Proton Decay Without GUT. Hitoshi Murayama (IAS) UCLA Dec 3, 2003

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1 Proton Decay Without GUT Hitoshi Murayama (IAS) UCLA Dec 3, 2003

2 Outline Why We Expect Proton Decay Story with Supersymmetry A Very Ambitious Model More on GUTs Conclusions Hitoshi Murayama UCLA

3 Why We Expect Proton Decay

4 Problem with Anti-Matter Anderson discovered positron e +, antimatter of electron in 1932 A very naïve question: Why doesn t proton decay p e + γ? Stückelberg (1939) made up a new conservation law: Baryon number must be conserved (later also by Wigner, 1949) Hitoshi Murayama UCLA

5 Lepton Family Number Similarly ad-hoc conservation law Neddermeyer-Anderson discovered muon in 1937 A very naïve question: Why doesn t muon decay µ e γ? Inoue-Sakata made up a new conservation law: Lepton Family number must be conserved Neutrino oscillations (SuperK & SNO) have disproven lepton family number conservation! Hitoshi Murayama UCLA

6 Sacred and secular laws Sacred conservation laws: consequences of fundamental principles such as gauge invariance, Lorentz invariance, unitarity e.g., electric charge, CPT, energy-momentum Secular conservation laws: Happen to be approximately true, but ultimately violated e.g., parity, CP, lepton family Hitoshi Murayama UCLA

7 Fate of Secular Conservation Laws Parity Charge Conjugation CP T Lepton Family Lepton Number Baryon Number Fallen 1956 Fallen 1956 Fallen 1964 Fallen 1999 Fallen 1998 (µ), 2002 (e) Still viable (0νββ?) Still viable Hitoshi Murayama UCLA

8 Baryon Number is Probably Violated Universe is made of baryons, no anti-baryons There must have been a process in early Universe that created this asymmetry via baryon number violation Such baryon number violation may (but not necessarily) lead to proton decay Old philosophy (e.g., Yang-Mills): all conserved quantities must be local gauge charges Quantum gravity (virtual blackholes, wormholes) violate global (non-gauge) charges Hitoshi Murayama UCLA

9 B is Violated Actually, SM violates B (but not B L). In Early Universe (T > 200GeV), W/Z are massless and fluctuate in W/Z plasma Energy levels for lefthanded quarks/leptons fluctuate correspondingly ΔL=ΔQ=ΔQ=ΔQ=ΔB=1 Δ(B L)=0 Hitoshi Murayama UCLA

10 But Anomaly is Small At zero temperature, the anomaly process occurs only via tunneling ΔB=ΔL=N g t Hooft (1976) estimated its effect on twogeneration case ΔB=ΔL=2 τ(d e + ν µ )~ years Three-generation case gives ΔB=ΔL=3 τ(t e + ν µ ν τ )~ years Need motivated model of B violation e.g., GUT (Note any new particles potential source of B viol.) Hitoshi Murayama UCLA

11 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 wellmotivated theories that lead to proton decay But doesn t have to be GUTs 11

12 Story with Supersymmetry

13 Supersymmetry and R-parity Supersymmetry predicts new particles Gauge invariance allows baryon- and leptonnumber violating interactions even within the MSSM Baryon number violation: W=udd Lepton number violation: W=QdL+LLe+LH u Baryon number is no longer conserved accidentally If both types present, they will induce proton decay Hitoshi Murayama UCLA

14 R-parity Violation If GUT, 10 5* 5* contains both udd & QdL If they exist with O(1) couplings: τ p ~m sq4 /m p5 ~10 12 sec! Product of two couplings < Impose R-parity = ( 1) 3B+L+2S Forbids baryon and lepton number violation W=udd+QdL+LLe+Lh u Stable Lightest Supersymmetric Particle Cold Dark Matter Hitoshi Murayama UCLA

15 Dirty Little Secret about Supersymmetry But R-parity is not enough! Once supersymmetry is there, with or without grand unification, Planck-scale physics can cause too-rapid proton decay Dangerous operators: Typically, h < , 10 7, respectively (Kakizaki, Yamaguchi) Hitoshi Murayama UCLA

16 But there are small numbers But remember that we actually do see small numbers in our daily life. Hitoshi Murayama UCLA

17 But there are small numbers But remember that we actually do see small numbers in our daily life. Yukawa couplings for 1st, 2nd generations are pretty small. Using λ~θ C ~0.22, h u /h t ~λ 8, h d /h b ~λ 4, h e /h t ~λ 5 Aren t they unnatural? Yes, of course! Hitoshi Murayama UCLA

18 Question of Flavor What distinguishes different generations? Same gauge quantum numbers, yet different Hierarchy with small mixings: Need some ordered structure Probably a hidden flavor quantum number Need flavor symmetry Flavor symmetry must allow top Yukawa Other Yukawas forbidden Small symmetry breaking generates small Yukawas Hitoshi Murayama UCLA

19 Broken Flavor Symmetry Flavor quantum numbers (SU(5)-like): 10(Q, u R, e R ) (+4, +2, 0) 5*(L, d R ) (+2, +2, +2) Flavor symmetry broken by a VEV λ ~0.22 M u ~ λ 8 λ 6 λ 4 λ 6 λ 4 λ 2, M ~ λ 4 λ 2 1 d λ 6 λ 6 λ 6 λ 4 λ 4 λ 4, M ~ λ 2 λ 2 λ 2 l m u :m c :m t ~ m d2 :m s2 :m b2 ~ m e2 :m µ2 :m τ 2 ~ λ 8 : λ 4 :1 λ 6 λ 4 λ 2 λ 6 λ 4 λ 2 λ 6 λ 4 λ 2 Hitoshi Murayama UCLA

20 Not bad! m b ~ 3m τ, m s ~ 3m µ, m d ~ 3m e m u :m c :m t ~ m d2 :m s2 :m b2 ~ m e2 :m µ2 :m τ 2 Hitoshi Murayama UCLA

21 Flavor Symmetry Suppresses Proton Decay, too! Once the quarks and leptons carry a new charge, it would forbid the dangerous proton decay operators. Proton decay may be suppressed because of the same reason why 1st and 2nd generation particles are light. (HM, D.B. Kaplan) Previous charge assignment gives h~λ 12 ~ Interesting number! Hitoshi Murayama UCLA

22 A Very Ambitious Model

23 Anomalous U(1) from String Theory Flavor symmetries tend to be anomalous. Isn t that a problem? Actually, string theory tends to give you an anomalous U(1) gauge symmetry Because it is anomalous, it gets broken shortly below the string scale Dynamically generates the seed hierarchy for fermion masses λ~<a>/m Pl Hitoshi Murayama UCLA

24 Anomalous U(1) from String Theory Anomalies actually cancelled by the Green Schwarz mechanism Still subject to strong constraints Given phenomenological constraints on quarks & lepton masses, CKM matrix, now even neutrino masses and MNS matrix, the charge assignments quite restricted Hitoshi Murayama UCLA

25 A Very Ambitious Attempt Use anomalous U(1) for everything The only symmetry beyond SU(3) C SU(2) L U(1) Y Only two right-handed neutrinos No new mass scales except for M Pl and m SUSY Quark masses and CKM matrix Lepton masses Right-handed neutrino masses (no GUT-scale) Left-handed neutrino masses and MNS matrix R-parity as an unbroken subgroup of U(1) Adequate suppression of proton decay? (Dreiner, HM, Thormeier) Hitoshi Murayama UCLA

26 Ansatz Successful masses and mixings Find U(1) charges consistent with this ansatz, anomaly cancellation, automatic R- parity four solutions Hitoshi Murayama UCLA

27 Consequence on Proton Decay The operators Suppression factors for all four viable models: h ~ λ 12 or λ 13 ~ cf. τ(p K + ν) > years (90% CL) (SK) cf. τ(p K + ν) > years (unpublished) Hitoshi Murayama UCLA

28 Consequence on Proton Decay p K + ν still dominant liquid Argon However, p K 0 µ +, K 0 π 0 π 0 γγγγ would be quite spectacular in water Cherenkov, presumably with a higher efficiency than ~10% for K + ν But nuclear absorption? Important lesson: many different modes are possible Hitoshi Murayama UCLA

29 Charges aren t nice But likely due to too restrictive phenomenological ansatz Hitoshi Murayama UCLA

30 Conclusions Baryon Number Violation is naturally expected at some level even without grand unification Supersymmetry connects proton decay to Planck-scale physics Proton decay suppression may well be due to the same reason why electron is light Models suggest rates at interesting levels Hitoshi Murayama UCLA

31 More on GUTs

32 Rest In Peace Minimal SUSY SU(5) GUT RGE analysis SuperK limit τ(p K + ν) > years (90% CL) M Hc > GeV Even if 1st, 2nd generation scalars decoupled, 3rd generation contribution (Goto, Nihei) M Hc > GeV (HM, Pierce) Hitoshi Murayama UCLA

33 It doesn t rule out SUSY-GUT Unfortunately, the prediction of the proton decay via D=5 operator is sensitive to the ugliest aspect of the SUSY-GUTs Triplet-doublet splitting Fermion mass relation m l =m d Any solution to these big problems is likely to modify the proton decay prediction. Hitoshi Murayama UCLA

34 Triplet-Doublet Splitting Flipped SU(5) Flipped SU(5) Ellis et al Not quite a unification SU(5) U(1) Broken by 10 1 (not 24) Triplet massive by W= H No triplet-doublet splitting problem Eliminates D=5 operator completely M GUT where SU(3) and SU(2) meet is ~10 15 GeV D=6 can be important SuperK: τ(p e + π 0 )> year (90% CL, 25.5 kt year) Minimal SUSY GUT: τ(p e + π 0 )= year (M V /10 16 GeV) 4 M V > GeV Flipped SU(5): τ(p e + π 0 )= year (M V /10 16 GeV) 4 M V > GeV (HM, Pierce) Hitoshi Murayama UCLA

35 Triplet-Doublet Splitting Orbifold GUT Breaking (Kawamura; Hall, Nomura) SU(5) SU(3) SU(2) U(1) normally achieved by <Σ(adjoint)> 0 New way to break SU(5) by boundary conditions on extra line segment S 1 /Z 2 Boundary conditions explicitly break SU(5) Still unitarity OK (Hall, HM, Nomura) Natural triplet-doublet splitting Gauge coupling unification improved No D=5 operator Compactification scale M c ~10 15 GeV Can have new D=6 operators on the fixed point ~1/M 2 c Hitoshi Murayama UCLA

36 p e + π 0 SuperK: τ(p e + π 0 )> year (90% CL, 25.5 kt year) Minimal SUSY GUT: τ(p e + π 0 )= year (M V /10 16 GeV) 4 M V > GeV Flipped SU(5): τ(p e + π 0 )= year (M V /10 16 GeV) 4 M V > GeV 5-D orbifold GUT: τ(p e + π 0 ) year May well be just around the corner 36

37 Fermion Mass Relation Georgi-Jarlskog Georgi-Jarskog relation m e ~m d /3 m µ ~m s *3 Can be achieved using Higgs in 45* rather than 5* Different Clebsch-Gordan factors D=5 operator worse by a factor of two 2 2 Hitoshi Murayama UCLA

38 Threshold Corrections Add an otherwise unmotivated additional 5+5* Split them using <Σ> in the opposite way from Higgs: Triplet lighter Doublet heavier Changes the threshold correction and allows M Hc raised (HM,Pierce) SO(10) models have many more fields at the GUTscale Typically worse than SU(5) But larger possible range in threshold correction Allows M Hc raised somewhat Just above the current limit τ(p K + ν)<10 34 yrs (Babu, Pati, Wilczek) Hitoshi Murayama UCLA