Xiangdong JiMaryland center for fundamental physicsU of Maryland

OCPA conference on Underground ScienceUniversity of Hong Kong, July 23, 2008

One of the most profitable themes in physics! Electricity and magnetism Light! Electromagnetism and weak force W,

Z and spontaneous symmetry breakingWill this trend continue?

Electroweak + strong? (GUTs) + gravity? (string theory)

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Pati-Salam SU(2) LSU(2) RSU(4) C

Georgi-Glashow SU(5)SO(10)Exceptional groups E6 and E8

Adding supersymmerty, extra dimension

…

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In a typical GUT, quarks and leptons are placed in the same representation of some unification group. SU(5) example F = (d1, d2, d3, , e)

ALL the particles in a multiplet are the “same stuff” that can be rotated into each other through gauge and Yukawa interactions.

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Hence the baryon and lepton numbers are no longer separately conserved and proton Is not absolutely stable!

Decay product: light leptons (muon and electron and

neutrinos) + light mesons (pions and kaons)

Example: P 0 + e+

A diamond will eventually dissolve into light + neutrinos + electrons

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GUT is a beautiful idea but the scale is very high, at least larger than 1015~16 GeV Can one really trust a theory

at that high-energy scale and pretend that nothing will happen in between?

Similar question for the sea-saw mechanism, where the R-handed scale is on 1014 GeV

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Opportunist: Neutrino mass and proton decay probe

physics at extremely high-energy scale, otherwise unreachable using the conventional particle accelerator.

Pragmatist:Whatever the new physics might be, one

can always probe the low-energy baryon/lepton number violating limit, which might or might not be signals for grand unification.

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Baryon and lepton numbers are known to be conserved to very good precision in low-energy experiments.

SM have baryon and lepton number as accidental symmetry.

These symmetries will likely be broken in beyond-SM theories, taken into account by new high-dimensional operators.

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Detector type Exposure (kt-

year)

Frejus Fe 2.0HPW H2O <1.0IMB H2O 11.2Kamiokande H2O 3.8KGF Fe <1.0NUSEX Fe <1.0Soudan 1 Fe <1.0Soudan 2 Fe 5.9Super-Kamiokande H2O 79.3

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41032

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In non-SUSY GUT, proton decay is mediated by dimension-6 operators

The lifetime is simply,

Given a unified coupling and GUT scale, one can predict the lifetime, which can be tested immediately in experiments. Non-SUSY SU(5) & SO(10) rule out!

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Adding supersymmetry improves the unification and pushes the unification scale to higher energy

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Unlike SM, it is easy to write down operators which violate B and L.

Dimension-2 operators mixes leptons and quarks with higginos FH

Dimension-3 operators ucdcdc, QLdc, LLec

They either violate B or L, but not both, generating huge lepton and baryon number violations.

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If we imposes R-parity on the SUSY GUT, dimension-3 and 4 operators can be entirely eliminated particles have +1 parity and sparticles

have parity -1. There is no deep theoretical reason why R-

parity shall be conserved (LR symmetry). Small B & L violation might be the strong

empirical reason from R-parity conservation.

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Proton decay can happen with dimension-5 operators of the following formd

QQQL, ucucdcec

which are suppressed only by color triplet mass Mc

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Y2/Mc

Higgs color-triplet that generates dim-5 operator must have masses on the order of GUT scale.

On the other hand, the weak SU(2) doublet which gives rise masses of SM particles must live on the scale of EW symmetry breaking

It is not trivial to generate this stable scale separation in theory Huge theoretical literature

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The dimension-5 operator can be dressed with gauginos or higgsino to generator SM dim-6 operators

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Y2/Mc MSUSY

Y2/MGUT MSUSY

Large, because 1/MSUSY Suppression through yukawa coupling Results depend on sensitively on flavor

structure of the GUT, which is least known. Models

SU(5): simplest version has been rule out SO(10), many different versions for Y-

couplings

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Unification of the gauge coupling constants depends on the color-triplet threshold. At two-loop level, this gives a constraint

for the success of unification 3.5 1014 GeV < MC < 3.6 1015 GeV p K+ limit constraints the mass scale to

be MC > 2 1017 GeV The conflicts rules out the simple SU(5)

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There are many SO(10) models on the market which claim to fit all fermion masses, mixings including neutrino mixing matrix.

Generally they predict fast proton decay rates

SUSY proton decay problem! Way out

Special flavor structure leading to cancellation? Larger unification scale? Split SUSY Extra dimension…

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Japan: Hyper-KUS: DUSEL (UNO or LAr)Europe: 100 kt LAr TPC, 1Mt WC

detector at Frejus.

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Proton decay has not yet been seen yet, but its longevity suggests baryon number violation is small and is perhaps related to GUT and small neutrino mass.

However, GUT model building is increasingly complicated. Along with SUSY flavor, CP problems, now we likely have a SUSY proton decay problem.

It is very exciting to push the current limit by another order of magnitude.

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