Physics at the LHC Higgs and Supersymmetry Part

Physics at the LHC: Higgs and Supersymmetry Part 7: Neutrino masses Manfred Jeitler SS 2020

remember: fermion masses § explicit mass term would not be invariant under SU(2)L § same SU(2)L gauge transformation acts on Higgs field and on left-handed fermions: L: left-handed chiral fermion spinor § combination is invariant under SU(2)L gauge transformations § combined with right-handed singlets: with “Yukawa coupling” or mass term coupling between electron and Higgs boson § mass for lower component of SU(2)L doublets (charged leptons, down-type quarks) 2

remember: fermion masses for up-type quarks § use conjugate doublet for up-type quarks: § gauge invariant mass term for the up-type quarks can be constructed = zero after symmetry breaking § or § could also construct neutrino masses in this way: § § remember: neutrinos are also the “upper component” of the SU(2) doublets “Dirac” mass § but their Yukawa couplings would be extremely small (< 10 -12) § look for other mechanism? 3

Majorana mass § right-handed neutrinos and left-handed antineutrinos transform as singlets under the Standard Model gauge transformations § can add terms from these fields into Langrangian without breaking the gauge invariance § Majorana mass term: right-handed (chiral) neutrino left-handed (chiral) antineutrino § does not break gauge invariance § but provides direct coupling between particle and antiparticle § neutrinos could be their own antiparticles! Wait a minute. . . what about lepton number conservation? mixing!! Who is she and who is he? 4

Seesaw mechanism § rewrite as hermitian conjugate same thing § combined Dirac and Majorana ( ) mass terms: or § for physical states, diagonalize mass matrix! 5

Seesaw mechanism § if M >> m. D : never mind the sign - flip in definition of fields ν N or § mass eigenstates: § look for neutrinoless double beta decay to check if this can be true M m. D 2/M 6

important questions of today’s particle physics (ongoing research) • Why are particle masses so different? • Is there an overall (hidden) symmetry such as Supersymmetry (SUSY) “mirror world” of all known particles? . • What is the nature of “Dark Matter” and “Dark Energy” in the universe? • Why is there more matter than anti-matter? • Why have neutrinos such small mass? • Is there a Grand Unification which combines all interactions, including gravitation? • Are there extra dimensions, D > 4 ? ( string theory, …) 7

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