Nucleon Decay Stuart Raby DUSEL 2010 Rapid City, SD October 2, 2010
Nucleon Decay Standard Model Baryon & Lepton number - anomalous global symmetries Weinberg - effective operators consistent with SM 1 M eg. ( * ) ( * µ ) b d 2 a µ uc 0 σ e σ u ε p e + π New physics at scale M breaks B & L eg. Grand unification M = M GUT eg. Universal large extra dims. abc p e π π νν + + M ~ TeV e e ( ) µ π ν + + +
Outline Evolution of SUSY GUTs 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions
Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions
The Goal of Beyond SM physics Reduce # fundamental parameters 18 parameters in Standard Model 13 charged fermion masses & mixing + 3 gauge couplings + 2 W & Higgs mass 27 including neutrino masses & mixing 28 including QCD θ parameter 29 including G N
Supersymmetric Grand Unified Theories M Z << M G natural Explains charge quantization & Families Unification of gauge couplings Yukawa coupling unification + family symmetry fermion mass hierarchy Neutrino masses via See-Saw LSP - dark matter candidate Baryogenesis via leptogenesis SUSY desert LHC probes physics at M Pl SUSY GUTs natural extension of SM Title of talk 6
u ν q=, u, d, l =, e, ν d e 1 4 2 Y :,,, 1, + 2, 0 3 3 3 H u + 0 h h, H 0 d = = h h + 1, 1 Q EM = T + 3 Y 2 Title of talk 7
All interactions of fermions & Higgs with gauge bosons fixed by their charges Y Dµ = ( µ + igst AGµ A + igtaw µ a + ig Bµ ) 2 Lgauge fermion = [ l i D l + ] + [ Tr( G G ) + ] 2 * µ 1 µν σ µ µν L = DH + DH + V 2 2 gauge Higgs µ u µ d Higgs L = λ le H + λ qd H ij ij Yukawa e i j d d i j d ij ij 1 + λu qu i j Hu + λν liν j Hu Mijνν i j 2 Title of talk 8
The MSSM is obtained by defining chiral superfields Ey (, θ) = ey ( ) + 2( θey ( )) + ( θθ) F( y) y µ = x µ iθσ µ θ, ( θey ( )) θ α ey ( ) 4 Y Lgauge matter = d θ [ Li exp( 2 [ gsvg + gvw + g VB ]) Li + ] 2 1 + θ [ ( ) + ] +.. 2 α d Tr W 2 g Wgα h c 8gs L = dθ [ λ LE H + λ QD H 2 ij ij Yukawa e i j d d i j d + λ QU H + λ U V Q =, U, D,L =, EV, D E LV H ij ij u i j u ν i j u 1 Mij Vi V j µ Hu Hd ] + h. c. 2 Title of talk 9 e α
Grand Unification & Charge Quantization u u u q= u = d = d d d l ν = e e ( u u u) ( d d d ) SU(4) SU(2) SU(2) C L R Q u u u ν u u u ν = Q d d d e = d d d e Q = B L + T + T 1 2 ( ) 3 3 EM L R
Pati-Salam - lepton # = 4 th color Quarks & leptons fit into two irreducible reps. Q= ( ql), Q= ( ql) SU(4) SU(2) SU(2) u ν q=, l = (4,2,1) (4,1, 2) d e The two Higgs doublets H = ( H H ) (1, 2, 2) d u C L R QHQ λ λ = λ = λ = λ λ t b τ ν τ Yukawa coupling unification Title of talk 11
Grand Unification - SO( 10 ) GUT 1 Georgi Fritszch & Minkowski spinor repsn. of SO( 10 ) 10 tensor product of 5 spin ½ w/even no. + signs 5 Title of talk Georgi & Glashow SU(5) 12
Gauge coupling unification Boundary conditions at M GUT A A a Y ggta G gst AG + gtaw + g' B 2 µ µ µ µ g,, ' 3 s = g g = g g = g 5 3 2 1 2 2 g ' 3 3 2 1, sin θ G W 2 2 g = g = g = g = = g + g' 8 Title of talk 13
Gauge coupling unification Dimopoulos, Raby & Wilczek PRD24, 1681 (1981) LEP data!! Amaldi, de Boer & Furstenau, PLB260, 447 (1991) Title of talk 14
ε 3 Title of talk 15
This assumes degenerate squarks and sleptons and degenerate gauginos at GUT scale. If, for example, even have ε. 3 0 M3 << M2 M1 then can See Raby, Ratz, Schmidt-Hoberg arxiv:0911.4249 [hep-ph] Title of talk 16
Proton decay - dim 6 operators c l i c d a Title of talk 17
p + e π 0 Title of talk 18
Super Kamiokande bound τ p + 0 1 10 Br( p e π ) 34 yrs Theory τ p M Br( p e + π ) g m 4 G 0 4 5 G p 3 2 4 37 0.012 GeV M X 10 16 α 3 10 GeV yrs Title of talk 19
Proton decay - dim 4 operators 10 5 5 λ UDD+ λ' Q L D + λ" EL L P p π π ν or ( π π, π π ) + 0 0 0 + + Title of talk 20 e
Γ p ( λλ' ) m 2 m 5 p 4 λλ' m 2 g G 32 2 26 m < 10 GeV λλ' < 10 M G 1TeV 2 2 2 2 matter parity excludes dim 4 operators F -F, H H Title of talk 21
Proton decay - dim 5 operators 10 1010 5 Q QQ L + UU DE p K ν Title of talk 22 +
λλ t ( LF) τ µ 16π + 2 2 1/2 2 2 m16 + cc Ap ( Kν ) (LF) eff M T M c ~ Yukawa couplings minimize LF maximize M T eff Eg. "Natural" D T splitting W 10 45 10 + (10 ) 45 G 2 X with M B L ( ) M T 0 M G 1 X 0 0 =, M eff 2 D MG X = MT M G 0 X Thus for eff X << M obtain M >> M G T G Title of talk 23
= + + Higgs GUT breaking 3 3 3 Higgs 3 eff 3α G M T = ln( ) 5π M G Minimal SU 5 : Proton decays toooo fast!! 33 τ > 2.3 10 yrs (92 ktyr) at 90% CL ( p K + ν ) ~ (1/3-3) 10 34 yrs Theory Title of talk 24
Minimal SU 5 excluded! Caveats: 1. Family structure is standard 2. ε 3 < 0 Title of talk 25
Minimal SO(10) Model 45 W 16 1016 + 16 10 16 + M Albright, Anderson, Babu, Barr, Barbieri, Berezhiani, Blazek, Carena, Dermisek, Dimopoulos, Hall, Pati, Raby, Romanino, Rossi, Starkman, Wagner, Wilczek, Wiesenfeldt, Willenbrock Effective higher dimension operators, Small rep s + Many predictions!! Possible UV completion to strings!! Title of talk 26
3 family SO 10 SUSY Model D 3 x U(1) Family Symmetry Superpotential Yukawa couplings χ 2 analysis Charged fermion masses & mixing Neutrino masses & mixing
Superpotential for charged fermion Yukawa couplings W = 16 1016 + 16 10χ ch. fermions 3 3 a a φ a φ a + χ Mχ χ + 45 163 + 45 16 + A16 M M a a a a φ φ 1 = φ2 φ Familon VEVs 0 = φ 2 assumed ( B ) 45 = L MG Title of talk 28
7 real para s + 4 phases SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family + 3 real Majorana Neutrino masses Dermisek & Raby PLB 622:327 (2005). Title of talk 29
Extend to neutrino sector ( λ λ ) W = 16 N 16 + N 16 neutrino 2 a a 3 3 3 ( SNN SNN) + + 1 2 a a a 3 3 3 S M S M a = = 16 = v a 3 3 16 Assume 3 new real para s Title of talk 30
Global χ 2 analysis 24 parameters at GUT scale compared to SM - 27 parameters CMSSM - 32 parameters Title of talk 31
χ 2 analysis including B physics Albrecht, Altmannshofer, Buras, Guadagnoli, & Straub JHEP 0710:055 (2007) Find good fits to quark, charged lepton & neutrino masses and mixing angles & test flavor violation in b physics some tension between b s γ & b s l + l - m 16 ~ 10 TeV Title of talk 32
+ What is the tension? ( SM ) χ µ A tan β sign 2 SM 7 t 7 7 C C C b t s A < 0 t χ χ γ C = C + C C SM SM 7 7 7 7 χ + BR(B X l l ) favors C + C + SM s 7 7 at 2 σ Title of talk 33
However C = C SM 7 7 B * + K l l Belle arxiv:0904.0770 Title of talk 34
Albrecht et al. JHEP 0710:055 (2007) Required SM 7 7 Title of talk 35 C = + C
MSO 10 SM & Large tan( β ) Predicts light Higgs with mass of order 120 130 GeV Predicts lighter 3 rd and heavy 1 st & 2 nd gen. squarks and sleptons (inverted scalar mass hier.) LFV bounds satisfied Enhances Br[ B s µ + µ ] Suppresses Br( B τ ν ) & M B s B X s γ, X s l + l - tension?? LHCb Title of talk 36
MSO 10 SM & Large tan( β ) predicts light gluinos ~ 300 500 GeV predicts light charginos and neutralinos LHC MSO 10 SM : Beautiful symmetry Many experimental tests!! Title of talk 37
Problems of SUSY GUTs GUT symmetry breaking Higgs doublet-triplet splitting Missing partner mechanism SU(5) W + M + H + H H + XH H 3 2 75 75 Hu 75 50 d 75 50 50 50 Missing VEV mechanism SO(10) ( ) 2 ( ) 4 2 W 45 + M 45 + X 16 16 + F X ( S S ) ( S S ) X ( ) + 16' 45 + 16 + 16' 45 + 16' + 10 4510' + ' 10' 1 2 Title of talk 38 2
Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions Title of talk 39
Orbifold GUTs in 5 or 6 dimensions GUT symmetry breaking Doublet-Triplet splitting Kawamura; Hall & Nomura; Contino, Pilo, Rattazzi & Trincherini; Altarelli, Feruglio & Masina; Dermisek & Mafi; H.D. Kim & Raby; Asaka, Buchmuller & Covi; Lee; Hebecker & March-Russell H.D.Kim, Raby & Schradin JHEP 0505:036 (2005) Title of talk 40
Hall & Nomura SU(5) GUT on M x S 1 /(Z 2 x Z 2 ) GUT symmetry breaking Suppress b-τ Yukawa Higgs D-T splitting proton decay unification via orbifold BCs 10 + 5 rd 3 family Brane states c ( H + H ) ( c H + H ) 1 st & 2 nd families in bulk Bulk states π R Title of talk 41
G.C. Unif. & Proton decay > 4D 5D Orbifold GUT KK modes 0 πr M c ~ 1/πR < M G < M * Dienes et al., Hall & Nomura, Kim & S.R., Feruglio et al. Title of talk 42
u G.C. Unif. & Proton decay Enhanced > 4D!! 5D Orbifold u GUT Dim 6 amp. ~ 1 / M C 2 u u } π 0 P 0 R M C Brane e d Proton 0 π + e + M c ~ 1/R < M G < M * γγ Title of talk 43
G.C. Unif. & Proton decay Suppressed > 4D!! Dim 6 amp. ~ 1 / M C 2 u 5D Orbifold u GUT u U } π 0 P 0 R M C Bulk E d Proton 0 π + e + M c ~ 1/R < M G < M * γγ Title of talk 44
Orbifold GUTs in 5 or 6 dimensions : GUT breaking via Orbifold Parity Higgs doublet - triplet splitting via Orbifold P NO proton decay via Dim 5 operators due to R symmetry Proton decay via Dim 6 operators can be suppressed, BUT typically enhanced (model dependent) Matter localization determines Yukawas Title of talk 45
Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions Title of talk 46
UV completion Orbifold GUTs in 5 or 6 dimensions Derived from heterotic string in 10 D Kobayashi, Raby & Zhang; Forste, Nilles, Vaudrevange & Wingerter; Buchmuller, Hamaguchi, Lebedev & Ratz; JE Kim, JH Kim & Kyae; Buchmuller, Ludeling & Schmidt Title of talk 47
Road to the MSSM with R-parity Lebedev et al. 0708.2691[hep-th] Find 15 models from orbifold compactification of E(8)xE(8) heterotic string MSSM spectrum at low energy Exact R parity Light Higgs Non-trivial charged fermion masses Neutrino masses via See-Saw Title of talk 48
Compactify E(8)xE(8) heterotic string on (T 2 ) 3 /(Z 3 ) + A 3 only ( R 5 >> l s ) SU(6) orbifold GUT BULK After Z 2 SU(5) brane Z 2 = Z 2 + A 2 SU(4)xSU(2) brane Title of talk 49
Bulk states SU( 6) SU( 5) 35 24 + 5 + 5 + 1 H + H Gauge Higgs unification! c t 20 20 ( 10 10 ) + + + Q = + t + b ( c ν 2 6 6 ) τ + L= + b τ Tree level coupling u d 3 rd family Title of talk 50 τ 20 35 20 c Q H t u
Benchmark model 1 - Spectrum S Title of talk 51
Yukawa couplings Effective higher dimension operators!! Neutrino masses via See-Saw!! Title of talk 52
4 3 2 R symmetry LR S V Q U D L E V H H R 4 1 1 1 1 1 1 0 0 u d Superpotential W has charge 2 Title of talk 53
Conclusions Evolution of SUSY GUT Model Building Bottom up 4D SUSY GUT + family symmetry test predictions via global χ 2 analysis Lift to 5D ( or 6D ) orbifold GUT Top down Derive from heterotic string, M or F theory includes Gravity!! Title of talk 54