Majorana Neutrinos: What, Why, Where? Francesco Vissani GSSI & LNGS WIN 2019 Conference, Bari, June 7, 2019 why known neutrinos could well be Majorana particles; the minimal formalism; relevance of the issue for the direct search of big-bang neutrinos MAJORANA’S HYPOTHESIS ON NEUTRINOS June 07, 2019 Francesco Vissani, GSSI & LNGS 2 direction of the momentum direction of the momentum 0 0 helicity distinguishes neutrinos from antineutrinos June 07, 2019 Francesco Vissani, GSSI & LNGS 3 direction of the momentum direction of the momentum 0 0 but in the rest frame there is only the spin! June 07, 2019 Francesco Vissani, GSSI & LNGS 4 direction of the momentum direction of the momentum 0 0 Majorana: in the rest frame the two states are the same June 07, 2019 Francesco Vissani, GSSI & LNGS 5 June 07, 2019 Francesco Vissani, GSSI & LNGS 6 June 07, 2019 Francesco Vissani, GSSI & LNGS 7 June 07, 2019 Francesco Vissani, GSSI & LNGS 8 June 07, 2019 Francesco Vissani, GSSI & LNGS 9 Francesco Vissani, GSSI & LNGS June 07, 2019 comments o recall: neutrino masses are necessary to explain oscillations o neutrino mass + V-A nature makes Majorana hypothesis plausible o “unusual appearance” means just “we are used to Dirac” next, one manifestation of Majorana mass – see M. Messina’s talk 10 direct search of big-bang neutrinos big-bang neutrinos produce 3 neutrino-capture lines for a radioactive target their positions depend on mi ; their 2 intensity on |Uei | 1 +βi Dirac 2 lightest neutrino gives the most R ∝U × νi C ei intense line for normal hierarchy 2 Needs Ø great energy resolution 2m Ø big target mass, ≥100g of tritium i 11 Francesco Vissani, GSSI & LNGS June 07, 2019 Majorana means more events Roulet & FV, 2018 & FV, 12 remarks on the features of the standard model (SM); effective operators that violate lepton and baryon numbers; observable manifestations ON SM EXTENSIONS June 07, 2019 Francesco Vissani, GSSI & LNGS 13 Francesco Vissani, GSSI & LNGS June 07, 2019 remarks on SM standard model o in SM B-L , Le – Lµ and Lµ – Lτ are exact symmetries refrains Le – Lµ and Lµ – Lτ are violated in oscillations -- which means that the SM needs to be modified/improved/extended. 14 Francesco Vissani, GSSI & LNGS June 07, 2019 remarks on SM standard model o in SM B-L , Le – Lµ and Lµ – Lτ are exact symmetries o But L – L and L – L are violated in oscillations e µ µ τ 15 Francesco Vissani, GSSI & LNGS June 07, 2019 remarks on SM standard model o in SM B-L , Le – Lµ and Lµ – Lτ are exact symmetries o But Le – Lµ and Lµ – Lτ are violated in oscillations conclusion: SM needs to be modified/improved/extended 16 Francesco Vissani, GSSI & LNGS June 07, 2019 SM effective operators (Weinberg; Wilczek & Zee 79) accept in the SM Lagrangian density also the operators with canonical dimension >4 that conserve gauge symmetry e.g. 17 Francesco Vissani, GSSI & LNGS June 07, 2019 SM effective operators (Weinberg; Wilczek & Zee 79) accept in the SM Lagrangian density also the operators with canonical dimension >4 that conserve gauge symmetry e.g. B-L and Li-Lj broken B & L broken B-L unbroken 18 manifestations p dim.6 π0 e+ e- n p n n n dim.5,7,9 p p p - p e 19 manifestations p dim.6 π0 e+ B=+1 , L=0 B=0 , L=-1 e- n p n n n dim.5,7,9 p p p - p e 20 manifestations p dim.6 π0 e+ B=+1 , L=0 B=0 , L=-1 e- n p n n n dim.5,7,9 p p p - p e B=A, L=0 B=A , L=2 21 manifestations p π0 e+ e- n p n n n p p p - p e 22 manifestations p π0 e+ e- n p n n n p p p - p e 23 the process of interest; connection with Majorana neutrino masses; theoretical discussion of the most plausible mechanism TESTING B-L SYMMETRY June 07, 2019 Francesco Vissani, GSSI & LNGS 24 Francesco Vissani, GSSI & LNGS June 07, 2019 the process of interest A very promising process to test B-L is, (A,Z) à (A,Z+2) + 2 e- Actively searched (see G. Gratta and next talks) ¤ It violates Le , also violated in oscillations (T2K, NOνA) ¤ It violates L , being a creation of two electrons ¤ It conserves B ¤ It violates B-L , of which we have no evidence 25 Francesco Vissani, GSSI & LNGS June 07, 2019 its selection rules The process we are interested to consider is, (A,Z) à (A,Z+2) + 2 e- Not yet observed, actively searched ¤ It violates Le , also violated in T2K & NOνA’s oscillations ¤ It violates L , being a creation of two electrons (NEW!) ¤ It conserves B ¤ It violates B-L, the residual SM symmetry (NEW!) ¤ Potentially due to many SM effective operators: dim.5, 7, 9 etc 26 Francesco Vissani, GSSI & LNGS June 07, 2019 its selection rules The process we are interested to consider is, (A,Z) à (A,Z+2) + 2 e- Not yet observed, actively searched ¤ It violates Le , also violated in T2K & NOνA’s oscillations ¤ It violates L , being a creation of two electrons ¤ It conserves B ¤ It violates B-L, the residual SM symmetry ¤ Potentially due to many SM effective operators: dim.5, 7, 9 etc 27 Francesco Vissani, GSSI & LNGS June 07, 2019 dim5 operator… Francesco Vissani, GSSI & LNGS June 07, 2019 …yields Majorana mass in SM! e- Majorana neutrinos p p n n and 0ν2β n p νe p p uu d d n n p d u n - W e- e- νM e- W- d u d d u u June 07, 2019 Francesco Vissani, GSSI & LNGS 30 Francesco Vissani, GSSI & LNGS June 07, 2019 discussion ¤ SM gauge symmetry constrains hypothetical phenomena that break L & B. These are described by higher-order operators, ordered in powers of new physics masses 31 Francesco Vissani, GSSI & LNGS June 07, 2019 discussion ¤ SM gauge symmetry constrains hypothetical phenomena that break L & B. These are described by higher-order operators, ordered in powers of new physics masses ¤ many operators can break B-L causing 0ν2β, w/o giving big contributions to neutrino masses 32 Francesco Vissani, GSSI & LNGS June 07, 2019 discussion ¤ SM gauge symmetry constrains hypothetical phenomena that break L & B. These are described by higher-order operators, ordered in powers of new physics masses ¤ many operators can break B-L causing 0ν2β, w/o giving big contributions to neutrino masses ¤ the lowest order operator causes 0ν2β (“neutrinoless double beta decay”) and gives Majorana mass: a plausible extension of the SM -- oscillations are explained 33 summary: the reasons of assuming light neutrino dominance o First, we have evidence of liGht neutrino masses and not of new physics at TeV scale. o Moreover, hiGher dimensional operators would point to new physics at TeV scale (Tello et al 2011) but would also indicate that the couplinGs of the neutrinos are rather different from the other ones – much smaller. June 07, 2019 Francesco Vissani, GSSI & LNGS 34 the relevant parameter - “electron neutrino mass”, aka “effective mass”, aka mββ; theoretical remarks on its value; again on alternative theoretical possibilities THEORETICAL REMARKS June 07, 2019 Francesco Vissani, GSSI & LNGS 35 the “electron neutrino” mass If light Majorana ν leads the transition, the parameter that counts for 0ν2β is, The first is the traditional symbol; the second, is the ee-element of the ν mass matrix. Sometimes indicated also as <mν> (there are also other symbols, that always indicate the very same thing!) the “electron neutrino” mass If light Majorana ν leads the transition, the parameter that counts for 0ν2β is, 2 2 Only the mass differences mi -mj and 2 electronic mixing |Uej | are measured by oscillations. Lightest neutrino mass & Majorana phases ξi aren’t. Francesco Vissani, GSSI & LNGS June 07, 2019 fourty years ago 38 Francesco Vissani, GSSI & LNGS June 07, 2019 twenty years ago 39 Francesco Vissani, GSSI & LNGS June 07, 2019 today 40 Francesco Vissani, GSSI & LNGS June 07, 2019 is mββ = | (mν)ee | predictable? ¤ Yes, in a definite theoretical context ¤ However, it is difficult to believe that this can be achieved w/o understanding charged fermions masses ¤ Which principles should be adopted? ¤ Do we have credible models to tackle such problems? ¤ To illustrate these considerations we discuss a few attempts 41 Francesco Vissani, GSSI & LNGS June 07, 2019 PDF 0.20 0.15 0.10 0.05 0.00 0 2 4 6 8 10 12 14 mββ [meV] (mν)ee ~ √Δmatm ×θC (guesswork) Vissani 1998-2001; Dell’Oro et al 2018 Francesco Vissani, GSSI & LNGS June 07, 2019 Altarelli Buccella et al 2009- et al 2019 et al 2013; Bertolini et al 2011; Ohlsson Dueck Joshipura et al 2005; et al 2013; Bajc 2011; et al 2012; minimal SO(10) (principled model) « 16-plet coupled to 10 and 126 higgs: heavy right-handed neutrinos « (Peccei Quinn symmetry to address strong CP and dark matter) Francesco Vissani, GSSI & LNGS June 07, 2019 Altarelli Buccella et al 2009- et al 2019 et al 2013; Bertolini et al 2011; Ohlsson Dueck Joshipura et al 2005; et al 2013; Bajc 2011; et al 2012; minimal SO(10) (principled model) « 16-plet coupled to 10 and 126 higgs: heavy right-handed neutrinos « (Peccei Quinn symmetry to address strong CP and dark matter) « neutrinos are massive and fermion masses constrained Francesco Vissani, GSSI & LNGS June 07, 2019 Altarelli Buccella et al 2009- et al 2019 et al 2013; Bertolini et al 2011; Ohlsson Dueck Joshipura et al 2005; et al 2013; Bajc 2011; et al 2012; minimal SO(10) (principled model) « 16-plet coupled to 10 and 126 higgs: heavy right-handed neutrinos « (Peccei Quinn symmetry to address strong CP and dark matter) « neutrinos are massive and fermion masses constrained « normal mass hierarchy; mββ in the few meV range Francesco Vissani, GSSI & LNGS June 07, 2019 Altarelli Buccella et al 2009- et al 2019 et al 2013; Bertolini et al 2011; Ohlsson Dueck Joshipura et al 2005; et al 2013; Bajc 2011; et al 2012; minimal SO(10) (principled model) « 16-plet coupled to 10 and 126 higgs: heavy right-handed neutrinos « (Peccei Quinn symmetry to address strong CP and dark matter) « neutrinos are massive and fermion masses constrained « normal mass hierarchy; mββ in the few meV range « (potentially interesting expectations for proton decay) Francesco Vissani, GSSI & LNGS June 07, 2019 another contribution from heavy (“right- handed”) neutrinos? naively, not a likely option with some gym, maybe -4 10 DELPHI -5 10 TRIUMF quenching Mitra CHARM g A 2016 PS 191 -6 correlations 10 range short 2 SHiP I 0nbb e -7 U 10 10-8 SHiP et al 2009’ E.O.I.