Muon Capture and the Nucleon's Axial Structure

1. Muon Capture and the Nucleon’s Axial StructureFirst Results and Future Plans of the MuCap Experiment L1A gP Peter Kammel “MuSun”project MuCap GF MuLan

2. MuCap Physics Context • Historical: V-A and m-e Universality • Today: EW current key probe for • Understanding hadrons from fundamental QCD • Symmetries of Standard Model • Basic astrophysics reactions • - + p  m+ n charged current

3. MuCap The Black Sheep of Form Factors T. Hemmert gP Muon Capture on the Proton • - + p  m+ n rateLSat q2= -0.88 mm2 Form factors + second class currentssuppressed by isospin symm. Lorentz, T invariance All form factors precisely known from SM symmetries and data apart from gP = 8.3 ± 50%

4. MuCap gpNN n p p Fp W m- nm Pseudoscalar Form Factor gP gP determined by chiral symmetry of QCD: gP= (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% • gP basic and experimentally least known EW nucleon form factor • solid QCD prediction via HBChPT (2-3% level) • basic test of QCD symmetries Recent reviews:V. Bernard et al., Nucl. Part. Phys. 28 (2002), R1T. Gorringe, H. Fearing, Rev. Mod. Physics 76 (2004) 31

5. MuCap 1 % LH2 100% LH2 pm ppμ ppmO ppμ pm ppmO ppmP ppmP time (ms) Interpretationof Experiments ? LT= 12 s-1 triplet (F=1) pμ↑↑ Lortho=506s-1 Lpara=200s-1 λop μ ppμ ppμ f λppm ortho (J=1) para (J=0) pμ↑↓ • Interpretation requires knowledge of ppm population • Strong dependence on hydrogen density f singlet (F=0) LS= 710s-1 n+n

6. Precise Theory vs. 45 Years of Exp. Efforts gP - + p  m+ n @ Saclay - + p  m+ n + g@TRIUMF ChPT mCapprecisiongoal TRIUMF 2006 exp theory lOP(ms-1) • no overlap theory & OMC & RMC • large uncertainty in lOP gP  50% ? MuCap

7. MuCap MuCap Experimental Strategy • Lifetime method • 1010m→enn decays • measure - to 10ppm, • S = 1/- - 1/+to 1% • Unambiguous interpretation at 1% LH2 density • Clean m stop definition in active target (TPC) to avoid wall stops • Ultra-pure gas system and purity monitoring at 10 ppb level • Isotopically pure “protium” m → enn LSreduces lifetime by 10-3 • + log(counts) • - μ+ μ – te-tm PSI, Switzerland fulfill all requirements simultaneouslyunique MuCap capabilities

8. m- Muons stop in active TPC target 10 bar ultra-pure hydrogen, 1.16% LH2 2.0 kV/cm drift field ~5.4 kV on 3.5 mm anode half gap bakeable glass/ceramic materialscontinuous gas circulation Observed muon stopping distribution E p e- 3D tracking w/o material in fiducial volume

9. MuCap 6 mm Inside TPC Time Spectra m-e impact parameter cut huge background suppression diffusion (deuterium) monitoring blinded master clock frequency variety of consistency checks

10. MuCap Results + from PDG and MuLan SMuCap = 725.0  13.7stat 10.7sys s-1 further sub percent theory required Average of HBChPT calculations of S: Apply new rad. correction (2.8%): Czarnecki, Marciano,Sirlin , PRL 2007 gP = 7.3 ± 1.1 (MuCap 2007)

11. MuCap gP Landscape after MuCap 07 • - + p  m + n + g Before MuCap experiments inconclusive and mutually inconsistent MuCap • MuCap result nearly model independent First precise and unambiguous result • Consistent with chiral prediction Does not confirm radiative muon capture (RMC) discrepancy • Final result (’06 and ’07 data) will reduce error twofold

12. m + d  n + n + n “Calibrating the Sun” via Muon Capture on the Deuteron “MuSun” model-independent connection via EFT & L1A • Goal • total md capture rate to 1% precision • Motivation • first precise measurement of basic EW reaction in 2N system, benchmark measurement with 10x higher precision • impact on fundamental astrophysics reactions (SNO, pp) • comparison of modern high precision calculations • high precision feasible by mCap technique and careful optimization

13. Reactions m + d  n + n + n basic solar fusion reaction p + p  d + e+ +  key reactions for SNO  + d  p + p + e- (CC)  + d  p + n +  (NC) … MECEFT L1A 10 20 30 En (MeV) 20 En (MeV) 40 50 pn(MeV/c) 60 70 80 90 En (MeV) MuSun Axial Currents in 2N System • Theory SNPA – EFT (HBChPT, pEFT, hybrid) • 1B NN description accurate • 2B not well constrained by theory EFT: Class of axial current reactions related by single parameter L1AQuest for L1A • Precision m+d experiment (PK, Chen) best determination of L1A from 2N system theory: precise enough? reaction soft enough for L1A? Ando, Park, Kubodera, Myhrer (2002) Chen, Inoue, Ji, Li (2005) experiment: 1% precision possible ?MuCap technique   En (MeV)

14. Precise experiment in 2N system needed Quest for L1A

15. MuSun Proposal planned 2007 measurement of absolute rate to <1% mSun I: mCap technique, 1% LD2, 300 K, measure time spectra of capture neutrons monitor populations with fusion and capture reactions First measurement of polarization observables in m+d capture? mSun II: new cryo TPC Kinetics requires optimized target conditions: T<50 K, >5% LD2 density 1% LD2300 K md() md() m3He time (ms) 30K, 5% 10% LD230 K New collaborators welcome !Meeting @ PSI Oct ‘07, US Nov ‘07Proposal deadline Jan ‘08

16. Various ideas: Fusion • hep: 3He + p → 4He + e+ + n m4He → t + n + nDalitz plot ? • ddm→ 4He + m + gp wave at low energies • d3Hem→ 4He+m+pTheoretical motivation should be clarifiedCan one extract the S factor, which precision needed ? sensitivity study based on MuCap data

17. Summary • MuCap: • First precise gP measurement with clear interpretation • Consistent with ChPT expectation, does not support RMC puzzle • Factor 2-3 additional improvement on theway • MuSun • muon-deuteron capture, needs gP as input • New benchmark in EW reactions in 2N system • MuLan: • First GF update in 23 years – 2.5x improvement, no surprise in result • Factor 10 additional improvement on the way 2008 projected 2006 20 ppm 10 ppm1 ppm log(counts) ?? 30 ppm10 ppm μ+ μ – time

18. http://www.npl.uiuc.edu/exp/mucapture/

19. Additional slides

20. MuCap

21. MuCap Error Budget

22. TPC tracks 2 different events seen by TDC and FADC system

23. 45 Years of Experiments to Determine gP • - + p  m+ n OMC BR~10-3 • 8 experiments, typical precision 10-15%, Saclay 4% • - + p  m+ n + g RMCBR~10-8, E>60 MeV • - + 3He  m+ 3H • Beta Decay Correlations 279±25 eventsBRg(k>60MeV)=(2.10±0.21)x10-8 Wright et al. (1998) … rad. corrections?

24. QCD • high q2 (q > some GeV) short distance <0.1 fm • Weakly interacting quarks and gluons asymptotic freedom • low q2 (q << 1GeV) long distance > 1 fm • QCD has chiral symmetry spontaneously brokenp is Nambu-Goldstone boson, weakly interacting chiral effective theory ↔ Nuclear Physics • Lattice QCD: ab initio calculations • issues: continuum transition, etc. • physical quark masses not reached Lattice QCD Edwards et al. LHPC Coll (2006)

25. Results cN, cO < 7 ppb, cH2O~18-30 ppb correction based on observed capture yield x t z Imp. Capture MuCap Unique Capabilities: Impurities • rare impurity capture mZ(Z-1)+n+n • LZ (C, N, O) ~ (40-100) x LS • ~10 ppb purity required • Hardware • CirculatingHydrogenUltrahighPurificationSystem • Gas chromatography • CRDF 2002, 2005 • Diagnostic in TPC

26. Results Directly from data cd= 1.49 ± 0.12 ppm AMS (2006) cd= 1.44 ± 0.15 ppm On-site isotopic purifier 2006 (PNPI, CRDF) MuCap Unique Capabilities: mp, md diffusion • mp + d  md + p (134 eV) • large diffusion range of md • < 1 ppm isotopic purity required m-e impact par cut mp md mp e- e- or to wall • Diagnostic: • l vs. m-e vertex cut • AMS, ETH Zurich World Record cd < 0.1 ppm

27. MuCap Axialvector Form Factor gA Lattice QCD Axial radius Exp. History n+N scattering consistent with p electroproduction (with ChPT correction) Bernard et al. (2002) Edwards et al. LHPC Coll (2006) PDG 2006 introduces 0.46% uncertainty to LS (theory)

28. MuCap gP MuCap Physics Case • EW current key probe • Understanding hadrons from QCD • Symmetries of Standard Model • Muon Capture • Formfactors • - + p  m+ n rateLSat q2= -0.88 mm2 The Black Sheep of Form Factors T. Hemmert + second class currentssuppressed by isospin symm. Lorentz, T invariance All form factors precisely known fromSM symmetries and data apart from gP = 8.3 ± 50%

29. Future

30. Quest for L1A Chen, Heeger, Robertson PRC 67 (2003) 25801 • process value (fm3) method • theory • Dim.arguments ±6 • 2 nucleon • n+d  e++n+n 3.6 ±4.6 reactor, optimistic • n +n +p ES, CC, NC 4.0±6.3 SNO self calibration m+d  n+n+n ±1 ? 1% L measurement theory uncertainty 1% 3 nucleon 3H  3He+e++n 4.2 ± 0.1 used by EFT*, not by pEFT m3He  3H+n ? gP from other source astro Helioseismology 7.0± 5.9 pp fusion, but no other SoMo uncertainties Precise experiment in 2N system needed

31. Various Ideas: Weak Interactions recoil polarization should be included ga sensitivitySerebrov dga~0.7% mp: H(n,F) mp: Laser md: Av

32. m3He

33. MuLan

34. MuLan MuLan Scientific Case • Fundamental electroweak parameters • GF • Implicit to all EW precision physics • Uniquely related to muon decay • PrecisionGF t relation no longer theory limited • GFaMZ 9 ppm 0.0007 ppm 23 ppm QED exp MuLan2004 theory 17 ppm 18 ppm 90 ppb 30 ppm9 ppm 18 ppm <0.3 ppm0.5 ppm 1 ppm <0.3 ppm van Ritbergen and Stuart: 2-loop QED corrections MuLan Goal

35. MuLan MuLan Experiment Real data Kicker On “Early-to-late” changes • Instrumental shifts Gain or threshold Time response • Effective acceptance Residual polarization or precession Pileup • Missing events PSI DC proton beam590 MeV, 1.7 mA Systematics Measurement Period Number (log scale) time Fill Period -12.5 kV 12.5 kV

36. MuLan This world average used for MuCap MuLan

37. MuLan MuLAN tm(MuLan) = 2.197 013(21)(11) ms (11ppm) tm(World) = 2.197 019(21) ms (9.6 ppm) GF = 1.166 371(6) x 10-5 GeV-2 (5 ppm) FAST tm= 2.197 083 (32) (15) mse-Print: arXiv:0707.3904 [hep-ex]

38. MuLan Error Budget