Measurements and Experiments in Muon Physics

1. Muon Lifetime Programme at PSI Fundamental Constants MuLan FAST Peter Kammel Basic QCD Symmetries “Calibrating the Sun” MuSun MuCap

2. MuLan Muon Lifetime • Fundamental electro-weak couplings • GF • Implicit to all EW precision physics • Uniquely defined by muon decay GFaMZ 9 ppm 0.0004 ppm 23 ppm q QED

3. MuLan Dramatic Progress in QED Calc. • Extraction of GF from tm not theory limited total MuLan2004 theory 17 ppm 18 ppm 90 ppb 30 ppm 9 ppm 18 ppm <0.3 ppm 0.5 ppm 1 ppm <0.3 ppm van Ritbergen and Stuart: 2-loop QED corrections MuLan Goal ExperimentsRAL, PSI dnm from dm2 Pak & Czarnecki (2008) -0.43 ppm reduction of tmdue to finite me effect

4. MuLan MuLan Experiment Real data Kicker On PSI DC proton beam590 MeV, 1.7 mA ~ 10 MHz m+ Measurement Period Number (log scale) time Fill Period -12.5 kV 12.5 kV

5. MuLan MuLan detector has 30 active “houses”, with 170 tile pairs e+ 80 pe/mip

6. MuLan Statistics & Systematics “Early-to-late” changes • Instrumental shifts Gain or threshold Time response Kicker and accidentals • Effective acceptance Residual polarization or precession • Pileup leads to missed events 2004 symmetric detector stray muons studied different targets

7. FAST Experiment • Fast imaging target of 4x4x200 mm3 scintillators, PSPMs • Trigger: L1 selects p, L2 selects p → m→ e decay chain • Essentially many small decay detectors in parallel • Proof-of-principle measurement 16 ppm published 2008, 30 kHz L2 • One year run in 2008 to obtain 2 ppm t result (with improved L2)

8. ±1 ppm  10 New World Situation GF = 1.166367(5) x 10-5 GeV-2(4.1 ppm)

9. MuCap Muon Capture on the Proton • 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 Lattice CalculationsChiral Effective Theories

10. MuCap Formfactors and gP - + p  m+ n rateLSat q2= -0.88 mm2 • Muon Capture • Formfactors + second class currentssuppressed by isospin symm. Lorentz, T invariance All form factors precisely known fromSM symmetries and data. CVC, n beta decay apart from gP = 8.3 ± 50%

11. MuCap Pseudoscalar Form Factor gP gP determined by chiral symmetry of QCD: gP = (8.74  0.23) – (0.48  0.02) = 8.26  0.23 ChPT leading order one loop two-loop <1% • gP basic and experimentally least known nucleon form factor • solid QCD prediction (2-3% level) • basic test of QCD symmetries T. Gorringe, H. Fearing, Rev. Mod. Physics 76 (2004) 31V. Bernard et al., Nucl. Part. Phys. 28 (2002), R1

12. 1 % LH2 100% LH2 pm ppμ ppmO ppμ pm ppmO ppmP ppmP time (ms) But m- is a heavy electron ! 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 MuCap

13. Precise Theory vs. Controversial Experiments 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

14. MuCap MuCap Experimental Strategy • Lifetime method • 1010m→enn decays • measure - to 10ppm, • S = 1/- - 1/+to 1% • Unambiguous interpretation at low target density • Clean m stop definition in active target (TPC) • 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 fulfill all requirements simultaneouslyunique MuCap capabilities

15. MuCap MuCap Detector

16. MuCap 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 materials Observed muon stopping distribution E p e- 3D tracking w/o material in fiducial volume

17. Results cN, cO < 5 ppb, cH2O~ 8-30 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 Circulating Hydrogen Ultrahigh Purification System(CHUPS) Gas chromatographyCRDF 2002, 2005 CHUPS Diagnostic in TPC

18. MuCap gP Landscape after MuCap 07 SMuCap = 725.0  13.7stat 10.7sys s-1 Czarnecki, Marciano,Sirlin , PRL 99 (2007) MuCap, PRL 99, 032001 (2007) - + p  m + n + g gP = 7.3 ± 1.1

19. Muon Capture on the DeuteronThe MuSun Experiment

20. Motivation • m- + d  n + n + nRateLd from md() atom • MeasureLdto < 1.5 % • Simplest weak interaction process in a nucleusallowing for precise theory & experiment • Close relation to neutrino/astrophysics • Broader Impact on modern nuclear physics • EFT relates m+d to strong processes like p+d  g + n +n, ann

21. m + d  n + n + nTheory • Axial current reaction • Gamow-Teller 3S1 1S0 • one-body currents well defined • two-body currents not well constrained by theory (short distance physics) • Methods • Potential model + MEC • hybrid EFT • Effective field theories model independent D p MEC EFT  L1A, dR Low Energy Constants

22. Connection to Neutrino/Astrophysics • Basic solar fusion reaction • p + p  d + e+ +  • Key reactions for Sudbury Neutrino Observatory • e + d  p + p + e- (CC) • x + d  p + n + x (NC) • Intense theoretical studies, scarce direct data • EFT connection to m+d capture via LEC L1A, • Muon capture soft enough to relate to solar reactions with L1A ~ 6 fm3

23. Precise Experiment Needed consistent ChPT pionless, needs L1A hybrid EFT Potential Model + MEC

24. Muon Kinetics Collisional processes density f dependent, e.g. hfs transition rate from q to d state = flqd densityf normalized to LH2 density Muon-catalyzed Fusion lq lqd ld md() md md() m3He complicated, can one extract fundamental weak parameters ?

25. Cryo-TPC Design

26. Observables • Observables in MuSun experiment • decay electrons main observable • fusion and capture essential as kinetics and background monitors Experience from MCF experiments mN capture 1.8 1010 109 5 105

27. Statistics + Systematics 1.81010 events Experiment approved PAC 2008

28. Summary and Outlook • MuLan: • First GF update in 23 years – 2.5x improvement, no surprise in result • Factor 10 additional improvement on the way • MuCap: • First precise gP with clear interpretation • Consistent with ChPT expectation, clarifies long-standing puzzle • Factor 3 additional improvement on the way • MuSun • Muon-deuteron capture with 10x higher precision • Calibrates basic astrophysics reactions and provides new benchmark in axial 2N reactions

29. Part of MuLan http://www.npl.uiuc.edu/exp/mucapture/ http://www.npl.uiuc.edu/exp/mulan/ http://www.npl.uiuc.edu/exp/musun/ Part of MuCap http://fast.home.cern.ch/fast/

31.  Quest for L1A, dR “Calibrate the Sun” • Precision m+d experiment • by far the best determination • of L1A in the theoretically clean • 2-N system

32. Bahcall & Pena-Garay 2004 • v fluxes from experiments + Luminosity constraint • Relevance of 7Be exp. • Relevance of pp experiment • SSM correct at 1%, n/g Luminosity(steady state, other energy generation?) • MSW-vacuum transition • Improvement q12

33. Impact for Solarand n Physics • SNO assumes 1.1% uncertainty in s(n+d)but Truhlik, Vogel et al. estimate 2-3% model dependence • SSM assumes 0.4% uncertainty in pp S-factor • Impact for both solar and n physics should be updatede.g. SNO III: Df(CC) from 6.3% to 4.0% • m+d capture: calibration of fundamental reactions based on first principles completely rests on hybrid EFT & 3-N A. B. Balantekin and H. Yuksel

34. Experimental Strategy • Two main conditions • Unambiguous physics interpretation • Muon kinetics  optimization of D2 conditions • Very high precision Ld to 1.2% (5 s-1) • Statistics: several 1010 events • Systematics !

35. Comments on Systematic Errors

36. 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 Edwards et al. LHPC Coll (2006) MuCap

37. Constraining Short Distance Nuclear Physics • ga axial current coupling to single-nucleon system • axial current coupling to two-nucleon system • Connection to N-p physics analogous to Goldberger-Treiman relation 1N sector • Applications • contribution to chiral 3N force from term • determination reduces ann uncertainty from theory • p + d → n + n + g ann= 18.90 ± 0.27(exp) ± 0.30(th) fm • future <0.05

38. Experiment Overview e eSC ePC2 ePC1 mPC Cryo-TPC m mSC

39. m + d Experiment m   d • Experimental Challenges • Dalitz Plot • Intensity at low Enn • ChPT covers most of DP • pEFT only pn< 90 MeV/c m → enn lm= 455162 s-1 mdq,d → n+n+nLq ~ 10 s-1, Ld = 400 s-1md() + d→ md() + dddm→ 3He + n + mrates ~ lm

40. Cryo-TPC Design Criteria

41. Technical Design Cryo-System Vibration free cooling Continuous cleaning

42. Gas Purity (Z-1)* + n • CirculatingHydrogenUltrahighPurificationSystem(CHUPS) • US CRDF 2002, 2005 • New: • cryo-TPC • cryo filter before TPC • continuous getter in gas flow for gas chromatography • Particle detection in TPC • much harder – fusionfor MuSun – m signal 1 MeV • excellent TPC resolution • full analog readout • tags – p after capture • – X-ray • protium measurement Rare impurity capture:md + Z d + mZ  (Z-1)* + n MuCap achieved: ~ 10 ppb purity and 0.1 ppb purity monitoring MuSun needs: ~ 1 ppb purity or 0.5 ppb purity monitoring

43. Impurity detection • Capture recoil 300-500 keV • f (MuSun) = 5 f (MuCap) • Separate mN signal with • Excellent energy resolution(30keV) • Additional tag • TPC signal topology • Coincident X-ray, neutron mN capture, cN = 41 ppb p

44. Muon Capture, Big Picture { gP, gA, ChPT } m + p m + d m + 3He { gP, gA, ChPT, L1A, ann } { gP, gA, hybrid EFT, L1A, 3N} Final MuCap 2-3x improvement Combinedanalysis

45. Solar • Sun Facts • Solar radius = 695,990 km = 109 Earth radii • Solar mass = 1.989 1030 kg = 333,000 Earth masses • Solar luminosity (energy output of the Sun) = 3.846 1033 erg/s • Surface temperature = 5770 K = 9,930º F • Surface density = 2.07 10-7 g/cm3 = 1.6 10-4 Air density • Surface composition = 70% H, 28% He, 2% (C, N, O, ...) by mass • Central temperature = 15,600,000 K = 28,000,000º F • Central density = 150 g/cm3 = 8 × Gold density • Central composition = 35% H, 63% He, 2% (C, N, O, ...) by mass • Solar age = 4.57 109 yr  

46. pp cycle

47. Solar n updates • Borexino 2008 • Kamland 2008

48. CHUPS cN, cO < 5 ppb, cH2O~ 8-30 ppb correction based on observed capture yield

49. 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%): gP = 7.3 ± 1.1 (MuCap 2007)

50. MuSun Solar Fusion and Neutrinos • Basic solar fusion reaction • p + p  d + e+ +  1.4x1010 yrs • d + p  3He + g 6 s • 3He + 3He  4He + 2p 106 yrs • Key reactions for Sudbury Neutrino Observatory • e + d  p + p + e- (CC) •  + d  p + n +  (NC) Solar neutrino problem solved by neutrino oscillation Intense theoretical studies, Very limited direct experimental info