Heavy Neutrinos and the Majorana vs. Dirac Question Boris Kayser CERN October 9, 2019 1 Based, with thanks to my collaborators, on — Baha Balantekin, André de Gouvêa, B.K. arXiv:1808.10518, Phys.Lett. B789 (2019) 488 Baha Balantekin, B.K. arXiv:1805.00922, Ann.Rev.Nucl.Part.Sci. 68 (2018) 313 B.K. arXiv:1805.07523, Proc.Moriond Electroweak (2018) 323 — and ongoing work by Jeffrey Berryman, Patrick Fox, André de Gouvêa, B.K., Kevin Kelly, Jennifer Raaf 2 The Majorana vs. Dirac Question Is each neutrino mass eigenstate νi — a Majorana fermion νi = νi or a Dirac fermion νi ¹ νi This question is particularly interesting because of its relation to another question: 3 What is the origin of the neutrino masses? In particular, do neutrinos, unlike the quarks and charged leptons, have Majorana masses? In terms of underlying neutrinos ν (not mass eigenstates), in terms of which the Standard Model, extended to include neutrino mass, is written, a Majorana mass has the effect — n n n n X and X Majorana Majorana mass mass 4 Then any mass eigenstate neutrino, such as n1, must be of the form — n1 = n + n, since this is the neutrino that the Majorana mass term sends back into itself, as required for any mass eigenstate particle: Mass n + n X n + n 5 Then any mass eigenstate neutrino, such as n1, must be of the form — n1 = n + n, Note that n1 = n1. since this is the neutrino that the Majorana mass term sends back into itself, as required for any mass eigenstate particle: Mass n + n X n + n When the underlying masses are Majorana masses, the mass eigenstates will be Majorana neutrinos. Neutrinos are Dirac No Majorana masses 6 When the neutrino mass eigenstates are Majorana neutrinos, there will be Majorana masses. If the neutrino mass eigenstates like ν1 are Majorana particles, we can have — Underlying neutrino This is a Majorana mass. Neutrinos are Majorana Majorana masses Neutrinos are Dirac No Majorana masses 7 The main approach to trying to demonstrate that neutrinos are Majorana particles has been the search for Neutrinoless Double Beta Decay [0νββ]. (Talks by Fedor Simkovic and Frank Deppisch) Observing 0νββ would prove that neutrinos are Majorana particles. Not observing 0νββ would not prove that neutrinos are Dirac particles. (Non-observation places a lower bound on the lifetime, but we do not really know what the lifetime is if neutrinos are Majorana particles.) 8 Another Approach If There Is a Heavy Neutrino N 9 Decays of a Heavy Neutrino Suppose there is a heavy neutrino N. (Talk by Marco Drewes) A chain like — q μ+ W+ e+ N q¢ π– would violate lepton number conservation, and signal that N is a Majorana neutrino. To look for this, a detector must have charge discrimination. 10 Very Neutral N Decay Modes The decays — N →ν + X ν1 ,ν2 ,orν3 X = X could also reveal whether neutrinos are Dirac or Majorana particles. Depending on the mass of N, we could have — 0 0 0 0 X = γ ,π , ρ , Z ,or H . 11 For each of these decay modes, Γ(N M →ν M + X ) = 2Γ(N D →ν D + X ) Majorana Dirac (Gorbunov and Shaposhnikov) This difference may not be too useful, because the decay rate also depends on unknown mixing angles. The angular distribution of the daughter X in the N rest frame, when N has been polarized by the mechanism that produced it, also depends on whether neutrinos are Majorana or Dirac particles. 12 General analysis: Baha Balantekin, André de Gouvêa, B.K. z ! p X θ λX We assume N s N is fully polarized. ! −p λ ν λ , λ are helicities. ν X ν 13 If neutrinos are Majorana particles: Rotational invariance cosθ M M d N X 2 Γ( → ν + ) " M ! M ! ∼ X (p,λX )ν (−p,λν ) H N (s ) = A + B sˆ ⋅ pˆ d cos ∑ ( θ ) λX , λν 2 ! M ! M ! ˆ ˆ = ∑ X (p,−λX )ν (−p,−λν ) H N (−s ) = A − B s ⋅ p CPT λX , λν invariance B = 0 The angular distribution is isotropic. Thanks to Samoil Bilenky for suggesting something like this way of explaining the isotropy. 14 The isotropy in the Majorana case does not depend on the details of the interaction driving the decay. What Is the Angular Distribution in the Dirac Case? This does depend on the interaction. What we assume ν MDM μ and EDM d γ N 15 ν ν π0 ρ0 Ζ0 Ζ0 N N ν ν Ζ0 H0 N N 16 The Angular Distributions in the Dirac Case Rotational {invariance dΓ(N D → ν D + X ) = Γ0 (1+α cosθ ), −1 ≤ α ≤ +1 d (cosθ ) In general, these angular distributions are far from isotropic. 17 N Decays to Charged Particles The decay modes N → ℓ∓ + X ± are probably advantageous: e or μ π or ρ Measuring the ! and X momenta would allow reconstruction of the N. One would know where the N rest frame is in each event, so the angular distribution of the daughter X in the N rest frame could be determined directly. A peak in the !X invariant mass distribution at the N mass would help get rid of backgrounds. 18 Assume that the particles N are produced in a neutrino beam facility via, e.g., — K + → ℓ+ + N and K − → ℓ− + N e or μ For most values of the N mass mN, the particles N will be quite highly polarized, with polarization P from K+ decay, and – P from K– decay. This polarization is independent of whether N is a Majorana particle or a Dirac one. 19 Suppose our detector has electric charge discrimination. One can then collect, for example, separate samples of N → µ − π + and N → µ + π − . If N is a Majorana fermion NM Γ(N M → µ−π + ) = Γ(N M → µ+π − ) There will be as many μ–π+ pairs as μ+π– ones from N decays. If N is a Dirac fermion ND N D → µ−π + but N D → µ+π − Neutrino-mode (focused K+) running will produce more μ–π+ than μ+π– pairs from N decays. Antineutrino-mode (focused K–) running will produce + – – + more μ π than μ π pairs from N decays. 20 Now suppose our detector, at some neutrino facility, does not have electric charge discrimination, although it can identify e, μ , and π. In that case, we can measure the sum of the N → μ–π+ and N → μ+π– decays. If N is a Majorana fermion NM M – + M + − dΓ N From K + → µ π dΓ N From K + → µ π ( ) + ( ) and d (cosθ ) d (cosθ ) M – + M + − dΓ N From K − → µ π dΓ N From K − → µ π ( ) + ( ) , d (cosθ ) d (cosθ ) and thus their sum, are all isotropic. 21 If N is a Dirac fermion ND D + − dΓ(N D → µ –π + ) dΓ(N → µ π ) = = Γ0 (1+αP cosθ ) , d (cosθ ) d (cosθ ) 2 2 2ε mN − m where α = µ ( µ ) , 2 2 2 (mN − mµ ) + ε µ (mN + mµ ) 2 2 mN − m − m with ε ≡ ( µ ) π . µ 2 2 (mN + mµ ) − mπ This angular distribution is not isotropic. Indeed, if mµ ≪ mN , α ≅ 1. 22 If neutrinos are Majorana particles, the decays of a heavy neutrino N could prove that. And if neutrinos are Dirac particles, the decays of N could prove that as well. 23 A heavy neutrino is being sought at CERN, J-PARC, and Fermilab. The discovery potential at Fermilab has been considered by Ballett, Pascoli, and Ross-Lonergan. Some of the physics of a heavy neutrino has been discussed by Ballett, Boschi, and Pascoli, by Hernandez et al., Caputo et al., and Han et al.. The angular distribution and related photon polarization in radiative neutrino decays has been considered in specific formalisms as a probe of whether neutrinos are Dirac or Majorana particles by — Li and Wilczek and by Shrock. 24 Conclusion The question of whether neutrinos are Majorana or Dirac particles bears on the question of the origin of the neutrino masses. If a heavy neutrino N should be discovered, experimental study of its decays could reveal the answer. 25.