1. A.Vorobyov on behalf of MuCap collaboration Determination of the nucleon’s pseudoscalar form factor in the MuCap experiment HSQCD 2014 Gatchina 30.06.2014

2. Overview Recent progress in studies of muon capture rates on proton, deuteron, and He3 made by the MuCap collaboration at PSI. First determination of the nucleon’s pseudoscalar form factor. Critical probe for Heavy Baryon Chiral Perturbation Theory. Determination of Low Energy Constants for Effective Field Theories of two and three nucleon systems

3. MuCap collaboration Petersburg Nuclear Physics Institute Paul Scherrer Institute, Switzerland University of Wasington, USA Regis University, USA University of Kentucky, USA Boston University, USA University of South Carolina, USA Université Catholique de Louvain, Belgium

4. 4 Muon Capture on Proton  - + p   + n Chiral Effective Theories

5. 5 Muon Capture on Proton  - + p   + n p n µ ν W

6. 6 Muon Capture on Proton  - + p   + n p n µ ν W

7.  - + p  µ + n  - + p  µ + n Muon Capture on Proton µ νµνµ pn W q c 2 = - 0.88 m µ 2 g v (q c 2 ) = 0.9755(5) values and q 2 dependence known from g M (q c 2 ) = 3.5821(25) EM form factors via CVC g A (q c 2 ) =1.251(4) g A (0)=1.2701(25) from neutron β-decay, g P (expt) = ? q 2 dependence from neutrino scattering ( ( µp-capture offers a unique way to determine g P (q c 2 )

8. Theoretical predictions for g P n  p --  g  NN FF Partial conservation of axial current (PCAC) Heavy Baryon chiral perturbation theory (ChPT) W g P (q c 2 ) = (8.74  0.23 ) – (0.48  0.02) = 8.26  0.23 PCAC pole term ChPT leading order one loop two-loop <1% Recent reviews: V. Bernard et al., Nucl. Part. Phys. 28 (2002), R1 T. Gorringe, H. Fearing, Rev. Mod. Physics 76 (2004) 31

9. 45 years of Efforts to Determine g P 9 “ Radiative muon capture in hydrogen was carried out only recently with the result that the derived g P was almost 50% too high. If this result is correct, it would be a sign of new physics... ’’ — Lincoln Wolfenstein (Ann.Rev.Nucl.Part.Sci. 2003) OMC RMC  - + p  n + + 

10. Emilio Zavattini 1927-2007 1969 Bologna-Pisa-CERN 1973 Dubna group H2 –target 8 atm Pioneers of muon capture experiments g P = 12 ± 5 g P = 9 ± 7 H2 –target 41 atm

11. Status of µp-capture experiments YearExptl.placeH 2 target Λ C, s -1 Method 1962 *) 1962 1963 1969 1974 1981 Chicago Columbia CERN Columbia CERN Dubna Saclay liquid gas, 8 atm gas, 41 atm liquid 428 ± 85 515 ± 85 450 ± 50 464 ± 42 651 ± 57 686 ± 88 460 ± 20 neutron detection - " – - " - Life time measurement  - + p  µ + n Br=0.16% Two experimental methods to measure Λ C *) First direct observation of µp-capture Neutron detectionLife time measurement Λ C = 1/τ µ+ - 1/τ µ- Λ C Nn/Nµ µ ± p → e ± ν e ν µ CPT inv

12.  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  λ pp  From which muonic state the muon capture occurs ?

13. Pµ - PPµ(ortho) - PPµ(para) population pp  P pp  O pp 100% LH 2 pp pp  P pp  O 1 % LH 2 time (  s)

14. Precise Theory vs. of Exp. Efforts ChPT OP (ms -1 ) gPgP  - + p   + n +  @ TRIUMF 1996 theory  - + p   + n @ Saclay 1981 g P = 12 ± 5 H2 –target 8 atm 1969 exp1 exp2

15. Main requirements The H2 gas pressure should not exceed 10 bar to provide dominant (µ - p) 1S state. The muon capture rate Λs in the reaction  - + p  (µ - p) 1S → µ + n BR=0.16% should be measured to 1% precision To reach such precision, one should measure the µ - life time in hydrogen with 10 -5 precision. ΛSΛS

16. Theory predicts g P with ~ 3% precision Uncertainties in other form factors set the limit : =0.45% or =3% To approach this limit, one should measure Λ S with ~0.5% precision Sensitivity of Λ S to form factors Contributes 0.45% uncertainty to measured  S Examples: 10% 56% 1.0% 6.1% 0.5% 3.8%

17. High precision muon capture experiments based on New experimental method developed at PNPI Unique muon channel at PSI MuCap setup PSI meson factory

18. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S

19. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S Lifetime method Λ S = 1/τ µ+ - 1/τ µ- 10 -5 precision both in µ - and µ+ life times→ δΛ S /Λ S = 1%

20. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S Lifetime method Λ S = 1/τ µ+ - 1/τ µ- 10 -5 precision both in µ - and µ+ life times→ δΛ S /Λ S = 1% >10 10 muon decay events High data taking rate

21. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S Lifetime method Λ S = 1/τ µ+ - 1/τ µ- 10 -5 precision both in µ - and µ+ life times→ δΛ S /Λ S = 1% >10 10 muon decay events High data taking rate Clean muon stop selectionNo wall effects

22. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S Lifetime method Λ S = 1/τ µ+ - 1/τ µ- 10 -5 precision both in µ - and µ+ life times→ δΛ S /Λ S = 1% >10 10 muon decay events High data taking rate Clean muon stop selectionNo wall effects Low background< 10 -4

23. Strategy of MuCap experiment H2 gas target at 10 atm (µ - p) 1S Lifetime method Λ S = 1/τ µ+ - 1/τ µ- 10 -5 precision both in µ - and µ+ life times→ δΛ S /Λ S = 1% >10 10 muon decay events High data taking rate Ultra clean protium impurities with Z>1 less than 10 ppb (1 ppb = 10 -9 ) deuterium concentration less than 100 ppb Clean muon stop selectionNo wall effects Low background< 10 -4

24. …………………...... E - 40kV µ G +5kV G Time projection chamber, TPC z Y x Cathode strips Anode wires 3D detection of muon track X- cathode strips Y- drift time Z- anode wires y x z Sensitive volume 15 x 12 x 28 cm 3 Muon stop selection inside the sensitive volume far enough from all chamber materials H2 gas 10 atm room temperature

25. …………………...... E 40kV µ G 5kV G Cathode strips Anode wires e ePC1 ePC2 eSC hodoscope µSC e-µ space correlation reduces background tµ = t eSC – t µSC µPC

28. Cryogenic circulation-purification hydrogen gas system N 2 less than 10 ppb O 2 less than 10 ppb Gas purification system TPC provides control for impurities on a level of 10 ppb

29. Isotopic purity of protium Deuterium concentration in hydrogen gas Natural gas 140 ppm Best on market 2 ppm Produced at PNPI for MuCap ≤ 6 ppb Cryogenic isotopic exchange column Accelerator mass spectrometry at ETH in Zurich Reached sensitivity 6 ppb

30. PSI muon channel can provide ~ 70 kHz muons MuCap could use only ~ 7kHz (to prevent pile up) New beam system (Muon-on-demand) constructed in 2005 allowed to increase the usable beam intensity up to 20 kHz -- +12.5 kV -12.5 kV Kicker Plates 50 ns switching time  detector TPC ~3 times higher rate Data taking rate Muon-on demand system run2006 10 000 hrs of beam time

31. µ e Reduction of background by µ-e vertex cut The impact cut can reduce the background to a level of 10 -4 -10 -5

32. Determination of  S 32 molecular formation bound state effect MuCap: precision measurement MuLan

33. Final result λµ– = 455854.6 ± 5.4stat ± 5.1syst s -1 (MuCap) λµ+ = 455170.05 ± 0.46 s -1 (μLAN experiment), Λ S MuCap = 714.9 ± 5.4stat ± 5.1syst s -1. MuCap collaboration, Phys. Rev. Lett. 110, 022504 (2013). *) Based on updated calculations of Λs from A. Czarnecki, W.J. Marciano, A. Sirlin, Phys. Rev. Lett., 99, 032003 (2007) g P MuCap (q c 2 ) = 8.06 ±0.48±0.28 *) g P HBCPT = 8.26  0.23 V. Bernard, L. Elouadrhiri, and U.-G. Meissner, J. Phys.G28, R1 (2002).

34. 34 g P (theory) = 8.26 ± 0.23 g P (MuCap) = 8.06 ± 0.55 The MuCap result does not depend on molecular OP-transitions

35. Axial Vector g A 35 PDG 2008 g A (0)= 1.2695±0.0029 PDG 2012 g A (0)= 1.2701 ±0.0025 Future ? g A (0)= 1.273 ? In this case g P MuCap = 8.24±0.55 g P Theory = 8.26±0.23 A. Garcia PDG12

36. Synopsis: Sizing Up Quark Interactions Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling gP V. A. Andreev et al. (MuCap Collaboration) Phys. Rev. Lett. 110, 012504 (2013) Published January 3, 2013 Even though the radioactive decay of nuclei is mainly driven by the weak force, interactions between the quarks that make up the protons and neutrons in the nucleus can also affect the process. Calculating these effects with quantum chromodynamics (QCD), the theory describing the strong force interactions between quarks, is, however, mathematically cumbersome at the low energies associated with the nucleus. Instead, calculations are more tractable using an effective QCD theory, in which interactions are between bound quarks (mesons, protons and neutrons). Now, researchers running the muon capture (MuCap) experiment at the Paul Scherrer Institute in Switzerland have confirmed a long-standing prediction of the theory, known as chiral perturbation theory, boosting confidence that it can be used to accurately describe quark interactions in simple nuclei. Muon capture is like a beta-decay process run in reverse: a muon (a particle with the same charge as an electron, but 200 times the mass) interacts with a proton to produce a neutron and a neutrino. Among other factors, a dimensionless quantity called the “pseudoscalar coupling,” determines the rate of the reaction. Chiral perturbation theory says the coupling factor has a value of Gp, without a lot of wiggle room. But experimental data going back to the 1960s have shown the coupling could be anywhere between and. The MuCap collaboration, which measures the rate of the muon capture process by stopping a beam of muons in a low-density gas of pure hydrogen, has analyzed 30 terabytes of data to extract the pseudoscalar coupling with unprecedented precision. The value of their result, reported in Physical Review Letters, is 8.06+/-0.55 —in excellent agreement with the theoretical prediction. – Jessica Thomas PHYSICS spotlighting exceptional research American Physical Society

37. Muon capture rates on deuteron and He3

38. 38 Quest for “unknown” Axial LEC LEC - low energy constants in Effective Field Theories  2-body system –1 LEC to be determined from µd capture –experimental information scarce: ~100% uncertainty –Measurement of µd capture rate to 1% precision will –Measurement of µd capture rate to 1% precision will reduce uncertainty to ~15%  3-body system –2 LECs and additional complexity enter –tritium beta decay –Muon capture on He3 potential current

39.  + d  n + n +  + d  n + n + model-independent connection via EFT & L 1A “MuSun” Next experiment Mesurement of muon capture rate with 1% precision  basic solar fusion reaction p + p  d + e + + key reactions for SNO + d  p + p + e - (CC) + d  p + n + (NC) MEC EFT L 1A

40. 40 Precise Experiment Needed

41. Muon Capture on He-3 µ - + 3 He → 3 H + ν µ E t = 1.9 MeV This capture rate was measured in MuCap experiment with 0.3 % precision Λ stat = 1496 ± 4 s -1 Physics Letters B417,224 (1998) The world precision was improved by a factor of 50 Since then, this result was a subject of various analyses with the goal to obtain the value of g p

42.  + 3 He → 3 H + MuCap: 1496±4 /s (0.3%) Pisa-JLab theory: 1494±21 /s  g P (q c 2 )=8.2±0.7   He capture 42

43. Conclusions The MuCap experiment is able to perform measurements of muon capture rates on proton and light nuclei on unprecedented level of precision. This allowed for the first time to measure with high precision the nucleon’s pseudoscalar form factor, thus providing a critical probe of the Heavy Baryon Chyral Perturbation Theory. The precision measurements of µd and µHe3 capture rates will allow to fix the Low Energy Constants in the Effective Field Theories of light nuclei.