Physics 662. Particle Physics Phenomenology. February 21, Physics 662, lecture 13 1

Transcription

1 Physics 662 Particle Physics Phenomenology February 21, 2002 Physics 662, lecture 13 1

2 Physics Beyond the Standard Model Supersymmetry Grand Unified Theories: the SU(5) GUT Unification energy and weak mixing angle Supersymmetric SU(5) Proton Decay Neutrino mass: Dirac and Majorano neutrinos Neutrino Oscillations Magnetic Monopoles Superstrings Reference: Donald H. Perkins, Introduction to High Energy Physics, Fourth Edition Physics 662, lecture 13 2

3 The Standard Model SU(3) C x SU(2) x U(1) Y no serious conflict with data shortcomings: can we further unify electroweak and strong interactions Grand Unified Theory (GUT) hierarchy problem quantum effects are important at the Planck scale of GeV new particles at the Planck scale would lead to divergences in the Higgs mass through virtual loops, unless something is done to cancel them Supersymmetric models are designed to do this left-handed (only) neutrinos means massless neutrinos but neutrinos appear to have mass gravity left out Supergravity?? Physics 662, lecture 13 3

4 Supersymmetry Supersymmetry could provide cancellations in the divergent amplitudes in the hierarchy problem Fermion-boson symmetry every fermion has a superpartner: a boson every boson has a superpartner: a fermion Broken symmetry Mass (superpartners ) >> Mass (original particles) However, radiative corrections from vitual boson and fermion loops are of opposite sign cancel for this to work, superpartner masses need to satisfy relation Associated production R parity M F2 -M B2 < 1 TeV 2 Lightest Supersymmetric Particle (LSP) stable photino??? Physics 662, lecture 13 4

5 Supersymmetry Minimal Supersymmetric Standard Model (MSSM) Two Higgs doublets 5 physical Higgs particles 4 higgsinos ( H 0 1,2 H ± ) mix with four gauginos (photino, winos, zino) to form 4 charginos χ ± 1,2 4 neutralinos χ 0 1,2,3,4 Physics 662, lecture 13 5

6 Supersymmetry Masses and couplings of the SUSY particles described by four parameters three masses and one mixing angle mixing angle: tanβ = v 1 /v 2 v 1 and v 2 are vacuum expectation values of the Higgs fields H 1 and H 2 Physics 662, lecture 13 6

7 Supersymmetry Physics 662, lecture 13 7

8 Grand Unified Theories: the SU(5) GUT Can we unified weak, EM and strong forces into one theory? SU(3) C x SU(2) x U(1) Y Considering the running of the coupling constants U(1) coupling g increases with energy (remember α increases with E) the non-abelian couplings decrease SU(2) g SU(3) g s do these couplings extrapolate to a common value at high energy? Assuming no new physics between EW scale and Planck scale Early, simple model was SU(5) of Georgi and Glashow in 1974 quarks and leptons brought together into multiplets leptons and quarks interact through heavy bosons, the Y and X Q = -1/3 Q = -2/3 12 new gauge bosons Physics 662, lecture 13 8

9 Grand Unified Theories: the SU(5) GUT Fermion multiplets Physics 662, lecture 13 9

10 Grand Unified Theories: the SU(5) GUT SU(5) has the following attractive features: fractionally charge quarks are natural since Σ i Q i = 0 in multiplet Equally of proton and electron charge explained Charge conservation automatic Similarity of lepton and quark weak doublet patterns explained u d u d Physics 662, lecture 13 10

11 Unification energy and weak mixing angle Since the Z and the photon are orthogonal, the following diagram must vanish Σ f Q f (I 3 f - Q f sin 2 θ W ) = 0 Σ f Q f I 3 f - Σ f Q f 2 sin 2 θ W = 0 sin 2 θ W = (Σ f Q f I 3 f ) / (Σ f Q f 2 ) = 3/8 since e = g sin θ W sin 2 θ W = e 2 /g 2 = 3/8 at unification IQ Q / /9 0 1/9 0 1/9 1/2 4/3 Physics 662, lecture 13 11

12 Unification energy and weak mixing angle The couplings of U(1), SU(2), and SU(3) are α 1 = 8 α em /3 = 8 (e 2 /4π)/3 α 2 = g 2 /4π α 3 = g s 2 /2π Unification at E = M X : n b = 0 [U(1)] 2 [SU(2)] 3 [SU(3)] n f = 3 Physics 662, lecture 13 12

13 Unification energy and weak mixing angle Unification fails Energy scale, GeV Physics 662, lecture 13 13

14 Supersymmetric SU(5) Supersymmetry introduces new elementary fermions and bosons, so the slopes of the coupling constants change there is also an energy scale where this evolution takes over, E SUSY For E SUSY = 1 TeV, unification appears at E GUT = 3 x GeV with α GUT = 1/24 α -1 Energy scale, GeV Physics 662, lecture 13 14

15 Proton Decay Grand Unification implies quarks can transform to leptons Note, B and L are not conserved, but B-L is conserved Consider non-susy unification: M X = 3 x GeV, α GUT = 1/43, A=1 Physics 662, lecture 13 15

16 Proton Decay No proton decay events have been seen, despite very sensitive experiments, like SuperK For p e + + π 0, τ P / BR > 5 x years Physics 662, lecture 13 16

17 Proton Decay Physics 662, lecture 13 17

18 Proton Decay Physics 662, lecture 13 18

19 Proton Decay Physics 662, lecture 13 19

20 Physics Beyond the Standard Model Supersymmetry Grand Unified Theories: the SU(5) GUT Unification energy and weak mixing angle Supersymmetric SU(5) Proton Decay Neutrino mass: Dirac and Majorano neutrinos Neutrino Oscillations Magnetic Monopoles Superstrings Reference: Donald H. Perkins, Introduction to High Energy Physics, Fourth Edition Physics 662, lecture 13 20