
(* Three-loop matching coefficient of the NRQCD vector current  *)
(* [Marquard, Piclum, Seidel, Steinhauser arXiv:1401.3004]      *)
(* Note: uncertainties in 3-loop coefficients are not included  *)
(* in the expressions below.                                    *)

(* matching coefficient for mu_r = m, cf. Eq. (6) *)
cv[m] = 1 + alphas[m]/Pi*cv1m + (alphas[m]/Pi)^2*cv2m + (alphas[m]/Pi)^3*cv3m;

(* matching coefficient for mu_r = mu *)
cv[mu] =
    1 +
    alphas[mu]/Pi*cv1m +
    (alphas[mu]/Pi)^2*( cv2m + beta0*cv1m*Log[mu^2/m^2] ) +
    (alphas[mu]/Pi)^3*( cv3m + beta0^2*cv1m*Log[mu^2/m^2]^2 +
		       ( beta1*cv1m + 2*beta0*cv2m )*Log[mu^2/m^2] );

beta0 = ( 11/3*CA - 4/3*TF*nl )/4;
beta1 = ( 34/3*CA^2 - 20/3*CA*TF*nl - 4*CF*TF*nl )/16;

(* coefficients for mu_r = m, cf. Eqs. (7) and (8) *)
cv1m = -2*CF;
cv2m =
    ( -151/72 + 89/144*Pi^2 - 5/6*Pi^2*Log[2] - 13/4*Zeta[3] )*CA*CF +
    ( 23/8 - 79/36*Pi^2 + Pi^2*Log[2] - 1/2*Zeta[3] )*CF^2 +
    ( 22/9 - 2/9*Pi^2 )*CF*TF*nh + 11/18*CF*TF*nl -
    1/2*Pi^2*( 1/2*CA + 1/3*CF )*CF*Log[mu^2/m^2];
cv3m =
    CF*( CF^2*cFFF + CF*CA*cFFA + CA^2*cFAA +
	TF*nl*( CF*cFFL + CA*cFAL + TF*nh*cFHL + TF*nl*cFLL ) +
	TF*nh*( CF*cFFH + CA*cFAH + TF*nh*cFHH ) );

cFFF =
    36.55 +
    ( -9/16 + 3/2*Log[2] )*Pi^2*Log[mu^2/m^2] - 5/32*Pi^2*Log[mu^2/m^2]^2;
cFFA =
    -188.10 +
    ( -59/108 - 3/4*Log[2] )*Pi^2*Log[mu^2/m^2] - 47/576*Pi^2*Log[mu^2/m^2]^2;
cFAA =
    -97.81 +
    ( -2/9 - 3/4*Log[2] )*Pi^2*Log[mu^2/m^2] + 1/6*Pi^2*Log[mu^2/m^2]^2;
cFFL = 46.691 + 25/108*Pi^2*Log[mu^2/m^2] - 1/18*Pi^2*Log[mu^2/m^2]^2;
cFAL = 39.624 + 37/144*Pi^2*Log[mu^2/m^2] - 1/12*Pi^2*Log[mu^2/m^2]^2;
cFHL = -557/162 + 26/81*Pi^2;
cFLL = -163/162 - 4/27*Pi^2;
cFFH = -0.846 - 1/20*Pi^2*Log[mu^2/m^2];
cFAH = -0.098;
cFHH = -427/162 + 158/2835*Pi^2 + 16/9*Zeta[3];

