Standard Model - Standard Model prediction (postulated that neutrinos are massless, consistent with observation that individual lepton flavors seemed to be conserved and total lepton number as well) - Why 3 families ? - Origin of masses and hierarchy of masses and mixing angles? - Phenomenon of neutrino oscillations? Barion number violation has been a powerful way to probe physics beyond the Standard Model.

A Brief History of Barion Number Problem with Anti-Matter Anderson discovered positron e +, anti-matter of electron in 1932 A very naive question: Why doesn’t proton decay p  e +  ? Stückelberg (1939) made up a new conservation law: Baryon number must be conserved (later also by Wigner, 1949)

Lepton Family Number Similarly ad-hoc conservation law Neddermeyer-Anderson discovered muon in 1937 A very naive question: Why doesn’t muon decay    e   ? Inoue-Sakata made up a new conservation law: Lepton Family number must be conserved Neutrino oscillations (SuperK, SNO, KamLAND) have disapproved lepton family number conservation!

4 Baryon Number as an Accidental Symmetry In the Standard Model, the proton is absolutely stable Baryon Number is an “accidental” symmetry, i.e., there is no renormalizable interaction you can write down that violates the baryon number with the minimal particle content But once beyond the Standard Model, there is no reason for baryon number to be conserved. Grand Unified Theories prime example of well-motivated theories that lead to nucleon decay

Gauge Coupling Unification There are many ways in which the SU(2), U(1), SU(3) symmetries could be incorporated into a more global gauge symmetry. The simplest grand unified symmetryis that of the group SU(5) – Georgi and Glashow (1974). A Minimal Supersymmetric Standard Model is a class of proposed supersymmetric extensions to the Standard Model. Minimal supersymmetry assumes that the interaction between particles conserves R-parity and every particle has one superpartner.

SU(5) Quarks and leptons in the same multiplet Gauge bosons Y and X ~ 10^15GeV Quarks can transform to leptons and antiquarks Cause proton decay via D=6 operators! p  e +  0 IMB excluded the original SU(5) GUT by setting the limit on proton decay Also, neutrinos are considered to be massless and occur in only one helicity state

SUSY GUTs Idea of symmetry between bosons and fermions Complete unification possible with symmetry group S(10) One universal gauge coupling α g One family of quarks and leptons

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Current Limits Super-Kamiokande bounds on nucleon lifetime: ( 79.3 ktyr exposure ) ( 61 ktyr exposure ) ( 79.3 ktyr exposure ) ( 61 ktyr exposure ) at 90% CL Minimal non-supersymmetric SU(5) the unification scale is Mg ~ Predict the most dominant decay mode to be: with a partial lifetime of IMB-3 Collaboration SNO limit:

Current Limits Nucleon decay channels and partial lifetime predictions have been calculated for variety of GUT models including: - non-minimal SU(5) - minimal and non-minimal SU(10) - E6 GUT model All fail on the basis of unification scale Mg ~ Implies too rapid nucleon decay rate as well as a prediction for That is inconsistent with the high precision LEP measurements. Non-minimal SUSY SO(10) – has predictions consistent with current limits

Supersymmetry postulates that for every Standard Model particle there is a corresponding supersymmetric particle (or ``sparticle'') which has a spin that is different by 1/2 unit. SUperSYmmetry Figure 1: A Higgs boson dissociating into a virtual fermion-antifermion pair Figure 2: A Higgs boson dissociating into a virtual sfermion-antisfermion pair; Figure 1 shows a Feynman diagram involving a Higgs boson. The Higgs boson gives masses to particles; this diagram is one of many that contributes to the Higgs boson's own mass. There are infinitely many such diagrams, involving more than one such fermion loop, and if one tries to calculate the Higgs mass correction, one gets a value which diverges to infinity The existence of particles with exactly the same properties as the Standard Model particles, except for different spins, helps solve the divergence problem (Higgs example). For every diagram like Figure 1 there is a diagram that looks like Figure 2; these diagrams have the same vertices and coupling constants, and hence the same magnitude for the amplitude. But since the particle spins are different, the amplitude has the opposite sign. So when calculating the cross section, the amplitudes cancel yielding a finite interaction probability.

There exists a quantum number known as R-parity. Unlike the additive quantum numbers, this is a multiplicative quantum number, where all normal particles have R=1 and SUSY particles have R= -1. It is postulated that at every vertex, the product of R for each particle must be +1. Figure shows the production of a pair of neutralinos. There are two vertices in the graph; each vertex involves one SM particle and two SUSY particles; thus the R for each vertex is 1. Figure 8: The production of a pair of neutralinos. A practical consequences of R-parity conservation is that every SUSY interaction must involve two SUSY particles. SUSY particles must be created in pairs, and a SUSY particle must decay into another SUSY particle and Standard Model particles. It also means that the lightest SUSY particle (LSP) cannot decay, since there is no lighter SUSY particle that it can decay into. SUperSYmmetry

In the Standard Model, we don't bother distinguishing between left- and right-handed fermions, since they have the same mass and can be easily converted into each other by flipping the spins. Their supersymmetric partners are spin-0, so the partner of the left-handed fermion can be completely unrelated to the partner of the right-handed fermion, so the sfermions appear as two different states with different masses. Exception: in the Standard Model, there are only left-handed neutrinos (although this isn't quite true if neutrinos have mass), so there is only one sneutrino from each generation.

References Grand Unified Theories. Written April 2002 by S. Raby (Ohio State University). Nucleon Decay in a Realistic SO(10) SUSY GUT Authors: Vincent Lucas, Stuart Raby (The Ohio State University) Journal-ref: Phys.Rev. D55 (1997) Vincent LucasStuart Raby