Proton Decay in SUSY GUT in Light of LHC

8/12/2019 Proton Decay in SUSY GUT in Light of LHC

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Proton decay in SUSY GUT in light of LHCPN

Northeastern University, Boston, MA 02115

International Symposium on Opportunities in UndergroundPhysics

24-27 May, 2013, Asilomar, California
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Unification and Proton decay

Grand unification leads to an explanation of the three coupling constants1, 2, 3 in terms of a single coupling at the GUT scale.

Quantization of charge

|1 + Qe

Qp| < O(1021).

Quark lepton unification1

Proton decay is a consequence of quark -lepton unification1, 2 and is a common

feature of high scale models3 .

4 D GUTs

5 D and 6D models

string and D brane models

1JC Pati, A. Salam, PRL 31, 661(1973); PRD 10, 275 (1974).

2H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).

3For a review on proton stability see

PN, P. Fileviez Perez, Phys. Report, Vol. 441, No.5-6,(2007).
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Why proton decay is of great importance for fundamental physics.

The main points about proton decay are

Observation of proton decay will test the basic idea of quark-lepton unification,i.e., that they are members of the same common multiplet. This phenomenon isnot testable in any other low energy process.

It will probe length scales which are extra-ordinarily small, i.e., O(1033)m.

Proton decay can provide a test for supersymmtry: In supersymmetry thedominant mode is typically p K+ and its observation will give support tothe existence of SUSY at the fundamental level.

Proton decay in principle can provide clues to the existence of strings and

possibly of extra dimensions.

Proton decay can provide a clue to the possible origin of matter generations.


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Proton decay from Lepto-quark exchange

For dim 6 operators arising from lepto-quark exchange the dominant decaymode is p e+0 and is predicted to have a lifetime5

p(p 0e+) =Cp 1.6 10

36yrs( MX

2 1016GeV)4 (1)

whereCp is model dependent but O(1).

In D-branes (Klebanov-Witten) the decay lifetime is

st(p e+0) =GUT(p e

+0)CstM4GM4X

whereCst is the string enhancement factor and estimates give

Cst = 0.5 1.2. The dominant process is p e+

L 0

while the decayp e

+R

0 is suppressed.

The current experimental limit is

st(p e+0) >1.4 1034yrs.

5p lifetime is sensitive to fermion mixing: P. Fileviez Perez,PLB595, 476(2004).
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(p e+0) could be much shorter than 1036 yr.

The lifetime of the proton in higher dimensional theories could be very different

than in 4D theories Thus compactification of higher dimensional theories givesrise to Kaluza -Klein modes whose inclusion can reduce the effective scale thatenters in p decay. This is the case for 5D orbifold GUTs6.

A similar situation occures for compactification of D=6 theory where

1

M2

Xeff

4M2

c ln(M

MC

) + 2.3 .Choosing Mc MG 2 10

16 GeV, and M 1017 GeV, leads to7

(p e+0) 1 1035yr.

Certain classes of GUT models also lead to a shorter lifetime for p e+0 8

Proton decay is sensitive to extra matter which can modify the p e+0

prediction9.

6S Rabys talk

7See. e.g., Buchmuller, Covi, Emmanuel-Costa, Wiesenfeldt, hep-ph/0407070

8Babu, Pati, Tavarkiladze, JHEP 1006 (2010) 084 + Babus talk

9 Hisano, Kobayashi, Nagata, Phys.Lett. B716 (2012) 406-412, arXiv:1204.6274[hep-ph].
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Brief intro to SUSY

SUSY is an extension of the space time symmetry. It isprimarily a high scale symmetry.

SUSY was discovered in the early seventies 10

However, SUSY is a global symmetry and difficult to break ina phenomenologically viable fashion.

Gauging of SUSY brings in gravity 11 and leads tosupergravity12.

10P Ramond, PRD 3, 2415 (1971); Y.A. Golfand and E. Likhtman, JETPLett. 13, 323 (1971); D.V. Volkov and V.P. Akulov, PLB 46, 109 (1973); J.

Wess and B.Zumino, PLB 49, 52 (1974).

11PN, R. Arnowitt, Phys.Lett. B56, 177 (1975)R. Arnowitt, PN, B. Zumino, Phys.Lett. B56, 81 (1975).

12D Z Freedman, P. van Nieuwenhuizen, S. Ferrara, Phys.Rev. D13 (1976)

3214-3218.
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SUGRA Unification, SUSY scale, proton decay

For the rest of the talk we will focus on SUGRA unification, the scale of SUSY andthe proton decay in light of the LHC data.

Supergravity grand unification (SUGRA) breaks SUSY via gravity mediation. 13It depends on three arbitrary functions

K(z, z), W(z), f

Under simplifying assumptions on K and f the parameter space is11, 14

m0, m1/2, A0, B0, 0. Under radiative breaking of the electroweak symmetry

one can redefine the parameter space of the universal SUGRA models

m0, m1/2, A0, tan , sign().

There are other possibilities for breaking of SUSY

Gauge mediation 15

Anomaly mediation 1613A H Chamseddine, R. Arnowitt, PN, Phys.Rev.Lett. 49 (1982) 970.14L. J. Hall, J. D. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983).15M. Dine, A. E. Nelson, Phys. Rev. D48, 1277 (1993); Further work: Nir,

Shirman, .16L. Randall and R. Sundrum, Nucl. Phys. B 557, 79 (1999); G. F. Giudice,

M. A. Luty, H. Murayama and R. Rattazzi, JHEP 9812, 027(1998).
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SUGRA, strings, branes

Low energy limit of string models and of brane models is N = 1

supergravity. Thus supergravity models encompass a broad class,the various models being discriminated by the choices of the Kahlerpotential, the superpotential and the gauge kinetic energy function.
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The LHC constraints on the sugra models with universalboundary conditions


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[GeV]0m

500 1000 1500 2000 2500 3000

[G

eV]

1/2

m

100

200

300

400

500

600

700

800900

1000

l~LEP2

1

LEP2

NoEW

SB

=LSP

Non-Conv

ergentR

GE's

)=500g~m(

)=1000g~m(

)=1500g~m(

)=2000g~m(

)=1000

q~m(

)=1500

q~m(

)=2000

q~m(

)=

2500

q~m(

Median Expected Limit1Expected Limit

Observed Limit(theory)1Observed

HAD Observed LimitLeptons Observed Limit

-1L dt = 4.7 fb= 7 TeVsCMS

Hybrid CLs 95% C.L. Limits

Razor Inclusive

NoEW

SBNon-C

onverge

ntRGE'

s

)=10tan(

= 0 GeV0A> 0= 173.2 GeVtm

=LSP
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Natural SUSY and proton stability

Some versions of the so called natural SUSY advocate a stop mass in the very lowmass region which was not yet eliminated by experiment. However, proton stabilitydoes not favor this region.

.
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Higgs boson discovery

ATLAS and CMS Collaborations have measured the mass of anew boson which lies between 125 and 126 GeV17. Whilemany properties of the new boson need still to be identified itis the general belief that the particle seen is the Higgs bosonwhich enters in the electroweak symmetry breaking

It is quite remarkable that the observed Higgs boson mass liesclose to the upper limit predicted in grand unified supergravitymodels which is roughly 130 GeV 18,19,20.

17CMS Collaboration, Phys. Lett. B, 716, (2012) 3061,arXiv:1207.7235ATLAS Collaboration, Phys. Lett. B, 716 (2012) 129. arXiv:1207.7214.

18S. Akula, B. Altunkaynak, D. Feldman, PN and G. Peim, PRD 85, 075001 (2012).19A. Arbey, M. Battaglia, A. Djouadi and F. Mahmoudi, JHEP 1209 (2012) 107,

arXiv:1207.1348 [hep-ph].20O. Buchmueller, R. Cavanaugh, A. De Roeck et al. Eur. Phys. J. C 72 (2012)

2020,arXiv:1112.3564.
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A comparison of mSUGRA, mGMSB, mAMSB and others

A. Arbey, M. Battaglia, A. Djouadi and F. Mahmoudi, JHEP 1209 (2012) 107,arXiv:1207.1348 [hep-ph].
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No-scale: m0 A0 0

cNMSSM: m0 0, A0 14 m1/2

VCMSSM: A0m0

NUHM: mSUGRA + two more inputs.

A. Arbeya, M. Battaglia, A. Djouadi, F. Mahmoudi and J. Quevillon, Phys.Lett.

B708 (2012) 162-169, arXiv:1112.3028.
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Implications of the 125 GeV Higgs boson

SM: Within the standard model the Higgs is a bit too light.

SUSY: Within SUSY the Higgs is a bit too heavy.
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125 GeV Higgs boson in SM

In the Standard Model vacuum stability puts a stringent constraint on the allowed

range of the Higgs mass.With the inclusion of both the theoretical error in the evaluation ofmhestimated at 1.0 GeV and the experimental errors on the top mass and sthe analysis 21

mh >129.4 1.8 GeV,

for the standard model to have vacuum stability up to the Planck scale. Thisexcludes the vacuum stability for the SM for mh0 < 126 GeV at the 2 level.

The Higgs mass of 125 GeV would give vacuum stability up to only scalesbetween 109 1010 GeV and stability up to the Planck scale would requirenew physics.

Vacuum stability is less problematic in supersymmetric theories22

21Degrassi, Di Vita, Elias-Miro, Espinosa, Giudice et al. JHEP, 1208, 098 (2012).22J. Hisano and S. Sugiyama, Phys.Lett. B696, 92 (2011), arXiv:1011.0260

[hep-ph]; Carena, S. Gori, I. Low, N. R. Shah and C. E. Wagner, JHEP 1302, 114(2013); T. Kitahara, JHEP 1211, 021 (2012), arXiv:1208.4792 [hep-ph].
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A Higgs mass 125 GeV implies a high SUSY scale

In MSSM the Higgs boson mass obeys at the tree level

mh < MZ

and a large loop correction is needed to pull it up to the experimental value.

The dominant one loop contribution arises from the top/stop sector and is givenby

m2h 3m4t22v2

lnM2Sm2t

+ 3m4t22v2

X2tM2S

X4t12M4S

+ .

v = 246 GeV (v is the Higgs VEV), MS is an average stop mass, andXt At cot .

An mh 125GeV implies MS in the several TeV region.

The large SUSY scale tends to stabilize p decay from B&L violatingdimension five operators.

P t d i t i l t Hi i h K+ d
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Proton decay via triplet Higgsino exchange: p K+ mode

Operators arising from triplet Higgsino exchange must be dressed by charginos,neutralinos and gluino exchanges to produce B&L violating dim 6 operators. All thesedressings have been computed fully23. The dim 5 proton decay has a significant modeldependence. Both high energy and low energy physics affect this decay24. There is a

rich literature on dim 5 decay 25

Dressing loop diagrams for p K+ decay from dimension five operators via exchange of charginos, squarks

and Higgsino color triplets.

Very crudely

(p K+) C(m4q/m2

tan

2 )

Formq in the sub TeV region, this could lead to too short a lifetime for this mode. This is specifically the case fornatural models which advocate Ms 300 500GeV.

23Arnowitt, Chamseddine, PN; Hisano, Murayama, Yanagida; Lucas, Raby; Goto, Nihei

24See, e.g., PN, P Fileviez Perez, Phys. Report, Vol. 441, No.5-6,(2007).

25Weinberg; Sakai, Yanagida; Dimopoulos, Raby Wilczek; Ellis, Nanopoulos, Rudaz; Arnowitt, PN; Babu,

Pati, Wilczek; Bajc, Fileviez Perez, Senjanovic; Dosner; Dermisek, Mafi, Raby;Emmanuel-Costa, Wiesenfeldt;

Dutta, Mimura, Mohapatra; Syed, PN; Babu, Pati, Tavartkiladze, .
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Suppression ofp K+ by cancellation

A suppression ofp K+ decay mode can arise by cancellations26 amongvarious contributions to dimension five operators.

An example of this occurs from operators arising from a new class ofSO(10)models where the Higgs structure at the GUT scale is of the form 27

144 + 144.

In SU(5) U(1) decomposition ofSO(10), 144 + 144 has higgsino tripletscoming from 5(3) +5(3)and 45(3) + 45(3) and the cancellation occursamong contributions arising from these.

In this class of models the SO(10) GUT symmetry breaks to the SM gaugegroup at one scale and one does not need different Higgs representations for

rank reduction and for a complete breaking of the GUT symmetry.

26PN, R. M. Syed, Phys. Rev. D 77, 015015 (2008) [arXiv:0707.1332 [hep-ph]].27K. S. Babu, I. Gogoladze, PN, R. M. Syed, Phys. Rev. D 72, 095011 (2005)

[hep-ph/0506312]; Phys. Rev. D 74, 075004 (2006) [hep-ph/0607244].
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Implications of the high Higgs mass for proton stabilityMengxi Liu, PN: arXiv:1303.7472

Higgs boson mass mh0 (GeV)

ProtonLife

time(yrs)

115 120 125 1301033

1034

1035

1036

Curve 1Curve 2Curve 3Experiment(Lower Limit)

A 5-10 GeV shift in the Higgs boson mass can result in a shift in the proton decay life time for the mode K+

by up to 2 orders of magnitude.
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exp(p K+) constraint on the SUGRA parameter spaceMengxi Liu, PN: arXiv:1303.7472

m0 (TeV)

Lifetime(yrs)

0 5 10 15 20 25 3010

30

1035

1040

Experiment(Lower Limit)

p K+ lifetime constraint on mSUGRA/CMSSM (left panel) and on non-universal SUGRA model with

gaugino mass non-universalities (right panel) where MeffH3 /MG = 50.

The discovery ofp K+ mode could occur even with a modest increase insensitivity.

28
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Projected sensitivities of Hyper-K28

1032

1033

1034

1035

1036

1037

10-2

10-1

1 10 102

103

Exposure (Megaton year)

PartialLifetime(years)

pK+sensitivity

with 20%coverage (90%CL)

Super-K limit

206ktyr

3.9 x 1033

yrs (90%CL)

Sensitivities of the Hyper-Kamiokande proton decay search as a function of detector exposure. Left Panel: for

p e+0 mode; Right Panel: for p K+ mode.

MICA point taken from talk by Elisa Resconi (TU Munich): Aspen Winter Workshop -New Directions in NeutrinoPhysics. http://indico.cern.ch/conferenceDisplay.py?confId=224351

28K. Abe, T. Abe, H. Aihara, Y. Fukuda, Y. Hayato, K. Huang, A. K. Ichikawa and M. Ikeda et al., Letter of

Intent: The Hyper-Kamiokande Experiment Detector Design and PhysicsPotential, arXiv:1109.3262

[hep-ex].

C fli i id f l
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Conflicting evidence from muon anomalous moment

The Brookhaven experiment E821 29 which measures a = 1

2(g 2) shows

a deviation from the Standard Model prediction 30 at the 3 level.

a = (287 80.) 1011 . (2)

The SUSY contribution31 arises from and 01 loops.

A rough estimate of the supersymmetric correction is

a sign()

130 1011100GeV

MSUSY

2tan . (3)

In order to obtain a SUSY correction of size indicated by the Brookhaven

experiment masses of sparticles in the loops, i.e., the masses of, , 01,must be only about a few hundred GeV.

29Muon G-2 Collaboration, Phys. Rev. D 73 (2006) 072003

30K. Hagiwara, R. Liao, A. D. Martin et al. J. Phys. G, 38 (2011) 085003, M. Davier, A. Hoecker,

B. Malaescu et al. Eur. Phys. J. C, 71 (2011) 1515.31

T. Yuan, R. L. Arnowitt, A. H. Chamseddine, P.N., Z. Phys. C, 26 (1984) 407; D. A. Kosower, L. M.Krauss, and N. Sakai, Phys. Lett. B 133 (1983) 305; S. Heinemeyer, D. Sto ckinger,andG.Weiglein, Nucl. Phys.

B 690 (2004) 62 -80.
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SUGRA unification with unconventional boundary conditions at high scale

As mentioned the experimental evidence points to color particles being much heavier than the uncolored particles.Thus we specify the boundary conditions for soft parameters by 32

m0, m3, A0, tan , sign()

while m1 = m2 > m0. Therenormalization group evolution of squarks is dominated by the gluino mass.

d

dt

m2H2m2Um2Q

= Yt

3 3 32 2 21 1 1

m2H2m2Um2Q

YtA2t

321

+

32m22 + 1m

21

163

3m23 +

169

1m21

163 3m

23 + 32m

22 +

19 1m

21

.

32S. Akula and PN., Gluino-driven Radiative Breaking, Higgs Boson Mass,Muon g 2,andtheHiggs

Diphoton Decay in SUGRA Unification, arXiv:1304.5526 [hep-ph].

S lit l SUSY t f SUGRA
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Split scale SUSY spectrum for gSUGRA.

105

1010

1015

102

10

3

104

RGE Scale Q (GeV)

Mass(GeV)

H1

H2

q

M1M2

M3

m0

m1/2

m20+

21/2

S. Akula and PN., arXiv:1304.5526 [hep-ph].
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Light and heavy spectrum of Split Scale SUSY

Particles with light masses

33

01, 02,

1, 1, 2, l

Particles with heavy masses

03, 04,

2, H

0, A0, H, q, g

An observation of the p K+ mode is possible inimproved p decay experiment in this Split Scale SUSYmodel.This is in contrast to split SUSY case.

33As a comparison the light spectrum of split susy (Arkani-Hamed, Dimopoulos,

JHEP 0506, 073 (2005)) consists of light Higgsinos

Hu,d,

B,

W, g and one Higgs

doublet but does not have light sfermions.
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A high scale solution

Mas

s

GeV

21

101

Posterior Mean

1 Credible Interval

2 Credible Interval

200

400

600

800

1000

12

Mas

s

TeV

gqt1

2H0

Posterior Mean

1 Credible Interval

2 Credible Interval

5

10

15

20

Figure: Split scale SUSY spectrum for gSUGRA.

Implications of LHC13 for the supersymmetric decay of the
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Implications of LHC13 for the supersymmetric decay of theproton

We have already seen that the measurement of the Higgs

boson mass has led to our revision of the proton decaylifetime predictions. LHC13 would put further severeconstraints on the SUGRA parameter space (see the exclusionplot in m0 m1/2 at LHC13.)The observation of sparticles, specifically squarks at the LHC

would give a strong hint that supersymmetric decay of theproton should be seen. The observation of some of thesparticles should allow us to estimate values ofm0, m1/2, A0, tan .

These estimates would allow us to make much more precisepredictions on the proton lifetime arising from dimension fiveoperators.

Thus there are strong direct implications of LHC13 forthe observation of SUSY decays oftheproton.

Projected discovery reach in m0 m1/2 at

s = 14 TeV
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Projected discovery reach in m0 m1/2 at

s = 14 TeVfor mSUGRA

(GeV)0m0 1000 2000 3000 4000 5000 6000 7000 8000

(G

eV)

1/2

m

400

600

800

1000

1200

1400

1600

1800

2000

=4TeV

q~m

=6TeV

q~

m

=2TeVq~

m

=2TeVg~m

=1.2TeVg~m

=3TeVg~m

=4TeVg~m=1 2 3 Ge V

h

m

=127

GeV

hm

-13000 fb

-11000 fb

-1300 fb

-1100 fb

LHC7excluded

= 172.6 GeV

t

> 0, m!= 10,, tan0

= -2m0A LHC14

From H. Baer, V. Barger, A. Lessa and X. Tata, Phys.Rev. D86 (2012) 117701,

arXiv:1207.4846 [hep-ph].
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Conclusion

Search for proton decay is central to understanding the nature of fundamental physics.It will do many things

Provide test of quark-lepton unification.

Probe length scales ofO(1033) m which are inaccessible to any otherexperiment.

Provide a test of supersymmetry.

Opens a window to observing possible effects of strings and branes and of extradimensions.

Could throw light on the possible origin of matter generations.

In summary there are overwhelming theoretical reasonsfor making a strong push for proton decay searches.

What about fine tuning?
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g

Fine tuning is a rather subjective issue and it depends on how you define fine tuning and also depends on whatphenomena are included in fine tuning. Generally, one considers just REWSB. But one should also incude otherphonomena such as FCNC, CP and proton decay. Here we consider REWSB and proton decay.

REWSB: Fine tuning in REWSB arises from the equation that determines the Z -boson mass

1

2M2Z =

2 + |mHu |2 +

If or |mHu | get too large, one needs a fine tuning to get the Zmass. An obvious ways to definedefine fine tuning in REWSB is

F2|mHu |

2

M2Z

Low soft masses are then preferred as large soft masses appear to lead to a large fine tuning.

Proton decay: Here we define fine tuning as

Fpd =4 1033yr

(p K+)yr. (4)

A more appropriate object to consider then is

F =

ni=i

Fi

1n

. (5)

In this circumstance a smaller fine tuning occurs at large m0.
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Fine tunings with inclusion of p decayMengxi Liu, PN: arXiv:1303.7472

m0 (TeV)

FineTuning

0 5 10 15 20 25 3010

4

102

10

0

102

104

106

F

FpdF

Top left: Fine tuning constraint from REWSB and from proton stability for the mode p K+

and the meanas a function ofm0 for mSUGRA. Right: A smooth curve through the averages34.

The combined fine tuning appears to favor larger m0.

34The analysis is similar in spirit to a recent work (Jaeckel, Khoze, arXiv:1205.7091 [hep-ph])where FCNC

and CP violation were included along with REWSB in the analysis of fine tuning.
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Proton Decay in SUSY GUT in Light of LHC