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forcer.h
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forcer.h
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#ifndef `FORCERHFILE'
#define FORCERHFILE
**
* The input can consist of the following symbols in a proper format.
* Any use of other symbols is at your own risk.
*
CF vx,ex;
V p1,...,p11,Q;
**
* The output will be given in terms of the following symbols.
*
S ep;
CF rat,GschemeConstants,Master;
S haha,no1,no2,no3,no6,lala,nono,bebe,cross,fastar2,nostar5,nostar6,
no,t105,t124,t145,t155;
S z2,z3,z4,z5,z6,z7,z8,z5z3,z9,z10,z7z3,z11,z5z3z3,z12,z9z3,z6z4z1z1;
**
* The internals.
*
#appendpath forcer
#define FORCERH
#include pathforcer.h
#include recognition.h
#include forcer-manual.h # FORCERD
#include forcer-manual.h # FromSpectator
#do i=1,14
#define POS`i' "pos_"
#define NEG`i' "neg0_"
#enddo
#do i=1,9
#define SKIP`i' ""
#enddo
S G10,G20,G30,G40,G50;
CF frat;
AutoDeclare S ALARM;
S order,xxx1,xxx2;
*--#[ Forcer : Forcer([options...])
**
* The main user interface of Forcer.
*
* Options
* -------
* gschemeexpand=off
* msbarexpand=off
* Do not expand the master integrals in ep (default).
*
* gschemeexpand=on
* gschemeexpand[=d]: d is int
* Expand the result in the G-scheme up to depth d (default: d=4, i.e.,
* up to ep^0 for 4-loops).
*
* msbarexpand=on
* msbarexpand[=d]: d is int
* Expand the result in the MSbar scheme up to depth d (default: d=4).
*
* keepzeta2[=on]
* keepzeta2=off
* Keep z2 for the expansions in the MSbar scheme (default: off).
*
* polyratfunexpand=off
* Do not expand rational coefficients at intermediate steps (default).
*
* polyratfunexpand=div
* Keep only the lowest power of ep in coefficients at intermediate steps.
*
* polyratfunexpand=n: n is int
* Expand coefficients with respect to ep up to ep^n at intermediate steps.
* Note that the result is not guaranteed to be correct up to ep^n due to
* (spurious) poles. The user should experimentally determine the depth that
* gives the correct result.
*
#procedure Forcer(?options)
* NOTE: this procedure overwrites MSBAR, KEEPZETA2 and POLYRATFUNEXPAND.
* Parse the arguments.
#$ForcerExpandScheme = 0;
#$ForcerExpandDepth = 0;
#$ForcerPolyRatFunExpand = -1;
#define KEEPZETA2 ""
#define gschemeexpand(n) "
#case gschemeexpand=`~n'
#$ForcerExpandScheme = 1;
#$ForcerExpandDepth = `~n';
#break
"
#define msbarexpand(n) "
#case msbarexpand=`~n'
#$ForcerExpandScheme = 2;
#$ForcerExpandDepth = `~n';
#break
"
#define polyratfunexpand(n) "
#case polyratfunexpand=`~n'
#$ForcerPolyRatFunExpand = `~n';
#break
"
#do a={`?options',}
#ifdef `a'
#switch `a'
#case gschemeexpand=off
#case msbarexpand=off
#$ForcerExpandScheme = 0;
#$ForcerExpandDepth = 0;
#break
#case gschemeexpand
#case gschemeexpand=on
#$ForcerExpandScheme = 1;
#$ForcerExpandDepth = 4;
#break
`gschemeexpand(0)'
`gschemeexpand(1)'
`gschemeexpand(2)'
`gschemeexpand(3)'
`gschemeexpand(4)'
`gschemeexpand(5)'
`gschemeexpand(6)'
`gschemeexpand(7)'
`gschemeexpand(8)'
`gschemeexpand(9)'
#case msbarexpand
#case msbarexpand=on
#$ForcerExpandScheme = 2;
#$ForcerExpandDepth = 4;
#break
`msbarexpand(0)'
`msbarexpand(1)'
`msbarexpand(2)'
`msbarexpand(3)'
`msbarexpand(4)'
`msbarexpand(5)'
`msbarexpand(6)'
`msbarexpand(7)'
`msbarexpand(8)'
`msbarexpand(9)'
#case keepzeta2
#case keepzeta2=on
#redefine KEEPZETA2
#break
#case keepzeta2=off
#redefine KEEPZETA2 ""
#break
#case polyratfunexpand=off
#$ForcerPolyRatFunExpand = -1;
#break
#case polyratfunexpand=div
#$ForcerPolyRatFunExpand = 0;
#break
`polyratfunexpand(1)'
`polyratfunexpand(2)'
`polyratfunexpand(3)'
`polyratfunexpand(4)'
`polyratfunexpand(5)'
`polyratfunexpand(6)'
`polyratfunexpand(7)'
`polyratfunexpand(8)'
`polyratfunexpand(9)'
`polyratfunexpand(10)'
`polyratfunexpand(11)'
`polyratfunexpand(12)'
`polyratfunexpand(13)'
`polyratfunexpand(14)'
`polyratfunexpand(15)'
`polyratfunexpand(16)'
`polyratfunexpand(17)'
`polyratfunexpand(18)'
`polyratfunexpand(19)'
`polyratfunexpand(20)'
`polyratfunexpand(21)'
`polyratfunexpand(22)'
`polyratfunexpand(23)'
`polyratfunexpand(24)'
`polyratfunexpand(25)'
`polyratfunexpand(26)'
`polyratfunexpand(27)'
`polyratfunexpand(28)'
`polyratfunexpand(29)'
`polyratfunexpand(30)'
`polyratfunexpand(31)'
`polyratfunexpand(32)'
`polyratfunexpand(33)'
`polyratfunexpand(34)'
`polyratfunexpand(35)'
`polyratfunexpand(36)'
`polyratfunexpand(37)'
`polyratfunexpand(38)'
`polyratfunexpand(39)'
`polyratfunexpand(40)'
`polyratfunexpand(41)'
`polyratfunexpand(42)'
`polyratfunexpand(43)'
`polyratfunexpand(44)'
`polyratfunexpand(45)'
`polyratfunexpand(46)'
`polyratfunexpand(47)'
`polyratfunexpand(48)'
`polyratfunexpand(49)'
`polyratfunexpand(50)'
#default
#message Error: Forcer(`?options'): unknown option `a'
#terminate
#break
#endswitch
#endif
#enddo
#ifdef `KEEPZETA2'
#if `$ForcerExpandScheme' != 2
#message Warning: Forcer(`?options'): keepzeta2 affects only in MSbar
#endif
#endif
#define POLYRATFUNEXPAND "`$ForcerPolyRatFunExpand'"
.sort:Forcer-start;
* Parform the reduction for each expression.
#if `numactiveexprs_' == 0
#elseif `numactiveexprs_' == 1
#define NAME "`activeexprnames_'"
#call ForcerImpl()
#else
#define ForcerExprNames "`activeexprnames_'"
Hide `ForcerExprNames';
.sort:Forcer-hide;
#do NAME={`ForcerExprNames'}
#ifdef `NAME'
Unhide `NAME';
#call ForcerImpl()
.sort:Forcer-end-`NAME';
Hide `NAME';
#endif
#enddo
.sort:Forcer-unhide;
Unhide `ForcerExprNames';
#endif
#endprocedure
#define ForcerNotationLoaded "0"
#procedure ForcerImpl()
#if `$ForcerExpandScheme' >= 1
* Count the number of loops.
id order = 1;
id vx(?a) = vx(?a)*xxx1*xxx2^nargs_(?a);
id xxx1^n1?*xxx2^n2? = order^(n2 / 2 - n1);
id ex(?a) = ex(?a)*order^nargs_(?a);
#endif
* Match the topology.
#if `ForcerNotationLoaded' == 0
.sort:Forcer-notation;
#call loadTopologies()
#redefine ForcerNotationLoaded "1"
#endif
#call matchTopologies(1)
* Convert dot products into the Forcer notation.
#call ToForcer()
* Compute the integrals.
#call DoForcer()
* Convert the output into the standard form.
* #call propagators(1)
id BasicNOIntegral = Master(no);
id BasicT1Integral = Master(t105)*rat(1,ep^2);
id BasicNOIntegral5 = Master(nostar5);
id BasicNOIntegral6 = Master(nostar6);
id BasicT1Integral55 = Master(t155);
id BasicT1Integral45 = Master(t145);
id BasicT1Integral24 = Master(t124);
* GC(0,0) GC(n,1) = GC(n,0) GC(n+1,0) (1-(n+2)ep) / (1-2ep)
id GschemeConstants(0,0)*GschemeConstants(2,1)
= GschemeConstants(2,0)*GschemeConstants(3,0)
*rat(1-4*ep,1-2*ep);
id GschemeConstants(0,0)*GschemeConstants(1,1)
= GschemeConstants(1,0)*GschemeConstants(2,0)
*rat(1-3*ep,1-2*ep);
#if `$ForcerExpandScheme' >= 1
* Expand the master inegrals.
#if `$ForcerExpandScheme' == 1
#define SchemeName "GScheme"
#elseif `$ForcerExpandScheme' == 2
#define SchemeName "MSBAR"
#endif
#do i=1,5
id GschemeConstants(`i',0)
= G`i'0*GschemeConstants(0,0)*rat(1-2*ep,1-{`i'+2}*ep);
#enddo
id GschemeConstants(0,0) = rat(1,ep);
.sort:To`SchemeName'-1;
PolyRatFun rat(expand,ep,12);
.sort:To`SchemeName'-2;
PolyRatFun;
id rat(x?) = x;
.sort:To`SchemeName'-3;
#if `$ForcerExpandScheme' == 2
#define MSBAR
#else
#define MSBAR ""
#endif
#call Masters(order,`$ForcerExpandDepth')
id order = 1;
.sort:To`SchemeName'-4;
#endif
#endprocedure
*--#] Forcer :
#endif
* vim: ft=form et ts=8 sts=2 sw=2 fdm=marker fmr=#[,#] fdc=4