UNPARTICLE PHYSICS Jonathan Feng UC Irvine Detecting the Unexpected UC Davis 16-17 November 2007.
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Transcript of UNPARTICLE PHYSICS Jonathan Feng UC Irvine Detecting the Unexpected UC Davis 16-17 November 2007.
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UNPARTICLE PHYSICS
Jonathan FengUC Irvine
Detecting the UnexpectedUC Davis
16-17 November 2007
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16 Nov 07 Feng 2
OVERVIEW
• New physics weakly coupled to SM through heavy mediators
• Many papers [hep-un]
• Many basic, outstanding questions
• Goal: provide groundwork for discussion, LHC phenomenology
SM
Mediators
CFT
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16 Nov 07 Feng 3
CONFORMAL INVARIANCE
• Conformal invariance implies scale invariance, theory “looks the same on all scales”
• Scale transformations: x e-x , ed
• Classical field theories are conformal if they have no dimensionful parameters: d = 1, d = 3/2
• SM is not conformal even as a classical field theory – Higgs mass breaks conformal symmetry
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16 Nov 07 Feng 4
CONFORMAL INVARIANCE
• At the quantum level, dimensionless couplings depend on scale: renormalization group evolution
• QED, QCD are not conformal
g
Q
g
Q
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CONFORMAL FIELD THEORIES
• Banks-Zaks (1982)
-function for SU(3) with NF flavors
For a range of NF, flows to a
perturbative infrared stable fixed point
• N=1 SUSY SU(NC) with NF flavors
For a range of NF, flows to a strongly coupled infrared stable fixed point Intriligator, Seiberg (1996)
16 Nov 07 Feng 5
g
Q
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UNPARTICLES• Hidden sector (unparticles)
coupled to SM through non-renormalizable couplings at M
• Assume unparticle sector becomes conformal at U, couplings to SM preserve conformality in the IR
16 Nov 07 Feng 6
Georgi (2007)
• Operator OUV , dimension dUV = 1, 2,… operator O, dimension d
• BZ d ≈ dUV, but strong coupling d ≠ dUV .
Unitary CFT d ≥ 1 for scalar O, d ≥ 3 for vector O. Mack (1977)
[Loopholes: unparticle sector is scale invariant but not conformally
invariant, O is not gauge-invariant.]
g
QMU
[ ][ ]
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UNPARTICLE INTERACTIONS
16 Nov 07 Feng 7
• Interactions depend on the dimension of the unparticle operator and whether it is scalar, vector, tensor, …
• There may also be super-renormalizable couplings: This is important – see below.
Cheung, Unparticle Workshop (2007)
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• The density of unparticle final states is the spectral density , where
• Scale invariance
• This is similar to the phase space for n massless particles:
• So identify n dU. Unparticle with dU = 1 is a massless particle. Unparticles with some other dimension dU looks like a non-integral number dU of massless particles Georgi (2007)
UNPARTICLE PHASE SPACE
16 Nov 07 Feng 8
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• An alternative (more palatable?) interpretation in terms of “standard” particles
• The spectral density for unparticles is
• For dU 1, spectral function piles up at P2 = 0, becomes a -function at m = 0. Recall: -functions in are normal particle states, so unparticle is a massless particle.
• For other values of dU, spreads out to higher P2. Decompose this into un-normalized delta functions. Unparticle is a collection of un-normalized particles with continuum of masses. This collection couples significantly, but individual particles couple infinitesimally, don’t decay.
UNPARTICLE DECONSTRUCTION
16 Nov 07 Feng 9
Stephanov (2007)
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TOP DECAY
• Consider t u U decay through
16 Nov 07 Feng 10
• 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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• Unparticle propagators are also determined by scaling invariance.
E.g., the scalar unparticle propagator is
• Propagator has no mass gap and a strange phase
• Becomes infinite at d = 2, 3, …. Most studies confined to 1 < d < 2
UNPARTICLE PROPAGATOR
16 Nov 07 Feng 11
Georgi (2007), Cheung, Keung, Yuan (2007)
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SIGNALSCOLLIDERS• Real unparticle production
– Monophotons at LEP: e+e- g U– Monojets at Tevatron, LHC: g g g U
• Virtual unparticle exchange– Scalar unparticles: f f U +- , , ZZ,…
[No interference with SM; no resonance: U is massless]– Vector unparticles: e+e- U +-, qq, …
[Induce contact interactions; Eichten, Lane, Peskin (1983) ]
LOW ENERGY PROBES• Anomalous magnetic moments• CP violation in B mesons• 5th force experiments
ASTROPHYSICS• Supernova cooling• BBN
16 Nov 07 Feng 12
Many Authors (2007)
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CONSTRAINTS COMPARED
High Energy (LEP)
11 Nov 07 Feng 13
Low Energy (SN)
Bander, Feng, Shirman, Rajaraman (2007) Hannestad, Raffelt, Wong (2007)
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CONFORMAL BREAKING• EWSB conformal symmetry
breaking through the super-renormalizable operator
• This breaks conformal symmetry at
16 Nov 07 Feng 14
Fox, Shirman, Rajaraman (2007)
• Unparticle physics is only possible in the conformal window
g
QMU
[ ][ ]
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CONFORMAL WINDOW
16 Nov 07 Feng 15
Many Implications
• Low energy constraints are applicable only in fine-tuned models
• Mass Gap
Fox, Shirman, Rajaraman (2007)
• Colored Unparticles
Cacciapaglia, Marandella, Terning (2007)
• Higgs Physics
Delgado, Espinoza, Quiros (2007)
• Unresonances Rizzo (2007)
Ba
nd
er, F
en
g, S
hirm
an
, Ra
jara
ma
n (2
00
7)
The window is narrow
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UNRESONANCES
16 Nov 07 Feng 16
Rizzo (20
07)
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MULTI-UNPARTICLE PRODUCTION
• Strongly interacting conformal sector multiple unparticle vertices don’t cost much
• LHC Signals
• Cross section is suppressed mainly by the conversion back to visible particles
16 Nov 07 Feng 17
Feng, Rajaraman, Tu (2007)
q
q OO
O
O
O
O
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3 POINT COUPLINGS
• 3-point coupling is determined, up to a constant, by conformal invariance:
16 Nov 07 Feng 18Photon pT
• E.g.: gg O O O
• Rate controlled by value of the (strong) coupling, constrained only by experiment
• Kinematic distributions are
predicted
• Many possibilities: ZZ, ee, , …
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16 Nov 07 Feng 19
SUMMARY
• Unparticles: conformal window implies high energy colliders are the most robust probes
• Virtual unparticle production rare processes
• Real unparticle production missing energy
• Multi-unparticle production spectacular signals
• Distinguishable from other physics through bizarre kinematic properties