proton&decay&in&susy&guts& revisited ·...

Proton Decay in SUSY GUTs revisited

J. Hisano (Nagoya Univ.)

2013 Interna,onal Workshop on Baryon and Lepton Number Viola,on (BLV2013):

From the Cosmos to the LHC April 8-‐11, 2013, MPIK Heidelberg, Germany

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International Workshop on ��Next Generation Nucleon Decay and Neutrino Detectors

NNN13

Nov.11-13, 2013

http://indico.ipmu.jp/indico/conferenceDisplay.py?confId=17

Kavli IPMU, Kashiwa, Japan

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 maMer 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.LeM. 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) •  UnificaAon of gauge groups •  UnificaAon of quarks and leptons In GUTs Electric charge quanAzaAon is automaAc.

PredicAon of GUTs: •  Gauge coupling unificaAon •  Proton decay

SU(3)C � SU(2)L � U(1)Y � SU(5), SO(10), E6

�(10) = (uL, dL, (uR)c, (eR)c)�(5�) = ((dR)c, �L, eL)

SU(5)

|Qp + Qe| < 10�21

4

Gauge coupling unificaAon •  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 2* 1016 GeV.

(From SUSY primer by S.MarAn)

Grand Desert from MSSM to SUSY GUTs has been considered the most promising paradigm for beyond SM acer 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 . EffecAve baryon-‐number violaAng operators are dim=6. When MSSM at TeV scale is assumed, From experimental bound, SuperKamiokande experiment is approaching close to the GUT scale.

�p � 1.2� 1035years��

MX

1016GeV

�4

X

q

q

q

l

p� e+�0

�p�e+�0 > 1.29� 1034years

MX > 0.6� 1016GeV

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 violaAng operators, which include squarks or sleptons, and they become dim=6 operators with SUSY parAcle exchange. Main decay mode is . Assuming Higgsino exchange dominates over gaugino ones, while experimental bound is . Various models are constructed to suppress the proton decay.

q

q

q

l

H̃C

q̃

l̃W̃, H̃

p� K+�̄

�p�K+� > 3.3� 1033years

�p � 2� 1031years� sin4 2�

�MHC

1016GeV

�2 �MSUSY

TeV

�2

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 Proposals to push up Higgs mass: •  TeV scale SUSY with large A term •  NMSSM •  Extra gauge interacAons •  Extra maMers coupled with Higgs boson •  High scale SUSY (sfermion masses are 102-‐3 TeV scale) •  etc…

m2h � m2

Z cos2 2� +3�2

m4t sin4 �

v2

�log

mt̃

mt+ a2(1� a2/12)

�

8


Higgs mass bound in MSSM.

m2h � m2

Z cos2 2� +3�2

m4t sin4 �

v2

�log

mt̃

mt+ a2(1� a2/12)

�

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 unificaAon is sAll beauAful.

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Proposals to push up Higgs mass: •  TeV scale SUSY with large A term •  NMSSM •  Extra gauge interacAons •  Extra maMers •  High scale SUSY (sfermion masses are 102-‐3 TeV scale) •  etc…

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Proposals to push up Higgs mass: •  TeV scale SUSY with large A term •  NMSSM •  Extra gauge interacAons •  Extra maOers •  High scale SUSY (sfermion masses are 102-‐3 TeV scale) •  etc…

Some hints for SUSY GUTs may be hidden in these ideas.

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2, Extra maMers AddiAonal extra maters to MSSM are someAmes proposed. •  RadiaAve correcAon to Higgs mass. •  Gauge mediaAon •  5 and 5* in E6 GUTs and extra family in string theories. IntroducAon of SU(5) complete mulAplets does not disturb the gauge coupling unificaAon.

Allowed region in GMSB with extra maMer (SUSY primer by S.MarAn)

Muon (g-‐2) 125GeV Higgs

(Hamaguchi et al(12)) 12

Extra maMers AddiAonal extra maters to MSSM are someAmes proposed. •  RadiaAve correcAon to Higgs mass. •  Gauge mediaAon •  5 and 5* in E6 GUTs IntroducAon of SU(5) mulAplets do not disturb the gauge coupling unificaAon.

Allowed region in GMSB with extra maMer

(Hamaguchi et al(12))

IntroducAon of extra maters enhances X-‐boson proton decay rate since the gauge coupling constant becomes stronger at the GUT scale.

(S.MarAn)

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Proton decay in SUSY SU(5) GUTs with extra maMer in intermediate scale

0.001

0.01

0.1

1

104 106 108 1010 1012 1014

Ratio

Mass (GeV)

5+5+10+10 0.001

0.01

0.1

1

104 106 108 1010 1012 1014

Ratio

Mass (GeV) 0.001

0.01

0.1

1

104 106 108 1010 1012 1014

Ratio

Mass (GeV)

5+5 10+10

IntroducAon of extra maMers enhances proton decay rate due to larger gauge coupling constants at GUT scale.

Suppression factors for proton lifeAme, compared with the case without extra maMers, as funcAons of mass for extra maMers.

Light gray and gray regions for , respecAvely are excluded.

MX = 1� 1016, 2� 1016GeV

(JH, Kobayashi, Nagata (12))

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# = 1, 2, 3, 4, 5 # = 1, 2, 3 # = 1, 2

RadiaAve correcAons to proton decay rates Larger coupling could enhance the proton decay rate by the radiaAve correcAon. The renormalizaAon group equaAons for Wilson coefficients for the D=6 operators are evaluated at one-‐loop level.

RadiaAve correcAon to lifeAme at one-‐loop one.

1

10

104 106 108 1010 1012 1014

Ratio

Mass (GeV)

5+5

W/

W/O

#(5� + 5) = 1, 2, 3, 4, 5

　　　　　 Extra maMer mass (GeV) 15

RadiaAve correcAons to proton decay rates We derive the renormalizaAon group equaAons for Wilson coefficients for the D=6 operators at two-‐loop level. We found that two-‐loop correcAon to the event rate quite small.

𝑅

This comes from accidental cancellaAon between two-‐loop correcAons to gauge coupling and Willson coefficients, while the correcAons could change the rate larger than O(10)%.

RadiaAve correcAon at two-‐loop level, compared with one-‐loop one.

Extra maMer mass (GeV)

(5 + 5�)

2� (5 + 5�)

3� (5 + 5�)

(JH, Kobayashi, Muramatsu, Nagata (12))

16

Threshold correcAon at GUT scale is now being evaluated at one loop level.

Tips EffecAve operator in Khaeler potenAal (without covariant derivaAve) Anomalous dimension for the operator is easily derived without evaluaAon of diagrams, if you use effecAve Khaeler potenAal for general Khaeler potenAal, with . Anomalous dimension at one-‐loop level is derived as where is Casimir for (or ) and are for fields in the operator. Now only gauge int. is considered. Two-‐loop level effecAve Khaeler potenAal is derived by Nibbelink, Groot and Nyawelo. We used it for two-‐loop anomalous dim.

�(1)O =

�

�

g2�

16�2

�4CO� � 2

�

i

C�(i)

�

KO = �†A(�†1,�

†2, · · · )[eV ]AB�B(�1,�2, · · · )

CO �A �B C(i)

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K =�

i

�†i eV �i �

�

i

�†i eV �i + KO

3, High-‐scale SUSY

mh<115.5GeV

mh>127GeV

120GeV125GeV

130GeV

135GeV

10 102 103 1041

10

MSUSYêTeVtanb

High-‐scale SUSY, in which scalar bosons except for the SM Higgs have mass around 102-‐3 TeV, is a possible soluAon for the Higgs mass. •  Squarks and slepton masses are

comparable to graviAno mass. •  Gaugino masses are one-‐loop

suppressed compared with graviAno masses (anomaly mediaAon).

•  Higgsino mass could be order of graviAno mass, though accidental symmetries suppress it.

•  LSP is Wino or Higgsino. The thermal relics for wino and Higgsino are good for mass 3 or 1TeV, respecAvely.

For Higgs mass 125GeV,

(Ibe, Matsumoto, Yanagida (12))

� =14(35g21 + g2) cos2 2�

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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 unificaAon, since differences among the gauge coupling const. at weak scale come from the mass differences among components in SU(5) mulAplets.

MS

M3 M2

•  Colored Higgs and SU(2) doublet Higgs mass difference

: Masses for Higgsino and Heavy Higgs boson in MSSM , : Masses for gluino and wino. •  Mass difference in gauge sector

, : X boson and adjoint Higgs masses, respecAvely. M�MX(JH, Kuwahara, Nagata (13))

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5�1(mZ)

� 3�2(mZ)

� 2�3(mZ)

=12�

�12 ln

�M2

XM�

m3Z

�+ 4 ln

�M2

mZ

�+ 4 ln

�M3

mZ

��

3�2(mZ)

� 2�3(mZ)

� 1�1(mZ)

=12�

�125

ln�

MHC

mZ

�� 2 ln

�MS

mZ

�+ 4 ln

�M3

M2

��,

GUT-‐scale mass spectrum

1015

1016

1017

1018

102 103

M Hc

MS (TeV)

M2 = 3TeV

M 3/M 2 = 3

M 3/M 2 = 9

M 3/M 2 = 30

tan! = 3

•  Squarks and sleptons are assumed to have masses equal to Higgsino and heavy Higgs bosons in MSSM, .

•  In pure anomaly mediaAon , while the raAo may be corrected by Higgs-‐Higgsino loops.

M3/M2 � 11MS

Low-‐energy SUSY predicts colored Higgs mass around 1015 GeV (blue bands in figs), while the gauge coupling unificaAon can be improved in high-‐scale SUSY.

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GUT-‐scale mass spectrum The GUT scale ( ) is slightly lowered when the gauginos are heavier. X boson proton decay may be accessible. When , .

1016

101

M GUT

M3 (TeV)

M2 = 300GeV

M2 = 3TeV

MS = 103TeVtan! = 3

MG

UT�

(M2 XM

�)1

/3

MGUT � (M2XM�)1/3

MX = MGUT �p � (Mgaugino)�8/9

21

Colored Higgs proton decay

(a)

qL

qL

qL (lL)

lL (qL)

W̃

q̃L l̃L (q̃L)

(b)

uRdR (sR)

(!!)L

"̃Rt̃R

sL (dL)

H̃u H̃d

HC HC

Qi

Qi

Qk

Ll

U i

Ej

Uk

Dl

HC HC

Colored Higgs exchange two types of dim=5 baryon-‐number violaAng operators; one is composed of lec-‐handed quarks and leptons and another is of right-‐handed ones. The proton decay diagrams include wino or Higgsino exchange, and amplitudes are proporAonal to wino or Higgsino mass.

22

1033

1034

1035

1036

102 103 104 105

lifetim

e (ye

ars)

MS (TeV)

tan! =

50

tan! =

3 tan! =

5 tan! =

10

tan! =

30

Colored Higgs proton decay MHC = 1016 GeV

Squark/slepton mass (TeV)

Higgsino mass is equal to squark/slepton mass. Wino mass is 3 TeV.

Colored Higgs proton decay escapes from experimental bound, and the minimal SUSY SU(5) GUT is sAll viable without introducing any mechanism. In addiAon, Future experiments may be accessible, depending on parameters.

�p�K+� > 3.3� 1033years

(JH, Kobayashi, Kuwahara, Nagata (13))

23

1033

1034

1035

1036

101 102 103

lifetim

e (ye

ars)

tan! = 10 tan! = 30

tan! = 50 tan! = 5

(TeV)"H

Colored Higgs proton decay MHC = 1016 GeV

Higgsino mass (TeV)

Squark/slepton masses are 103 TeV. Wino mass is 3 TeV.

The Higgsino exchange dominates over the wino exchange.

�p�K+� > 3.3� 1033years

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Summary

In my talk, I discuss proton decay in SUSY SU(5) GUTs. My personal opinion is that the gauge coupling unificaAon is sAll beauAful. If the Higgs boson is elementary, SUSY, which may involve the Grand Desert, is sAll interesAng. I consider two cases. •  IntroducAon extra maMer at intermediate scale •  High-‐scale SUSY In both cases, the proton decay may be enhanced compared with tradiAonal MSSM. Future proton decay searches may give important informaAon for SUSY and GUTs.

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