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

2. 2 Muon Lifetime n Fundamental electro-weak couplings nGFnGF Implicit to all EW precision physics Uniquely defined by muon decay 9 ppm 0.0004 ppm 23 ppm G F  M Z QED MuLan q

3. 3 Dramatic Progress in QED Calc. Extraction of G F from   not theory limited MuLan 2004 MuLan Goal theory 17 ppm 18 ppm 90 ppb 30 ppm 9 ppm 18 ppm <0.3 ppm 0.5 ppm 1 ppm <0.3 ppm 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 total   from  m 2 MuLan Pak & Czarnecki (2008) -0.43 ppm reduction of   due to finite m e effect Experiments RAL, PSI

4. 4 PSI DC proton beam 590 MeV, 1.7 mA ~ 10 MHz  + Kicker On Fill Period Measurement Period time Number (log scale) -12.5 kV 12.5 kV Real data MuLan Experiment MuLan

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

6. 6 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 symmetric detector stray muons studied different targets MuLan yeartargetgeometryelectronicsbeamevents 2004 PRL 2007 Ferromag AK3 beam MWPC, He bag TDC2 MHz1.8 E10 2006AK3vacuum to target500 MHz WFD8 MHz~ 1 E12 2007Quartzvacuum to target500 MHz WFD8 MHz~ 0.3 E12 2004

7. 7 FAST Experiment Fast imaging target of 4x4x200 mm 3 scintillators, PSPMs Trigger: L1 selects , L2 selects  →  → 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  result ( with improved L2)

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

9. 9  Historical: V-A and  -e Universality  Today: EW current key probe for Understanding hadrons from fundamental QCD Symmetries of Standard Model Basic astrophysics reactions Muon Capture on the Proton charged current MuCap  - + p   + n Lattice Calculations Chiral Effective Theories

10. 10  Muon Capture  Formfactors Formfactors and g P MuCap  - + p   + n rate   S at q 2 = -0.88 m  2 Lorentz, T invariance + second class currents suppressed by isospin symm. apart from g P = 8.3 ± 50% All form factors precisely known from SM symmetries and data. CVC, n beta decay

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

12. 12 But  - is a heavy electron !  T = 12 s -1 pμ ↑↓ singlet (F=0)  S = 710 s -1 n+ triplet (F=1) μ pμ ↑↑ ppμ para (J=0)ortho (J=1) λ op  ortho =506 s -1  para =200 s -1 ppμ Interpretation requires knowledge of pp  population Strong dependence on hydrogen density  pp  P pp  O pp 100% LH 2 pp pp  P pp  O 1 % LH 2 time (  s)  λ pp  MuCap

13. 13 no overlap theory & OMC & RMC large uncertainty in OP  g P  50% ? no overlap theory & OMC & RMC large uncertainty in OP  g P  50% ? Precise Theory vs. Controversial Experiments ChPT OP (ms -1 ) gPgP  - + p   + n +  @ TRIUMF  Cap precision goal exp theory TRIUMF 2006  - + p   + n @ Saclay MuCap

14. 14 n Lifetime method 10 10  →e decays measure   to 10ppm,     S = 1/   - 1/    to 1%  n Unambiguous interpretation at low target density Clean  stop definition in active target (TPC) Ultra-pure gas system and purity monitoring at 10 ppb level n Isotopically pure “protium” MuCap Experimental Strategy fulfill all requirements simultaneously unique MuCap capabilities MuCap log(counts) t e -t  μ+μ+ μ –        S reduces lifetime by 10 -3  → e

15. 15 MuCap Detector MuCap

16. 16 3D tracking w/o material in fiducial volume Muons stop in active TPC target p -- Observed muon stopping distribution E e-e- 10 bar ultra-pure hydrogen, 1.16% LH 2 2.0 kV/cm drift field ~5.4 kV on 3.5 mm anode half gap bakeable glass/ceramic materials MuCap

17. 17 MuCap Unique Capabilities: Impurities Results n c N, c O < 5 ppb, c H2O ~ 8-30 ppb n correction based on observed capture yield Hardware Circulating Hydrogen Ultrahigh Purification System (CHUPS) Gas chromatography CRDF 2002, 2005 rare impurity capture  Z  (Z-1)+n+  Z (C, N, O) ~ (40-100) x  S ~10 ppb purity required Diagnostic in TPC Imp. Capture x z t CHUPS

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

19. 19 Muon Capture on the Deuteron The MuSun Experiment Muon Capture on the Deuteron The MuSun Experiment

20. 20 Motivation   + d  + n + n Rate  d from  d(  ) atom Measure  d to < 1.5 % n Simplest weak interaction process in a nucleus allowing for precise theory & experiment n Close relation to neutrino/astrophysics n Broader Impact on modern nuclear physics EFT relates  +d to strong processes like  +d   + n +n, a nn

21. 21  + d  + n + n Theory Axial current reaction Gamow-Teller 3 S 1  1 S 0 n one-body currents well defined n two-body currents not well constrained by theory (short distance physics) n Methods Potential model + MEC hybrid EFT Effective field theories model independent MEC L 1A, d R EFT    Low Energy Constants

22. 22 n Basic solar fusion reaction p + p  d + e + + n Key reactions for Sudbury Neutrino Observatory e + d  p + p + e - (CC) x + d  p + n + x (NC) n Intense theoretical studies, scarce direct data EFT connection to  +d capture via LEC L 1A, Muon capture soft enough to relate to solar reactions Connection to Neutrino/Astrophysics with L 1A ~ 6 fm 3

23. 23 Precise Experiment Needed Potential Model + MEC pionless, needs L 1A hybrid EFT consistent ChPT

24. 24 Muon Kinetics Collisional processes density  dependent, e.g. hfs transition rate from q to d state =  qd density  normalized to LH 2 density complicated, can one extract fundamental weak parameters ? Muon-catalyzed Fusion q d qd  d(  )  d(  ) dd   He

25. 25 Cryo-TPC Design

26. 26 Observables Observables in MuSun experiment decay electrons main observable fusion and capture essential as kinetics and background monitors Experience from MCF experiments  N capture 1.8 10 10 10 9 5 10 5

27. 27 Statistics + Systematics  d (Hz) -- Statistics3.4 Systematics3.3 ++ from MuLan0.455 total  d uncertainty 4.8 Hz 1.2 %  d 10 ppm  1.8  10 10 events Experiment approved PAC 2008

28. Summary and Outlook MuLan: First G F update in 23 years – 2.5x improvement, no surprise in result Factor 10 additional improvement on the way MuCap: First precise g P 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. 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/ Part of MuLan

31. 31 Quest for L 1A, d R Precision  +d experiment by far the best determination of L 1A in the theoretically clean 2-N system  “Calibrate the Sun”

32. 32 Bahcall & Pena-Garay 2004 v fluxes from experiments + Luminosity constraint Relevance of 7 Be exp. Relevance of pp experiment SSM correct at 1%,  Luminosity (steady state, other energy generation?) MSW-vacuum transition Improvement  12

33. 33 SNO assumes 1.1% uncertainty in  ( +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 physics should be updated e.g. SNO III:  (CC) from 6.3% to 4.0%  +d capture: calibration of fundamental reactions based on first principles Impact for Solar  and Physics A. B. Balantekin and H. Yuksel completely rests on hybrid EFT & 3-N

34. 34 Experimental Strategy Two main conditions Unambiguous physics interpretation Muon kinetics  optimization of D 2 conditions Very high precision  d to 1.2% (5 s -1 ) Statistics: several 10 10 events Systematics !

35. 35 Comments on Systematic Errors Source2004 (ppm)2006 Extinction Stability3.5Higher extinction beam tune detailed kicker measurements Errant Muon Stops2.0Replaced He bag with vacuum TDC Response1.0WFD Response Gain Stability1.8WFD, laser gain measurements Deadtime Correction2.0Scales as √(deadtime/stats) Duplicate Data1.0n/a (new electronics) Queuing Losses0.7n/a (new electronics) Multiple Hit Timing Shifts0.8Laser timing measurements Total Systematic5.2<1 ppm Statistics11.0~1.1 ppm

36. 36 QCD High q 2 (q > some GeV)short distance <0.1 fm Weakly interacting quarks and gluons asymptotic freedom Low q 2 (q 1 fm QCD has chiral symmetry spontaneously broken  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. 37 Constraining Short Distance Nuclear Physics g a axial current coupling to single-nucleon system axial current coupling to two-nucleon system Connection to N-  physics analogous to Goldberger-Treiman relation 1N sector Applications contribution to chiral 3N force from term determination reduces a nn uncertainty from theory  + d → n + n +  a nn  18.90 ± 0.27(exp) ± 0.30(th) fm future <0.05

38. 38 Experiment Overview Experiment Overview  PC  SC ePC2 ePC1 eSC Cryo-TPC e 

39. 39  + d Experiment Experimental Challenges Dalitz Plot Intensity at low E nn ChPT covers most of DP  EFT only p < 90 MeV/c  → e   = 455162 s -1  d q, d → n+n+ q ~ 10 s -1,  d = 400 s -1  d(  ) + d→  d(  ) + d dd  → 3 He + n +  rates ~    d  

40. 40 Cryo-TPC Design Criteria n Recombination n Drift Velocity n Equation of State n Specs

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

42. 42 Gas Purity Circulating Hydrogen Ultrahigh Purification System (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 – fusion for MuSun –  signal 1 MeV excellent TPC resolution full analog readout tags – p after capture – X-ray protium measurement Rare impurity capture:  d + Z  d +  Z  (Z-1)* + MuCap achieved: ~ 10 ppb purity and 0.1 ppb purity monitoring MuSun needs: ~ 1 ppb purity or 0.5 ppb purity monitoring (Z-1)* +

43. 43 Impurity detection Capture recoil 300-500 keV  (MuSun) =    (MuCap) Separate  N signal with Excellent energy resolution (30keV) Additional tag TPC signal topology Coincident X-ray, neutron  N capture, c N = 41 ppb p

44. 44 Muon Capture, Big Picture  + p  + d  + 3 He { g P, g A, ChPT } { g P, g A, ChPT, L 1A, a nn }{ g P, g A, hybrid EFT, L 1A, 3N} Final MuCap 2-3x improvement Combined analysis

45. 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 10 9 yr

46. 46 pp cycle

47. 47 Solar updates Borexino 2008 Kamland 2008

48. 48 CHUPS c N, c O < 5 ppb, c H2O ~ 8-30 ppb correction based on observed capture yield

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

50. 50 Solar Fusion and Neutrinos Basic solar fusion reaction p + p  d + e + + 1.4x10 10 yrs d + p  3 He +  6 s 3 He + 3 He  4 He + 2p 10 6 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 MuSun

51. 51 Time Spectra  -e impact parameter cut huge background suppression diffusion (deuterium) monitoring blinded master clock frequency variety of consistency checks 6 mm Inside TPC MuCap

52. 52 Theory and Sensitivities PCAC: q 2 =0 GT relation: g  NN (0) F  =M g A (0) q 2 <0g p (q 2 )= 2 m M/(m  2 -q 2 ) g A (0) g P =8.7 Sensitivity of capture rate: error from  V ud = 0.16 % assuming optimistic 20% g P error assuming g T <0.1

53. 53 Parameters

54. 54 Nucleon charged current at q 2 = - 0.88 m  2 J  = V  - A  V   g V (q 2 )   + ig M (q 2 )/2M   q  + g S (q 2 )/m q  A   g A (q 2 )     + g P (q 2 ) q  /m   + ig T (q 2 )/2M   q    Vector current in SM determined via CVC g V (0)=1, g(q 2 )=1+q 2 r 2 /6, r V 2 =0.59 fm 2 g M (0)=  p -  n -1=3.70589, r M 2 =0.80 fm 2 q 2 dependence from e scatt. Axial vector FF from experiment g A (0)=1.2670(35), r A 2 =0.42±0.04 fm 2 q 2 dependence from quasi-elastic scattering,  e-production 2 nd class FF g S, g T forbidden by G symmetry, e.g. g T /g A =-0.15 ±0.15 (exp), -0.0152 ±0.0053(QCD sum rule, up-down mass difference) error from  V ud = 0.16 % nucleon weak formfactors g V, g M, g A determined by SM symmetries and data contribute <0.4% uncertainty to  S g V = 0.9755(5) g M = 3.5821(25) g A = 1.245(3) remains g P = ?  Cap

55. 55 Results Directly from data c d = 1.49 ± 0.12 ppm AMS (2006) c d = 1.44 ± 0.15 ppm On-site isotopic purifier 2006 (PNPI, CRDF)  p + d   d + p (134 eV)  large diffusion range of  d < 1 ppm isotopic purity required MuCap Unique Capabilities:  p,  d diffusion Diagnostic: vs.  -e vertex cut AMS, ETH Zurich e-e- e-e- pp p dp d or to wall  -e impact par cut World Record c d < 0.1 ppm

56. 56 45 Years of Experiments to Determine g P  - + p   + n OMC BR~10 -3 8 experiments, typical precision 10-15%, Saclay 4%  - + p   + n +  RMC BR~10 -8, E>60 MeV  - + 3 He   + 3 H n Beta Decay Correlations … 279±25 events BR  (k>60MeV)=(2.10±0.21)x10 -8 Wright et al. (1998) authors  stat (s -1 ) comment theory 1993Congleton & Fearing13041B theory 1996Congleton & Truhlik1502±321B + 2B exp 1998Ackerbauer et al1496.0±4.0 3 He TPC theory 2002Marcucci et al.1484±81B+2B, T beta constraint rad. corrections?

57. 57    MuLan  = 2.197 013(21)(11)  s (11ppm)   ( World ) = 2.197 019(21)  s (9.6 ppm) G F = 1.166 371(6) x 10 -5 GeV -2 (5 ppm)    MuLan  = 2.197 013(21)(11)  s (11ppm)   ( World ) = 2.197 019(21)  s (9.6 ppm) G F = 1.166 371(6) x 10 -5 GeV -2 (5 ppm) arXiv:0704.1981v1 [hep-ex] MuLan 6/5/07 accepted PRL

58. 58 2007 2009 MuLan PRL 0.5 G F improvements over the years “Mu Law” MuLan on tape FAST submitted

59. 59 Note: Experimental limits on  (non SM) are largest uncertainty of Fermi constant 70 ppm uncertainty on G F Access to  through transverse polarization measurement of outgoing positron Danneberg et al, PRL 94 021802 (2005) G F depends on  Update Sept. 2005: New model-independent result for  PP P  Fetscher expt. PSI

60. 60 The pp-chain 99,77% p + p  d+ e + + e 0,23% p + e - + p  d + e 3 He+ 3 He  +2p 3 He+p  +e + + e ~2  10 -5 %84,7% 13,8% 0,02%13,78% 3 He + 4 He  7 Be +  7 Be + e -  7 Li + e 7 Be + p  8 B +  d + p  3 He +  7 Li + p ->  +  pp I pp III pp II hep hep 8 B  8 Be*+ e + + e 2 