Weak and rare nuclear processes. Doron Gazit

Transcription

1 Weak and rare nuclear processes Doron Gazit

2 Outline The role of theory in calculating rare nuclear processes. Calculating weak reactions in chiral EFT. Gamow-Teller transitions within chiral EFT: from 3 H through 6 He to medium-mass nuclei. 0nbb decay rates at medium-heavy nuclei. Spin-dependent WIMP scattering on nuclei. Summary. 2

3 Weak and rare nuclear processes Nuclear weak processes play a major role in: Nuclear structure: Giant Gamow-Teller resonance, Fermi and GT Strength Functions. Superallowed Fermi transitions: isospin symmetry breaking, CKM matrix unitarity. 3 H single b-decay: measurement of the neutrino mass 0nbb decay: Lepton Number Conservation, Majorana nature of neutrinos Astrophysical phenomena. Dark matter as a weakly interacting massive particle. 3

4 The role of theory Rare processes are usually hard to measure. Accurate, parameter free predictions are needed to : Constrain fundamental symmetries of QCD. Quantify beyond the standard model effects for experiments and assessing the feasibility of experiments. Describe the microscopic dynamics of astrophysical phenomena. Connecting reactions and structure in the nuclear domain. Understanding the nuclear regime from first principles is essential for a correct interpretation of natural phenomena and experiments. 4

5 Introduction Low energy electromagnetic reaction l μ k 2 q 0 m Pf E f,pf g k 1 P i E i,p i l 5

6 Introduction Low energy weak reaction l μ k 2 q 0,q Pf E f,pf k 1 0 W,Z P i E i,p i l W,Z propagator = g mn + q m q n M W 2 q 2 + M W 2 6

7 INT - "Light nuclei from first principles" Introduction Neutrino-less double beta-decay 7 Figure taken from P. Vogel

8 INT - "Light nuclei from first principles" Introduction Neutralino scattering off a nucleus l μ k 2 H,Z 0 Pf E f,pf q k 1 P i E i,p i l 8

9 INT - "Light nuclei from first principles" All happy families are alike, every unhappy family is unhappy in its own way Low energy weak reactions l μ k 2 q 0,q Pf E f,pf k 1 0 W,Z P i E i,p i l W,Z propagator = g mn + q q m n 2 M W q M W g mn M W 2 9

10 Introduction Low energy reactions Ĥ W ~ d 3 + ò x ĵ m ( x) Ĵ m - ( x) l Probe current of known symmetry Nuclear current of the same symmetry μ k 2 Pf E f,pf O ˆ ~ i J f k 1 P i E i,p i Scattering operator l Currents in the nucleus 10

11 Low energy nuclear reactions induced by an external probe Same symmetry will induce the same structure of the nuclear current. Differences lie in coupling constants. The currents are reflections of the symmetries and properties of the nuclear interaction, in particular can be used to characterize the elusive three nucleon force. Thus, one can relate electro-weak properties and reaction rates with non-trivial properties not only of the target, but also of the fundamental theory leading to its structure! 11

12 Chiral Effective Field Theory Symmetries are important NOT degrees of freedom. In QCD an approximate chiral symmetry: The u and d quarks are (almost) massless (~5-10 MeV). SU 2 SU 2 SU 2 L R V The SU(2) V symmetry is the isospin symmetry. The pions are the Nambu-Goldstone bosons of the spontaneous chiral symmetry breaking. The order-parameter is the pion-decay constant: L QCD =4pf p Identify Q the momentum scale of the process. In view of Q-identify the effective degrees of freedom: Write a Lagrangian composed of ALL possible operators invariant under symmetries of the underlying theory. 12

13 Chiral Effective Field Theory Find a systematic way to organize diagrams according to their contribution to the observable. Expand in the inverse of the nucleon s mass (take L a ~M N ) Heavy Baryon cpt! Weinberg s Power Counting: Each Feynman diagram can be characterized by: Weinberg showed that n is bound from below. Issues! Q n L 20 years of debate led by: Weinberg, Kaplan, Savage, Wise, van-kolck, Nogga, Timmermans, Birse, Meissner, Epelbaum, Machleidt 13

14 cpt approach for low-energy EW nuclear reactions: Nuclear potential QCD Low energy EFT Chiral EFT Lagrangian Nöther current Wave functions Weak current Nuclear Matrix Element 14

15 Unites phenomena: 3 body forces and reactions L ~ N a NNN 4 5 pnn absorption Nöther current Nuclear potential Same LEC appears in the potential and in the current! 15 van Kolck (1995); van Kolck, Ordonez (1995); Gårdestig, Phillips (2006); DG, Quaglioni, Navratil (2009)

16 Forces in pionfull ceft The leading order NNN forces are at N 2 LO. They include 2 new contact parameters. No new parameters at N 3 LO. Weinberg, van Kolck, Ordonez, Meissner, Epelbaum, Nogga, Bernard, Kaiser, Krebs, Machleidt, Entem 16

17 Differences from D-full 17 Figure adopted from Ulf Meissner.

18 ceft axial weak currents to O(Q 3 ) Single nucleon current 1 pion exchange Contact term O(Q 0 ), O(Q 2 ) O(Q 3 ) 18 T.-S. Park et al, Phys. Rev. C 67, (2003); DG PhD thesis arxiv:

19 ceft axial weak currents to O(Q 3 ) Single nucleon current 1 pion exchange Contact term O(Q 0 ), O(Q 2 ) O(Q 3 ) 19 T.-S. Park et al, Phys. Rev. C 67, (2003); DG PhD thesis arxiv:

20 ceft axial weak currents to O(Q 3 ) Single nucleon current 1 pion exchange Contact term O(Q 0 ), O(Q 2 ) O(Q 3 ) Fermi operator Gamow- Teller operator 20 T.-S. Park et al, Phys. Rev. C 67, (2003); DG PhD thesis arxiv:

21 ceft axial weak currents to O(Q 3 ) Single nucleon current 1 pion exchange Contact term O(Q 0 ), O(Q 2 ) O(Q 3 ) ˆd R Nucleon-pion interaction, NO new parameters Contact term 21 T.-S. Park et al, Phys. Rev. C 67, (2003); DG PhD thesis arxiv:

22 ceft axial weak currents to O(Q 3 ) Single nucleon current 1 pion exchange Contact term O(Q 0 ), O(Q 2 ) O(Q 3 ) ˆd R Nucleon-pion interaction, NO new parameters Contact term 22 Gårdestig, Phillips, Phys. Rev. Lett. 98, (2006); DG, Quaglioni, Navratil, Phys. Rev. Lett. T.-S. 103, Park et al, (2009). Phys. Rev. C 67, (2003); DG PhD thesis arxiv:

23 Nuclear b decays Typically, a very low momentum transfer. ft M V 2 = 1 2J i +1 y i = é ët T +1 2p ln 2 / m 3 3 e V 1 A G V D F M 1 D g M F ud R V V R A A A å k=1 ± t k ( ) -T Z ( T z +1) y f 2 ù û 1-d C = ( ) M A 2 = yi E 1 A / g A y f 2 = 1 3p 2J i +1 ( ) A å y i s k t k ± k=1 y f 2 + corrections 23

24 Step 1: use the trinuclei binding energies to find a c D -c E relation 24 Navratil et al., Phys. Rev. Lett. 99, (2007).

25 Step 2: calibrate c D according to the triton half life. 0.3 c D 0.1 c E 0.220, N 3 LO EM 550 DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, (2009)

26 A prediction of 4 He properties 26

27 A closer look into the weak axial correlations in 3H Contact Specific character of the force has minor effect Is this the origin for the success of EFT*? MEC a 2% effect on the matrix element NNN are not important??? Without the contact interaction - a disaster OPEC 27

28 EFT* approach for low-energy weak reactions: Phenomenological Hamiltonian Solution of Schrödinger equation QCD Low energy EFT Chiral Lagrangian Nöther current Wave functions Weak current Nuclear Matrix Element T.-S. Park et al, Phys. Rev. C 67, (2003), M. Rho arxiv: nucl-th/

29 e n e M A 2 = y i GT y f 2 A å GT LO = s i t i ± i=1 ft V 1 A G V D F M 1 D g M K F ud R V V R A A GAMOW-TELLER TRANSITIONS 29

30 mow-teller quenching Gamow-Teller Quenching Theoretical calculations need to quench the Gamow-Teller coupling J n,1b = g A σ n n, A = qg A, q 0.75 sd shell pf shell to reproduce experimental lifetimes and strength functions in regions where the spectroscopy is well reproduced g eff Large quenching Model thal et al. PRC (1983) ez-pinedo et al. PRC (1996) =) gy Density Functional Methods Chou, Warburton, Brown, Phys. Rev. C47, 163 (1993) r et al. PRC (2002) QRPA calculations reach similar results. uez et al. PRL (2010) Energy Density Functional Methods Martinez-Pinedo et al, Phys. Rev. C53, 2602 (1996) Alvarez-Rodriguez et al, Phys. Rev. C70, (2004) Bender et al, Phys. Rev. C65, (2002) Rodriguez et al, Phys. Rev. Lett. 105, (2010) Problem approx. many-body method, incomplete operator, or both? Quenching needed in regions where spectroscopy is well reproduced. Javier Menéndez 2B currents and weak transitions 30

31 Gamow-Teller Quenching Sesano et al, Phys. Rev. C79, (2009); Yako et al, Phys. Lett. B615, 193 (2005) (much debated) Measurements of Ikeda sum-rule in 90 Zr up to high energies, show very small quenching! Small quenching Suggesting: many body approximations responsible for the discrepancy. The quenching puzzle attracted many theoreticians: Arima, Rho, Towner, Bertsch and Hamamoto, Wildenthal and Brown Revisit in the framework of Chiral EFT! 31

32 6 He b decay We use the HH method to solve the 6 body problem, with JISP16 NN potential. We use ceft axial MEC with c D fixed using triton b decay Very rapid convergence: E ( 6 He)=28.70(13) MeV E exp ( 6 He)= MeV E ( 6 Li)=31.46(5) MeV E exp ( 6 Li)= MeV GT LO =2.225(2) GT=2.198(2) 32 Vaintraub, Barnea, DG, Phys. Rev. C, (2009); Lupo, Barnea, DG, work in progress

33 6 He b decay OPEC Contact 33 Vaintraub, Barnea, DG, Phys. Rev. C, (2009).

34 6 He b decay OPEC Contact The contact interaction that does not exist in pheno. MEC, has an 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) 34 Vaintraub, Barnea, DG, Phys. Rev. C, (2009).

35 6 He b decay and a hint to heavier nuclei The inclusion of ceft based MEC is helpful, even when one uses phen. interaction. The need of ceft based MEC is observed in capture on light nuclei. DG, Phys. Lett. B666, 472 (2008), Marcucci et al., Phys. Rev. C 83, (2011). The conclusion is that the weak correlations inside the nucleus can lead to (at least part of) the observed suppression. Going to heavier nuclei demands approximations. 35

36 Intermission: b-decay and fundamental symmetries 6 Li daughter nucleus DI=1 Pure GT e - Electron p dw a E dw SM e e 6 ( He) cos q 1 3 p E e e cos q 6 He 6 Li e e q n e Electron anti-neutrino Theoretical input needed! 6 He produced using a BeO target enormous SARAF 36

37 WIRED - beta decay of 6He 10/24/2012 SARAF Phase Soreq Center - Israel Commissioning of Phase-I is approaching finalization 1 ma CW proton beam has been accelerated up to an energy of 3.7 MeV Low duty cycle (~0.2 ma ) deuteron beam has been accelerated up to an energy of 4.3 MeV Phase-II up to 40 MeV (2015) Beam Dump PSM Target beam line

38 WIRED - beta decay of 6He 10/24/2012 The case of 16 N Pure E2 transition: 1. No MEC contribution pinpointing suppression origin 2. Different bncorrelation properties! GT 16 N is produced simultaneously with 6 He, and with a comparable yield, in the BeO target 16 O(p,n) 16 N Experiment: Hass, Vaintraub (2013) Theory: DG (2012) in preparation. Vary, DG, Maris, Schwenk, WIP

39 TO MEDIUM-HEAVY NUCLEI LAND 39

40 Effective 2-body current eff J n,2b = -g A s n t n - r m N f p 2 F r,c 3,c 4,c D, p ( ) leading GT 40 Menendez, DG, Schwenk, Phys. Rev. Lett. 107, (2011)

41 Long range GT and quenching 41 Menendez, DG, Schwenk, PRL 107, (2011)

42 Short range contributions to GT and quenching 42

43 Short range contributions to GT and quenching Menendez, DG, Schwenk, PRL 107, (2011) 43

44 GT p dependence 44 Menendez, DG, Schwenk, PRL 107, (2011)

45 Neutrino-less double beta decay Double b-decay only appears when regular b-decay is energetically forbidden or hindered by large J difference. 45

46 Neutrino-less double beta decay 0nbb decay needs also massive Majorana neutrinos detection would prove Majorana nature of neutrinos. Nuclear Matrix element, biggest uncertainty due to g A : Relevant momentum transfer: p~100mev. T 0nbb 4 1/2 µ g Ā m bb = å k U 2 ek m k Common debate: Is g A quenched at these momenta? 46

47 relevant p for 0nbb ME 47 Menendez, DG, Schwenk, Phys. Rev. Lett. 107, (2011)

48 ME predictions 48 Menendez, DG, Schwenk, Phys. Rev. Lett. 107, (2011)

49 Conclusions for 0nbb ME 49

50 Spin-dependent WIMP scattering on nuclei More than 20% of the energy density of the Universe is understood as dark matter. Promising candidates are WIMPs, such as neutralinos. This has spurred direct detection of cold dark matter via elastic scattering off nuclei, requiring detailed knowledge of the response to WIMP induced currents in nuclei. This presents a challenging problem, because even if the coupling of to quarks is known, it needs to be evaluated at the nucleus level in the nonperturbative regime of quantum chromodynamics Chiral EFT provides an ideal theoretical framework since the typical momentum transfers in direct dark matter detection are of the order of 100 MeV/c. 50

51 Dark matter 51

52 WIMP-nucleus scattering At low energies: Spin dependent Spin independent Spin dependent: When moving to the nucleon level: In the nucleus level the Isoscalar isovector part Isovector has 2b corrections identical to the weak current! 52

53 Spin dependent WIMP scattering 53 Menendez, DG, Schwenk, PRD (in press) (2012)

54 Spin dependent WIMP scattering 54

55 55

56 Summary Constrain the Nuclear interaction and structure. Extract microscopic information about the fundamental theory and its symmetries. Using cpt to calculate weak reactions with nuclei can be useful to: Predict in-medium evolution of nuclear properties. Probe the limits of the standard model. Nuclear theory is in the process of building a unified fundamental understanding of reactions and structure, which can shed light on many physical mysteries. 56

57 Collaborators Achim Schwenk, J. Menéndez Sofia Quaglioni Petr Navratil, Sonia Bacca Nir Barnea, Sergiu Lupo, Hilla Deleon Michael Hass, Sergey Vaintraub James Vary, Pieter Maris 57 Supported in part by: BMBF ARCHES.