Signatures of confinement in Landau gauge QCD
J.~M. Pawlowski
We summarise an analysis of the infrared regime of Landau gauge QCD by means of a flow equation approach \cite{Pawlowski:2003hq}. The infrared behaviour of gluon and ghost propagators is evaluated. The results provide further evidence for the Kugo-Ojima confinement scenario. We also discuss their relation to results obtained with other functional methods as well as the lattice.
aipcheck.tex
%
% $Id: aipcheck.tex,v 1.7 2002/01/11 19:50:46 frank Exp $
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Testing for potential problems with this class
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\ifproblem
\newif\iftimesok

\makeatletter
\def\IfStandaloneCheck{\def\next{aipcheck}
  \edef\currjob{\jobname}
  \edef\next{\meaning\next}
  \edef\currjob{\meaning\currjob}
  \ifx\currjob\next
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
}
\makeatother

\typeout{***********************************************}
\typeout{*}
\typeout{* Testing if all files required for the aipproc}
\typeout{* class are available ...}
\typeout{*}
\typeout{***********************************************}

\typeout{*}
\typeout{* Looking for LaTeX2e ... }
\ifx\documentclass\undefined
 \typeout{*}
 \typeout{* Sorry this is a fatal error:}
 \typeout{*}
 \typeout{* The aipproc class can only be used with LaTeX2e which is}
 \typeout{* the standard LaTeX since 1994!}
 \typeout{*}
 \typeout{* Please make sure that your version of LaTeX is up-to-date}
 \typeout{* before attempting to use this class.}
 \typeout{*}
 \expandafter\stop
\else
 \typeout{* ... ok }
\fi


\def\next#1/#2/#3\next{#1#2}
\typeout{*}
\typeout{* Testing that LaTeX2e is not too old ... }
\ifnum\expandafter\next\fmtversion\next<199612 \relax
 \typeout{* ... what a vintage! }
 \typeout{*}
 \typeout{* Sorry this is a fatal error:}
 \typeout{*}
 \typeout{* The aipproc class can only be used with a recent version}
 \typeout{* of LaTeX2e. Your version is dated \fmtversion\space --- but}
 \typeout{* at least the 1996/12/01 version is required!}
 \typeout{*}
 \typeout{* Please make sure that your version of LaTeX is up-to-date}
 \typeout{* before attempting to use this class.}
 \typeout{*}
 \expandafter\stop
\else
 \ifnum\expandafter\next\fmtversion\next<199806 \relax
   \typeout{* ... probably ok }
   \typeout{*}
   \typeout{* Your version of LaTeX2e is quite old --- the aipproc class}
   \typeout{* hasn't been tested with your release.}
   \typeout{*}
   \typeout{* We believe that it will probably work, but if you encounter}
   \typeout{* problems you will need upgrade your installation.}
   \typeout{*}
   \typein{* Type <return> to continue ...}
   \problemtrue
 \else
   \typeout{* ... ok }
 \fi
\fi


\typeout{*}
\typeout{* Looking for aipproc.cls ... }
\IfFileExists{aipproc.cls}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* Before you can use the aipproc class you have to unpack}
     \typeout{* it from the documented source.}
     \typeout{*}
     \typeout{* Run LaTeX on the file 'aipproc.ins', e.g.,}
     \typeout{*}
     \typeout{* \space\space latex aipproc.ins}
     \typeout{*}
     \typeout{* or whatever is necessary on your installation to process}
     \typeout{* a file with LaTeX. This should unpack a number of files for you:}
     \typeout{*}
     \typeout{* aipproc.cls \space and \space aip-*.clo}
     \typeout{*}
     \typeout{* After that retry processing this guide.}
     \typeout{*}
     \stop
}

\typeout{*}
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\IfFileExists{aipxfm.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The aipxfm.sty file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}

\typeout{*}
\typeout{* Looking for aip-8s.clo ... }
\IfFileExists{aip-8s.clo}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The aip-8s.clo file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}

\typeout{*}
\typeout{* Looking for aip-8d.clo ... }
\IfFileExists{aip-8d.clo}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The aip-8d.clo file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}


\typeout{*}
\typeout{* Looking for aip-6s.clo ... }
\IfFileExists{aip-6s.clo}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The aip-6s.clo file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}


\typeout{*}
\typeout{* Looking for aip-arlo.clo ... }
\IfFileExists{aip-arlo.clo}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The aip-arlo.clo file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}

\typeout{*}
\typeout{* Looking for fixltx2e.sty ... }
\IfFileExists{fixltx2e.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying fix2col.sty instead ... }
     \typeout{*}
     \IfFileExists{fix2col.sty}
	 {
	  \typeout{* ... ok }
	 }
	 {
	  \typeout{* ... not found! }
	  \typeout{*}
	  \typeout{* Sorry this is a fatal error:}
	  \typeout{*}
	  \typeout{* Your LaTeX distribution contains neither fixltx2e.sty}
	  \typeout{* nor fix2col.sty.}
	  \typeout{*}
	  \typeout{* This means that it is either too old or incompletely}
	  \typeout{* installed.}
	  \typeout{*}
	  \typeout{* fixltx2e.sty is part of the standard LaTeX distribution}
	  \typeout{* since 1999; fix2col.sty is an earlier version of this}
	  \typeout{* package.}
	  \typeout{*}
	  \typeout{* Best solution is to get the latest LaTeX distribution.}
	  \typeout{* If this is impossible for you, download fix2col.sty.}
	  \typeout{* You can get this software from a CTAN host.}
          \typeout{* Refer to http://www.ctan.org and search for "fix2col".}
	  \typeout{*}
	  \typeout{* After you have updated your LaTeX distribution}
	  \typeout{* retry processing this guide.}
	  \stop
     }
}

\typeout{*}
\typeout{* Looking for fontenc.sty ... }
\IfFileExists{fontenc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The fontenc package, which is part of standard LaTeX}
     \typeout{* (base distribution) has to be installed at the site to}
     \typeout{* run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* improperly.}
     \typeout{*}
     \typeout{* Please make sure that your version of LaTeX is okay}
     \typeout{* before attempting to use this class. The LaTeX distribution}
     \typeout{* contains the file "ltxcheck.tex" which can be used to}
     \typeout{* test the basic functionality and integrity of your installation.}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for calc.sty ... }
\IfFileExists{calc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The calc package, which is part of standard LaTeX}
     \typeout{* (tool distribution) has to be installed at the site}
     \typeout{* to run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* Please make sure that the tools distribution of LaTeX}
     \typeout{* is installed before attempting to use this class.}
     \typeout{*}
     \typeout{* (You might be able to get calc.sty separately for your}
     \typeout{* installation if you are unable to upgrade to a recent}
     \typeout{* distribution for some reason.)}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for varioref.sty ... }
\IfFileExists{varioref.sty}
    {
     \typeout{* ... ok }
     \gdef\variorefoptionifavailable{varioref,}
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    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The varioref package, which is part of standard LaTeX}
     \typeout{* (tool distribution) is not installed at this site.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot make use of the options "varioref" or "nonvarioref".}
     \typeout{*}
     \typeout{* Please also note that the aipguide.tex documentation}
     \typeout{* normally uses the "varioref" option to show its}
     \typeout{* effects (which  will now fail).}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\variorefoptionifavailable{}
     \let\vpageref\pageref
     \let\vref\ref
    }

\typeout{*}
\typeout{* Looking for times.sty ... }
\IfFileExists{times.sty}
    {
     \begingroup
% load times and forget it immediately again
       \RequirePackage{times}
       \global\expandafter\let\csname ver@times.sty\endcsname\relax    
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       \else
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     \typeout{* ... obsolete! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) is obsolete at this site.}
     \typeout{*}
     \typeout{* The fact that it contains incorrect code either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts with old files remaining!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but}
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typeout{* You can also try using the class in the following way:}
     \typeout{*}
     \typeout{* \space\space \string\documentclass[cmfonts]{aipproc}}
     \typeout{* \space\space \string\usepackage{times}}
     \typeout{* \space\space ...}
     \typeout{*}
     \typeout{* With luck this will result in Times Roman output but chances}
     \typeout{* are that you will get a larger number of error messages in}
     \typeout{* which case you have to remove the \string\usepackage declaration.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
          \problemtrue
          \gdef\psnfssproblemoption{cmfonts}
          \def\textdegree{$^\circ$}            % used below but now
                                               % not setup
       \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{cmfonts,}
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\iftimesok % don't bother testing other font options if times already
           % bad

\typeout{*}
\typeout{* Looking for t1ptm.fd or T1ptm.fd ... }
\IfFileExists{t1ptm.fd}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying T1ptm.fd ... }
     \IfFileExists{T1ptm.fd}
          {
           \typeout{* ... ok }
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          {
           \typeout{* ... not found}
           \typeout{* Serious problem detected:}
           \typeout{*}
           \typeout{* The times package, which is part of standard LaTeX}
           \typeout{* (psnfss distribution) is available but the corresponding}
           \typeout{* .fd file (defining how to load Times Roman) is missing.}
           \typeout{*}
           \typeout{* The fact that this package is only partially installed}
           \typeout{* means that you LaTeX installation is unable to use Times}
           \typeout{* Roman fonts!}
           \typeout{*}
           \typeout{* You can use the aipproc class without this package but }
           \typeout{* you have to specify the option "cmfonts" which result in}
           \typeout{* documents which are not conforming to the AIP layout}
           \typeout{* specification!}
           \typeout{*}
           \typein{* Type <return> to continue ...}
           \problemtrue
           \timesokfalse
           \gdef\psnfssproblemoption{cmfonts,}
          }
    }

\fi


\newcommand\CheckFDFile[3]{%
  \typeout{*}
  \typeout{* Looking for #1#3.fd or #2#3.fd ... }
  \IfFileExists{#1#3.fd}
    {
     \typeout{* ... ok }
    }
    {
     \IfFileExists{#2#3.fd}
      {
       \typeout{* ... ok }
      }
      {\problemtrue
       \typeout{* ... not found! }
      }
    }
}

\iftimesok % don't bother testing other font options if Times already bad

%\CheckFDFile{ot1}{OT1}{ot1ztmcm}
%\CheckFDFile{oml}{OML}{omlztmcm}
%\CheckFDFile{oms}{OMS}{omsztmcm}
%\CheckFDFile{omx}{OMX}{omxztmcm}

\typeout{*}
\typeout{* Looking for mathptm.sty ... }
\IfFileExists{mathptm.sty}
    {
     \typeout{* ... ok }
     \CheckFDFile{ot1}{OT1}{ptmcm}
     \CheckFDFile{oml}{OML}{ptmcm}
     \CheckFDFile{oms}{OMS}{pzccm}
     \CheckFDFile{omx}{OMX}{psycm}
     \ifproblem
      \typeout{*}
      \typeout{* Problem detected:}
      \typeout{*}
      \typeout{* The mathptm package, which is part of standard LaTeX}
      \typeout{* (psnfss distribution) was found but some or all of its}
      \typeout{* support files describing which fonts to load are missing!}
      \typeout{*}
      \typeout{*}
      \typeout{* The fact that this package is only partially installed}
      \typeout{* means that the mathptm package cannot be used!}
      \typeout{*}
      \typeout{* You can use the aipproc class without this package but }
      \typeout{* you have to specify the option "nomathfonts" so that}
      \typeout{* math formulas will be typeset using Computer Modern.}
      \typeout{*}
      \typein{* Type <return> to continue ...}
      \problemtrue
      \gdef\psnfssproblemoption{nomathfonts,}
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      \typeout{*}
      \typeout{* Looking for mathptmx.sty ... }
      \IfFileExists{mathptmx.sty}
       {
        \typeout{* ... ok }
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        \CheckFDFile{oml}{OML}{ztmcm}
        \CheckFDFile{oms}{OMS}{ztmcm}
        \CheckFDFile{omx}{OMX}{ztmcm}
        \ifproblem
	  \typeout{*}
	  \typeout{* Problem detected:}
	  \typeout{*}
	  \typeout{* The mathptmx package, which is part of standard LaTeX}
	  \typeout{* (psnfss distribution) was found but some or all of its}
	  \typeout{* support files describing which fonts to load are missing!}
	  \typeout{*}
	  \typeout{*}
	  \typeout{* The fact that this package is only partially installed}
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	  \typeout{*}
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	  \typeout{* you have to specify the option "mathptm" (no x) so that}
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	  \typeout{*}
	  \typein{* Type <return> to continue ...}
	  \problemtrue
	  \gdef\psnfssproblemoption{mathptm,}
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       {
	\typeout{* ... not found! }
	\typeout{*}
	\typeout{* Problem detected:}
	\typeout{*}
	\typeout{* The mathptmx package, which is part of standard LaTeX}
	\typeout{* (psnfss distribution) can not be found.}
	\typeout{*}
	\typeout{* This is unfortunate but not a disaster as the older}
	\typeout{* version of the package "mathptm" (no x) seems to exist.}
	\typeout{*}
	\typeout{* You can use the aipproc class without this package but }
	\typeout{* you have to specify the option "mathptm" so that}
	\typeout{* math formulas use the older version with upright greek letters.}
	\typeout{*}
	\typein{* Type <return> to continue ...}
	\problemtrue
	\gdef\psnfssproblemoption{mathptm,}
       }
      \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The mathptm package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "nomathfonts" so that}
     \typeout{* math formulas will be typeset using Computer Modern.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{nomathfonts,}
    }

\typeout{*}
\typeout{* Looking for mathtime.sty ... }
\IfFileExists{mathtime.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* The mathime package can not be found.}
     \typeout{*}
     \typeout{* This is not a serious problem because this package is}
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     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use the "mathtime" option of the class.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
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\typeout{*}
\typeout{* Looking for graphicx.sty ... }
\IfFileExists{graphicx.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The graphics package, which is part of standard LaTeX}
     \typeout{* (graphics distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use commands like \protect\includegraphics
                or \protect\resizebox}
     \typeout{* in this case.}
     \typeout{*}
     \typeout{* Please note that you will get a further error message below}
     \typeout{* about: "graphicx.sty not found" because the class will try}
     \typeout{* to load this package! Type return in response to that error.}
     \typeout{*}
     \typeout{* As a result the illustrations in aipguide will look strange.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \gdef\resizebox##1##2{}
     \gdef\includegraphics{\textbf{graphics package missing:}}
     \problemtrue
    }

\typeout{*}
\typeout{* Looking for textcomp.sty ... }
\IfFileExists{textcomp.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The textcomp package, which is part of standard LaTeX}
     \typeout{* (base distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you will always get the error: "textcomp.sty not found"}
     \typeout{* because the class will try to load this package!}
     \typeout{* Type return in response to that error.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \def\textdegree{$^\circ$}         % used below but now
                                       % not set up
     \problemtrue
    }


\typeout{*}
\typeout{* Looking for url.sty ... }
\IfFileExists{url.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The url package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you will not be able to use the \string\url}
     \typeout{* command. Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.ctan.org and search for "url".}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }


\makeatletter

\typeout{*}
\typeout{* Looking for natbib.sty ... }
\IfFileExists{natbib.sty}
    {
     \IfStandaloneCheck
       {\begingroup
        \let\@listi\relax
        \let\thebibliography\@empty
        \let\bibstyle\@empty
        \RequirePackage{natbib}
        \@ifpackagelater{natbib}{1999/05/29}
	  {
           \typeout{* ... ok }
	  }{
           \typeout{* ... might be too old! }
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\begin{document}
%preprint{FAU-TP3-04-05}
%preprint{HD-THEP-04-55}
\title{Signatures of confinement in Landau gauge QCD}

\classification{05.10.Cc, 11.15.Tk, 12.38.Aw}
\keywords      {confinement, gluon propagator, ghost propagator, flow equation}

\author{J.~M. Pawlowski
}{address={Institute for Theoretical 
Physics, University of 
Heidelberg, 69120 Heidelberg, Germany}
}

\author{D.~F.~Litim}{
  address={Theory Group, CERN, CH-1211 Geneva 23; 
SPA, U. Southampton, Southampton SO17 1BJ, U.K.}
}

\author{S.~Nedelko}{
  address={BLTP, JINR, 141980 Dubna, Russia}
}

\author{L.~von Smekal}{address={Institute for Theoretical 
Physics III, 
Universit\"at Erlangen, D-91058 Erlangen, Germany}
}


\begin{abstract}
We summarise an analysis of the infrared regime of Landau gauge QCD by
means of a flow equation approach \cite{Pawlowski:2003hq}. 
The infrared behaviour of gluon and
ghost propagators is evaluated. The results provide further evidence
for the Kugo-Ojima confinement scenario. We also discuss their
relation to results obtained with other functional methods as well as the 
lattice.


\end{abstract}

\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% MAINMATTER
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
In gauge fixed formulations of QCD the infrared behaviour of ghost and
gluon propagators provide signatures of confinement: in Landau gauge
QCD the confinement scenarios of Kugo-Ojima \cite{Kug79} and
Gribov-Zwanziger, e.g.\  \cite{Zwanziger:2001kw}, entail an infrared
enhancement for the ghost propagation and an infrared suppression for
the gluon propagation. This behaviour was first seen within a
functional approach using Dyson-Schwinger equations (DSE)
\cite{Sme97}, giving access to the full momentum regime. It was later
confirmed within lattice studies down to scales about 1 GeV.  However,
in the deep infrared below 1 GeV, lattice studies encounter problems
due to finite size effects. This situation calls for an independent
confirmation of the infrared behaviour seen in DS-studies.  Ideally
such a method would still share enough structure with other functional
methods such as DSEs in order to benefit from insights and results
obtained from these equations. The above features are precisely given
for the flow equation, a particular advantage of which is its
flexibility when it comes to approximations. So far this approach has
been used in Landau gauge QCD for high and intermediate momenta
\cite{Ellwanger:1996qf}.

Here we present results of a flow equation approach to the infrared
regime of Landau gauge QCD \cite{Pawlowski:2003hq}. 
Our analysis is based on an integrated flow equation
that reads for the scale-dependent effective action $\Gamma_k$, 
\begin{equation}\label{eq:flow}
\Gamma_0-\Gamma_k = 
\frac{1}{2}\, \int_0^k d k\,  
{\rm Tr}\,\frac{1}{\Gamma^{(2)}_k+R}\,\partial_k R\,.  
\end{equation}
The scale $k$ is an infrared scale below which $\Gamma_k$ has no
propagating degrees of freedom and $\Gamma^{(n)}$ stands for its $n$th
derivative w.r.t.\ the fields. Consequently $\Gamma=\Gamma_0$ is the
full effective action. Flows for Green functions are obtained by
taking field derivatives of \eq{eq:flow}. The resulting equations
share many features with DSEs and stochastic quantisation for Green
functions. However, in contradistinction to those approaches built on
dressed {\it and} bare quantities, the flow equation \eq{eq:flow}
links dressed vertices and propagators exclusively. Moreover, the flow
equation and its $k$-integral \eq{eq:flow} are manifestly ultraviolet
and infrared finite, no additional renormalisation is required even
within truncations.  Therefore the flow equation offers an interesting
functional method for accessing the infrared regime: its close
relation to DSEs makes many of the truncation schemes and results of
DSEs accessible to flow equation studies; its qualitative differences
and complementary advantages provide additional support for results
obtained within both approaches. 


We evaluate the integrated flow \eq{eq:flow} of ghost and gluon 
propagators in the deep infrared 
\begin{eqnarray}\label{eq:IR1}
p^2 \ll \Lambda_{\rm QCD}^2\,,
\end{eqnarray}
where $\Lambda_{\rm QCD}$ is the dynamical mass scale of QCD. For
these momenta the integrated flow \eq{eq:flow} tends to zero as the
flow reaches a (trivial) fixed point at $ k=0$. This enables us to
study the leading infrared behaviour of the propagators by means of a
fixed point argument developed in \cite{Pawlowski:2003hq}.  For
momenta in the regime \eq{eq:IR1} and for $k^2\ll \Lambda_{\rm QCD}^2$
we can expand $n$-point functions at finite $k$ about that at $k=0$
with
\begin{eqnarray}\label{eq:IR2}
\Gamma_k^{(n)}=\Gamma_0^{(n)}(1+\delta Z_n)\,,
\end{eqnarray} 
where $\delta Z_n$ only depend on ratios $p_i/k$ with
$i=1,...,n-1$. \Eq{eq:IR2} is valid up to order $p_i/\Lambda_{\rm
QCD}$. Indeed, \eq{eq:IR2} can be proven by iterating the integrated 
flow \eq{eq:flow} about $\delta Z_n\equiv 0$. So far we have not relied on any 
approximation. For the explicit computation we resort to a truncation with 
dressed vertices with trivial momentum dependence, an 
approximation which is well in accord with consistency considerations 
\cite{Schleifenbaum:2004id} as well as lattice studies 
\cite{Cucchieri:2004sq}. We allow for a general momentum dependence on 
$x=p^2/k^2$ in the ghost and (transversal) gluon two point functions 
$\Gamma_{k,C}^{(2)}$ and $\Gamma_{k,A}^{(2)}$ 
\begin{eqnarray}\nonumber 
\Gamma_{k,C}^{(2)}(x)& \simeq & z_{C}\, p^2\, x^{\kappa_{C}} 
(1+\delta Z_{C}(x))
\,,\\ 
\Gamma_{k,A}^{(2)}(x)& \simeq 
& z_{A}\, p^2\, x^{-2 \kappa_{C}} (1+\delta Z_{A}(x))
\,, \label{eq:IR3}\end{eqnarray} 
where we dropped the Lorentz and group structure of the propagators. 
In \eq{eq:IR3}, $\Gamma_0^{(2)}= z\,x^\kappa=\hat z p^{2\kappa}$ are
the leading infrared terms for $k=0$ with $k$-independent prefactor
$\hat z$. The functions $\delta Z$ entail the transition between the
physical infrared regime, $x\gg 1$, and the cutoff regime, $x\ll1$. 
In \eq{eq:IR3} we have also used that non-renormalisation 
of the ghost-gluon vertex at
vanishing $k$ entails $\kappa_A=-2\kappa_C$ and
$\alpha_s=g^2/(4\pi\, z_Az_C^2)$ \cite{Lerche:2002ep}. 
Inserting the propagators \eq{eq:IR3} in \eq{eq:flow} leads to
two integral equations for $\delta Z_{A}$ and $\delta Z_C$ of the form
\begin{eqnarray}\label{eq:fixed}
\delta Z_{A/C}(x)=F_{A/C}[\delta Z_{A/C},\kappa_{C},\alpha_s]\,.
\end{eqnarray}
Explicit expressions for the integrals $F$ are given in
\cite{Pawlowski:2003hq}. The equations \eq{eq:fixed} are solved
iteratively for $\delta Z_{A}$, $\delta Z_C$, $\kappa_C$ and $
\alpha_s$, leading to 
\begin{eqnarray}\label{eq:result}
\kappa_C=0.59535\cdots\,,\qquad \qquad \alpha_s=2.9717\cdots\,.
\end{eqnarray}
The values in \eq{eq:result} are achieved by also invoking an
optimisation procedure developed in \cite{Pawlowski:2003hq} for
eliminating the regulator-dependence. 

The results \eq{eq:result} agree with the analytic results obtained
within DSEs \cite{Lerche:2002ep} and
stochastic quantisation \cite{Zwanziger:2001kw}. For the present
truncation within an optimised cut-off scheme one can indeed formally
link the integrated flow \eq{eq:flow} to a set of DSEs with explicit
renormalisation, see \cite{Pawlowski:2003hq}. We expect a mild $R$-dependence 
for the results as we have resorted to a truncation. Indeed, 
for general cut-off 
functions $R$, the results for $\kappa_C$ mildly vary in the interval 
\begin{eqnarray}\label{eq:interval}
\kappa_C\in [0.539\,,\,0.595]\,. 
\end{eqnarray} 
Both bounds have physical interpretations. The upper bound, as we
have already discussed, relates to the physical infinite volume result
whereas the lower bound can be linked to a finite volume computation.
The related regulator is a sharp cut-off that strictly allows no
propagation of modes with momenta $p^2$ smaller than $k^2$.  This is
as close to a finite volume (e.g.\ in lattice studies) as one can get 
with local momentum cut-off functions.
Interestingly, the lower bound $\kappa_C=0.539$ compares well to very
recent lattice results \cite{Oliveira:2004gy}.
A further interesting consequence of our analysis is the evaluation of
renormalisation procedures for DSEs stemming from the integrated flow
\eq{eq:flow}: for DSEs in the present truncation and subject to a
general consistent renormalisation it is impossible to achieve a
masslike behaviour for the gluon propagator, $\kappa_C=1/2$. More
generally $\kappa_C\in\!\!\!\!\!\!\!\slash\ [0,1/2]$, see 
\cite{Pawlowski:2003hq}. 
With multiplicative renormalisation this was already 
shown in \cite{Lerche:2002ep}. 

The above analysis allows for many interesting extensions. The most
important open question in the present truncation concerns the
detailed analysis of the transition between ultraviolet and infrared
regime. Unfortunately this question has not been resolved completely in
subsequent flow studies \cite{Kato:2004ry}. Moreover dynamical quarks
are investigated which opens the door towards a description of
dynamical chiral symmetry breaking.

\begin{theacknowledgments}
  JMP thanks the organisers of Quark Confinement and the Hadron
  Spectrum for making this interesting conference possible. This work
  has been supported by a grant from the Ministry of Science, Research
  and the Arts of Baden-W\"urttemberg (Az: 24-7532.23-19-18/1 and
  24-7532.23-19-18/2), EPSRC, and the DFG under contracts SM70/1-1 and 
GI328/1-2.


\end{theacknowledgments}

\begin{thebibliography}{99}

%\cite{Pawlowski:2003hq}
\bibitem{Pawlowski:2003hq}
J.~M.~Pawlowski, D.~F.~Litim, S.~Nedelko and L.~von Smekal,
%``Infrared behaviour and fixed points in Landau gauge QCD,''
Phys.~Rev.~Lett.~{\bf 93} (2004) 152002 [hep-th/0312324].
%%CITATION = HEP-TH 0312324;%%

\bibitem{Kug79}
T.~Kugo, I.~Ojima,
  Prog. Theor. Phys. Suppl. \textbf{66} (1979) 1.
%%CITATION = PTPSA,66,1;%%

\bibitem{Zwanziger:2001kw}
D.~Zwanziger,
%``Non-perturbative Landau gauge and infrared critical exponents in QCD,''
Phys.\ Rev.\ D {\bf 65} (2002) 094039 
[hep-th/0109224].
%%CITATION = HEP-TH 0109224;%%




\bibitem{Sme97}
L.~von Smekal, A.~Hauck, and R.~Alkofer,
  Phys. Rev. Lett. \textbf{79} (1997) 3591 [hep-ph/9705242].
%%CITATION = HEP-PH 9707327;%%
%%CITATION = HEP-PH 9705242;%%

\bibitem{Ellwanger:1996qf}
U.~Ellwanger, M.~Hirsch and A.~Weber,
Z.\ Phys.\ C {\bf 69} (1996) 687 
[hep-th/9506019]; 
Eur.\ Phys.\ J.\ C {\bf 1} (1998) 563 
[hep-ph/9606468]; 
%\cite{Bergerhoff:1997cv}
%\bibitem{Bergerhoff:1997cv}
B.~Bergerhoff and C.~Wetterich,
%``Effective quark interactions and QCD propagators,''
Phys.\ Rev.\ D {\bf 57} (1998) 1591 [hep-ph/9708425].
%%CITATION = HEP-TH 9506019;%%
%%CITATION = HEP-PH 9606468;%%
%%CITATION = HEP-PH 9708425;%%





%\cite{Schleifenbaum:2004id}
\bibitem{Schleifenbaum:2004id}
W.~Schleifenbaum, A.~Maas, J.~Wambach and R.~Alkofer,
%``Infrared behaviour of the ghost gluon vertex in Landau gauge Yang-Mills
%theory,''
hep-ph/0411052.
%%CITATION = HEP-PH 0411052;%%

%\cite{Cucchieri:2004sq}
\bibitem{Cucchieri:2004sq}
A.~Cucchieri, T.~Mendes and A.~Mihara,
%``Numerical study of the ghost-gluon vertex in Landau gauge,''
hep-lat/0408034.
%%CITATION = HEP-LAT 0408034;%%




%\cite{Lerche:2002ep}
\bibitem{Lerche:2002ep}
C.~Lerche, L.~von Smekal,
%``On the infrared exponent for gluon and ghost propagation in Landau  gauge QCD,''
Phys.\ Rev.\ D {\bf 65} (2002) 125006 
[hep-ph/0202194].
%%CITATION = HEP-PH 0202194;%%



%\cite{Oliveira:2004gy}
\bibitem{Oliveira:2004gy}
O.~Oliveira and P.~J.~Silva,
%``The infrared Landau gauge gluon propagator from lattice QCD,''
these proceedings, hep-lat/0410048.
%%CITATION = HEP-LAT 0410048;%%


%\cite{Kato:2004ry}
\bibitem{Kato:2004ry}
J.~Kato,
%``Infrared non-perturbative propagators of gluon and ghost via exact
%renormalization group,''
hep-th/0401068; 
%\cite{Fischer:2004uk}
%\bibitem{Fischer:2004uk}
C.~S.~Fischer and H.~Gies,
%``Renormalization flow of Yang-Mills propagators,''
JHEP {\bf 0410} (2004) 048
[hep-ph/0408089].
%%CITATION = HEP-PH 0408089;%%
%%CITATION = HEP-TH 0401068;%%

\end{thebibliography}


\end{document}


%%
%% End of file `conVI.tex'.



hep-th0412326.extracted_bib
\begin{thebibliography}{99}

%\cite{Pawlowski:2003hq}
\bibitem{Pawlowski:2003hq}
J.~M.~Pawlowski, D.~F.~Litim, S.~Nedelko and L.~von Smekal,
%``Infrared behaviour and fixed points in Landau gauge QCD,''
Phys.~Rev.~Lett.~{\bf 93} (2004) 152002 [hep-th/0312324].
%%CITATION = HEP-TH 0312324;%%

\bibitem{Kug79}
T.~Kugo, I.~Ojima,
  Prog. Theor. Phys. Suppl. \textbf{66} (1979) 1.
%%CITATION = PTPSA,66,1;%%

\bibitem{Zwanziger:2001kw}
D.~Zwanziger,
%``Non-perturbative Landau gauge and infrared critical exponents in QCD,''
Phys.\ Rev.\ D {\bf 65} (2002) 094039 
[hep-th/0109224].
%%CITATION = HEP-TH 0109224;%%




\bibitem{Sme97}
L.~von Smekal, A.~Hauck, and R.~Alkofer,
  Phys. Rev. Lett. \textbf{79} (1997) 3591 [hep-ph/9705242].
%%CITATION = HEP-PH 9707327;%%
%%CITATION = HEP-PH 9705242;%%

\bibitem{Ellwanger:1996qf}
U.~Ellwanger, M.~Hirsch and A.~Weber,
Z.\ Phys.\ C {\bf 69} (1996) 687 
[hep-th/9506019]; 
Eur.\ Phys.\ J.\ C {\bf 1} (1998) 563 
[hep-ph/9606468]; 
%\cite{Bergerhoff:1997cv}
%\bibitem{Bergerhoff:1997cv}
B.~Bergerhoff and C.~Wetterich,
%``Effective quark interactions and QCD propagators,''
Phys.\ Rev.\ D {\bf 57} (1998) 1591 [hep-ph/9708425].
%%CITATION = HEP-TH 9506019;%%
%%CITATION = HEP-PH 9606468;%%
%%CITATION = HEP-PH 9708425;%%





%\cite{Schleifenbaum:2004id}
\bibitem{Schleifenbaum:2004id}
W.~Schleifenbaum, A.~Maas, J.~Wambach and R.~Alkofer,
%``Infrared behaviour of the ghost gluon vertex in Landau gauge Yang-Mills
%theory,''
hep-ph/0411052.
%%CITATION = HEP-PH 0411052;%%

%\cite{Cucchieri:2004sq}
\bibitem{Cucchieri:2004sq}
A.~Cucchieri, T.~Mendes and A.~Mihara,
%``Numerical study of the ghost-gluon vertex in Landau gauge,''
hep-lat/0408034.
%%CITATION = HEP-LAT 0408034;%%




%\cite{Lerche:2002ep}
\bibitem{Lerche:2002ep}
C.~Lerche, L.~von Smekal,
%``On the infrared exponent for gluon and ghost propagation in Landau  gauge QCD,''
Phys.\ Rev.\ D {\bf 65} (2002) 125006 
[hep-ph/0202194].
%%CITATION = HEP-PH 0202194;%%



%\cite{Oliveira:2004gy}
\bibitem{Oliveira:2004gy}
O.~Oliveira and P.~J.~Silva,
%``The infrared Landau gauge gluon propagator from lattice QCD,''
these proceedings, hep-lat/0410048.
%%CITATION = HEP-LAT 0410048;%%


%\cite{Kato:2004ry}
\bibitem{Kato:2004ry}
J.~Kato,
%``Infrared non-perturbative propagators of gluon and ghost via exact
%renormalization group,''
hep-th/0401068; 
%\cite{Fischer:2004uk}
%\bibitem{Fischer:2004uk}
C.~S.~Fischer and H.~Gies,
%``Renormalization flow of Yang-Mills propagators,''
JHEP {\bf 0410} (2004) 048
[hep-ph/0408089].
%%CITATION = HEP-PH 0408089;%%
%%CITATION = HEP-TH 0401068;%%

\end{thebibliography}