The Mudcat Café TM
Thread #59418   Message #2282361
Posted By: Rapparee
07-Mar-08 - 03:20 PM
Thread Name: BS: The Mother of all BS threads
Subject: RE: BS: The Mother of all BS threads
Oh, fer...Amos, back in 2000 Roux and Torma wrote, in part:

...The situation at such high scales is that fermions are (effectively) massless so that a chiral symmetry exists. Above the electroweak scale there would not be any 2-point functions that involve fermions with electroweak quantum numbers, because these would break the electroweak symmetry. The same applies to any other n-point function that breaks the electroweak symmetry. There are however some 4-point functions involving fermions with electroweak quantum numbers that are allowed at scales above the electroweak scale. One can
distinguish five such 4-point functions on the basis of the chiralities of their external lines: three are chirality preserving and two are chirality changing. The chirality preserving 4-point functions can obviously respect any chiral symmetry. The chirality changing 4-point functions can be invariant under a chiral isospin symmetry, which may contain the SU(2)L of the electroweak symmetry, but these 4-point functions break larger chiral symmetries. If it can be generated nonperturbatively, such a 4-point function would signal the following breaking pattern

SU(Nf )R × SU(Nf )L ! SU(2)R × SU(2)L × SU(Nf /2)V . (1)

(The subscript V indicates a vectorial symmetry.)

Hence, these chirality changing 4-point functions act as order parameters for this partial breaking of chiral symmetries, which may occur at scales high above the electroweak scale. (Note that all fermions transform nontrivially under chiral isospin, which implies that masses are not allowed.) The significance of this is that the partial chiral symmetry breaking gives a new scale high above the
electroweak scale. The surviving chiral isospin symmetry can contain the SU(2)L of the electroweak symmetry, which means that this mechanism can exist for standard model fermions. It is therefore
not necessary to introduce new non-standard model fermions to produce flavor scale physics. As a result dynamical models may become simpler.
For 4-point functions to act as order parameters they must appear at higher scales than 2-point functions do. One can imagine that for certain combinations of number of colors, Nc, and number of
flavors, Nf , the critical coupling for the formation of 2-point functions may be higher than the critical coupling for the formation of 4-point functions. In an asymptotically free theory the 4-point functions would then be formed at a higher scale than the 2-point functions.


You KNOW this. Wuffo you bringing up that other stuff?