Re: your questions

[Douglas Beck <dhbeck@uiuc.edu>]

Hi Peter,

Thanks for the careful thoughts.  The way I would think about the 
pseudoscalar decay via the W is that, as you said, it is the momentum 
transfer that plays the key role (no suppression) - coupling that vector 
with the axial vector piece of the W gives the necessary pseudoscalar; 
if the quarks are massless there could be no momentum transfer and the 
process would be forbidden.  I am not sure about Scott's comment about 
the scalar part of the W - maybe this is the same as the A-q coupling.

BTW, I meant radiative correction in the generic sense of beyond tree 
level, in our case the diagrams don't turn out to be small at all.

Thanks again.

Doug

Professor Douglas H. Beck
Department of Physics
University of Illinois at Urbana-Champaign
1110 West Green Street
Urbana, IL 61801-3080
(217) 244-7994
(217) 333-1215 (FAX)

Peter Kammel wrote:
> Dear Doug,
> 
> As I understood, you had two questions conc the peseudoscalar
> term:
> 
> i)  how can the W couple to a pion?
> ii) why are two pion diagrams, like rho/omega exchange not dominant?
> 
> As regards i) pion decay proceeds purely through the axial vector
> part of the weak interaction. This can be easily seen as it is
> a transition between the 0+ vacuum and a pseudoscaler 0-. Or
> one explicitly constructs the hadronic matrix element to
> be proportional to the momentum transfer (the only quantity
> to form a Lorentz scalar with the lepton current). Then you
> need the axial vector to get the pseudoscalar to vector transition.
> 
> I did not understand why the W interaction with a axial
> current should be supressed. The standard model constructs
> the W vertex with quarks/leptons with maximum parity violation.
> In the low energy limit there is no difference if one
> couples the lepton current directly or with an intermediate
> boson.
> 
> As regards ii) I should emphasize that the pseudoscalar term
> is part of the general axial current. If one constructs a
> naive model with intermediate boson exchange,
> the intermediate bosons should carry the pseudoscalar
> spin parity. For single vector meson exchange this cannot
> be achieved. Also the scalar sigma does not have the right
> quantum numbers.
> The situation is different for the vector current which can
> couple directly to vector mesons and the approximate
> mechanism of vector meson dominance plays an important role.
> 
> Finally you mentioned that in your case the diagrams are
> radiative corrections. That is not the case here, as these
> are QCD diagramatic calculations.
> 
> But maybe I missed some subtle question. As these issues
> are heart of the form factor discussions, I am always
> interested to learn more.
> 
> With best regards
> 
> Peter