
New physics weakly coupled to sm through heavy mediators

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New physics weakly coupled to SM through heavy mediators Many papers [hepun] 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 ex , 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
BanksZaks (1982) BanksZaks (1982) function for SU(3) with NF flavors 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 nonrenormalizable couplings at M Hidden sector (unparticles) coupled to SM through nonrenormalizable 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 nonintegral 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 unnormalized delta functions. Unparticle is a collection of unnormalized particles with continuum of masses. This collection couples significantly, but individual particles couple infinitesimally, don’t decay.
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
 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 ASTROPHYSICS Supernova cooling BBN
High Energy (LEP)
EWSB conformal symmetry breaking through the superrenormalizable operator EWSB conformal symmetry breaking through the superrenormalizable 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
3point coupling is determined, up to a constant, by conformal invariance: 3point 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 Multiunparticle production spectacular signals Distinguishable from other physics through bizarre kinematic properties
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