FeynCalc manual (development version)

FCMatchSolve

FCMatchSolve[expr, {notvar1, notvar2, ...}] assumes that expr is a sum that must vanish term-wise and converts it to a system of linear equations. The function automatically determines which variables to solve for, excluding notvar1, notvar2, ... from the list.

FCMatchSolve can also handle overdetermined systems of equations. This function is useful e.g. for determining renormalization constants or matching coefficients, where looking at each term separately and determining the values of the constants/coefficients by hand is too tedious.

The input (say a sum or a difference of amplitudes) should be prepared using Collect2 by collecting w.r.t distinct objects, e.g. matrix elements or coupling constants so that each term must vanish separately.

See also

Overview, Collect2, Solve2, Solve3.

Examples

FCMatchSolve[-1/8*(tauPref*(-128 + 64*nc + 160*nc^2 - 8*nc*zz14 + 4*nc*zz44 - 
         16*evFlag[4, 3, 1] + 8*nc*evFlag[4, 3, 1] - 16*evFlag[5, 3, 1] + 8*nc*evFlag[5, 3, 1] + 
         nc*evFlag[9, 3, 1] - 2*evFlag[10, 3, 1] + nc^2*evFlag[10, 3, 1])*OP[Q])/nc + 
   (tauPref*(-96*nc - 96*nc^2 + 4*nc*zz24 - 4*nc*zz44 - 16*evFlag[4, 3, 1] + 
        24*nc*evFlag[4, 3, 1] + 16*nc^2*evFlag[4, 3, 1] + 16*evFlag[5, 3, 1] - 
        8*nc*evFlag[5, 3, 1] - nc*evFlag[9, 3, 1] + nc*evFlag[9, 4, 1] + 2*evFlag[10, 3, 1] - 
        nc^2*evFlag[10, 3, 1] - 2*evFlag[10, 4, 1] + nc^2*evFlag[10, 4, 1])*OP[QS])/(4*nc), 
  {OP[_], nc, evFlag[__], tauPref}]

FCMatchSolve: Solving for: {zz14,zz24,zz44}\text{FCMatchSolve: Solving for: }\{\text{zz14},\text{zz24},\text{zz44}\}

FCMatchSolve: A solution exists.\text{FCMatchSolve: A solution exists.}

{zz24→14  nc(−16  nc2  evFlag(4,3,1)−nc2  evFlag(10,4,1)−32  nc  evFlag(4,3,1)−nc  evFlag(9,4,1)+32  evFlag(4,3,1)+2  evFlag(10,4,1)−64  nc2+8  nc  zz14+32  nc+128),zz44→14  nc(nc2(−evFlag(10,3,1))−8  nc  evFlag(4,3,1)−8  nc  evFlag(5,3,1)−nc  evFlag(9,3,1)+16  evFlag(4,3,1)+16  evFlag(5,3,1)+2  evFlag(10,3,1)−160  nc2+8  nc  zz14−64  nc+128)}\left\{\text{zz24}\to \frac{1}{4 \;\text{nc}}\left(-16 \;\text{nc}^2 \;\text{evFlag}(4,3,1)-\text{nc}^2 \;\text{evFlag}(10,4,1)-32 \;\text{nc} \;\text{evFlag}(4,3,1)-\text{nc} \;\text{evFlag}(9,4,1)+32 \;\text{evFlag}(4,3,1)+2 \;\text{evFlag}(10,4,1)-64 \;\text{nc}^2+8 \;\text{nc} \;\text{zz14}+32 \;\text{nc}+128\right),\text{zz44}\to \frac{1}{4 \;\text{nc}}\left(\text{nc}^2 (-\text{evFlag}(10,3,1))-8 \;\text{nc} \;\text{evFlag}(4,3,1)-8 \;\text{nc} \;\text{evFlag}(5,3,1)-\text{nc} \;\text{evFlag}(9,3,1)+16 \;\text{evFlag}(4,3,1)+16 \;\text{evFlag}(5,3,1)+2 \;\text{evFlag}(10,3,1)-160 \;\text{nc}^2+8 \;\text{nc} \;\text{zz14}-64 \;\text{nc}+128\right)\right\}