g-2 phase study from GEANT simulation

1. g-2 phase study from GEANT simulation Qinzeng Peng Advisor: James Miller Boston University Sep 28, 2004 Muon g-2 collaboration at BU: Lee Roberts, Rober Carey, Jon Paley, Xiaobo Huang Institutes: BU, BNL, UIUC, Univ. of Minnesota, Yale Univ.

2. Outline • Brief introduction to g-2 • Experimental set up and simulation • Simulation results and analysis

3. What is g-2? magnetic moment gyromagnetic ratio spin • Dirac equation predicts g=2 • in nature radiative correction makes g≠2 where aμ(SM) = aμ(QED) + aμ(hadronic) + aμ(weak) aμ(New Physics)= aμ(Measured) −aμ(SM) Studied Muon instead of Electron due to

4. Experimental Setup – Muon storage Polarization Momentum Idealorbit Kicker Modules R=711.2cm d=9cm Electric Quadrupoles Protons Pions Inflector (from AGS) p=3.1GeV/c Target (1.45T) Injection orbit • Muon polarization • Muon storage ring • injection & kicking • focus by Quadrupoles Storage ring

5. DET magic γ= 29.3 spin precession and muon decay • muons move in circle with constant speed • spin precession (Thomas + Larmor) • electrons decay mostly along the spin • direction and boosted by Pmuon • fitting by 5-parameter function to get N(t,E) = N0(E)e-t/τ(1+A(E)Cos(ωat+Φ(E))

6. Phase shift on ωa uncertainty What if φ is not a constant? Take an example: if And measuring time is about 600 μs, then

7. Idealorbit g2Geant simulation Hugh Brown • Muons generation • Spin polarization Beam-line simulation Jon Paley Inflector p≈3.1GeV/c g2Track • Inflection • Kicking • scraping Robert Carey g2GEANT Simulates nearly all geometric set up in the storage ring DET

8. Vert. on DET Vert. in Beam Radial in Beam Radial on DET tdecay-tmeasure=drift time Beam-line / Calorimeter alignment vertical Beam in the ring Calorimeter horizontal

9. Data selection • Energy cut: En >1.8GeV • Detector dependence: average over 24 detectors • Drift time: offset of g-2 phase

10. Ф vs. detector vertical position DET Beam 3cm ypc1 • Symmetric about center • Energy dependent • ΔΦbig : -80 ~ +80 mrad • Φ(all) small : about 5 mrad • Φ change sign at 3cm

11. inward outward 3cm outward and inward decay

12. Ф vs. detector radial position • ΔΦ smaller, 30 mrad • Φ≈0 on outside • Φ >0 on detector

13. Ф vs. beam vertical/radial position • ΔΦ smaller • Φ≈0 on inside • Φ >0 • symmetric about center of beam • ΔΦ big • Φ≈0 at center

14. Beam vertical shift • ΔΦ ≈0 • Φ is detector dependent, 4 groups --- 4 Quads

15. Beam width change idea: change beam vertical distribution by a weighting factor Result : 1 percent width change / 0.1 mrad phase shift

16. Beam upper cut – muon losses 9cm • Muon losses: 1.64% • ΔΦ = -0.323 mrad

17. DET Vert. Detector gain shift 1.05 E 0.95 E E • very small effect • 10% gain shift / • ΔΦ = 0.014 mrad

18. Beam / detector vertical alignment • 0.11%/1.0% width change • 0.9mm/1.0mm shift

19. CBO modulation • Betatron Oscillation • Coherent Betatron Oscillation • Combine 23 detectors in one CBO period Time = MOD ( time - DET# /24*Tcbo, Tcbo)

20. Sampling  Tcbo=2.4μs

21. CBO effect Combine 23 detectors

22. CBO modulation Number modulation Asymetry modulation, 0.22%

23. phase modulation, 0.358 mrad dt modulation, 0.175 mrad

24. conclusions • Simulation results consistent with Real data, like FSD studies. • Phase shift due to the geometric set up is a small effect on ωa . • CBO effect is a small effect.