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 I. Brief introduction to g-2 II. Experimental set up and simulation III. Simulation results and analysis

3 What is g-2? magnetic momentgyromagnetic ratiospin Dirac equation predicts g=2 in nature radiative correction makes g≠2 a μ (SM) = a μ (QED) + a μ (hadronic) + a μ (weak) a μ (New Physics) = a μ (Measured) − a μ (SM) where Studied Muon instead of Electron due to

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

5 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 P muon fitting by 5-parameter function to get N(t,E) = N 0 (E)e -t/τ (1+A(E)Cos(ω a t+Φ(E)) DET magic γ= 29.3

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

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

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

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

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

11 outward and inward decay outward < 0 Φ < 0 dt longer inward > 0 Φ > 0 dt shorter 3cm outward inward

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 symmetric about center of beam ΔΦ big Φ ≈0 at center ΔΦ smaller Φ ≈0 on inside Φ >0

14 Beam vertical shift ΔΦ ≈0 Φ is detector dependent, 4 groups 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 Muon losses: 1.64% ΔΦ = mrad 9cm

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

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

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

20 Sampling  T cbo =2.4μs

21 Combine 23 detectors CBO effect

22 CBO modulation Number modulation Asymetry modulation, 0.22%

23 phase modulation, mrad dt modulation, mrad

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