16th Neutrino Platform Week 2019: Hot Topics in Neutrino Physics CERN, Switzerland, Switzerland, 7– 11 October 2019 Matrix Elements for Neutrinoless Double Beta Decay Fedor Šimkovic OUTLINE I. Introduction (Majorana ν’s) II. The 0νββ-decay scenarios due neutrinos exchange (simpliest, sterile ν, LR-symmetric model) III. DBD NMEs – Current status (deformation, scaling relation?, exp. support, ab initio… ) IV. Quenching of gA (Ikeda sum rule, 2νββ-calc., novel approach for effective gA ) V. Looking for a signal of lepton number violation (LHC study, resonant 0νECEC …) Acknowledgements: A. Faessler (Tuebingen), P. Vogel (Caltech), S. Kovalenko (Valparaiso U.), M. Krivoruchenko (ITEP Moscow), D. Štefánik, R. Dvornický (Comenius10/8/2019 U.), A. Babič, A. SmetanaFedor(IEAP SimkovicCTU Prague), … 2 After 89/63 years Fundamental ν properties No answer yet we know • Are ν Dirac or • 3 families of light Majorana? (V-A) neutrinos: •Is there a CP violation ν , ν , ν ν e µ τ e in ν sector? • ν are massive: • Are neutrinos stable? we know mass • What is the magnetic squared differences moment of ν? • relation between • Sterile neutrinos? flavor states • Statistical properties and mass states ν µ of ν? Fermionic or (neutrino mixing) partly bosonic? Currently main issue Nature, Mass hierarchy, CP-properties, sterile ν The observation of neutrino oscillations has opened a new excited era in neutrino physics and represents a big step forward in our knowledge of neutrino10/8/2019 properties Fedor Simkovic 3 Symmetric Theory of Electron and Positron Nuovo Cim. 14 (1937) 171 CNNP 2018, Catania, October 15-21, 2018 10/8/2019 Fedor Simkovic 4 ν ↔ ν- oscillation (neutrinos are Majorana particles) 1968 Gribov, Pontecorvo [PLB 28(1969) 493] oscillations of neutrinos - a solution of deficit10/8/2019 of solar neutrinos in HomestakeFedor Simkovic exp. 5 Standard Model (an astonishing successful theory, based on few principles) However, we know that ν’s do have mass from the ν-oscillation experiments! => Thus10/8/2019 the neutrino mass indicatesFedor that Simkovic there is something new = BSM physics6 ! Majorana ν-mass => Lepton number violation The absence of the RH ν fields in Majorana Neutrinos . the SM is the simplest, most LN violating . c economical scenario. The ν-masses ν = ν . c and mixing are generated by the ν = νL + (νL) L-number violating Majorana mass term coming from dimension-5 effective Weinberg operator: Weinberg, 1979: d=5 10/8/2019 Fedor Simkovic 8 II. The 0νββ-decay scenarios 10/8/2019 Fedor Simkovic 9 Nuclear double-β decay (even-even nuclei, pairing int.) 2νββ Phys. Rev. 48, 512 (1935) Two-neutrino double-β decay – LN conserved - - (A,Z) → (A,Z+2) + e + e + νe + νe Goepert-Mayer – 1935. 1st observation in 1987 0νββ Nuovo Cim. 14, 322 (1937) Phys. Rev. 56, 1184 (1939) Neutrinoless double-β decay – LN violated - - 10/8/2019(A,Z) → (A,Z+2) + e + e (FurryFedor Simkovic1937) 10 Not observed yet. Requires massive Majorana ν’s 06/08/17 A. Schukraft | FNAL 11 short range: d=9 (d=11) Beyond the SM physics Amplitude for long range: d=7 (A,Z)→(A,Z+2)+2e- can be divided into: mass mechanism: d=5 Valle Weinberg,10/8/2019 1979 Babu,Fedor Leung: Simkovic 2001 12 de Gouvea, Jenkins: 2007 If 0νββ is observed the ν is a Majorana particle Schechter, Valle: PRD 1982 Different 0νββ-decay scenarios ν mass n mechanism p Considering Can we say i. Sterile ν something about e- long-range ii. Different LNV scales content e- iii. Right-handed currents of the black box? iv. Non-standard n short-range p ν-interactions v. …. 10/8/2019 Fedor Simkovic 13 - - 0νββ-decay (V-A SM int., light ν-exchange) (A,Z) → (A,Z+2) + e + e Phase factor Uei well understood ? mi NME must be evaluated using tools of nuclear theory Uei Effective Majorana mass can be evaluated. It depends on m1, m2, m3, θ12, θ13, α1, α2 (3 unknown parameters: m1/m3, α1, α2) 14 0νββ –half lives for NH and IH with included uncertainties in NMEe unquenched gA (gA=1.27) NH IH NH: IH: 15 Lightest ν-mass equal to zero 10/8/2019 Fedor Simkovic 16 II.b Nuclear medium effect on the light neutrino mass exchange mechanism of the 0νββ-decay S.G. Kovalenko, M.I. Krivoruchenko, F. Š., Phys. Rev. Lett. 112 (2014) 142503 ν q Low energy 4-fermion ∆L ≠ 0 Lagrangian g 2 gO’A L= ( qO q )(νν O′ ), mMχ > W . gOA eff 2 ∑ AA ~ m A χ χ q ν oscillation experiments, tritium β-decay density cosmology q 0νββ-decay χ vac medium Σ=×ν , Σν = ×+ Area 〈χ〉g1 [eV] and blue -0.05 between Complementarity green 0 cosmological red 1 IH IH measurements measurements β NH NH - decay, decay, might be spoiled might 0νββ – decay 10/8/2019 Fedor Simkovic 18 II.c. The sterile ν mechanism of the 0νββ-decay (D-M mass term, V-A,SM int.) Interpolating formula Dirac-Majorana Mixing of mass term active-sterile neutrinos small ν masses due to see-saw mechanism Light ν mass ≈ (mD/mLNV) mD Heavy ν mass ≈ mLNV Neutrinos masses offer a great opportunity to jump beyond the EW framework via see-saw ... Different motivations for the LNV scale Λ eV keV Fermi TeV GUT Planck light sterile ν hot DM LHC -6 10-6 10/8/2019GeV 10 GeV 10-6 GeVFedor Simkovic103 GeV 1016 GeV 1019 GeV19 Left-handed neutrinos: Majorana neutrino mass eigenstate N with arbitrary mass mN Faessler, Gonzales, Kovalenko, F. Š., PRD 90 (2014) 096010] General case light ν exchange heavy ν exchange Particular cases 10/8/2019 Fedor Simkovic 20 Interpolating formula 10/8/2019 Fedor Simkovic 21 Faessler, Gonzales, Kovalenko, F. Š., PRD 90 (2014) 096010] Interpolating formula is justified by practically no dependence <p2> on A A. Babič, S. Kovalenko, M.I. Krivoruchenko , F.Š., PRD 98, 015003 (2018) 10/8/2019 Fedor Simkovic 22 0ν 76 25 26 T 1/2( Ge) ≥ 3.0 10 yr ⇒ 0.9 10 yr Exclusion plot 0ν 136 25 ⇒ 26 2 T 1/2( Xe) ≥ 3.4 10 yr 1.1 10 yr in |UeN| – mN plane QRPA (constrained Hamiltonian by 2νββ half-life, self-consistent treatment of src10/8/2019, restoration of isospin symmetryFedor Simkovic …) 23 II.d. The 0νββ-decay within L-R symmetric theories (interpolating formula) (D-M mass term, see-saw, V-A and V+A int., exchange of heavy neutrinos) A. Babič, S. Kovalenko, M.I. Krivoruchenko , F.Š., PRD 98, 015003 (2018) Mixing of light and heavy neutrinos Effective LNV parameter within LRS model (due interpolating formula) 10/8/2019 Fedor Simkovic 24 6x6 PMNS see-saw ν-mixing matrix (the most economical one, prediction for 6x6 neutrino mass matrix mixing of heavy neutral leptons) Basis 6x6 matrix: 15 angles, 10+5 CP phases 3x3 matrix: 3 angles, 1+2 CP phases 3x3 block matrices U, S, T, V are generalization of PMNS matrix Assumptions: i) the see-saw structure ii) mixing between different generations is neglected see-saw parameter 6x6 matrix: 3 angles, 1+2 CP phases, 1 see-saw par. 10/8/2019 A. Babič, S. Kovalenko, FedorM.I. Krivoruchenko Simkovic , F.Š., PRD 98, 015003 (2018) 25 6x6 PMNS see-saw ν-mixing matrix (the most economical one) A. Babič, S. Kovalenko, M.I. Krivoruchenko , F.Š., PRD 98, 015003 (2018) Assumption about heavy neutrino masses Mi (by assuming see-saw) Inverse MR depends on proportional ββ “Dirac” CP phase δ unlike “Majorana” CP phases α1 and α2 Proportional 10/8/2019 R Fedor Simkovic 26 Heavy Majorana mass M ββ depends on the “Dirac” CP violating phase δ See-saw scenario Normal spectrum Inverted spectrum 10/8/2019 27 A. Babič, S. Kovalenko, M.I. Krivoruchenko , F.Š., PRD 98, 015003 (2018) III. 0νββ decay NMEs 2004 (factor 10) 2019 (factor 2-3) few groups, 2 nuclear many groups, many nuclear structure methods: structure methods: Nuclear Shell Model, Nuclear Shell Model, QRPA, QRPA Interacting Boson Model, Energy Density Functional Attempts (light nuclear systems): Ab initio calculations by different approaches – No Core Shell Model, Green’s Function Monte Carlo, Coupled Cluster Method, Lattice QCD Bahcall, Maruyama, Pena-Garay, 10/8/2019PRC 70, 033012 (2004) Fedor Simkovic 28 J. Engel, J. Menendez, Rept. Prog. Phys. 80, 046301 (2017) νββ (updated 2019) 0 -decay NME status 2019 All models missing essential physics Impossible to assign unquenched gA rigorous uncertainties Nuclear Shell Model (Madrid-Strasbourg, Michigan, Tokyo): Relatively small model space (1 shell), all correlations included, solved by direct diagonalization QRPA (Tuebingen-Bratislava-Calltech, Jyvaskyla, Chapel Hill, Lanzhou, Prague): Several Shells, only simple correlations included Interacting Boson Method (Yale-Concepcion): Small space, important proton-neutron Pairing correlations missing Energy10/8/2019 Density Functional theory (Madrid,Fedor Beijing): Simkovic >10 shells, important proton-neutron29 pairing missing Suppression of the ββ-decay 0νββ-decay NMEs within deformed QRPA NMEs due to different deformation with partial restoration of isospin symmetry of initial and final nuclei Agreement by a chance? D. Fang, A. Faessler, F.Š., PRC 97, 045503 (2018) Systematic study of the deformation effect on the 2νββ-decay NME Within deformed QRPA F.Š., Pacearescu, Faessler, NPA 733 (2004) 321 10/8/2019 Fedor Simkovic 30 New QRPA calculations based on 2ν restoration of the SU(4) symmetry (M GT-cl=0) 10/8/2019 Fedor Simkovic 31 F. Š., A. Smetana, P. Vogel, PRC 98, 064325 (2018) Ab Initio Nuclear Structure Nucleons, pions. Sufficient below (Often starts with chiral effective-field theory) chiral symmetry breaking scale. Expansion of operators in power of Q/Λχ. Q=mπ or typical nucleon momentum.