The Weak Structure of the Nucleon from Muon Capture on 3He D. Gazit, Phys. Lett. B 666, 472 (2008). The Weak Structure of the Nucleon from Muon Capture on 3He Doron Gazit Institute for Nuclear Theory University of Washington

The decay of a muonic 3He: competition 3He(m-,nm) p+2n 10% 3He(m-,nm) 3H 70% 3He 3He(m-,nm) d+n 20% 3He p+2n The rates become comparable for Z~10. The Z4 law has deviations – mainly due to nuclear effects. In order to probe the weak structure of the nucleon, one has to keep the nuclear effects under control.

In other words… Solve the nuclear problem from the nucleonic degrees of freedom. However: This is possible only for light nuclei. The nuclear effects inside the nucleus are complicated – in particular the weak interaction of the muon with meson currents in the nucleus. However, a parameter free, percentage level accuracy calculation of the process is a great challenge to nuclear physics. The MuCap collaboration (PSI) measuring: For the (exclusive) process 3He(m-,nm) 3H an incredible measurement (0.3%): Expecting to achieve 1% accuracy. MuCap, Phys. Rev. Lett. 99, 032002 (2007). Ackerbauer et al, Phys. Lett. B417, 224 (1998).

Muon weak interaction with the nucleus Lepton current Nuclear current PANIC08

Previous calculations… Some calculations look at the nuclei as spin ½ doublet. However, too many free parameters. 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. The modern point of view – chiral perturbation approach, with nucleons and pions as explicit degrees of freedom – an effective theory for low energy QCD. PANIC08

cPT approach for low-energy nuclear reactions: Low energy EFT QCD The problem – for now: Nuclear potentials were developed only recently, and only to third order. Chiral Lagrangian Nuclear Hamiltonian + Solution of Schrödinger equation Nöther current Wave functions Weak current PANIC08

EFT* approach for low-energy nuclear reactions: Low energy EFT QCD Phenomenological Hamiltonian (with correct long-pion tail) Chiral Lagrangian Nöther current Solution of Schrödinger equation Wave functions Weak current PANIC08 T.-S. Park et al, Phys. Rev. C 67, 055206 (2003), M. Rho arXiv: nucl-th/061003.

The Nuclear Wave Functions Barnea, Leidemann, Orlandini, PRC, 63 057002 (2001); Nucl. Phys. A, 693 (2001) 565. The Nuclear Wave Functions Previous calculations [Marcucci et. al] showed no significance sensitivity to the nuclear potential [±2 Hz], as long as the energies are reproduced. Consistent cPT investigations show that the pion tail in the Hamiltonian is the important part, whereas short range correlations in the wave functions do not affect GT type of operators. [DG, Quaglioni, Navratil] We use: AV18+UIX, and solve using EIHH approach PANIC08

EFT* approach for low-energy nuclear reactions: Low energy EFT QCD Phenomenological Hamiltonian (with correct long-pion tail) Chiral Lagrangian Nöther current Solution of Schrödinger equation Wave functions Weak current PANIC08 T.-S. Park et al, Phys. Rev. C 67, 055206 (2003), M. Rho arXiv: nucl-th/061003.

cPT based weak currents to fourth order Single nucleon current Contact term 1 pion exchange No free parameters in the meson exchange currents – We can investigate the nucleon. Nucleon-pion interaction, NO free parameters Contact term: ONE free parameter. Calibrated using triton b decay PANIC08 T.-S. Park et al, Phys. Rev. C 67, 055206 (2003); DG PhD thesis arXiv: 0807.0216

Single Nucleon Currents p' q Vector Axial Magnetic Induced Pseudo-Scalar Second class currents p Weinberg Phys. Rev., 112, 1375 (1958)

Second class terms - G parity breaking G parity is the symmetry to a combined charge conjugation and rotation in isospin space: Due to the fact that isospin is an approximate symmetry, we expect a non vanishing result - Using QCD sum rules: Shiomi, J. Kor. Phys. Soc., 29, S378 (1996)

Conserved Vector Current Hypothesis The weak vector current is an isospin rotation of the electromagnetic current, and in particular conserved. So, if CVC holds then: PANIC08

Result ? PANIC08

Radiative corrections to the process Beta decay has prominent radiative corrections. Why not for muon capture? Czarnecki, Marciano, Sirlin, showed that radiative corrections increase the cross section by 3.00.4%. This worsens the good agreement of the old calculations. But… PANIC08 Czarnecki, Marciano, Sirlin, Phys. Rev. Lett 99, 032003 (2007)

Final result: PANIC08

Constraints on the weak structure of the nucleon PANIC08

Induced pseudo-scalar: From PT [Bernard, Kaiser, Meissner, PRD 50, 6899 (1994); Kaiser PRC 67, 027002 (2003)]: From muon capture on proton [Czarnecki, Marciano, Sirlin, PRL 99, 032003 (2007); V. A. Andreev et. al., PRL 99, 032004(2007)]: This work: PANIC08

Induced Tensor: From QCD sum rules: Experimentally [Wilkinson, Nucl. Instr. Phys. Res. A 455, 656 (2000)]: This work: PANIC08

Induced scalar (limits CVC): “Experimentally” [Severijns et. al., RMP 78, 991 (2006)]: This work: PANIC08

Final remark The current formalism correctly describes the weak process A great success to the theory – correct structure of currents The calculation is done without free parameters, thus - a prediction. A fully consistent cPT calculation, when possible, could: Decrease nuclear model dependence. Increase reliability. A more accurate estimate of radiative corrections is needed. PANIC08