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Home , Proton decay

Proton Decay in SUSY GUTs revisited

J. Hisano (Nagoya Univ.)

2013 Internaonal Workshop on and Number Violaon (BLV2013): From the Cosmos to the LHC April 8-11, 2013, MPIK Heidelberg, Germany 1 NNN13 International Workshop on Next Generation 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, Introducon of SUSY GUTs Does Higgs with mass 126 GeV mean existence of Grand Desert to SUSY GUTs? 2, SUSY SU(5) GUTs with extra maer in intermediate scale boson 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, Introducon 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 In GUTs SU(5) c c (10)=(uL,dL, (uR) , (eR) ) c (5 ) = ((dR) ,L,eL) Electric charge quanzaon is automac. 21 Q + Q < 10 | p e|

Predicon of GUTs: • Gauge coupling unificaon • Proton decay 4 Gauge coupling unificaon • (SUSY), which is a symmetry between boson and fermion, is needed for the gauge hierarchy problem. The (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.Marn)

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 are SU(5) partners of SM gauge bosons. Main decay mode is . p e+0 Effecve baryon-number violang operators are dim=6. q q X q l When MSSM at TeV scale is assumed, M 4 1.2 1035years X p 1016GeV 34 From experimental bound, p e+0 > 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 parcle exchange. q q q˜ ˜ ˜ H˜C W, H ˜l q l Main decay mode is . p K+¯ Assuming exchange dominates over ones, M 2 M 2 2 1031years sin4 2 HC SUSY p 1016GeV TeV 33 while experimental bound is . p K+ > 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 m˜ m2 m2 cos2 2 + t log t + a2(1 a2/12) h Z 2 v2 m t

Proposals to push up Higgs mass: • TeV scale SUSY with large A term • NMSSM • Extra gauge interacons • Extra maers coupled with • High scale SUSY ( 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 m˜ m2 m2 cos2 2 + t log t + a2(1 a2/12) h Z 2 v2 m t

My personal opinion; If the Higgs boson is elementary, SUSY is sll interesng. If SUSY exits, theories may involve the Grand Desert. In fact, the gauge coupling unificaon is sll beauful.

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 interacons • 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 interacons • 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 Addional extra maters to MSSM are somemes proposed. • Radiave correcon to Higgs mass. • Gauge mediaon

• 5 and 5* in E6 GUTs and extra family in string theories. Introducon of SU(5) complete mulplets does not disturb the gauge coupling unificaon.

(SUSY primer by S.Marn) Allowed region in GMSB with extra maer

Muon (g-2) 125GeV Higgs

12 (Hamaguchi et al(12)) Extra maers Addional extra maters to MSSM are somemes proposed. • Radiave correcon to Higgs mass. • Gauge mediaon

• 5 and 5* in E6 GUTs Introducon of SU(5) mulplets do not disturb the gauge coupling unificaon. (S.Marn) Allowed region in GMSB with extra maer Introducon 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 Introducon of extra maers enhances proton decay rate due to larger gauge coupling constants at GUT scale.

Suppression factors for proton lifeme, compared with the case without extra maers, as funcons 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 respecvely are excluded. 14 Radiave correcons 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 correcon to lifeme 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 correcons 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 correcon to the event rate quite small.

This comes from accidental Radiave correcon at two-loop level, cancellaon between two-loop compared with one-loop one. correcons to gauge coupling and Willson coefficients, while the correcons could change the rate (5 + 5) larger than O(10)%. � (JH, Kobayashi, Muramatsu, Nagata (12)) 2 (5 + 5) 3 (5 + 5) Threshold correcon at GUT scale is now being evaluated at one Extra maer mass (GeV) loop level. 16 Tips Effecve operator in Khaeler potenal (without covariant derivave) V K =† (1†,2†, )[e ]ABB(1,2, ) O A ··· ··· Anomalous dimension for the operator is easily derived without evaluaon of diagrams, if you use effecve Khaeler potenal for V V general Khaeler potenal, with . K = i†e i i†e i + K O i i Anomalous dimension at one-loop level is derived as 2 (1) g = 2 4CO 2 C(i) O 16 i where is CO Casimir for (or ) and are for fields in the A B C(i) operator. Now only gauge int. is considered.

Two-loop level effecve Khaeler potenal 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 soluon For Higgs mass 125GeV, for the Higgs mass. 1 3 2 2 2 = ( g1 + g ) cos 2 4 5

• Squarks and slepton masses are mh>127GeV comparable to gravino mass. 10 b

• Gaugino masses are one-loop tan 135GeV suppressed compared with gravino masses (anomaly mediaon). 130GeV 125GeV • Higgsino mass could be order of 120GeV mh<115.5GeV gravino 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, respecvely. 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) mulplets.

• Colored Higgs and SU(2) doublet Higgs mass difference 3 2 1 1 12 M M M = ln HC 2ln S +4ln 3 , (m ) (m ) (m ) 2 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.

• Mass difference in gauge sector 5 3 2 1 M 2 M M M = 12 ln X +4ln 2 +4ln 3 (m ) (m ) (m ) 2 m3 m m 1 Z 2 Z 3 Z Z Z Z

, : X boson and MX M adjoint Higgs masses, respecvely. 19 (JH, Kuwahara, Nagata (13)) GUT-scale mass spectrum • Squarks and sleptons are assumed to have masses equal to Higgsino and heavy Higgs bosons in MSSM, . MS • In pure anomaly mediaon , while the rao may be M /M 11 3 2 corrected by Higgs-Higgsino loops.

1018

= 3 Low-energy SUSY predicts /M 2 17 M 3 colored Higgs mass around 10 15 = 9 10 GeV (blue bands in figs), /M 2 Hc M 3 M while the gauge coupling 16 10 = 30 unificaon can be improved in /M 2 M 3 M2 = 3TeV high-scale SUSY. tanβ = 3 1015

102 103 20 MS (TeV) GUT-scale mass spectrum 2 1/3 The GUT scale ( ) is slightly lowered when the MGUT (MX M) are heavier. X boson proton decay may be accessible. 8/9 When , . MX = MGUT p (Mgaugino)

3 3 MS = 10 TeV /

1 β

) tan = 3 M 2 X GUT

M M2 = 300GeV ( M

1016 M2 = 3TeV GUT M 101 M3 (TeV) 21 Colored Higgs proton decay Colored Higgs exchange two types of dim=5 baryon-number violang operators; one is composed of le-handed quarks and leptons and another is of right-handed ones.

Qi Qk U i U k

HC HC HC HC

E Qi Ll j Dl The proton decay diagrams include wino or Higgsino exchange, and amplitudes are proporonal to wino or Higgsino mass.

qL qL (lL) dR (sR) uR

˜ q˜L lL (˜qL) t˜R τ˜R

˜ ˜ W˜ Hu Hd

22 qL lL (qL) sL (dL) (ντ )L (a) (b) Colored Higgs proton decay 16 MHC =10 GeV Higgsino mass is equal to squark/slepton mass. Wino mass is 3 TeV. (JH, Kobayashi, Kuwahara, Nagata (13)) 1036

tanβ = 3

Colored Higgs proton decay tanβ = 5 1035 escapes from experimental tanβ = 10 bound, and the minimal tanβ = 30

tanβ = 50 SUSY SU(5) GUT is sll 34 viable without introducing 10 any mechanism. In addion, lifetime (years)

Future experiments may be 33 33 10 p K+ > 3.3 10 years accessible, depending on parameters. 102 103 104 105 Squark/MsleptonS (TeV) mass (TeV23 ) Colored Higgs proton decay 16 MHC =10 GeV Squark/slepton masses are 103 TeV. Wino mass is 3 TeV.

36 10 tanβ = 5 tanβ = 10

35 The Higgsino exchange 10 tanβ = 30 dominates over the wino tanβ = 50 exchange. 1034 lifetime (years)

33 33 p K+ > 3.3 10 years 10

101 102 103 24 Higgsinoμ mass (H (TeV)TeV) Summary

In my talk, I discuss proton decay in SUSY SU(5) GUTs. My personal opinion is that the gauge coupling unificaon is sll beauful. If the Higgs boson is elementary, SUSY, which may involve the Grand Desert, is sll interesng. I consider two cases.

• Introducon extra maer at intermediate scale • High-scale SUSY

In both cases, the proton decay may be enhanced compared with tradional MSSM. Future proton decay searches may give important informaon for SUSY and GUTs.

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