Weak Structure of the Nucleon

1. From a few body physicist’s perspective Weak Structure of the Nucleon Doron Gazit Institute for Nuclear Theory University of Washington, Seattle.

2. Outline • Motivation. • Interaction of weak probes with nuclei. • Part I: Weak structure of the nucleon. • Part II: Some studies of weak interaction in light nuclei. • Application to astrophysics. • Summary and outlook. See S. Bacca’s talk Doron Gazit - The weak structure of the nucleon

3. Why is the weak structure of the nucleon interesting? • The response of anucleon to an external weak probe at low energy • Only the probe is perturbative. • One would like to constrain the non-perturbative response: • To study the fundamental theory • To acquire a predictive quality. Doron Gazit - The weak structure of the nucleon

4. A few body physicist’s perspective: • A precision era: • Available accurate ab-initio methods. • Consistent currents and potentials from cPT. • Allow parameter free calculations with sub-percentage accuracy, with nucleonicdof. Doron Gazit - The weak structure of the nucleon

5. Nuclear weak processes Lepton current Nuclear current Doron Gazit - The weak structure of the nucleon

6. Electroweak currents in the standard model • The standard model dictates the quark currents: • When sandwiched between nucleonic/nuclear states, the strong interaction induces form factors. • cPT offers a venue to characterize these form factors, at low energies. See J. S. Real’s talk Doron Gazit - The weak structure of the nucleon

7. cPT approach for low-energy EW nuclear reactions: Low energy EFT QCD Chiral Lagrangian Nuclear Hamiltonian Nöther current Wave functions Weak current Nuclear Matrix Element Doron Gazit - JLab Theory seminar

8. Forces in D-lesscPT See H. Krebs’ talk • The leading order NNN forces are at N2LO. • They include 2 new contact parameters. • No new parameters at N3LO. Weinberg, van Kolck, Ordonez, Meissner, Epelbaum, Nogga, Bernard, Kaiser, Krebs, Machleidt, Entem… Doron Gazit - The weak structure of the nucleon

9. D-lesscPT based weak currents to fourth order See T.-S. Park’s talk 1 pion exchange Single nucleon current Contact term Nucleon-pion interaction, NO new parameters Contact term Gårdestig, Phillips, Phys. Rev.Lett. 98, 232301 (2006); DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, 102502 (2009). Doron Gazit - The weak structure of the nucleon T.-S. Park et al, Phys. Rev. C 67, 055206 (2003); DG PhD thesis arXiv: 0807.0216

10. The Weak Structure of the nucleon Single nucleon current p' Second class currents Weak magnetism Induced scalar Vector p Induced Pseudoscalar Induced Pseudotensor Axial Weinberg Phys. Rev., 112, 1375 (1958) Doron Gazit - The weak structure of the nucleon

11. Second class currents • The quark currents have a specific behavior under G-parity Cexp(-iπT2). • Since isospin is not a symmetry of the strong force, induced second class currentsare allowed in nuclear reactions. • They are expected to be suppressed by a factor: • No experimental evidence for second class currents! Doron Gazit - The weak structure of the nucleon

12. Vector structure of the nucleon. Doron Gazit - The weak structure of the nucleon

13. Determination of Vector couplings • At zero momentum transfer: • The fact that FV is not renormalized at low energies, led to the Conserved Vector Current hypothesis. Doron Gazit - The weak structure of the nucleon

14. Conserved Vector Current (CVC) hypothesis • CVC hypothesizes: • The vector parts of the charge changing current and the isovector piece of the electromagnetic curret are three components of a vector in isospace. • All 3 components are conserved. • The vector and induced-weak-magnetic form factors are equal to their electromagnetic counter parts, including the momentum dependence. • The induced scalar form factor vanishes. • CVC implies that Siegert theorem holds for weak reactions. • An excellent approximation in the nuclear sector. • According to cPT, CVC holds to 2×10-4. Gerstein, Zeldovich, Sov. Phys. JETP 2, 576 (1956) Feynman, Gell Mann, Phys. Rev. 109, 193 (1958) Kaiser, Phys. Rev. C, 64, 028201 (2001) Doron Gazit - The weak structure of the nucleon

15. Tests of CVC – Nuclear b decay • 0+0+ • Only vector current contributes. • The nuclear matrix element: • Towner & Hardy define “nucleus independent” half-life: e ne Superallowed transitions Doron Gazit - The weak structure of the nucleon

16. Latest survey of superallowedb decays Miller & Schwenk, Phys. Rev. C 78, 035501 (2008). Hardy & Towner, Phys. Rev. C 79, 055502 (2009) Doron Gazit - The weak structure of the nucleon

17. Superallowed decay of 10C – an outstanding problem for few-body physics • “Needs” a nuclear correction of 0.72%. • T&H suggest 0.52±0.04%. • An existing NCSM calculation: (0+,1) (1.4645(19)%) 10C (0+,1) E*=1.7415 EB=15.6988(4) MeV (98.53(2)%) Caurieret al., Phys. Rev. C 66, 024314(2002) (1+,0) E*=0.71835 (3+,0) 10B EB=12.0507(4) MeV ft=3041.7±4.3 Doron Gazit - The weak structure of the nucleon

18. Axial structure of the nucleon Doron Gazit - The weak structure of the nucleon

19. Axial structure of the nucleon • Assuming no second class current. • The axial current is not conserved, even in the chiral limit. • Partial conservation of the axial current (PCAC): • The axial constant is renormalized, in a relativistic manner: See O. Zimmer and S. Ando’s talks Bernard, Elouadrhiri, Meissner, J. Phys. G: Nucl. Part. Phys. 28,R1 (2002). Doron Gazit - The weak structure of the nucleon

20. Lattice calculations of the axial constant Doron Gazit - The weak structure of the nucleon

21. Axial constant from AdS/QCD correspondence • One can asses the axial constant through AdS/QCD correspondence – using a conformal “cousin” theory of QCD which has a gravitational analogue in 5 dimensions. • A systematic way of including weak interactions into the AdS/QCD dictionary was recently proposed. • Using Sakai-Sugimoto model one gets a parameter free prediction: gA≅1.3. • Calculations of other weak form factors as well as nucleon forces are underway. DG, Yee, Phys. Lett. B670, 154 (2008). Doron Gazit - The weak structure of the nucleon

22. Axial current in nuclei • The axial current is not conserved! • Thus, its extension to nuclei is not trivial. Doron Gazit - The weak structure of the nucleon

23. A calculation of 3H b decay using cPT interaction and currents The calculation uses Idaho N3LO NN potential, Combined with N2LO NNN force. DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, 102502 (2009) Doron Gazit - The weak structure of the nucleon

24. Step 1: use the trinuclei binding energies to find a cD-cE relation Navratilet al., Phys. Rev. Lett. 99, 042501 (2007). Doron Gazit - The weak structure of the nucleon

25. Step 2: calibrate cD according to the triton half life. Doron Gazit - The weak structure of the nucleon

26. A prediction of 4He Doron Gazit - JLab Theory seminar

27. A closer look into the weak axial correlations in 3H • The NNN force has a negligible effect. • Specific character of the NN force has minor effect, as long asit is “state of the art” • Caliration of cD is robust – depends weakly on the force. • Is this the origin for the success of EFT*? NNN are not important??? Doron Gazit - The weak structure of the nucleon

28. Other checks Doron Gazit - The weak structure of the nucleon

29. EFT* approach for low-energy nuclear reactions: Low energy EFT QCD Phenom. Hamiltonian Chiral Lagrangian Nöther current Solution of Schrödinger equation Wave functions Weak current T.-S. Park et al, Phys. Rev. C 67, 055206 (2003), M. Rho nucl-th/061003; DG, NirBarnea, Phys. Rev. Lett. 98, 192501 (2007); O’Connor, DG et al. Phys. Rev. C (2008). PANIC08

30. Conclusions • Consistent calculations of weak and strong effects are possible. • The weak sensitivity of the weak decay to the NNN force make it an ideal candidate to constrain the NNN parameters. • The calibration of cD looks robust, whereas the value of cE will probably change when including 3NF N3LO potential. Now we’re ready to look at the axial constant evolution in nuclei. Doron Gazit - The weak structure of the nucleon

31. Surveys of β-decay rates of nuclei suggest that gA is gradually suppressed from ~1.27 to 1 (fully utilized A≅40). Quenching of gA in nuclear matter? b decay of 6He 0+1+: • gA(q0)=1 in the quark level. • gA(q0)=1.27 in the nucleon level. • gA(q0)1 inside nuclei??? Vaintraub, Barnea, DG, Phys. Rev. C, 79 065501 (2009). Doron Gazit - The weak structure of the nucleon

32. gA Quenching in nuclear matter • This is not surprising: • Axial current is not conserved. • Nucleons interact in nuclei. • However: • A VMC calculation of the β decay 6He(0+)6Li(1+) used AV18/UIX with phenomenological MEC and found: • Single nucleon GT strength overestimates by 4% the experimental strength. • Adding MEC worsens the discrepancy to 5.4%. • Are the VMC wave functions to blame? • Are the MEC to blame? • An exotic effect? Pervin et al., Phys. Rev. C76, 064319 (2007). Doron Gazit - The weak structure of the nucleon Schiavilla and Wiringa, Phys. Rev. C 65, 054302 (2002).

33. 6He b decay • We use the HH method to solve the 6 body problem, with JISP16 NN potential. • We use fourth order axial MEC calibrated in the triton. • Very rapid convergence: See A. Shirokov’s talk E∞(6He)=28.70(13) MeV Eexp(6He)=29.269 MeV E∞(6Li)=31.46(5) MeV Eexp(6Li)=31.995 MeV GT|LO=2.225(2) GT=2.198(2) Doron Gazit - The weak structure of the nucleon

34. 6He b decay • The contact interaction that does not exist in pheno. MEC, has a opposite sign with respect to the long range one. • The final GT is just 1.7% away from the experimental one! • MEC brings the theory closer to experiment! • No dependence on the cutoff! OPEC Contact |GT|JISP16(6He)=2.198(7) |GT|exp(6He)=2.161(5) Doron Gazit - The weak structure of the nucleon

35. 6He b decay and a hint to heavier nuclei • The inclusion of cPT based MEC is helpful, even when one uses phen. interaction. • The conclusion is that the weak correlations inside the nucleus can lead to the observed suppression. • RPA surveys of m capture showed that suppression is needed only in GT channel – consistent with MEC. • cPT estimation for the suppression of gA in infinite nuclear matter: • dgA/gA~+8% - +13% due to long range MEC. • dgA/gA~-28% due to contact interaction. • dgA/gA~-15% - -20% total. Zinner, Langanke, Vogel, Phys. Rev. C 74, 024326 (2006). Park, Jung, Min, Phys. Lett. B409, 26 (1997). Doron Gazit - The weak structure of the nucleon

36. Weak structure of the nucleon from m capture m capture on 3He DG, Phys. Lett. B666, 472 (2008). Doron Gazit - The weak structure of the nucleon

37. Induced Pseudoscalar • In QCD, the induced pseudoscalar form factor gP depends on the axial form factor. • Adler, Dothan and Wolfenstein: • HBcPT verified this result and connected it to QCD, as well as allowed corrections to the formula. • A comparison to experiment needs higher momentum than b decays – mcapture. Adler, Dothan, Phys. Rev. 151, 1257 (1966). Bernard, Kaiser, Meissner, Phys. Rev. D 50,6899 (1994), Kaiser, Phys. Rev. C 67, 027002 (2003). Doron Gazit - The weak structure of the nucleon

38. Ordinary muon capture • Since m is close to the atom so the capture probability is bigger: . • The rates become comparable for Z~10. • In proton, 0.16% branching ratio of OMC. m nm e Doron Gazit - The weak structure of the nucleon

39. RadiativeMuon Capture • The branching ration is very small (10-8 in hydrogen). nm g Doron Gazit - The weak structure of the nucleon

40. Muon capture on the proton • Due to the huge effects of the nuclear structure, studying the weak structure of the nucleon in muon capture processes has reduced to the proton. • Studies of OMC and RMC on hydrogen are hard: • Depend on the transition rate between ortho- and para-hydrogen. • Have small branching ratios. Doron Gazit - The weak structure of the nucleon

41. Induced pseudo scalar from m-p • The MuCap result:is consistent with cPT prediction:but with far bigger uncertainty. • The RMC result clearly deserves more work, though probably in the atomic side. • More information is needed from other nuclei. RMC: G. Jonkmans et al., Phys. Rev. Lett. 77, 4512 (1996) OMC: V. A. Andreev et al., Phys. Rev. Lett. 99, 0322002 (2007). Doron Gazit - The weak structure of the nucleon

42. OMC by 3He: 3He(m-,nm) 3H • For the (exclusive) process 3He(m-,nm) 3Han incredible measurement (0.3%) exists: • ab-initio calculations, based on phenomenological MEC or excitation: • Congleton and Truhlik [PRC, 53, 956 (1996)]: 150232 Hz. • Marcucci et. al. [PRC, 66, 054003(2002)]: 14844 Hz. • The main critique – too much freedom, without microscopic origin. • Did not include radiative corrections increase the cross section by 3.00.4%. Ackerbaueret al, Phys. Lett. B417, 224 (1998). Czarnecki, Marciano, Sirlin, Phys. Rev. Lett 99, 032003 (2007) Doron Gazit - The weak structure of the nucleon

43. OMC on 3He: 3He(m-,nm) 3H • Using the EIHH method to solve for the wave functions, with AV18/UIX potential: • Only free parameter calibrated using triton half-life. • To be compared with: • The dependence on the nuclear model is negligible. • The role of MEC ~ 12%! (compare to the 2% in triton b decay where it was calibrated). • This allows to constrain the weak structure of the nucleon. Doron Gazit - The weak structure of the nucleon

44. Resulting form factors: H. Shiomi, J. Korean Phys. Soc. 29 (1996) S378. Doron Gazit - The weak structure of the nucleon

45. Conclusions and Outlook • Few body nuclear physics acts as a pivot between QCD and heavy nuclei. • The current precision era in few-body nuclear physics provides an opportunity to study the weak structure of the nucleon: • Using precision measurements of weak interactions in nuclei one can constrain the bare form factors, as well as their “evolution” inside nuclei, without free parameters. • Constraints on strong properties are possible. • In particular, the upcoming MuSun measurement of m capture on the deutron will enable:to calibrate the 3NF at the 2-body level! Doron Gazit - The weak structure of the nucleon

46. Conclusions and Outlook • Going to heavier nuclei, mainly A=6-8 and A=10, within cPT, should be a holy grail, as it will open the door to new constraints of CVC and second class currents. • Microscopic understanding of weak reactions validates cross-sections predicted for astrophysics, which are out of reach experimentally. • Using AdS/QCD for the calculation of weak couplings of the nucleon seems like a good approximation! • Open questions: • Role of D excitations in weak reactions within cPT? • Role of a1? • How far can we go in momentum transfer within cPT? Doron Gazit - The weak structure of the nucleon

47. Doron Gazit - The weak structure of the nucleon

48. Precision era in few-body nuclear physics • Available methods for solving exactly the Schrödinger equation for few body systems, from their nucleonic degrees of freedom. • HH • NCSM • GFMC • FY • High precision nuclear interaction, phenomenological or cPT based. • Consistent microscopic approach for the construction of (meson exchange) currents in the nucleus. ab-initio calculations HBcPT • Allows parameter free calculations of nuclear wave functions and low-energy reaction rates, with sub-percentage accuracy. • Allows extraction of the weak structure of the nucleon from the strongly-correlated nuclear wave function. • Offers a hint on the in-medium evolution of the weak structure. Doron Gazit - The weak structure of the nucleon

49. The axial constant • Contrary to the vector coupling, the axial constant is renormalized. • Had the quarks were non-relativistic: • The deviation is a reflection of the relativistic dynamics of the u and d quarks in the nucleon. • Thus, its numerical calculation is a test for our understanding of QCD. • Still, experiment provides the most accurate result. See O. Zimmer and S. Ando’s talks Doron Gazit - The weak structure of the nucleon

50. Axial radius – cPT success I • At finite momentum: • From neutrino scattering: • From pion-electroproduction: • This axial radius discrepancy was solved in Baryon cPT, which allowed including finite pion mass in the pion-electroproduction. • The “radius” measured in pion-electroproduction: Bernard, Kaiser, Meissner, Phys. Rev. Lett. 691,877 (1992). Doron Gazit - The weak structure of the nucleon