gauge model of unparticles discovering the unexpected

GAUGE MODEL OF UNPARTICLES

Discovering the Unexpected

Gennady A. Kozlov

Bogolyubov Laboratory of Theoretical Physics

JINR, Dubna

22.04.23 GA Kozlov 2

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?


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


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


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


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


• 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


CONFORMAL INVARIANCE• At the quantum level, dimensionless couplings

depend on scale: renormalization group evolution

QED QCD are not conformal theories

g

Q

g

Q


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

22.04.23 GA Kozlov 10

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

22.04.23 GA Kozlov 11

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 ~

22.04.23 GA Kozlov 12

• 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

22.04.23 GA Kozlov 13

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.

22.04.23 GA Kozlov 14

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)

22.04.23 GA Kozlov 15

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

~

22.04.23 GA Kozlov 16

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, , …

22.04.23 GA Kozlov 17

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

22.04.23 GA Kozlov 18

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)

22.04.23 GA Kozlov 19

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

22.04.23 GA Kozlov 20

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

22.04.23 GA Kozlov 21

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

22.04.23 GA Kozlov 22

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

22.04.23 GA Kozlov 23

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

22.04.23 GA Kozlov 24

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,

22.04.23 GA Kozlov 25

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

22.04.23 GA Kozlov 26

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

22.04.23 GA Kozlov 27

“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

22.04.23 GA Kozlov 28

“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

22.04.23 GA Kozlov 29

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!

22.04.23 GA Kozlov 30

“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

22.04.23 GA Kozlov 31

“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

22.04.23 GA Kozlov 32

“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

22.04.23 GA Kozlov 33

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)

22.04.23 GA Kozlov 34

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

22.04.23 GA Kozlov 35

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

22.04.23 GA Kozlov 36

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

gauge model of unparticles discovering the unexpected

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