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

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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. August 2009 Doron Gazit - The weak structure of the nucleon2 See S. Bacca’s talk

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August 2009 Doron Gazit - The weak structure of the nucleon3 The response of a nucleon 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.

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August 2009 Doron Gazit - The weak structure of the nucleon4 The response of a nucleon 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.

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August 2009 Doron Gazit - The weak structure of the nucleon5 A precision era: ◦ Available accurate ab-initio methods. ◦ Consistent currents and potentials from PT. ◦ Allow parameter free calculations with sub- percentage accuracy, with nucleonic dof.

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6 Nuclear current Lepton current August 2009 Doron Gazit - The weak structure of the nucleon

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The standard model dictates the quark currents: When sandwiched between nucleonic/nuclear states, the strong interaction induces form factors. PT offers a venue to characterize these form factors, at low energies. August 2009 Doron Gazit - The weak structure of the nucleon7 See J. S. Real’s talk

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PT approach for low-energy EW nuclear reactions: Weak current Chiral Lagrangian QCD Low energy EFT Nöther current Wave functions Wave functions Nuclear Hamiltonian Nuclear Matrix Element 8Doron Gazit - JLab Theory seminar

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The leading order NNN forces are at N 2 LO. They include 2 new contact parameters. No new parameters at N 3 LO. August 2009 Doron Gazit - The weak structure of the nucleon9 Weinberg, van Kolck, Ordonez, Meissner, Epelbaum, Nogga, Bernard, Kaiser, Krebs, Machleidt, Entem… See H. Krebs’ talk

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August 2009 Doron Gazit - The weak structure of the nucleon10 Contact term 1 pion exchange Nucleon-pion interaction, NO new parameters T.-S. Park et al, Phys. Rev. C 67, 055206 (2003); DG PhD thesis arXiv: 0807.0216 Contact term Single nucleon current Gårdestig, Phillips, Phys. Rev. Lett. 98, 232301 (2006); DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, 102502 (2009). See T.-S. Park’s talk

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11 Vector Axial Weak magnetism Induced Pseudoscalar Second class currents Weinberg Phys. Rev., 112, 1375 (1958) p' p Induced scalar Induced Pseudotensor August 2009 Doron Gazit - The weak structure of the nucleon

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The quark currents have a specific behavior under G-parity Cexp(-iπT 2 ). Since isospin is not a symmetry of the strong force, induced second class currents are allowed in nuclear reactions. They are expected to be suppressed by a factor: No experimental evidence for second class currents! August 2009 Doron Gazit - The weak structure of the nucleon12

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August 2009 Doron Gazit - The weak structure of the nucleon13

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At zero momentum transfer: The fact that F V is not renormalized at low energies, led to the Conserved Vector Current hypothesis. August 2009 Doron Gazit - The weak structure of the nucleon14

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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 PT, CVC holds to 2×10 -4. August 2009 Doron Gazit - The weak structure of the nucleon15 Gerstein, Zeldovich, Sov. Phys. JETP 2, 576 (1956) Feynman, Gell Mann, Phys. Rev. 109, 193 (1958) Gerstein, Zeldovich, Sov. Phys. JETP 2, 576 (1956) Feynman, Gell Mann, Phys. Rev. 109, 193 (1958) Kaiser, Phys. Rev. C, 64, 028201 (2001)

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Superallowed transitions 0+0+0+0+ Only vector current contributes. The nuclear matrix element: Towner & Hardy define “nucleus independent” half-life: August 2009 Doron Gazit - The weak structure of the nucleon16 e e

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August 2009 Doron Gazit - The weak structure of the nucleon17 Hardy & Towner, Phys. Rev. C 79, 055502 (2009) Miller & Schwenk, Phys. Rev. C 78, 035501 (2008).

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“Needs” a nuclear correction of 0.72%. T&H suggest 0.52±0.04%. An existing NCSM calculation: August 2009 Doron Gazit - The weak structure of the nucleon18 10 C 10 B E B =12.0507(4) MeV E B =15.6988(4) MeV ft=3041.7±4.3 (98.53(2)%) (1.4645(19)%) Caurier et al., Phys. Rev. C 66, 024314(2002) (0 +,1) (0 +,1) E*=1.7415 (1 +,0) E*=0.71835 (3 +,0)

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August 2009 Doron Gazit - The weak structure of the nucleon19

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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: August 2009 Doron Gazit - The weak structure of the nucleon20 Bernard, Elouadrhiri, Meissner, J. Phys. G: Nucl. Part. Phys. 28, R1 (2002). See O. Zimmer and S. Ando’s talks

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August 2009 Doron Gazit - The weak structure of the nucleon21

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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: g A ≅ 1.3. Calculations of other weak form factors as well as nucleon forces are underway. August 2009 Doron Gazit - The weak structure of the nucleon22 DG, Yee, Phys. Lett. B670, 154 (2008).

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The axial current is not conserved! Thus, its extension to nuclei is not trivial. August 2009 Doron Gazit - The weak structure of the nucleon23

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DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, 102502 (2009) August 2009 Doron Gazit - The weak structure of the nucleon24 The calculation uses Idaho N 3 LO NN potential, Combined with N 2 LO NNN force.

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August 2009 Doron Gazit - The weak structure of the nucleon25 Navratil et al., Phys. Rev. Lett. 99, 042501 (2007).

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August 2009 Doron Gazit - The weak structure of the nucleon26

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Doron Gazit - JLab Theory seminar27

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August 2009 Doron Gazit - The weak structure of the nucleon28 MEC – a 2% effect on the matrix element Without the contact interaction - a disaster NNN are not important??? Specific character of the force has minor effect Caliration of c D is robust – depends weakly on the force. Is this the origin for the success of EFT*? Specific character of the force has minor effect Caliration of c D is robust – depends weakly on the force. Is this the origin for the success of EFT*?

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August 2009 Doron Gazit - The weak structure of the nucleon29 NNN are not important??? The NNN force has a negligible effect. Specific character of the NN force has minor effect, as long as it is “state of the art” Caliration of c D is robust – depends weakly on the force. Is this the origin for the success of EFT*? The NNN force has a negligible effect. Specific character of the NN force has minor effect, as long as it is “state of the art” Caliration of c D is robust – depends weakly on the force. Is this the origin for the success of EFT*?

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August 2009 Doron Gazit - The weak structure of the nucleon30

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PANIC0831 EFT* approach for low-energy nuclear reactions: Weak current Chiral Lagrangian QCD Low energy EFT Nöther current Wave functions Phenom. Hamiltonian Solution of Schrödinger equation T.-S. Park et al, Phys. Rev. C 67, 055206 (2003), M. Rho nucl-th/061003; DG, Nir Barnea, Phys. Rev. Lett. 98, 192501 (2007); O’Connor, DG et al. Phys. Rev. C (2008).

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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 c D looks robust, whereas the value of c E will probably change when including 3NF N 3 LO potential. Now we’re ready to look at the axial constant evolution in nuclei. August 2009 Doron Gazit - The weak structure of the nucleon32

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decay of 6 He August 2009 Doron Gazit - The weak structure of the nucleon33 Vaintraub, Barnea, DG, Phys. Rev. C, 79 065501 (2009). Surveys of β-decay rates of nuclei suggest that g A is gradually suppressed from ~1.27 to 1 (fully utilized A ≅ 40). Surveys of β-decay rates of nuclei suggest that g A is gradually suppressed from ~1.27 to 1 (fully utilized A ≅ 40). 0+1+:0+1+: g A (q 0)=1 in the quark level. g A (q 0)=1.27 in the nucleon level. g A (q 0) 1 inside nuclei???

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This is not surprising: ◦ Axial current is not conserved. ◦ Nucleons interact in nuclei. However: ◦ A VMC calculation of the β decay 6 He(0 + ) 6 Li(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? August 2009 Doron Gazit - The weak structure of the nucleon34 Schiavilla and Wiringa, Phys. Rev. C 65, 054302 (2002). Pervin et al., Phys. Rev. C 76, 064319 (2007).

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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: August 2009 Doron Gazit - The weak structure of the nucleon35 See A. Shirokov’s talk E ∞ ( 6 He)=28.70(13) MeV E exp ( 6 He)=29.269 MeV E ∞ ( 6 He)=28.70(13) MeV E exp ( 6 He)=29.269 MeV E ∞ ( 6 Li)=31.46(5) MeV E exp ( 6 Li)=31.995 MeV E ∞ ( 6 Li)=31.46(5) MeV E exp ( 6 Li)=31.995 MeV GT| LO =2.225(2) GT=2.198(2) GT| LO =2.225(2) GT=2.198(2)

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August 2009 Doron Gazit - The weak structure of the nucleon36 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! |GT| JISP16 ( 6 He)=2.198(7) |GT| exp ( 6 He)=2.161(5) |GT| JISP16 ( 6 He)=2.198(7) |GT| exp ( 6 He)=2.161(5) Contact OPEC

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The inclusion of PT 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 capture showed that suppression is needed only in GT channel – consistent with MEC. PT estimation for the suppression of g A in infinite nuclear matter: ◦ g A /g A ~+8% - +13% due to long range MEC. ◦ g A /g A ~-28% due to contact interaction. ◦ g A /g A ~-15% - -20% total. August 2009 Doron Gazit - The weak structure of the nucleon37 Zinner, Langanke, Vogel, Phys. Rev. C 74, 024326 (2006). Park, Jung, Min, Phys. Lett. B409, 26 (1997).

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capture on 3 He August 2009 Doron Gazit - The weak structure of the nucleon38 DG, Phys. Lett. B666, 472 (2008).

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In QCD, the induced pseudoscalar form factor g P depends on the axial form factor. Adler, Dothan and Wolfenstein: HB PT verified this result and connected it to QCD, as well as allowed corrections to the formula. A comparison to experiment needs higher momentum than decays – capture. August 2009 Doron Gazit - The weak structure of the nucleon39 Adler, Dothan, Phys. Rev. 151, 1257 (1966). Bernard, Kaiser, Meissner, Phys. Rev. D 50, 6899 (1994), Kaiser, Phys. Rev. C 67, 027002 (2003). Adler, Dothan, Phys. Rev. 151, 1257 (1966). Bernard, Kaiser, Meissner, Phys. Rev. D 50, 6899 (1994), Kaiser, Phys. Rev. C 67, 027002 (2003).

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Since 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. August 2009 Doron Gazit - The weak structure of the nucleon40 e

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The branching ration is very small (10 -8 in hydrogen). August 2009 Doron Gazit - The weak structure of the nucleon41

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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. August 2009 Doron Gazit - The weak structure of the nucleon42

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August 2009 Doron Gazit - The weak structure of the nucleon43 The MuCap result: is consistent with PT 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). RMC: G. Jonkmans et al., Phys. Rev. Lett. 77, 4512 (1996) OMC: V. A. Andreev et al., Phys. Rev. Lett. 99, 0322002 (2007).

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For the (exclusive) process 3 He( ) 3 H an 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%. August 2009 Doron Gazit - The weak structure of the nucleon44 Ackerbauer et al, Phys. Lett. B417, 224 (1998). Czarnecki, Marciano, Sirlin, Phys. Rev. Lett 99, 032003 (2007)

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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 decay where it was calibrated). This allows to constrain the weak structure of the nucleon. August 2009 Doron Gazit - The weak structure of the nucleon45

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August 2009 Doron Gazit - The weak structure of the nucleon46 Form FactorThis workTheoretical estimation Experimental Pseudo-scalar g P (q 2 =-0.954m 2 ) 8.13±0.5 7.99±0.2 (HB PT) g P (q 2 =-0.88m 2 )= 7.3±1.1 Induced scalar m e F S /F V (0.5±2)×10 -4 - -0.0011±0.0013 (Towner & Hardy) Induced pseudo- tensor G T QCD sum rules H. Shiomi, J. Korean Phys. Soc. 29 (1996) S378.

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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 capture on the deutron will enable: to calibrate the 3NF at the 2-body level! August 2009 Doron Gazit - The weak structure of the nucleon47

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◦ Going to heavier nuclei, mainly A=6-8 and A=10, within PT, 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 excitations in weak reactions within PT? ◦ Role of a 1 ? ◦ How far can we go in momentum transfer within PT? August 2009 Doron Gazit - The weak structure of the nucleon48

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August 2009 Doron Gazit - The weak structure of the nucleon49

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ab-initio calculationsHB PT 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 PT based. Consistent microscopic approach for the construction of (meson exchange) currents in the nucleus. August 2009 Doron Gazit - The weak structure of the nucleon50 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.

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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. August 2009 Doron Gazit - The weak structure of the nucleon51 See O. Zimmer and S. Ando’s talks

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At finite momentum: From neutrino scattering: From pion-electroproduction: This axial radius discrepancy was solved in Baryon PT, which allowed including finite pion mass in the pion-electroproduction. The “radius” measured in pion- electroproduction: August 2009 Doron Gazit - The weak structure of the nucleon52 Bernard, Kaiser, Meissner, Phys. Rev. Lett. 691, 877 (1992).

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Schindler et al. have included a 1 in their manifestly Lorentz invariant PT. They showed that it has an effect only at higher energy. August 2009 Doron Gazit - The weak structure of the nucleon53 Schindler et al, Phys. Rev. C, 75, 025202 (2007)

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Renormalization of g V (q 0) Renormalization of g A (q 0) F V (q 0)=1 in the quark level. F V (q 0)=1 in the nucleon level. F V (q 0)=1 inside nuclei. g A (q 0)=1 in the quark level. g A (q 0)=1.27 in the nucleon level. g A (q 0) 1 inside nuclei??? August 2009 Doron Gazit - The weak structure of the nucleon54 “Restoration of axial symmetry”. The implications are immense, e.g., weak reaction rates in supernovae.

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