1 Measurement of the Rate of Muon Capture in Hydrogen Gas and Determination of the Proton’s Pseudoscalar Coupling Steven Clayton Dissertation Talk June 15, 2007  + p  n +  Outline Theory MuCap experiment Data analysis Systematic effects Results

2  - Stopping in Hydrogen Quickly forms a  p atom, transitions to ground state, transitions to singlet hyperfine state. Bohr radius a ≈ a 0 m e /m  ≈ a 0 /200 Most of the time, the  decays: Occasionally, it nuclear captures on the proton:  - + p   + n rate  S BR~10 -3  - + p   + n +  BR~10 -8, E>60 MeV  -   + e - + e rate 0  1/   + BR≈0.999 Complications: molecular formation/transitions, transfer to impurity atoms, … The goal of  Cap is  s to 1% precision:  s = - 1/   +

3 Nucleon Form Factors G-parity CVC EM FF’s = 0 nucleon level quark level n-decay

4 Gives an expression in terms of form factors g V, g M, g A, g P. W.f.s are solutions to the Dirac equation.  in bound state: Non-relativisitic expansion to order v nucleon /c: –effective Hamiltonian in terms of “Primikoff factors” and Pauli matrices. –particle states in terms of 2-spinors (  –results in an explicit expression for the transition rate W: Phenomenological Calculation, total  p spin dependence  S =  T =  p(  ) singlet  p(  ) triplet

5 g P = (8.74  0.23) – (0.48  0.02) = 8.26  0.23 PCAC pole term Adler, Dothan, Wolfenstein ChPT leading order one loop two-loop <1% N. Kaiser Phys. Rev. C67 (2003) g P determined by chiral symmetry of QCD: solid QCD prediction via ChPT (2-3% level) basic test of QCD symmetries solid QCD prediction via ChPT (2-3% level) basic test of QCD symmetries Recent reviews: T. Gorringe, H. Fearing, Rev. Mod. Physics 76 (2004) 31 V. Bernard et al., Nucl. Part. Phys. 28 (2002), R1 Pseudoscalar Form Factor g p n  p --  g  NN FF W

6 Sensitivity of  S to Form Factors Contributes 0.45% uncertainty to  S (theory) g p vs.  S Examples: 2.4% 13.6% 1.0% 6.1% 0.5% 3.8% gpgp  S (s -1 ) slope = s (w/rad. corr.)

7 Muon Atomic/Molecular State in Experiment must be known to connect with theory.  p(F=0) H 2 density  pp  OP  s ≈ 700 s -1 p  p(J=1) Ortho  om ≈ ¾  s p  p(J=0) Para  = 1 (Liquid) Rel. Population Time after  p Formation  = 0.01 (~10 bar gas) Time after  p Formation Rel. Population  pm ≈ ¼  s

8 Previous Data on g p No common region of overlap between both expts. and theory g P basic and experimentally least known weak nucleon form factor (p  p ortho-para transition rate) HBChPT MuCap Goal

9 Muon Atomic Transitions  pp  OP  p(F=0) ss p  p(J=1) Ortho  om p  p(J=0) Para  pm   p(F=1) TT c d pd c d dd dd c Z pZ c Z ZZ  Z ~  S Z 4 n +  + (Z-1)* H 2 must be pure isotopically and chemically: c d < 1 ppm, c Z < 10 ppb

10 Experimental Challenges 2) All neutral final state of muon capture is difficult to detect. It would require absolute calibration of neutron detectors. 1) Unambiguous interpretation requires low- density hydrogen target.  p diffusion into Z > 1 material.  liquid (LH 2 )gas (1% LH 2 density)  stop distribution broad  stop distribution

11 slope =    ≡ 1/    TT Log N events  Cap Method: Lifetime Technique  Cap measures the lifetime of  - in 10 bar Hydrogen. -- e-e- T zero T electron slope =    ≡ 1/    Data Acquisition TT Repeat times for a 10 ppm precision lifetime measurement. H2H2       S   S to 1% precision Compare to  + lifetime:

12 3D tracking w/o material in fiducial volume 10 bar ultra-pure hydrogen, 1% LH kV/cm drift field >5 kV on 3.5 mm anode half gap bakable glass/ceramic materials Time Projection Chamber (TPC) Beam ViewSide View  Beam  Stop y xz y

13 p Tracking in the Time Projection Chamber E e-e- z x y -- 1)  entrance, Bragg peak at stop. 2) ionization electrons drift to MWPC. 3) projection onto zx plane from anodes and strips. 4) projection onto zy plane from anodes and drift time. 5) projection onto zy plane from strips and drift time.

14  Cap Method: Clean  Stop Definition Each muon is tracked in a time projection chamber. -- e-e- T zero T electron Data Acquisition TT Only muons stopped well-away from non-hydrogen are accepted. H2H2 anodes strips

15  Cap Detailed Diagram  Tracking of Muon to Stop Position in Ultrapure H 2 Gas  Tracking of Decay Electron

16 Commissioning and First Physics Data in 2004 (Target Pressure Vessel, Pulled Back)

17 Muon Definition time of signal arrival at MWPC (  s) 2D clustering stop identification fiducial vol. cut

18 Electron Definition timing from scintillator (eSC) temporal and spatial coincidences with wire chamber planes: full 3D tracking

19 Impact Parameter Cuts e  stop position interpolated e-track aluminum pressure vessel  Stop Position  -e Vertex Cut (also known as  -e vertex cuts) b (electron view) The impact parameter b is the distance of closest approach of the e-track to the  stop position. point of closest approach

20 Lifetime Spectra Normalized residuals (“pull”)

21 Internal corrections to  - (statistical uncertainty of  - : 12 s -1 )

22 Gas impurities (Z > 1) are removed by a continuous H 2 ultra-purification system (CHUPS). Commissioned 2004 c N2, c O2 < 0.01 ppm

23 In situ detection of Z > 1 captures  Beam  Stop Z>1 Capture (recoil nucleus) Capture Time TPC (side view)

24 The final Z > 1 correction  Z is based on impurity-doped calibration data. 0 Production Data Calibration Data (oxygen added to production gas) Extrapolated Result Observed capture yield Y Z Some adjustments were made because calibration data with the main contaminant, oxygen (H 2 O), were taken in a later running period (2006). Lifetime deviation is linear with the Z>1 capture yield.

25 Internal corrections to  - (statistical uncertainty of  - : 12 s -1 )

26  d Diffusion into Z > 1 Materials  d scattering in H 2 displacement (from  - stop position) at time of decay Ramsauer-Townsend minimum in the scattering cross section  d can diffuse ~10 cm before muon decay, possibly into walls. MuCap uses deuterium-depleted hydrogen (c d  1.5 ppm). Residual effects are accounted for by a zero-extrapolation. (Monte Carlo)

27 Residual deuterium content is accounted for by a zero-extrapolation procedure. d Concentration (c d )0 Production Data (d-depleted Hydrogen) Calibration Data (Natural Hydrogen) Extrapolated Result from fits to data (f = N e - t + B) This must be determined.

28 c d Determination: Data Analysis Approach  Stop Position  Decay Position  d Diffusion Path  -e Vertex Cut  d can diffuse out of acceptance region:  signal proportional to number of  d, and therefore to c d. Impact Parameter Cut b cut [mm] [s -1 ] Fits to Lifetime Spectra diffusion “signal” for 40-mm cut c d (Production) c d (Natural H2) = ± *after accounting for  p diffusion (electron view) natural hydrogen (c d  120 ppm) d-doped target (c d  17 ppm) production target (c d ~ 2 ppm)

29 Consistency Checks lifetime vs. variations in parameters not expected to change the results

30 Lifetime vs eSC segment Beam view of MuCap detector eSC Sum over all segments

31 Lifetime vs. Non-Overlapping Fiducial Volume Shell Included in standard fiducial cut z y Example TPC fiducial volume shells (red areas) outside the standard fiducial cut outer inner outerinner

32 Start Time Scan

33 Stop Time Scan

34 Lifetime vs. Chronological Subdivisions Oct. 9, 2004Nov. 4, 2004

35 MuCap  S from the   lifetime   bound-state effect  + decay rate molecular formation Averaged with UCB result gives

36  S Calculations and MuCap (2007) Result rad. corrections Czarnecki Marciano Sirlin (2006)  R = 2.8% MuCap agrees within ~1  with  S theory HBChPT

37 Updated g P vs. op MuCap 2007 result (with g P to 15%) is consistent with theory. This is the first precise, unambiguous experimental determination of g P (contributes 3% uncertainty to g p MuCap )

38 MuCap Collaboration V.A. Andreev, T.I. Banks, B. Besymjannykh, L. Bonnet, R.M. Carey, T.A. Case, D. Chitwood, S.M. Clayton, K.M. Crowe, P. Debevec, J. Deutsch, P.U. Dick, A. Dijksman, J. Egger, D. Fahrni, O. Fedorchenko, A.A. Fetisov, S.J. Freedman, V.A. Ganzha, T. Gorringe, J. Govaerts, F.E. Gray, F.J. Hartmann, D.W. Hertzog, M. Hildebrandt, A. Hofer, V.I. Jatsoura, P. Kammel, B. Kiburg, S. Knaak, P. Kravtsov, A.G. Krivshich, B. Lauss, M. Levchenko, E.M. Maev, O.E. Maev, R. McNabb, L. Meier, D. Michotte, F. Mulhauser, C.J.G. Onderwater, C.S. Özben, C. Petitjean, G.E. Petrov, R. Prieels, S. Sadetsky, G.N. Schapkin, R. Schmidt, G.G. Semenchuk, M. Soroka, V. Tichenko, V. Trofimov, A. Vasilyev, A.A. Vorobyov, M. Vznuzdaev, D. Webber, P. Winter, P. Zolnierzcuk Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia Paul Scherrer Institute (PSI), Villigen, Switzerland University of California, Berkeley (UCB and LBNL), USA University of Illinois at Urbana-Champaign (UIUC), USA Université Catholique de Louvain, Belgium TU München, Garching, Germany University of Kentucky, Lexington, USA Boston University, USA

39 Extra Slides

40 Sensitivity of  S to Form Factors Contributes 0.45% uncertainty to  S (theory) g p vs.  S Examples: 2.4% 13.6% 1.0% 6.1% 0.5% 3.8% gpgp  S (s -1 ) slope = s (w/rad. corr.)

41 g p from  S MuCap =  17.4 s -1 Average HBChPT calculations of  S : Apply new rad. correction (2.8%): (MuCap 2007, Final) Note: uncertainty in theory (~0.5%) not propagated.

42 Axialvector Form Factor g A  Asymmetry Axial radius  +N scattering consistent with  electroproduction (with ChPT correction) Introduces 0.45% uncertainty to  S (theory) PDG 2006 Bernard et al. (2002) Lifetime Neutron Decay Experiments Severijns et al. (2006) RMP

43  p Diffusion Effect  Stop Position  Decay Position  p Diffusion Path  -e Vertex Cut (b cut ) Impact Parameter Distribution F(b) b (mm) b cut early decays later decays b (ideal) b (obs.) Later decays are less likely than early decays to pass the impact parameter cut. The effect is calculated based on: 1) the observed F(b), 2) a thermal diffusion model, 3) the requirement of consistency of the c d ratio vs. b cut (prev. slide). (electron view)

44 Lifetime vs. e-definition All e acceptedOne e gated b<12cmno b-cutb<12cmno b-cut CathOR CathAND eSC Only CathOR CathAND CathOR CathAND eSC Only CathOR CathAND (impact par. cut) (treatment of detector planes) (e-multiplicity)

45 Lifetime deviations   due to Z > 1 impurities can be calculated. Muon decay time t Log N events Fit Function: f(t) = A exp(  t) Based on full kinetics solution: y e (t) Fit y e (t) to a single exponential or calculate first moment.

46 Impurity correction scales with Z > 1 capture yield.  Z =  Z /Y Z is similar for C, N, and O. We can correct for impurities based on the observed Z > 1 capture yield, if we know the detection efficiency  Z.

47  Cap Method: Clean  Stop Definition Each muon is tracked in a time projection chamber. -- e-e- T zero T electron Data Acquisition TT Only muons stopped well-away from non-hydrogen are accepted. H2H2 … TPC T1T1 T2T2 T3T3 0 <  T i < 22  s