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					GAUGE MODEL OF UNPARTICLES
        Discovering the Unexpected


            Gennady A. Kozlov

    Bogolyubov Laboratory of Theoretical Physics

                    JINR, Dubna
   SM: problems with HIGGS
  NO explanation of HIGGS potential (Origin?)

  NO prediction for HIGGS-boson mass

  Doesn’t predict fermion masses and mixings

  HIGGS mass unstable to quantum corrections

  Doesn’t account for three generations


    HIDDEN WORLD ?
    Particle mass ? Gap or Continuous distrib’n?
2011-12-03                    GA Kozlov            2
             UNPARTICLES

   WHAT DO WE KNOW ABOUT UNPARTICLE PHYSICS ?

     MANY? TOO MANY? (SINCE 2007) NOTHING …

   UNPARTICLE PHYSICS IS NOT UNPHYSICS BUT RATHER
    A NEW GLANCE TO HIGH ENERGY PHYSICS




2011-12-03           GA Kozlov                   3
              UNPARTICLES
 SPECULATION ON A POSSIBLE EXISTENCE OF A HIDDEN
  HIGH SCALE CONFORMAL SECTOR WHICH MAY COUPLE
  TO VARIOUS MATTER FIELDS, GAUGE FIELDS OF THE SM

 A STAFF OF THIS HIDDEN SECTOR IS SETTLED DOWN BY
  UNPARTICLES – Un-STAFF

 THE PHASE SPACE OF Un-STAFF:
  AT NON-INTEGER SCALE DIMENSION THE Un-STAFF
  LOOKS LIKE A NON-INTEGER NUMBER OF INVISIBLE
  OBJECTS

 Un-STAFF IS A PARTICULAR CASE OF A FIELD WITH
  CONTINUOUSLY DISTRIBUTED MASS
 2011-12-03              GA Kozlov                   4
                      SHORT OVERVIEW

 New physics (CFT) weakly coupled to SM through heavy mediators

                          Mediators, M

             SM, m                             CFT, m=0



 A lot of papers [hep-un] since      H. Georgi, P.R.L.98 (2007) 221601

 Many basic, outstanding questions

 Goal: provide groundwork for discussions and physical realization
        LHC & ILC phenomenology

2011-12-03                    GA Kozlov                           5
                  CONFORMAL INVARIANCE

   Conformal invariance implies scale invariance

                theory “looks the same on all scales”

   Scale transformations: x  e  x,   e d

   Basic feature of CT: NO MASSES in the theory

   Standard Model is not conformal even as a classical field theory:

             HIGGS MASS BREAKS CONFORMAL SYMMETRY



2011-12-03                     GA Kozlov                            6
  • The very high energy theory contains the fields of the
    SM and Banks-Zaks fields of a theory with a
    nontrivial IR fixed point.

 The two set interact via heavy particles of mass M
                                           1
inducing effective interactions below M :    k
                                               OSM OBZ
                                          M
 Dimensional transmutation occurs at U in SI sector
 Effective int. below U : U 4dSM dU OSM OU
 U defines a border energy where U  staff can affect the SM fields
 When dU  1  couplings too weak to be observed in Nature
    2011-12-03                     GA Kozlov                    7
     CONFORMAL INVARIANCE
• At the quantum level, dimensionless couplings
  depend on scale: renormalization group evolution



             g                      g


                       Q                 Q
                 QED                           QCD
                       are not conformal theories
2011-12-03                   GA Kozlov               8
   CONFORMAL FIELD THEORIES. ONE EXAMPLE

 Banks-Zaks (1982)  -function for SU  3 with N F flavors
   CFT: defined by QCD with many massless fundamental fermions
                                                        
                  g3          g5                        g7
                                                          ,     N ,... i  0 ,1, 2
    g    0       1                  2
              16                                     i 
                     2                  2              3          i   F

                           16 2                16 2
                                                         

 For a range of N F , flows to a perturbative IR stable fixed point

  gIR  Q  Q0   const

 Approx. CT, m f  0                                 g
 Introduce m f  0 CInv. broken

                                                                 Q
2011-12-03                                  GA Kozlov                                 9
             UNPARTICLES. IDEA & REALIZATION

   Hidden sector (unparticles) coupled to SM through
    non-renormalizable couplings at some UV scale M Georgi (2007)

   Assumed: unparticle sector becomes conformal at scale  U ,
    couplings to SM preserve conformality in the IR

   Operator OUV , dim. dUV =1,2,…        operator OU , dim. d

   BZ  d  dUV , however strong coupling  d  dUV

   Unitary CFT  d  1 (scalar OU ), d  3 (vector OU )     Mack (1977)

   Loopholes: unparticle sector is scale invariant but not conformally
    invariant. OU is NOT gauge-invariant
2011-12-03                     GA Kozlov                              10
  CONFORMAL Symmetry Breaking & High energy scale
3 characteristic scales: M , U , U
-Hidden sector couples at M
                 ~
- Conformal U  E  U
- EWSB  CSB at E  U

                                 g


                                                 U
                                                            Q
                                            U         M


• Unparticle physics is only possible in the conformal window
• Width of this window depends on d , U , U , M
  2011-12-03                    GA Kozlov                  11
             UNPARTICLE PHASE SPACE

• The density of unparticle final states is the spectral density U



• Scale invariance 

• This is similar to the phase space for n massless particles:




•   “Unparticle” with dU = 1 is a massless particle. “Unparticles” with some
    other dimension dU look like a non-integral number dU of massless
    particles               Georgi (2007)

2011-12-03                       GA Kozlov                              12
                              SIGNALS

Colliders Tevatron, LHC, ILC
  Real U -staff production
    - monojets           (Tevatron, LHC)          gg  gU
    - monophotons        (ILC)                    e  e   gU
                                            [missing energy signals]
   Virtual extra gauge bosons                  gg  Z   ZU ,  U

   Virtual U -staff exchange

       - scalar U -staff:               ff  U      ,  , ZZ , ...
         [No interference with SM, No resonances, U -staff massless]

      - vector U -staff:                e  e   U      , qq, ...
        [Induce contact interactions, Eichten, Lane, Peskin (1983)]
 U -staff decay in SM particles.      Higgs decay in U -staff.
2011-12-03                      GA Kozlov                              13
              TOP-quark DECAY
• Consider t  u U decay
  through




                                                  Georgi (2007)
• For dU  1, recover 2-body decay kinematics,
  monoenergetic u- jet.

• For dU > 1, however, get continuum of energies; unparticle
  does not have a definite mass
 2011-12-03                GA Kozlov                        14
                  TOP-quark DECAY
• Consider t  u U decay
  through



                                     dU 2              2
   1 d                                     EU   
         ~ dU dU  11  2 U
                            E
mt              2
                                
                                            
                                             m     
                                                    
    dEU                   mt               t           Georgi (2007)
 • For dU  1, recover 2-body decay kinematics,
   monoenergetic u- jet.

 • For 2>dU > 1, however, get continuum of energies;
   unparticle does not have a definite mass
  2011-12-03                                   GA Kozlov              15
               3 POINT COUPLINGS
• 3-point coupling is determined, up to a constant, by
  conformal invariance:




• E.g., LHC: gg  O  O O  

• Rate controlled by value of the
  (strong) coupling, constrained only
  by experiment

• Many possibilities: ZZ, ee, ,
  …


  2011-12-03                      GA Kozlov   Photon pT   16
                            Effective Field Theory

 Hidden sector lying beyond the SM.                         Modeled by O  M 

                                     c0  M 
Leff  M  ~ c  M ,   O  M                 OM 
                                         d 4           ,    SM ~ O  v  246 GeV 
                
  (Heavy messenger encoded)
                                                 ! Physics: M  M IR   SM
 Singlet-Doublet mixing:

        ~ OU HH   OU HH  ,
                     2
                                       1  d  2,        Re H   h  v  / 2

 Energy region: U ( IR )  E  U (UV )
 Two effects: mixing & invisible decays
 Unbroken symmetry: U -singlets stable, weak interacting
2011-12-03                                 GA Kozlov                                17
  UNPARTICLE INTERACTIONS




• Interactions depend on the dimension of the unparticle
  operator and whether it is scalar, vector, tensor, …

• Super-renormalizable couplings:
  Most important (model will follow)
 2011-12-03                 GA Kozlov                      18
 Our goal: U - staff in gauge theories           KGA 0903.5252 hep-ph
                                                      0905.2272 hep-ph
    U coupling to SM singlet/doublet

    U carries SM-like charges

    SM criteria, however non-canonical d  dUV

    Renormalizability ( Re N )

                 HIGGS GUARANTEE Re N

    Higgs serve as portal to HIDDEN sector

    Dilaton field   x   H  H  x  for light Higgs
      Conformal compensator with definite (small) mass

2011-12-03                        GA Kozlov                              19
             AN EXTENDED HIGGS-U TOWER MODEL

  L  Lgauge  LUH

             1 2              
            F   D OU D OU   OU  0 OU
                     2              2  4   2              2
 Lgauge
             4
                                                      2            2        2
                                             LUH  a H OU  b H OU
   ,  , 0 , a, b : d U -dependent

  Ignoring Higgs-U weak couplings will lead to unability of
   “observation” of U -staff
  Scaling properties of HIDDEN SECTOR depends on scaling
   properties of couplings

  SM limit:     OU  x     x  at   U ,       dU  d SM  1
2011-12-03                       GA Kozlov                             20
              INFINITE TOWER MODEL TM 
   Nature of U -staff unknown. Model(s)?
                        
    TM  : OU  O   f k  k ,      mk  k  2 as   0 Stephanov (2007)
                                        2

                        k 1
                            1 2
L( OU , H )  L( O, H )   F   2 D OU D  OU  V  k , H 
                                                   

                            4
                          2
              1   N
                       2   1 N 2 2             N                  N
V  k , H      k    mk k  a H  f k k  b H  k
                                             2                  2      2

              4  k 1  2 k 1                k 1               k 1



                               1              av 2 f k                  v
   Minimization:  k     k                              ,    H 
                               2        N 2             
                                 m     l  b
                                         2
                                                    v 2                 2
                                         k
                                        l 1            
   Interaction term a H OU with a  0 ensures  k  0 !
                        2


   Scale invariance is broken by controlled manner by splitting the
    spectrum of states as mk  k  2
                           2



2011-12-03                      GA Kozlov                               21
                           PROPAGATOR OF U -staff

                 
                                0  m 2 ,d 
            
                           2
                       dm
      D p 2 ,d  
                     0
                        2 p 2  m 2  i

 Two ways:
                                               
                                                           d 2
1. Scale invariance:  0 m ,d  Ad m
                               2                       2


                                     16 5 / 2   d  1 / 2 
                           1
                                   
 Ad  ? N.C.  0 m ,d  1  2  Ad 
                       2

                                       2    d  1   2d 
                                                                                           Georgi
                                     
                                           2d
                           m

                                              2   m                          0 O 0 
                                                                                                 2
2. Expansion over rel. states  0 m            2                      2
                                                                           m
                                                                             2

                                                                  



                                                                       
                                                                 Ad          d 2
                               0 O  0  k
                                                   2
  Combined result:                                          f 
                                                               2     2
                                                                    mk               2
                                                                 2
                                                              k




2011-12-03                                 GA Kozlov                                        22
                                       V.E.V. OF U -staff.

     In the continuum limit:
        
                              v2          f 2  s          Ad 2
         s  f  s  ds                                    av  1 z d 2  d  1   2  d 
                                                                        d 1
OU
       0
                              2    
                                   0       zs
                                                      ds 
                                                             4

                                                                   2
 IR-regularized mass (gap) induced by H OU :

                            N
 zm     2
         IRR    bv    l2
                    2

                           l 1


 Result: IRR mass is provided by EWSB ( v  0)
                  does cutoff the IR divergence of U -staff.

That’s NEW understanding how to avoid the IR trouble
                                       b  2
                      For real physics:  2  V  k , H 
                                        v
2011-12-03                                     GA Kozlov                                        23
                       GAUGE “unHiggs” MODEL


            1 2              
           F   D OU D OU   OU  0 OU
                    2              2  4   2                 2
Lgauge
            4

                                                         ,  , 0 are f’s ( d )
     Invariance A  x   A  x      x 
                   OU  x   exp   i e   x   OU  x  ,
                                                                  x  0

! Phase space U in decay to U -staff           for decay of d part’s ( m  0 )

Generating current: K   x ,       A  x    U    A  x 

                         1,   U SM
  Hidden parameter:  U 
                          1,   U
     2011-12-03                         GA Kozlov                                  24
           GAUGE “unHiggs” MODEL: equations of motion

To find a solution:
OU  21 / 2     i   ,            OU  21 / 2     i  
                                          


                             
                      real fields

   ,     0 ,   ,          0
 Aim: Canonical quantization

 L  OU   L  ,    Equations of motion:

    (  2   2 )  0 ,  2  2 2 2
       m  A  0 , m  e
    A   U    A  m 2 A   m     0
   2011-12-03                         GA Kozlov                        25
                                           SPECTRUM

1. U -staff     dipole field
                                    x   0 resembles Froissart model (1959)
                                2
  lim                 2
   2 0


2. Massive gauge bosons
                         1  U 
  A  x   B  x     1           x
                       m        m 2
                                       
               
 B : m 2 B  0;   B   0;  B  x  ,   y   0
                                                   
 U -staff NO LONGER REMAINS SCALE-INV.  EWSB !
 Generating current:
              2            1  U              
K   x   m  B  x               x  , m  e
                             m3                
                    
                                       A
                                                                 
                                                                      d 2
                   s  f  s  ds  d av 2  1                           d  1   2  d 
                                                     d 1
     OU                                                   2
                                                          m IRR
                 0
                                       4
  2011-12-03                                  GA Kozlov                                               26
                   “UnHiggs” field: Formal View & CCR

                                                   b
                                                                     
  CCR    x  ,   y    i bd E  x  y   d sign x 0  x 2
                                                8 i
  TPWF   x  y   0   x    y  0                    S   ,
                                                                   4
                                                                         x  0
                                                                             2


  Lorentz inv. req.                  x   b1 E   x   b2 E   x   const

                                                    i   1
 E  x  E   
                   x  E   
                                  x ,    E  x  2 2
                                             
                                                                 ,           2
                                                                                 E x  0
                                                   4 x  i x 0


             
    i                        i 
          ln 2
                l2
                         
                             4  
                                                                      
                                    ln  2 x 2  i sign x 0  x 2 
                                                                   
  4       x  i x 0   
        2                        2




                                                            
                                                                       
    x  ,   y    i bd E  x  y   2 i sign x 0 b1 x 2  b2 x 2 
                                                                                   
2011-12-03                                GA Kozlov                                   27
                                “UnHiggs” propagator

                                                              
   W  x   0 T   x    0 0   x0   x     x 0    x   
                                                      1            
                                 = b1 ln 2
                                           l2
                                         x  i
                                                                            
                                                  b2  2  i x 2   const
                                                      x            
                                           
                                   Main contribution
                                 (long range forces of “unHiggs”)

             e 
                     2
                         1    l2
W  x=                  ln 2        const
        1   U  4  2
                            x  i
               

             x  ,    0    0  i 3  x  ;     x     0   x   mA0  x 
Fixed by
                                    x 0

  2011-12-03                              GA Kozlov                                     28
                     GOLDSTONE THEOREM

     Main object         K   x  ,   y 
                                             


  i 3
  e  d x  K 0  x  ,   0 x0 0   v.e.v. of “unHiggs” staff
                             

                                     e
    
      i 0  K   x  ,   0  0 
                                   2             
                                           sign x 0  x 2 
                                                             
                                                 
                      
        ~ p sign p0  p2  Fourier transformation
                        
                      Consequence of the Goldstone theorem!


2011-12-03                        GA Kozlov                           29
                “UnHiggs” propagator. 4 space. Result I

                            e 
                                    2
                                        1          l2
 4 space: W  x                           ln 2         d 4 p e  ipx W  p 
                           1   U  4 2       x  i
 4 space:
                                                                               l2     
                                                                       ln 
                                 1  e                                     x 2  i 
                                                         2
                 2
                                                                                      
  W  p  2 H  p , H  p 
                               16 2 1   U 
                                               d 4 x e ipx
          p                                                               x 2  i

 Desired propagator W  p  . Two representations:


                                1
             Case A. W  p    i 
                                                                        
                                          ln e 2  p 2 l 2  i / 4  
                                             2
                                                                       
                                       2                                
                                4    p            p 2  i           
                                                                        

2011-12-03                              GA Kozlov                                30
                    “UnHiggs” propagator. 4 space. Result I. Cont’d

                                                1
        Desired propagator: Case B. W  p    i
                                                       
                                                      p ln  p  i
                                                                 2 2
                                                                                   
                                                                                     
                                                2 p                                 
                                                                      2

                                                           p 2  i                    

    Where is d -dependence ?
                               Regularized length


        e 
                2
                                  1  1
!            ,     d  ,   e 2 l ,    1 0.577
        1  U                    2

                                                1                     
                                                            ln  2 p 2  i  
IR div. avoiding:       d 4 pW  p  f  p   2 i  d 4 p  p2  i 2 p p f  p 
                                                                  
! EXTRA POWER OF p REMOVES IR DIVERGENCE AT SMALL p



     2011-12-03                             GA Kozlov                                        31
             “UnHiggs” propagator. 4 space. Result II

                           e 
                                   2
                                            1              l2
  space: W  x 
      4
                                                     ln 2         d 4 p e  ipx W  p 
                          1   U  4 2                x  i


 4 space: lim
             2
                0    d4 p e
                                  ipx

                                           p   2
                                                      1
                                                       i
                                                       2
                                                                
                                                                    2
                                                                        
                                                                             i
                                                                            8 2
                                                                                      
                                                                                   K 0   x 2  i   

    z 0
                                            
 lim K 0  z  ln  2 / z     O z 2 ,z 2 ln z          
Finally:
                                                                            
                  e 
                        2
                                           1               1      2 4
       W  p           lim                                 ln 2   p  
                                       
                 1   U  2  0  i p 2   2  i        
                                                         4               
                                                    2         2

                                                                            
      defined on subspace of S  4  for test functions f  p  0   0
2011-12-03                                  GA Kozlov                                             32
                                        PRICES
    Prices that must be paid for maintaining new results:

                                                      
         F.T. of TPWF’s    x  contains   p2 -function

                     
E   x   i  2 p 0   p 2 e  ipx d 4 p  
                                                     i 
                                                    2  
                                                                               
                                                           ln  2 x 2  i sign x 0  x 2 
                                                                                          
                                                  
                                                        2



                                                             
     Non-unitarity character of the model;   p2 isn’t a measure

                                           
        Spectral function of  p; 2 gives an indefinite metric
         Translations become pseudounitarity                      R. Ferrari (1974)




   2011-12-03                           GA Kozlov                                   33
        Energy (potential) of “unHiggs” charge. CONFINEMENT

    Static limit                                 KGA arXiv 0903.5252 [hep-ph]

                                             
     E  r  x ;   i  d 3 p e i p r W p 0  0 , p;      
                            e 
                                  2
                                           9                       
                                        r  ln 2  2  3 ln  r   ,   U ,  U  1
                         8 1   U      2                       

                                  e 
                                         2

     iW p   0
                  0 , p;  
                                               2
                                                 1
                               2 1   U   p  i  2
                                                         

                      4 p 2   p 2 l 2  i 2      6 p2    
                  1  2      ln           e  2          1
                     p  i         4           p  i 
     E  r ;   0 as   0 , U  1                  
                                                     U        
                       ! THE ENERGY GROWS AS r AT LARGE DISTANCES
   2011-12-03
                        Hidden - “unHiggs” CONFINEMENT
                                       GA Kozlov                 34
                       CONCLUSION. Theory view
                                                           2
1. Physical motivated way : Lagrangian term ~ OU H

2. IR cutoff m IRR  d   const v 2    d  gives   d   OU  0
               2




3. TPWF for “unHiggs”- staff solution: transition HE  LE “unHiggs”

4. Canonical quantization. New dipole solutions. Goldstone th. verified

5. Massive vector field B  x  with d - dependent mass m   e  d 

6. U -staff propagator W  p;d  valid in the window U  E  U

7. U -staff (ghost-like) propagator is the most general argument in
   favor of (free) energy E  r ; ;d  of “unHiggs” staff

2011-12-03                       GA Kozlov                               35
               SUMMARY. For experimentalists

• Unparticles: conformal energy window implies high energy colliders are
  the most useful machines

• Real unparticle production  missing energy

As for Emis of the SM particles is concerned, U - staff production looks the
   same as production of d massless particles

• Multi-unparticle production  spectacular signals

• Virtual unparticle production  rare processes

• Unparticles: Quite distinguishable from other HE physics through own
  specific kinematic properties

  2011-12-03                       GA Kozlov                               36

				
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