Cosmological Constraints on

R-Parity violating SUSY

under Lepton Flavor Violation

岩本 祥 [Sho Iwamoto]

2010/02/20

KEK-PH 2010 @ KEK/筑波 [Tsukuba]

along the paper

M. Endo, K. Hamaguchi and SI.

Cosmological Constraints on R-parity violation.

arXiv: 0912.0585 [hep-ph] (2009).

The University of Tokyo

Outline

1. R-Parity violating SUSY

2. Cosmological Constraints

3. Our Results

4. Application for LHC

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along the paper

M. Endo, K. Hamaguchi and SI.

Cosmological Constraints on R-parity violation.

arXiv: 0912.0585 [hep-ph] (2009).

(about to be published)

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1. R-parity violating SUSY

“To avoid the Proton Decay in the MSSM,

we usually impose the R-parity.

But actually, we have other two choices. ”

INDEX

MSSM and R-parity

MSSM

Hierarchy problem → solved!

Proton decay problem

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(Minimal Supersymmetric Standard Model)

Why does Proton decay?

Superpotential of the MSSM

Both and Proton Decay

Proton Decay Problem

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R-parity

Superpotential of the MSSM

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( s: spin )

with R-Parity conservation

Both and Proton Decayis stable.

SUSY without R-parity

However, since proton decay needs both and ,

we have other two possibilities!

To forbid with Baryon-parity etc.

To forbid with Lepton-parity etc.

with assuming

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(Allowing )

(Allowing )

SUSY without R-parity

That is, we can install RpV interactions additionally.

MSSM with R-parity →

-MSSM →

-MSSM →

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MSSM without R-parity

Introductive Diagram

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Standard Model

Supersymmetry

MSSM

Dark Matter!!

R-parity

conservation

MSSM with R-parity

-MSSM

-MSSM

B-conservation

MSSM without R-parity

L-conservation

(Here we need other DM candidates.)

What I studied

Can we constraint such exotic couplings?

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Collider experiments → various constraints

of order .

We analyzed cosmological constraints

→ much more stringent!(as we will see later…)

YES!!

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2. Cosmological Constraints

“The violation of R-parity may spoil

the current Baryon Asymmetry of the Universe.”

INDEX

Baryon Asymmetry of the Universe

Current universe:

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There’s Baryon,and no anti-baryon.

Baryon

Baryon Asymmetry of the Universe

Note:

Today we assume that

Current Baryon Asym. is generated

before EWPT.

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Baryon Asymmetry of the Universe

Current universe:

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There’s Baryon,and no anti-baryon.

Baryon

Wash-out with B-viol.

However, if we have interaction,

in the early universe.

And if frequently enough,

→ achieve Equilibrium :

→ No Baryon Asymmetry!

→ must be small enough!

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“WASH-OUT”

Wash-out with B-viol.

That is, if

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LARGE , then

“WASH-OUT” occurs!!

Bouquet and Salati, 1987

But this is a bit naïve view…

We have to consider “sphaleron.”

Sphaleron

In the early universe (temperature )

→ the sphaleron process is frequent. (by thermal effects)

Sphaleron converts

Baryon Anti-lepton

→ Equilibrium.

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Kuzmin, Rubakov, Shaposhnikov, 1985; Ringwald, 1988

Manton, 1983; Klinkhamer and Manton, 1984; ’t Hooft, 1976

Sphaleron’s Effect

If Baryon is short…

sphaleron works right to left

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sphaleron

(anti-lepton)

(baryon)

Sphaleron’s Effect

If Baryon is short…

sphaleron works right to left

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(anti-lepton)(baryon)

and achieve Equilibrium.

Sphaleron’s Effect

Also when (anti-)Lepton is short,

sphaleron does left to right

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sphaleron

(anti-lepton)(baryon)

Sphaleron’s Effect

Also when (anti-)Lepton is short,

sphaleron does left to right

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(anti-lepton)(baryon)

and achieve Equilibrium.

Wash-out with B-viol.

Thus, actually the previous wash-out by

is…

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(anti-lepton)(baryon)

Wash-out with B-viol.

Thus, actually the previous wash-out by

is…

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sphaleron

(anti-lepton)

(baryon)

Wash-out with B-viol.

Thus, actually the previous wash-out by

is…

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(anti-lepton)(baryon)

“WASH-OUT”

Wash-out with L-viol.

This story

does not end here!

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Kuzmin, Rubakov and Shaposhnikov, 1985Campbell, Davidson, Ellis and Olive, 1992

Wash-out with L-viol.

If

large (in the sphaleron era),

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(anti-lepton)(baryon)

Wash-out with L-viol.

If

large (in the sphaleron era),

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sphaleron

(anti-lepton)(baryon)

Wash-out with L-viol.

If

large (in the sphaleron era),

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(anti-lepton)(baryon)

Wash-out occurs!!

Wash-out with L-viol.

But

NOTE ONE IMPORTANT POINT!

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Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

(anti-lepton)(baryon)

Wash-out with L-viol.

Imagine this case.

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Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

If the Lepton Flavor is NOT violated,

and

if at least one of is conserved,

Wash-out with L-viol.

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Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

Wash-out with L-viol.

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sphaleron

Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

Wash-out with L-viol.

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Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

Wash-out with L-viol.

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sphaleron

Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

Wash-out with L-viol.

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Baryon SURVIVES!!!

Campbell, Davidson, et al., 1992; Dreiner and Ross, 1983

Wash-out with L-viol.

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Baryon Survives.Wash-out!

The “leptonic” wash-out needs three sif there’s no LFV.

Wash-out with L-viol.

But remember!

In MSSM,

We have LFVs in general!!!

The Standard Model The MSSM

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Endo, Hamaguchi, and SI, 2009

As Shimomura-san mentioned.

Wash-out with L-viol.

Therefore,

Only One would…

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(anti-lepton)(baryon)

Wash-out with L-viol.

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sphaleron

(anti-lepton)(baryon)

Therefore,

Only One would…

Wash-out with L-viol.

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(anti-lepton)(baryon)

Do “WASH-OUT”!!

Therefore,

Only One would…

Wash-out with L-viol.

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(baryon)

Therefore,

Only One would…

Wash-out with L-viol.

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(baryon)

Therefore,

Only One would…

Now We Know

To avoid the WASH-OUT,

All must be small enough, and

If all flavors are mixed

→ All must be small enough.

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These are what we studied!

Now We Know

To avoid the WASH-OUT,

All must be small enough, and

If all flavors are mixed

→ All must be small enough.

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These are what we studied!

How SMALL must be?

When MIX?

Now We Know

To avoid the WASH-OUT,

All must be small enough, and

If all flavors are mixed

→ All must be small enough.

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And we will claim that…

This is naturally expected!

All of them areseverely constrained!

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3. Our Results

INDEX

Methods

We calculated

by Boltzmann Eq.

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Lepton number density in i-th generation

Large LFV Tiny LFV

(All must be small.)

Methods

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LFV

Generally NOT diagonal

As Shimomura-san discussed.

Methods

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LFV

Diagonalizeby rotation

“mixing angle”

LFV

Methods

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For example

(We know , because we know the lepton masses.)

LFV causes Mixing.

Not mixed

Result

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Fully Mixed!

“Mixed”

Conclusion

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→ MIXED

This corresponds to

Remember:

By the way,

Conclusion

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Right-handed neutrino

SU(5) GUT (Colored Higgs)

Conclusion

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→ MIXED

Expected Value

Naturally Expected!Experimental Reach

Now We Know

To avoid the WASH-OUT,

All must be small enough, and

If all flavors are mixed

→ All must be small enough.

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This is naturally expected!

These are ALLseverely constrained!

Constraints on RpVs

In a similar manner…

→ calculated by the Boltzmann Eq.

We obtained the bounds for

R-parity violating couplings.

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Just the results…

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(For all i, j, k)

For

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4. Application for LHC

“Now we have a good tool

to study LHC phenomenology of RpV-MSSM.”

INDEX

SUSY Detection @ LHC

SUSY detection in LHC is important.

R-parity is Conserved → LSP Signal

Then if not?

→ LSP decays!How to detect RpV-SUSY?

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Application for LHC

Stringent RpV-constraint of order

→ LSP is a bit “long-lived.”

Example: ( -LSP)

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Decay Length

(cf. tau-lepton: )

To be a good signal of RpV-SUSY?→ Future works!

That’s all.

Thank you

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Summary

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MSSM

& areALL small.

LFV!!

LSP would bea bit long-livedeven if

NO R-Parity.

R-parity is not a must.

Appendices

A) Hierarchy Problem

B) Weak points of RpV-MSSM

C) Collider Constraints

D) The RpV Results

E) Several Details

F) Experimental LFV Bounds

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INDEX

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A. Hierarchy Problem

“In the Standard Model,

the quantum correction for the mass of the Higgs

requires a miraculous cancellation as

”

INDEX

APPENDICES

Hierarchy Problem

In the

Standard Modelwith Higgs,

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Hierarchy Problem

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Hierarchy Problem

In

MSSM(or other SUSY models),

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Hierarchy Problem

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And its superpartner goes round! Cancelled!

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B. Weak Points of RpV-MSSM

“The RpV-MSSM has some weak points,

but anyway important for the SUSY detection.”

INDEX

APPENDICES

Weak point of “RpV-MSSM”

Weak Points

Anyway we need “some symmetry.”

Dark Matter → left unsolved.

GUT compatibility… (´・ω・｀)

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C. Collider Constraints

“The RpV interactions are constrainedby several experimental facts.”

INDEX

APPENDICES

Constraints

The RpV parameters

→ experimental constraints

And the constraints are important

to study RpV-MSSM.

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Constraints

Example:

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Standard Model RpV-MSSM

Additional Contribution!

Constraints

Example:

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Standard Model RpV-MSSM

Additional Contribution!

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D. RpV Results

INDEX

APPENDICES

RpV Result

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[GeV]

RpV Result

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[GeV]

RpV Result

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[GeV]

RpV Result

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[GeV]

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E. Several Details

Approximations we used

Set up

MSSM; before EWPT (sphaleron era: )

Approximations

We consider only the decay of Higgsino

and the antiparticles’ processes.

Mass of Higgs bosons → Ignored

Fermi/Bose distribution → Boltzmann distribution

Sphaleron → Shut off at .

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Some Loophole

We can avoid any “wash-out”

with creating the current B-asymmetry

HERE.

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F. Experimental LFV Bounds

MEGA Result / MEG Prospect

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