Proton Stability in Low-Scale Extra-Dimensional

Grand Unified Theories

Mitsuru Kakizaki (University of Toyama)

February  13,  2014   Mitsuru  KAKIZAKI 1  

The 2nd Winter Toyama Mini-Workshop on Particle Physics and Cosmology "Basis of the Universe with Revolutionary Ideas 2014 (BURI 2014)”

February 13, 2014, University of Toyama

  Ref.: MK, Phys. Rev. D88, 095017 (2013)

Contents

1.  Motivation 2.  Localizing Fermions in Extra Dimensions (Review)

3.  Localizing X-bosons and Proton Stability

4.  Summary

February  13,  2014   Mitsuru  KAKIZAKI 2  

1. Motivation

February  13,  2014   Mitsuru  KAKIZAKI 3  

  Discovery of a Higgs boson at the CERN LHC   The Standard Model (SM) is established

as a low-energy effective theory below GeV O(100)

  Theoretical puzzles of the SM include   Unexplained structure of the

SM gauge bosons and fermions   Quantization of the electric charges

We  need  a  more  fundamental  theory  [www.physics.gla.ac.uk]

  Idea of Grand unified theories (GUTs)   Unification of gauge groups:   Unification of quarks and leptons:

Charge quantization

SU(3)C × SU(2)L ×U(1)Y ⊂G(Q,UC,EC ) =10 (DC,L) = 5*

This talk

February  13,  2014   Mitsuru  KAKIZAKI 4  

  Ordinary GUTs:

  This work   The X-bosons are localized in extra dimensions   SM fermions are displaced to different locations

The GUT scale can be as low as

  Proton decay constraint:

MX ~O(10)TeV

XgX gX

u e+

dp u

dd

Proton Decay

π 0τ p(p→ e+π 0 )> 8.2×1033 yr

MX / gX ≥1015GeV

[Super-Kamiokande,2009]

MX ~1014−16GeVgX ~1 : Beyond the reach of experiments

gX <<1

G XX W

!

"##

$

%&&⊕ B = 24

  New gauge bosons in GUTs:

Interlude: Idea of extra dimensions

February  13,  2014   Mitsuru  KAKIZAKI 5  

  Thread:   Macroscopic:

1-dimensional object   Microscopic:

Object with internal structure

x

x

y

E 2 = p2→

+ (p52 + p6

2 ++m2 )  Generic dispersion relation for a higher dimensional particle:

Momentum in the extra dim. = Mass in the 4D viewpoint

  Our world：   Macroscopic:

4-dimensional space-time   Microscopic:

Higher-dimensional space-time z

2. Localizing fermions in extra dimensions

February  13,  2014   Mitsuru  KAKIZAKI 6  

[Jackiw,Rebbi,1976;Rubakov,Shaposhnikov,1983; Arkani-Hamed,Schmaltz,2000]

  -invariant real scalar theory in 5D space-time ： xM = (xµ, y)

  Idea: Chiral fermions are localized due to a kink in extra dimensions

Z2

V (φ) : Double well

  Classical domain wall solution:

Translational invariance along the extra dimension is broken

φ ∝ yAround the origin:

Profile of a fermion wave function

February  13,  2014   Mitsuru  KAKIZAKI 7  

  5D Fermion coupled to the domain wall : φ = 2µ 2yΨ

Localization of the zero mode fermion:

  Location: Zero of φ +m  The right-handed component

is killed

  Profile: Gaussian

4D left chiral fermion Wave function

Coupling Constants in Four Dimensional Theories

February  13,  2014   Mitsuru  KAKIZAKI 8  

  Coupling constants in 4D theories = Overlap integrals of the relevant wave functions

  e.g.) 4D Yukawa couplings:

Locations of fermion and Higgs fields can account for the fermion mass hierarchy

  Idea: Kink background of an adjoint Higgs field Different profiles in the same GUT multiplets

3. Localizing X-bosons and Proton Stability

February  13,  2014   Mitsuru  KAKIZAKI 9  

[MK,2013]

  -invariant Lagrangian for an adjoint real scalar in 5D SU(5) GUTs: Z2

  Classical domain wall solution:

Translational invariance along the extra dimension and SU(5) are simultaneously broken

GUT relations are easily violated in the 4D viewpoint

Σ(24)

Localizing massive X-bosons

February  13,  2014   Mitsuru  KAKIZAKI 10  

  Equations of motion for the X-bosons:

  Equations of motion for the SM gauge bosons : c.f.) Wave equation

X-bosons are localized with Gaussian profiles [c.f. Hamada,Kobayashi,2012]

(G,W,B)

Zero mode wave functions: Gaussian profiles

Zero mode wave functions: Flat profiles

c.f.) Quantum harmonic oscillator X-bosons

Zero mode mass:

Zero mode mass: Massless

X boson Fermions<YY>

<S>

SM gauge bosons

x5

Proton Stability

February  13,  2014   Mitsuru  KAKIZAKI 11  

  Separation between the X-bosons and fermions

l

gX is exponentially suppressed

Successful Configuration

[c.f. Hamada,Kobayashi,2012]

4D -fermion coupling:

X (0)

Proton stability

  No symmetry is imposed to suppress the coupling gX

~ m−1

  is achieved even with a small X-boson mass

GUT Scale

February  13,  2014   Mitsuru  KAKIZAKI 12  

103104105106107108109

101010111012101310141015

0 1 2 3 4 5

MX(0

) (GeV

)

ml

MX(0) / gX

(0)

c = 10

105 GeV

1010 GeV

1015 GeV

1020 GeV

1025 GeV

  Effective X-boson mass:

  Non-observation of exotic colored particles

  To suppress proton decay:

  Contributions from higher KK X-bosons are also suppressed by a bit larger separation

MX

(0) / gX(0) >1015GeV

Inverse of the size of the extra dimension: L−1 ≥1TeV4 /m < l < L MX

(0) >10TeV

The X-boson effects may be probed at future experiments

  We proposed a new mechanism to localize GUT X-bosons in extra dimensions

4. Summary

February  13,  2014   Mitsuru  KAKIZAKI 13  

  The GUT scale can be as low as

  By separating the X-bosons and fermions, proton decay can be extremely suppressed without imposing symmetries

O(10)TeV

X boson Fermions<YY>

<S>

SM gauge bosons

x5