## Re: do tree-level results in effective potential incorporate loop

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On 2005-05-24, Xiao &lt;noncommutate@yahoo.com.cn&gt; wrote:\n&gt; Many thanks.\n&gt; So the second derivative of the effective potentail with respect to the\n&gt; field phi gives phi\'s physical mass which is scale independent, since\n&gt; there are no longer loop diagrams here?\n&gt; The second derivative is usually a polynomial of the parameters which\n&gt; is scale dependent. So if the second derivative is the physical mass,\n&gt; it implies that there are some automatic cancellations between the\n&gt; scale dependent quatities in the polynomial?\n\nI\'ll assume that by scale dependent, you mean dependent on the\nrenormalization scale. Since the coefficients, of the terms in the\neffective potential are taken to be renormalized scattering amplitudes,\nthey will in general be scale dependent. However, during renormalization\nthe coefficient of the effective mass term is tuned to be the physical\nmass at the renormalization momentum scale. Thus the effective mass term\nwill be scale independent in as much as it is momentum independent.\n\nHope this helps.\n\nIgor\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>On $2005-05-24,$ Xiao <noncommutate@yahoo.com.cn> 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