GAUGE MODEL OF UNPARTICLES Discovering the Unexpected
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Transcript of GAUGE MODEL OF UNPARTICLES Discovering the Unexpected
GAUGE MODEL OF UNPARTICLES
Discovering the Unexpected
Gennady A. Kozlov
Bogolyubov Laboratory of Theoretical Physics
JINR, Dubna
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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?
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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
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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
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SHORT OVERVIEW
New physics (CFT) weakly coupled to SM through heavy mediators
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
SM, m
Mediators, M
CFT, m=0
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CONFORMAL INVARIANCE
Conformal invariance implies scale invariance
theory “looks the same on all scales” Scale transformations: dx e x, e
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
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• The very high energy theory contains the fields of the SM and Banks-Zaks fields of a theory with a nontrivial IR fixed point.
4
The two set interact via heavy particles of mass
inducing effective interactions below
Dimensional transmutation occurs at in SI sector
Effective int. below
1:
:
SM U
SM BZk
U
d dU U SM
M
M O OM
O affect the d 1
U
U
U
defines a border energy where U staff can SM fieldsWhen couplings too weak to be observed in
O
Nature
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CONFORMAL INVARIANCE• At the quantum level, dimensionless couplings
depend on scale: renormalization group evolution
QED QCD are not conformal theories
g
Q
g
Q
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CONFORMAL FIELD THEORIES. ONE EXAMPLE
Banks-Zaks (1982) -function for 3SU with FN flavors CFT: defined by QCD with many massless fundamental fermions
3 5 7
0 1 22 32 2 216 16 16
g g gg
, 0 1 2i i FN ,... i , ,
For a range of FN , flows to a perturbative IR stable fixed point
0IRg Q Q const Approx. CT, 0fm Introduce 0fm CInv. broken
g
Q
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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 UVO , dim. UVd =1,2,… operator UO , dim. d BZ UVd d , however strong coupling UVd d Unitary CFT 1d (scalar UO ), 3d (vector UO ) Mack (1977) Loopholes: unparticle sector is scale invariant but not conformally
invariant. UO is NOT gauge-invariant
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CONFORMAL Symmetry Breaking & High energy scale3 characteristic scales:-Hidden sector couples at M- Conformal - EWSB CSB at
• Unparticle physics is only possible in the conformal window• Width of this window depends on
g
QMUU
U UM , ,
U E
U Ud , , , M
UU E ~
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• The density of unparticle final states is the spectral density
• 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)
UNPARTICLE PHASE SPACE
U
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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.
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TOP-quark DECAY • Consider t u U decay
through
• 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
Georgi (2007)
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TOP-quark DECAY • Consider t u U decay
through
• 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
Georgi (2007)
22
2 2111
t
Ud
t
UUU
Ut m
EmEdd
dEdm
U
~
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3 POINT COUPLINGS• 3-point coupling is determined, up to a constant, by
conformal invariance:
Photon pT
• E.g., LHC: gg O O O
• Rate controlled by value of the (strong) coupling, constrained only by experiment
• Many possibilities: ZZ, ee, , …
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Effective Field Theory
Hidden sector lying beyond the SM. Modeled by O M
04eff d
c ML M ~ c M , O M O M
, 246SM ~ O v GeV
(Heavy messenger encoded) ! Physics: IR SMM M Singlet-Doublet mixing: 2 1 2 2U U~ O HH O HH , d , Re H h v / Energy region: U U( IR ) E (UV ) Two effects: mixing & invisible decays Unbroken symmetry: U -singlets stable, weak interacting
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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)
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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 UVd d Renormalizability ( Re N )
HIGGS GUARANTEE Re N Higgs serve as portal to HIDDEN sector
Dilaton field xHHx for light Higgs
Conformal compensator with definite (small) mass
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AN EXTENDED HIGGS-U TOWER MODEL
gauge UHL L L
4 22 2 2 20
14gauge U U U UL F D O D O O O
2 2 2
UH U UL a H O b H O 0, , , a , b : Ud -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: UO x x at U , 1U SMd d
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INFINITE TOWER MODEL TM
Nature of U -staff unknown. Model(s)?
TM: 2 2
1U k k k
k
O O f , m k
as 0 Stephanov (2007)
2 214U U U kL( O ,H ) L( O,H ) F D O D O V ,H
2
2 22 2 2 2
1 1 1 1
1 14 2
N N N N
k k k k k k kk k k k
V ,H m a H f b H
Minimization: 2
2 2 2
1
12 2
kk k N
k ll
av f v, Hm b v
Interaction term 2
Ua H O with 0a ensures 0k ! Scale invariance is broken by controlled manner by splitting the
spectrum of states as 2 2km k
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PROPAGATOR OF U -staff
2202
2 20 2
m ,ddmD p ,dp m i
Two ways:
1. Scale invariance: 22 20
d
dm ,d A m
dA ? N.C.
5 22
0 22
1 21 1611 22
/
d d
d /m ,d A
m d d
Georgi
2. Expansion over rel. states 2
2 2 20 2 0 0m m m O
Combined result: 2 22 2 20 02
ddk k k
AO f m
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V.E.V. OF U -staff.
In the continuum limit:
22
12 2
00
1 1 22 4
d ddU
f s AvO s f s ds ds av z d dz s
IR-regularized mass (gap) induced by 2UH O :
2 2 2
1
N
IRR ll
z m b v
Result: IRR mass is provided by EWSB ( 0v ) does cutoff the IR divergence of U -staff.
That’s NEW understanding how to avoid the IR trouble
For real physics: 2
2 kb V ,H
v
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GAUGE “unHiggs” MODEL
4 22 2 2 2
014gauge U U U UL F D O D O O O
0, , are f’s (d ) Invariance A x A x x U UO x exp i e x O x , 0x
! Phase space U in decay to U -staff for decay of d part’s ( 0m ) Generating current: UK x, A x A x
Hidden parameter: 1
1U
UU
, SM,
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GAUGE “unHiggs” MODEL: equations of motion
To find a solution: 1 2 1 22 2/ /
U UO i , O i
real fields 0 0, , , Aim: Canonical quantization UL O L , Equations of motion:
2 2 2 2 20 2( ) , 0m A , m e 2 0UA A m A m
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SPECTRUM
1. U -staff dipole field
2
22
00lim x
resembles Froissart model (1959)
2. Massive gauge bosons
2
11 UA x B x xm m
2 0 0 0B : m B ; B ; B x , y
U -staff NO LONGER REMAINS SCALE-INV. EWSB ! Generating current:
23
1 UK x m B x x , m em
212 2
0
1 1 24
dddU IRR
AO s f s ds av m d d
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“UnHiggs” field: Formal View & CCR
CCR 0 2
8d
dbx , y i b E x y sign x x
i
TPWF 4 20 0 0x y x y S , x
Lorentz inv. req. 1 2x b E x b E x const
22 2 0
22 2 0 2
2 22 0
1 04
4 4
iE x E x E x , E x , E xx i x
i l iln ln x i sign x xx i x
0 2 2
1 22dx , y i b E x y i sign x b x b x
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“UnHiggs” propagator
0 0
22
1 22 2
0 0 0
1
W x T x x x x x
l = b ln b i x constx i x
Main contribution (long range forces of “unHiggs”)
2 2
2 2
11 4U
e lW x = ln constx i
Fixed by 0
3
00
xx , i x
; 0 0x x mA x
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GOLDSTONE THEOREM
Main object K x , y
0
30 0
0x
i d x K x ,e
v.e.v. of “unHiggs” staff
0 20 0 02ei K x , sign x x
0 2~ p sign p p Fourier transformation Consequence of the Goldstone theorem!
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“UnHiggs” propagator. 4 space. Result I
4 space:
2 2
42 2
11 4
ipx
U
e lW x ln d p e W px i
4 space:
2
2 224
2 2 2
116 1
ipx
U
llne x i
W p H p , H p d x e p x i
Desired propagator W p . Two representations:
Case A. 2 2 22
2 2
414
ln e p l i /W p i
p p i
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“UnHiggs” propagator. 4 space. Result I. Cont’d
Desired propagator: Case B.
2 2
22
12
p ln p iW p i
p p i
Where is d -dependence ? Regularized length
! 2 1
21 1 0 5771 2U
e, d , e l , .
IR div. avoiding:
2 2
4 4 22
12
ln p id pW p f p i d p p f p
pp i
! EXTRA POWER OF p REMOVES IR DIVERGENCE AT SMALL p
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“UnHiggs” propagator. 4 space. Result II
4 space:
2 2
42 2
11 4
ipx
U
e lW x ln d p e W px i
4 space: 2
202 22 20
18
ipx4
ilim d p e K x ip i
2 2
002
zlim K z ln / z O z ,z ln z
Finally:
2
2 24
2 2 22 20
1 11 4U
eW p lim ln p
i p i
defined on subspace of 4S for test functions 0 0f p
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PRICES
Prices that must be paid for maintaining new results: F.T. of TPWF’s x contains 2p -function
0 2 2 2 0 24 22
2ipx iE x i p p e d p ln x i sign x x
Non-unitarity character of the model; 2p isn’t a measure
Spectral function of 2p; gives an indefinite metric Translations become pseudounitarity R. Ferrari (1974)
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Energy (potential) of “unHiggs” charge. CONFINEMENT
Static limit KGA arXiv 0903.5252 [hep-ph]
03
2
0
9 2 2 3 18 1 2
i p r
U UU
E r x ; i d p e W p , p;
e r ln ln r , ,
20
22
2 2 2 22
2 2
102 1
4 61 14
U
eiW p , p;
p i
p p l i p ln ep i p i
0E r ; as 0 1U U, ! THE ENERGY GROWS AS r AT LARGE DISTANCES Hidden - “unHiggs” CONFINEMENT
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CONCLUSION. Theory view
1. Physical motivated way : Lagrangian term ~ 2
UO H
2. IR cutoff 2 2IRRm d const v d gives 0Ud O
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 UE 7. U -staff (ghost-like) propagator is the most general argument in
favor of (free) energy E r ; ;d of “unHiggs” staff
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SUMMARY. For experimentalists
• Unparticles: conformal energy window implies high energy colliders are the most useful machines
• Real unparticle production missing energy
As for of the SM particles is concerned, - staff production looks the same as production of massless particles
• Multi-unparticle production spectacular signals
• Virtual unparticle production rare processes
• Unparticles: Quite distinguishable from other HE physics through own specific kinematic properties
misE Ud