Unparticle PhysicsMike Berger

September 6, 2007

3-loop beta function for SU(3)

b0=0 b1=0

2-loop beta function has a zero (fixed point) if

Results can be generalized to group G with rep R

QEDBeta function

= 1/2= 11 – (2/3)NF

= 102 – (38/3)NF

= 33/2 =16.5 = 153/19 = 8.05

fundamental representation

IR UV

Dimensional transmutation

QCD (without quark masses) is a classically scale invariant theory

= 11 – (2/3)NF

LQCD

Banks-Zaks fields with infrared fixed point interact with SM fields

Dimensional transmutation of BZ fields

The operator dimension dU can be non-integral

Explicit example in SQCD with strongly coupled fixed point:

3/2 NC < NF < 3 NC for SU(NC) gauge group

Feynman rules (scalar)