22
SUPERSYMMETRY BREAKING ,R-SYMMETRY BREAKING ,AND METASTABLE VACUA IN SUPERGRAVITY Yuji Omura (Kyoto Univ.) Hiroyuki Abe (YITP,Kyoto Univ.) Tatsuo Kobayashi(Kyoto Univ.)

Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity

  • Upload
    taylor

  • View
    58

  • Download
    0

Embed Size (px)

DESCRIPTION

Yuji Omura (Kyoto Univ.) Hiroyuki Abe ( YITP,Kyoto Univ.) Tatsuo Kobayashi(Kyoto Univ.). Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity. Supersymmetry (SUSY) is one of the key ingredients - PowerPoint PPT Presentation

Citation preview

Page 1: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

SUPERSYMMETRY BREAKING ,R-SYMMETRY BREAKING ,AND METASTABLE VACUA IN SUPERGRAVITY

Yuji Omura (Kyoto Univ.)Hiroyuki Abe (YITP,Kyoto Univ.)Tatsuo Kobayashi(Kyoto Univ.)

Page 2: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

INTRODUCTION Supersymmetry(SUSY) is one of the key ingredientsto study physics beyond the SM :the hierarchy

between the Planck scale and the weak scale , dark matters , and etc……

On the other hand ,SUSY must be broken. Nelson and Seiberg showed “Generally there is broken SUSY if there is an R-symmetry.”

We discuss SUSY Models with a global U(1)R symmetry.

Page 3: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

THE SUSY MODELS WITH U(1)R SYMMETRY

U(1)R symmetry must be broken to make nonvanishing Majorana gaugino masses .

Nelson and Seiberg’s argument in global SUSY is

But spontaneous R symmetry breaking causes massless Goldstone boson ,R-axion.

SUSY breaking vacuum is metastable in O’Raifeartaigh Model.

R-symmetry breaking SUSY breaking

explicit R-symmetry breaking

In global SUSY

Intriligator,Seiberg and Shih showed in global SUSY

Page 4: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

SUSY breaking vacuum has a positive vacuum energy in global SUSY.

supergravity effect should be considered

to realize a Minkowski vacuum (V=0).

0|| 2WV global

)3(| ||| 22 WDWeV K

local

R-symmetry in supergravity

1. Are there relations between R-breaking and SUSY breaking like the Nelson and Seiberg’s argument?

R-symmetry should be broken for Majorana gaoujino masses to exist.

R-symmetry should be broken explicitly to avoid R-axion and …. 2. In O’Raifeartaigh Model ,which generally has SUSY

breaking vacua,are SUSY breaking vacua metastable ?

Page 5: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

Contents of our study and this talk

1. the relation between R-symmetry and Supersymmetry breaking in supergravity(SUGRA)

(based on the study of Nelson and Seiberg)2. the metastability of a supersymmetry breaking

Mikowski vacuum in O’Raifeartaigh Model in SUGRA. (Intriligator ,Seiberg and Shih argued this

metastability in global SUSY.)3. Conclusion

We discuss,

Page 6: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

“The Nelson and Seiberg argument in global SUSY”

the generic R-symmetric superpotential is rewritten

;R[W]=2,R[X]=qX.If there are R-breaking SUSY vacua( ),

There is not a solution of these equations. R-symmetry breaking SUSY breaking

1.The relation between R-symmetry and SUSY breaking in SUGRA

N+1 equations with N unknowns

(i=1,2,…,N)

Page 7: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

In SUGRA ,F-flat conditions are modified

That is ,as long as , Nelson and Seiberg’s argument still holds.For example, in the model with and , R-symmetry breaking SUSY

breaking. But most of R-symmetric Models don’t cause R-

breaking. We considered O’Raifeartaigh Model which is known as the R-symmetric Model drawing SUSY breaking.

Page 8: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

3.The metastability of SUSY breaking vacua

We argue explicit R-symmetry breaking makes SUSY breaking vacua metastable in O’Raifeartaigh Model.

Before the main topic,

: a=1,2,…,r and i=1,2,…,s. And r>s . In global SUSY, F-flat conditions for X are

so that there is no supersymmetric vacuum.

Introduction of generic O’Raifeartaigh Model

r equations with s(<r) unknowns

Page 9: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

Intriligator ,Seiberg and Shih’s argument

They added explicit R breaking terms to the generic O’Raifeartaigh Model to avoid R-axion.

In global SUSY, F-flat conditions for X areThere are solutions

depending on f.

SUSY breaking vacuum is metastable!

Explicit R-breaking

V

X

R-symmetric

SUSYSUSY

Page 10: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

and add

SUSY breaking vacuum:

SUSY vacuum:

The SUSY breaking vacuum is metastable and long-lived for .

Example in global SUSYV

XSUSYSUSY

)/1( O

Page 11: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

The metastability in SUGRA Generic O’Raifeartaigh Model in SUGRA

F-term flat conditions for X are

If there is no solution of ,

there is no SUSY vacuum .For example, K is canonical.

This potential can be

negative

r equations with s(<r) unknowns

Page 12: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

And if Kahler is canonical, V>0 .

Explicit R-breaking terms are required not only to avoid R-axion but also to make a Minkowski vacuum

under this condition about K.

This adding makes SUSY breaking vacuum metastable!

This adding makes the solutions of these equations exist.

The points satisfying the F-flat conditions are in V<0.

..

Page 13: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

By adding more generic explicit R-breaking terms,

Even if SUSY vacuua actually exist.

But this constant |c| must be set to tune V to 0.

There is a possibility the SUSY breaking Minkowski vacuum is not metastable .

SUSY vacua appear like the analyses in global SUSY.

If c is small, this is the same as in global SUSY!

Page 14: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

case 1 : By integrating out and , SUSY breaking vacuum(V=0): SUSY vacuum:case 2 : SUSY breaking vacuum (V=0) :

SUSY vacuum : ( )

In these cases, SUSY vacuum cannot exist!

Example(1)

Page 15: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

The situations to avoid the metastable

More generally ,the solutions of F-flat conditions can be expressed.In this case , the condition for SUSY vacua to exist is

In Polonyi –like Model,

SUSY breaking vacuum(V=0):

,this condition is

SUSY vacua can’t exist.

Page 16: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

(2)

The parameters are set ; SUSY breaking vacuum(V=0)

SUSY vacuum

V

XSUSY

SUSY

)/1( O

This term is added to (1).

Example 2

Page 17: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

SUSY vacua appear , . 0 makes the SUSY breaking vacuum

long-lived .

Even if = 0 , It is possibile that a SUSY vacuum exist . But the constant |c| is fixed to tune V to 0 ,so that there is a possibility that a SUSY Minkowski vacuum is

stabilized.

That is,…… cXfW ),( R

We found Polonyi-like models can avoid the metastable.

Page 18: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

4.ConclusionNelson and Seiberg argument “In the model with global U(1)R symmetry,R-symmetry breaking SUSY

breaking “This argument is also satisfied in SUGRA under the special condition , .(R[X]= )For example , The R-charges of all fields are positive , and .

Page 19: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

We considered R-symmetric Model with SUSY

breaking dynamics, O’Raifeartaigh Model.To make gauginos massive and avoid R-axion,R-symmetry should be broken explicitly.In global SUSY ,Intriligator Seiberg and Shih

showed the requirements cause the metastability of SUSY breaking vacua.

We discussed the metastability in supergravity.

Page 20: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

If Kahler potential is canonical, V >0 in O’Raifeartaigh Model in

supergravity. Explicit R-symmetry breaking terms are required not only to avoid R-axion but also make Minkowski vacua.

The explicit R-symmetry breaking causes the metastable Minkowski vacuum under the condition .We verified there are the points which satisfy SUSY stational conditions in the explicit R-symmetry breaking models.It is possible that the metastability of the SUSY breaking Minkowski vacuum is avoided ,for example, in Polonyi-like Model. Fin

.

.

Page 21: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity

Appendix

There is a R solution satisfying SUSY stational conditions in the case R-charge of X is negative.

A solution which doesn’t satisfy the NS condition.

SUSY :

SUSY :

X

V

SUSY

qx<0

Page 22: Supersymmetry  breaking ,R-symmetry breaking ,and  metastable vacua  in  supergravity