Unparticle and Supersymmetry Physics

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Unparticle and Supersymmetry Physics

• Hao Zhang
• School of Physics, Peking
  University
• (In collaboration with Chong Sheng Li and Zhao Li)

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Outline

• What is unparticle?
• How do SUSY couple with unparticle in a natural
  way?
• General coupling form
• Some examples
• Conclusion and Outlook

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What is unparticle?

• HistoryBanks and Zaks found that for some
  fermion number the non-abelian Klein-Yang-Mills
  theory might have a nontrivial infrared fixed
  point. (Banks,Zaks,Nucl.Phys.B196(1982) 189)
• It means that the theory is an asymtotically
  conformal field theory in infared limit.

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• There are also some theory which is conformal
  invariant such as N4 SYM.But are there any
  relations between them and our world?
• Who knows)

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Georgis scheme(Georgi,hep-ph/0703260)

• The most important thing is how we will know if
  we see it.
• Assume the high energy theory contains two parts.
  One contains fields of the SM, the other has an
  infrared fixed point. These two parts interact
  through the exchange of particles with a large
  mass scale MU.

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• We will have a effective theory below the scale
  MU. The interactions between the two parts have a
  generic form
• In the effective theory below some scale the BZ
  operators match to unparticle operators(go to the
  infrared fixed point)

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• We have the effective interactions
• Georgi showed that Unparticle stuff with scale
  dimension dU looks like a non-integral number dU
  of invisible particles.

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• This means that an unparticle stuff with scale
  dimension dU in final state looks like dU
  massless particles. Because the n-body phase
  space integral is
• While an unparticle phase space density is

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How do SUSY couple with unparticle in a natural
way?

• There are many interesting problems with
  unparticle.
• Georgi,hep-ph/0703260
• Georgi,hep-ph/0704.2457
• Kingman Cheung,Wai-Yee Keung,Tzu-Chiang
  Yuan,hep-ph/0704.2588
• Mingxing Luo,Guohuai Zhu,hep-ph/0704.3532
• Gui-Jun Ding,Mu-Lin Yan,hep-ph/0705.0794
• Stephanov,hep-ph/0705.3049
• etc.

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• A very important new physics at TeV scale is
  supersymmetry. This is a symmetry between boson
  and fermion which was first introduced in 1960s
  in string theory by Ramond and was first used in
  4D field theory by Wess and Zumino in western
  world in 1974 and by Golfand and Likhtman in
  Union of Soviet Socialist Republics in 1971.

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• Since supersymmetry is a important condidate of
  new physics, we are interesting in what we will
  see if there are couplings between unparticle and
  MSSM.
• The first problem is how to construct a effective
  coupling. Although it has a big uncertainty, we
  want to construct a more natrual interaction term.

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• We want the MSSM current to have such property,
  it should have both particle and sparticle field
  operators. Or it will still be a SM current just
  adds its scurrent.
• There is such a current in MSSM. It is the
  supercurrent.
• What is supercurrent? And how to understand it?

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• We all know the physics states construct a dense
  subset of a Hilbert. This Hilbert space is a
  representation of symmetry group. When we have a
  continue symmetry we get some charges(as Lie
  algebras representation) and their conservation
  currents. So when we have SUSY we get super
  charges(as Lie super algebras representation)
  and supercurrent.

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• Because SUSY is only a symmetry of the action. So
  when we have calculated terms like
• we still need to calculate the variation of
  the Lagrangian density.
• Since supersymmetry transformation connects
  particle and its superpartner,it must have the
  form

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• Let us write down a simple form of supercurrent
  which only has chiral superfield
• Now let us write down the coupling
• where S is the MSSM supercurrent and O is a
  spin-3/2 unparticle operator.

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Decay of sparticles with the coupling

• As examples we calculated some decay processes of
  sparticles.
• We are primarily interested in the shape of the
  curve.

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Sfermion fermion unparticle decay

• The first example is a sfermion decay to a
  fermion and an unparticle. We calculated a stop
  decay to a top quark and an unparticle,and a stau
  decay to a tau lepton and an unparticle. The
  vertex is

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Sfermion fermion unparticle decay
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Neutrilino(chargino) gauge boson unparticle decay

• In our model there is a special decay process. A
  neutrilino can decay to a photo and an
  unparticle. It looks strange that a photo can
  couple with two neutral particles.

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• In fact such an unparticle is like a gravitino.
  In gravity theory, two photos can couple with a
  graviton. When we consider a SUSY gravity (SUGRA)
  we change two of three particles in a vertex to
  their superpartners. That is why we have this
  vertex
• This will be a very important signal at colliders.

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Neutrilino photo unparticle decay
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Conclusion and outlook

• We have shown a natural couplings between
  unparticle and SUSY, and also used it calculating
  some decay processes of sparticle.
• The new coupling has some interesting
  phenomenology result. If we can see them at new
  colliders, it can help us to understand both SUSY
  and unparticle.

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• Although there are many problems about a theory
  which has a nontrivial infrared fixed point and
  conformal field theory,we should prepare to
  discovery it.
• SUSY is an important candidate of TeV new
  physics.If unparticle exists, it would be
  interesting to see whether there are some
  relation between them.

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• Since these couplings contains supercurrent, they
  might have some relations with SUSY breaking.
  This topic is very interesting for us. I think we
  can do something in this field next step.

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• If we only consider MSSM, the coupling is obvious
  SUSY breaking and R-parity breaking. But if we
  introduce suitable SUSY transformation of the
  unparticle that means we introduce SUSY to
  unparticle part, it will have a larger symmetry.
  We think it will look like a SUGRA theory.
• As Stephanov said in his paper(hep-ph/0705.3049),
  there might be some similiar between unparticle
  and AdS. We do not know whether it has relation
  to AdS/CFT and SUGRA.

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References

• 1. Banks,Zaks,Nucl.Phys.B196(1982) 189
• 2. Georgi,hep-ph/0703260
• 3. Georgi,hep-ph/0704.2457
• 4. Kingman Cheung,Wai-Yee Keung,Tzu-Chiang
  Yuan,hep-ph/0704.2588
• 5. Stephanov,hep-ph/0705.3049
• 6. Weinberg,The Quantum Theory of Fields,Vol III
• 7. Nieuwenhuizen,Supergravity,Phys.Rep68.No.4(1981
  ) 189

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Thank You!