Re: do tree-level results in effective potential incorporate loop effects?
- From: Igor Khavkine <igor.kh@xxxxxxxxx>
- Date: Wed, 25 May 2005 01:02:16 +0000 (UTC)
On 2005-05-24, Xiao <noncommutate@xxxxxxxxxxxx> wrote:
> Many thanks.
> So the second derivative of the effective potentail with respect to the
> field phi gives phi's physical mass which is scale independent, since
> there are no longer loop diagrams here?
> The second derivative is usually a polynomial of the parameters which
> is scale dependent. So if the second derivative is the physical mass,
> it implies that there are some automatic cancellations between the
> scale dependent quatities in the polynomial?
I'll assume that by scale dependent, you mean dependent on the
renormalization scale. Since the coefficients, of the terms in the
effective potential are taken to be renormalized scattering amplitudes,
they will in general be scale dependent. However, during renormalization
the coefficient of the effective mass term is tuned to be the physical
mass at the renormalization momentum scale. Thus the effective mass term
will be scale independent in as much as it is momentum independent.
Hope this helps.
Igor
.
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