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Proton decay?

Are diamonds really forever?

OCPA conference on Underground Science University

of Hong Kong, July 23, 2008

- Xiangdong Ji
- Maryland center for fundamental physics
- U of Maryland

Grand unification

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

spontaneous symmetry breaking - Will this trend continue?
- Electroweak strong? (GUTs)
- gravity? (string theory)

Candidates for GUT

- Pati-Salam SU(2) L?SU(2) R?SU(4) C
- Georgi-Glashow SU(5)
- SO(10)
- Exceptional groups E6 and E8
- Adding supersymmerty, extra dimension

Almost all GUTs allow proton decay

- 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.

Proton decay

- 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

GUT and B L violation scale

- GUT is a beautiful idea but the scale is very

high, at least larger than 101516 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

.

Two attitudes

- 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.

B L violation

- 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.

Experiments

- Detector type

Exposure -

(kt-year) - Frejus Fe

2.0 - HPW H2O lt1.0
- IMB H2O

11.2 - Kamiokande H2O 3.8
- KGF Fe

lt1.0 - NUSEX Fe

lt1.0 - Soudan 1 Fe lt1.0
- Soudan 2 Fe

5.9 - Super-Kamiokande H2O 79.3

4?1032

Current limits

Non-SUSY GUT

- 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!

SUSY

- Adding supersymmetry improves the unification and

pushes the unification scale to higher energy

SUSY GUT

- 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.

R-parity

- 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.

Effective Dimension-5 operator

- Proton decay can happen with dimension-5

operators of the following formd - QQQL, ucucdcec
- which are suppressed only by color triplet

mass Mc

Y2/Mc

Doublet-triplet splitting

- 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

Dressing of Dim-5 operator

- The dimension-5 operator can be dressed with

gauginos or higgsino to generator SM dim-6

operators

Y2/Mc MSUSY

Magnitude of the dim-5 contribution

- 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

SUSY SU(5)

- 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 lt MC lt 3.6 ? 1015 GeV
- p ?K? limit constraints the mass scale to be
- MC gt 2 ? 1017 GeV
- The conflicts rules out the simple SU(5)

SO(10) models

- 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

Future experimental opportunities

- Japan Hyper-K
- US DUSEL (UNO or LAr)
- Europe 100 kt LAr TPC, 1Mt WC detector
- at Frejus.

How far can one go in this game?

Exp. vs. theory

Conclusion

- 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.