Proton decay?

1. Xiangdong Ji Maryland center for fundamental physics U of Maryland Are diamonds really forever? Proton decay? OCPA conference on Underground Science University of Hong Kong, July 23, 2008

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) Proton decay

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 • … Proton

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. Proton decay

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 Proton decay

6. GUT and B & L violation scale • 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 . Proton decay

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. Proton decay

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. Proton decay

9. Experiments Detector type Exposure (kt-year) Frejus Fe 2.0 HPW H2O <1.0 IMB H2O 11.2 Kamiokande H2O 3.8 KGF Fe <1.0 NUSEX Fe <1.0 Soudan 1 Fe <1.0 Soudan 2 Fe 5.9 Super-Kamiokande H2O 79.3 41032 Proton decay

10. Current limits Proton decay

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! Proton decay

12. SUSY • Adding supersymmetry improves the unification and pushes the unification scale to higher energy Proton decay

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. Proton decay

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. Proton decay

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 Proton decay

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 Proton decay

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 Proton decay

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 Proton decay

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 < 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) Proton decay

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… Proton decay

21. Future experimental opportunities • Japan: Hyper-K • US: DUSEL (UNO or LAr) • Europe: 100 kt LAr TPC, 1Mt WC detector at Frejus. Proton decay

22. How far can one go in this game? Proton decay

23. Exp. vs. theory Proton decay

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. Proton decay