Minimal SUSY SU(5) GUT in High- scale SUSY

Minimal SUSY SU(5) GUT in High- scale SUSY Natsumi Nagata Nagoya University 22 May, 2013 Planck 2013 Based on J. Hisano, T. Kuwahara, N. Nagata, 1302.2194 (accepted for publication in PLB). J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata, 1304.3651.

SUSY SM Supersymmetric (SUSY) Standard Model (SM) scale TeV SUSY parbcles EW SM parbcles

SUSY SM Supersymmetric (SUSY) Standard Model (SM) scale [GeV] m 1/2 700 600 MSUGRA/CMSSM: tan! = 10, A = 0, µ>0 0 ATLAS -1 " L dt = 4.7 fb, Combined s=7 TeV SUSY Observed limit (±1# ) theory Expected limit (±1# exp ) TeV 500 SUSY parbcles 400 q (1000) q (1400) q (1800) -1 PLB 710 (2012) 67-85, 1.04 fb $% LSP LEP Chargino No EWSB g (1200) g (1000) EW SM parbcles 300 200 q (600) g (600) g (800) 500 1000 1500 2000 2500 3000 3500 4000 m 0 [GeV] Direct search

SUSY SM Supersymmetric (SUSY) Standard Model (SM) scale Events / 2 GeV 3000 2500 2000 1500 TeV 1000 EW g 3500 ATLAS 500 200-1 s=7 TeV, Ldt=4.8fb -1 s=8 TeV, Ldt=5.9fb (a) Data Sig+Bkg Fit (m =126.5 GeV) H Bkg (4th order polynomial) 500 SUSY parbcles 400 H 126 GeV 300 Higgs boson 200 SM parbcles [GeV] m 1/2 700 600 MSUGRA/CMSSM: tan! = 10, A = 0, µ>0 0 q (600) q (1000) q (1400) q (1800) ATLAS -1 " L dt = 4.7 fb, Combined LEP Chargino No EWSB g (1200) g (600) s=7 TeV SUSY Observed limit (±1# ) theory Expected limit (±1# exp ) -1 PLB 710 (2012) 67-85, 1.04 fb $% LSP g (1000) g (800) 500 1000 1500 2000 2500 3000 3500 4000 m 0 [GeV] Direct search

SUSY SM Supersymmetric (SUSY) Standard Model (SM) scale High- scale SUSY?? Events / 2 GeV 3000 2500 2000 1500 TeV 1000 EW g 3500 ATLAS 500 200-1 s=7 TeV, Ldt=4.8fb -1 s=8 TeV, Ldt=5.9fb (a) Data Sig+Bkg Fit (m =126.5 GeV) H Bkg (4th order polynomial) 500 SUSY parbcles 400 H 126 GeV 300 Higgs boson 200 SM parbcles [GeV] m 1/2 700 600 MSUGRA/CMSSM: tan! = 10, A = 0, µ>0 0 q (600) q (1000) q (1400) q (1800) ATLAS -1 " L dt = 4.7 fb, Combined LEP Chargino No EWSB g (1200) g (600) s=7 TeV SUSY Observed limit (±1# ) theory Expected limit (±1# exp ) -1 PLB 710 (2012) 67-85, 1.04 fb $% LSP g (1000) g (800) 500 1000 1500 2000 2500 3000 3500 4000 m 0 [GeV] Direct search

AMracBve features High- scale SUSY scenario has a lot of fascinabng aspects from a phenomenological point of view. 126 GeV Higgs boson can be achieved SUSY flavor & CP problems are relaxed GraviBno problem is avoided DM candidates (wino/higgsino) Gauge coupling unificabon (sufficient radiabve correcbons) (suppressed by sfermion masses) (heavy gravibno) w/ light fermions (chiral symmetries)

Today s topic Proton decay problem in the minimal SUSY SU(5) GUT. In the minimal SUSY GUT, the dominant decay mode of proton is induced by the exchanges of the color- triplet Higgs mulbplet. Predicted lifebme (in low- scale SUSY): Experimental constraints: Minimal SUSY GUT is excluded T. Goto and T. Nihei (1999), H. Murayama and A. Pierce (2001). Super- Kamiokande, arxiv: 1109.3262. needs some extensions to suppress the decay mode (PQ symmetry, higher- dimensional models, etc.)

Today s topic Proton decay problem in the minimal SUSY SU(5) GUT. In the minimal SUSY GUT, the dominant decay mode of proton is induced by the exchanges of the color- triplet Higgs mulbplet. Predicted lifebme (in low- scale SUSY): Experimental constraints: Minimal SUSY GUT is excluded T. Goto and T. Nihei (1999), H. Murayama and A. Pierce (2001). Super- Kamiokande, arxiv: 1109.3262. needs some extensions to suppress the decay mode (PQ symmetry, higher- dimensional models, etc.) Decoupling can revive the minimal SUSY SU(5) GUT Simple solubon. No need for addibonal mechanism.

Mass spectrum On the assumpbon of a generic Kahler potenbal and no singlet field in the SUSY breaking sector Scalar Par cles Gravi no Higgsinos M S = 10 (2-3) TeV Gauginos Gluino Anomaly mediation (Loop suppressed) Bino L. Randall and R. Sundrum (1998) G.F. Giudice, M.A. Luty, H. Murayama, R. RaMazzi (1998) Wino 126 GeV Higgs boson mass can be achieved Thermal relic (2.7-3TeV) is consistent with energy density of dark mamer

Dim- 5 effecbve operators Q i Q k U i U k H C H C H C H C LLLL Q i L l E j D l RRRR Exchanges of color- triplet Higgs mulbplets induce the dimension- five baryon- number violabng operators. EffecBve superpotenbal RRRR LLLL

RGE analysis The superheavy parbcles yield threshold correcbons to the SM gauge couplings at the GUT scale (μ GUT ) α i - 1 (μ GUT ) = α G - 1 (μ GUT ) + threshold correcbons Unified gauge coupling depending on the masses of superheavy parbcles obtained through the renormalizabon group equabons (RGEs) Indirect method By using the relabon, we can esbmate the masses of superheavy parbcles at the GUT scale. J. Hisano, H. Murayama, T. Yanagida (1992).

Threshold correcbons @ GUT scale Threshold correcbons (1- loop in DR scheme) Then, we have We evaluate M HC by using the relabon. 2- loop RGEs + 1- loop threshold correcbons (μ GUT scale)

M HC vs. SUSY scale M Hc 10 18 10 17 10 16 M 3 /M 2 = 3 M 3 /M 2 = 9 M 3 /M 2 = 30 μ H = M S M 2 = 3TeV tanβ = 3 Errors come from the strong coupling constant Low- energy SUSY case 10 15 (M S : sfermion mass) 10 2 10 3 M S (TeV) M HC increases as M S grows while it decreases when M 3 /M 2 becomes large M HC can be around 10 16 GeV in high- scale SUSY scenario J. Hisano, T. Kuwahara, N. Nagata (2013).

Dim- 5 effecbve operators q L q L ll ( q L ) W q L (l L ) d R (s R ) t R H u Hd τ R u R Although it is induced in the flavor changing process, its contribubon is sizable because of the large Yukawa couplings of the third generabon fermions q L (a) LLLL Loop funcbon l L (q L ) s L (d L ) (b) RRRR (ν τ ) L T. Goto and T. Nihei (1999) V. Lucas and S. Raby (1997) Chiral flip [M = wino mass (M 2 ) or higgsino mass (μ H )] Suppressed by sfermion mass (decoupling) In the case of μ H >> M 2, the higgsino exchange contribubon dominates the wino exchange one.

Proton decay lifebme For μ H = M S, the proton lifebme is approximately given as RenormalizaBon factors The proton lifebme is significantly reduced with large tanβ. The lifebme can be well above the current experimental limit: Decoupling can revive the minimal SUSY SU(5) GUT!

Results lifetime (years) 10 36 10 35 10 34 M S = μh 16 M 2 = 3 TeV M = 1.0 10 GeV tanβ = 3 tanβ = 5 Hc tanβ = 10 tanβ = 30 tanβ = 50 10 33 Experimental limit 10 2 10 3 10 4 10 5 M S (TeV) Proton decay lifebme in high- scale SUSY scenario can evade the experimental constraints, especially for small tanβ. J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata (2013).

Results 10 36 M S = μh 15 M 2 = 3 TeV M = 1.0 10 GeV Hc lifetime (years) 10 35 10 34 tanβ = 3 tanβ = 5 tanβ = 10 tanβ = 30 10 33 Experimental limit 10 2 10 3 10 4 10 5 M S (TeV) Even in this case, the resultant proton decay lifebme can evade the experimental constraints. J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata (2013).

Summary We discuss the minimal SUSY SU(5) GUT in the high- scale SUSY scenario Dimension- 5 proton decay can evade the current experimental limits We look forward to future proton decay experiments

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1- loop results First, we derive simpler formulae by using Results 1- loop RGEs for gauge couplings 1- loop threshold correcbons Features M HC gets larger as M S is taken to be higher. (M S : scalar mass, μ H = M S ) It originates from the mass difference among the components of the fundamental Higgs mulbplets. M HC depends only on the rabo of M 2 and M 3.

EffecBve 4- Fermi operators Loop funcbon (A R (i,j), A R : renormalizabon factors)