New physics weakly coupled to sm through heavy mediators

New physics weakly coupled to SM through heavy mediators

• New physics weakly coupled to SM through heavy mediators

• Many papers [hep-un]

• Many basic, outstanding questions

• Goal: provide groundwork for discussion, LHC phenomenology

Conformal invariance implies scale invariance, theory “looks the same on all scales”

• 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

At the quantum level, dimensionless couplings depend on scale: renormalization group evolution

• At the quantum level, dimensionless couplings depend on scale: renormalization group evolution

• QED, QCD are not conformal

Banks-Zaks (1982)

• 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)

Hidden sector (unparticles) coupled to SM through non-renormalizable couplings at M

• 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

The density of unparticle final states is the spectral density , where

• 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)

An alternative (more palatable?) interpretation in terms of “standard” particles

• 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.

Consider t  u U decay through

• Consider t  u U decay through

Unparticle propagators are also determined by scaling invariance.

• 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

COLLIDERS

• COLLIDERS

• 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

High Energy (LEP)

• High Energy (LEP)

EWSB  conformal symmetry breaking through the super-renormalizable operator

• EWSB  conformal symmetry breaking through the super-renormalizable operator

• This breaks conformal symmetry at

Strongly interacting conformal sector  multiple unparticle vertices don’t cost much

• 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

3-point coupling is determined, up to a constant, by conformal invariance:

• 3-point coupling is determined, up to a constant, by conformal invariance:

Unparticles: conformal window implies high energy colliders are the most robust probes

• 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