Proton Decay in SUSY GUTs revisited J. Hisano (Nagoya Univ.) 2013 Interna,onal Workshop on Baryon and Lepton Number Violaon (BLV2013): From the Cosmos to the LHC April 8-11, 2013, MPIK Heidelberg, Germany 1 NNN13 International Workshop on ! Next Generation Nucleon Decay and Neutrino Detectors Nov.11-13, 2013 Kavli IPMU, Kashiwa, Japan http://indico.ipmu.jp/indico/conferenceDisplay.py?confId=17 2 Contents of my talk 1, IntroducAon of SUSY GUTs Does Higgs boson with mass 126 GeV mean existence of Grand Desert to SUSY GUTs? 2, SUSY SU(5) GUTs with extra maer in intermediate scale X boson Proton decay 3, SUSY SU(5) GUTs with high-scale SUSY Colored Higgs Proton decay X boson Proton decay 4, Summary This talk is based on recent works, JH, Kobayashi, and Nagata, Phys.Le. B716 (2012) 406-412 JH, Kobayashi, Muramatsu, and Nagata, arXiv:1302.2194 JH, Kuwahara, and Nagata, arXiv:1304.0343 JH, Kobayashi, and Kuwahara, Nagata, arXiv:1304.xxxx 3 1, IntroducAon Grand Unified Thories (GUTs) • Unificaon of gauge grouPs SU(3)C SU(2)L U(1)Y SU(5),SO(10),E6 × × ⊂ • Unificaon of quarks and lePtons In GUTs SU(5) c c ψ(10)=(uL,dL, (uR) , (eR) ) c φ(5 ) = ((dR) ,νL,eL) Electric charge quanAzaon is automac. 21 Q + Q < 10− | p e| Predicon of GUTs: • Gauge couPling unificaon • Proton decay 4 Gauge couPling unificaon • SuPersymmetry (SUSY), which is a symmetry between boson and fermion, is needed for the gauge hierarchy Problem. The standard model (SM) should be suPersymmetric around TeV scale in the GUTs. • If the minimal suPersymmetric standard model (MSSM) is realized at TeV scale, the three SM gauge couPling couPling constants meets at 16 2* 10 GeV. (From SUSY primer by S.MarAn) Grand Desert from MSSM to SUSY GUTs has been considered the most Promising Paradigm for beyond SM aer LEP I exPeriments. 5 X boson Proton decay in SUSY SU(5) GUTs X bosons are SU(5) Partners of SM gauge bosons. Main decay mode is . p e+π0 → EffecAve baryon-number violang oPerators are dim=6. q q X q l When MSSM at TeV scale is assumed, M 4 τ 1.2 1035years X p × × 1016GeV 34 From exPerimental bound, τp e+π0 > 1.29 10 years → × 16 MX > 0.6 10 GeV × SuPerKamiokande exPeriment is apProaching close to the GUT scale. 6 Colored Higgs Proton decay in SUSY SU(5) GUTs Colored Higgses are SU(5) Partners of SU(2) doblet Higgses in MSSM. Colored Higgs exchange induces dim=5 baryon-number violang oPerators, which include squarks or slePtons, and they become dim=6 oPerators with SUSY ParAcle exchange. q q q˜ ˜ ˜ H˜C W, H ˜l q l Main decay mode is . p K+ν¯ → Assuming Higgsino exchange dominates over gaugino ones, M 2 M 2 τ 2 1031years sin4 2β HC SUSY p × × 1016GeV TeV 33 while exPerimental bound is . τp K+ν > 3.3 10 years → × Various models are constructed to suPPress the Proton decay. 7 “The discovery of the Higgs with a mass of 125 GeV makes ProPonents of the MSSM nervous.” (from MSSM Higgs mass in WikiPedia) Higgs mass bound in MSSM 4 4 3 m sin β m˜ m2 m2 cos2 2β + t log t + a2(1 a2/12) h ≤ Z π2 v2 m − t ProPosals to Push uP Higgs mass: • TeV scale SUSY with large A term • NMSSM • Extra gauge interacAons • Extra maers couPled with Higgs boson • High scale SUSY (sfermion masses are 102-3 TeV scale) • etc… 8 “The discovery of the Higgs with a mass of 125 GeV makes ProPonents of the MSSM nervous.” (from MSSM Higgs mass in WikiPedia) Higgs mass bound in MSSM. 4 4 3 m sin β m˜ m2 m2 cos2 2β + t log t + a2(1 a2/12) h ≤ Z π2 v2 m − t My Personal oPinion; If the Higgs boson is elementary, SUSY is sAll interesAng. If SUSY exits, theories may involve the Grand Desert. In fact, the gauge couPling unificaon is sAll beauAful. 9 “The discovery of the Higgs with a mass of 125 GeV makes ProPonents of the MSSM nervous.” (from MSSM Higgs mass in WikiPedia) ProPosals to Push uP Higgs mass: • TeV scale SUSY with large A term • NMSSM • Extra gauge interacAons • Extra maers • High scale SUSY (sfermion masses are 102-3 TeV scale) • etc… 10 “The discovery of the Higgs with a mass of 125 GeV makes ProPonents of the MSSM nervous.” (from MSSM Higgs mass in WikiPedia) ProPosals to Push uP Higgs mass: • TeV scale SUSY with large A term • NMSSM • Extra gauge interacAons • Extra maers • High scale SUSY (sfermion masses are 102-3 TeV scale) • etc… Some hints for SUSY GUTs may be hidden in these ideas. 11 2, Extra maers AddiAonal extra maters to MSSM are someAmes ProPosed. • Radiave correcAon to Higgs mass. • Gauge mediaon • 5 and 5* in E6 GUTs and extra family in string theories. IntroducAon of SU(5) comPlete mulAPlets does not disturb the gauge couPling unificaon. (SUSY primer by S.MarAn) Allowed region in GMSB with extra maer Muon (g-2) 125GeV Higgs 12 (Hamaguchi et al(12)) Extra maers AddiAonal extra maters to MSSM are someAmes ProPosed. • Radiave correcAon to Higgs mass. • Gauge mediaon • 5 and 5* in E6 GUTs IntroducAon of SU(5) mulAPlets do not disturb the gauge couPling unificaon. (S.MarAn) Allowed region in GMSB with extra maer IntroducAon of extra maters enhances X-boson Proton decay rate since the gauge couPling constant becomes stronger at the GUT scale. 13 (Hamaguchi et al(12)) Proton decay in SUSY SU(5) GUTs with extra maer in intermediate scale IntroducAon of extra maers enhances Proton decay rate due to larger gauge couPling constants at GUT scale. SuPPression factors for Proton lifeAme, comPared with the case without extra maers, as funcAons of mass for extra maers. (JH, Kobayashi, Nagata (12)) 1 1 1 0.1 0.1 0.1 Ratio Ratio Ratio 0.01 0.01 0.01 #=1, 2, 3, 4, 5 #=1, 2, 3 #=1, 2 5+5 10+10 5+5+10+10 0.001 0.001 4 6 8 10 12 14 0.001 4 6 8 10 12 14 10 10 10 10 10 10 104 106 108 1010 1012 1014 10 10 10 10 10 10 Mass (GeV) Mass (GeV) Mass (GeV) 16 16 Light gray and gray regions for , MX =1 10 , 2 10 GeV resPecAvely are excluded. × × 14 Radiave correcAons to Proton decay rates Larger couPling could enhance the Proton decay rate by the radiave correcon. The renormalizaon grouP equaons for Wilson coefficients for the D=6 oPerators are evaluated at one-looP level. Radiave correcAon to lifeAme at one-looP one. W/ 10 W/O #(5 + 5)=1, 2, 3, 4, 5 Ratio 5+5 1 104 106 108 1010 1012 1014 Extra maer mass (Mass (GeV) GeV) 15 Radiave correcAons to Proton decay rates We derive the renormalizaon grouP equaons for Wilson coefficients for the D=6 oPerators at two-looP level. We found that two-looP correcAon to the event rate quite small. This comes from accidental Radiave correcAon at two-looP level, cancellaon between two-looP comPared with one-looP one. correcAons to gauge couPling and Willson coefficients, while the correcAons could change the rate (5 + 5) larger than O(10)%. � (JH, Kobayashi, Muramatsu, Nagata (12)) 2 (5 + 5) × 3 (5 + 5) × Threshold correcAon at GUT scale is now being evaluated at one Extra maer mass (GeV) loop level. 16 Tips EffecAve oPerator in Khaeler PotenAal (without covariant derivave) V K =Φ† (φ1†,φ2†, )[e ]ABΦB(φ1,φ2, ) O A ··· ··· Anomalous dimension for the oPerator is easily derived without evaluaon of diagrams, if you use effecAve Khaeler PotenAal for V V general Khaeler PotenAal, with . K = φi†e φi φi†e φi + K → O i i Anomalous dimension at one-looP level is derived as 2 (1) gα γ = 2 4CαO 2 Cα(i) O 16π − α i where is CO Casimir for (or ) and are for fields in the ΦA ΦB C(i) oPerator. Now only gauge int. is considered. Two-loop level effecve Khaeler PotenAal is derived by Nibbelink, Groot and Nyawelo. We used it for two-looP anomalous dim. 17 3, High-scale SUSY High-scale SUSY, in which scalar bosons excePt for the SM Higgs have mass around 102-3 TeV, is a Possible soluAon For Higgs mass 125GeV, for the Higgs mass. 1 3 2 2 2 λ = ( g1 + g ) cos 2β 4 5 • Squarks and slePton masses are mh>127GeV comParable to graviAno mass. 10 b • Gaugino masses are one-looP tan 135GeV suPPressed comPared with graviAno masses (anomaly mediaon). 130GeV 125GeV • Higgsino mass could be order of 120GeV mh<115.5GeV graviAno mass, though accidental 1 symmetries suPPress it. 10 102 103 104 MSUSY TeV • LSP is Wino or Higgsino. The thermal (Ibe, Matsumoto, Yanagida (12)) relics for wino and Higgsino are good ê for mass 3 or 1TeV, resPecAvely. 18 GUT-scale mass sPectrum In the minimal SUSY SU(5) GUT, suPerheavy states are X boson, colored Higgses, and SU(5) breaking adjoint Higgs. The mass sPectrum can be constrained from the gauge couPling unificaon, since differences among the gauge couPling const. at weak scale come from the mass differences among comPonents in SU(5) mulAPlets. • Colored Higgs and SU(2) doublet Higgs mass difference 3 2 1 1 12 M M M = ln HC 2ln S +4ln 3 , α (m ) − α (m ) − α (m ) 2π 5 m − m M 2 Z 3 Z 1 Z Z Z 2 : Masses for MS Higgsino and Heavy Higgs boson in MSSM , : Masses for M3 M2 gluino and wino.