Proton decay?

1
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

2
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)

3
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

4
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.

5
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

6
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

.
7
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.

8
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.

9
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
10
Current limits
11
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!

12
SUSY

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

13
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.

14
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.

15
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
16
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

17
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
18
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

19
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)

20
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

21
Future experimental opportunities

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

22
How far can one go in this game?
23
Exp. vs. theory
24
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.