± 0.85 ± 0.29 (0.90) KLOE: 375.6 ± 0.8 ± 4.9 (5.0) Average 46.97 ± 0.73 ± 0.45 (0.86) 376.5 ± 0.6 ± 1.5 (1.7) energy interval 1040 – 1380 MeV Group aµ(), 10-10 OLYA 7.49 ± 0.18 ± 0.83 (0.83) CMD-2 7.01 ± 0.10 ± 0.16 (0.19) Average 7.03 ± 0.09 ± 0.16 (0.18)

  24. π/μ separation 440 MeV  480 MeV  320 MeV  360 MeV  230 MeV  280 MeV  Iron yoke Iron yoke 130 MeV  170 MeV  CSI CSI LXE LXE Vertical axis - radius(in cm) where pions and muons penetrate • At any energiesπ and μescapeLXE – it is bad • At energies aboveφ meson – muon range system will serve to suppress cosmic events, below to mark muon events • At energies below 2*400 MeV π /μ does not escape CsI calorimeter – it is fine

  25. Systematic error 0.6% (95)/ 0.8% (98) 1.2-4.2% 0.7% Pion formfactor (CMD-2) ~ 9105 +- events

  26. > 0.6GeV < 0.6 GeV Event separation (CMD2) ee   • e// separation using particles momentum • can measure N()/N(ee) • and compare to QED • e// separation is based on energy deposition in calorimeter • N()/N(ee) is fixed according to QED

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