
(* /x1/chet/Ageficom4/gfc3/form/fin/mnc40/DIS/jvud/ABC.res *)


 (* results and some auxiliary formulas from the paper 

Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order
alpha_s^4 in a General Gauge Theory

(Authors: P.A. Baikov, K.G. Chetyrkin, J.H. Kuehn.
Published in: Phys. Lett. B714 : (2012) 62-65. 
TTP preprint: TTP12-017 
)


in a form readable for Mathematica 


 *)


 (* Notations:



as =\alpha_s/Pi


beta3 <-- the function \beta(as) in three-loop approximation


Kas4 <--  K(as)

CBJpolas4  <--  C^{Bjp}(as)

CNS    <--  C^{NS}(as)
CSi    <--  C^{Si}(as)


ADNSas4    <--  D^{NS}(as)
ADSIas4    <--  D^{SI}(as)



RNSas4     <--- R^{NS}(s)

RSIas4     <--- R^{NS}(s)


Eq. (2.12) reads:

R(s) = (\sum_f q_f^2)* RNSas4 + (\sum_f q_f)^2 * RSIas4 


LMQ        <--- Log[\mu^2/Q^2]

LMS        <--- Log[\mu^2/s  ]

nf         <--  number of  quark flavours 

QCD4 and QED4 <-- rules to transform generic colour factors to the ones specific for QCD and QED 

respectively

 *)


  (* auxiliary functions *)

Ex[General`Private`x_] := Expand[General`Private`x];

cut[General`Private`x_, {General`Private`n1_, General`Private`n2_}] := 
   Module[{General`Private`r, General`Private`p}, 
     General`Private`r = #1*General`Private`x^1000; General`Private`r = 
       Ex[General`Private`r] /. 
        General`Private`x^(General`Private`p_Integer) /; General`Private`p < 
           1000 + General`Private`n1 -> 0; General`Private`r = 
       Ex[General`Private`r] /. 
        General`Private`x^(General`Private`p_Integer) /; General`Private`p > 
           1000 + General`Private`n2 -> 0; 
	  Ex[General`Private`r/General`Private`x^1000]] & ;





beta3 = as*( 
     (as*((-11*ca)/3 + (4*nf*tr)/3))/4 + 
     (as^2*((-34*ca^2)/3 + (20*ca*nf*tr)/3 + 4*cf*nf*tr))/16 + 
     (as^3*((-2857*ca^3)/54 + (1415*ca^2*nf*tr)/27 + (205*ca*cf*nf*tr)/9 - 
        2*cf^2*nf*tr - (158*ca*nf^2*tr^2)/27 - (44*cf*nf^2*tr^2)/9))/64
          );


 

KNSas4 = (as*((-21*cf)/8 + 3*cf*z3) + as^2*((-629*ca*cf)/32 + (397*cf^2)/96 - 
       (77*ca*cf*LMQ)/16 + (163*cf*nf*tr)/24 + (7*cf*LMQ*nf*tr)/4 + 
       (221*ca*cf*z3)/12 + (17*cf^2*z3)/2 + (11*ca*cf*LMQ*z3)/2 - 
       (19*cf*nf*tr*z3)/3 - 2*cf*LMQ*nf*tr*z3 - 15*cf^2*z5) + 
     as^3*((-406043*ca^2*cf)/2304 + (99757*ca*cf^2)/2304 + (2471*cf^3)/768 - 
       (7633*ca^2*cf*LMQ)/128 + (4367*ca*cf^2*LMQ)/384 - 
       (847*ca^2*cf*LMQ^2)/128 + (1055*ca*cf*nf*tr)/9 - 
       (7729*cf^2*nf*tr)/1152 + (3995*ca*cf*LMQ*nf*tr)/96 - 
       (13*cf^2*LMQ*nf*tr)/6 + (77*ca*cf*LMQ^2*nf*tr)/16 - 
       (307*cf*nf^2*tr^2)/18 - (163*cf*LMQ*nf^2*tr^2)/24 - 
       (7*cf*LMQ^2*nf^2*tr^2)/8 + (18007*ca^2*cf*z3)/144 + 
       (8285*ca*cf^2*z3)/96 + (61*cf^3*z3)/8 + (2737*ca^2*cf*LMQ*z3)/48 + 
       (187*ca*cf^2*LMQ*z3)/8 + (121*ca^2*cf*LMQ^2*z3)/16 - 
       (2521*ca*cf*nf*tr*z3)/36 - (917*cf^2*nf*tr*z3)/16 - 
       (475*ca*cf*LMQ*nf*tr*z3)/12 - (43*cf^2*LMQ*nf*tr*z3)/4 - 
       (11*ca*cf*LMQ^2*nf*tr*z3)/2 + (203*cf*nf^2*tr^2*z3)/18 + 
       (19*cf*LMQ*nf^2*tr^2*z3)/3 + cf*LMQ^2*nf^2*tr^2*z3 - 
       (77*ca^2*cf*z3^2)/4 - 2*ca*cf*nf*tr*z3^2 + 9*cf^2*nf*tr*z3^2 + 
       (2975*ca^2*cf*z5)/48 - (1555*ca*cf^2*z5)/12 - (715*cf^3*z5)/8 - 
       (165*ca*cf^2*LMQ*z5)/4 - (125*ca*cf*nf*tr*z5)/3 + 
       (125*cf^2*nf*tr*z5)/2 + 15*cf^2*LMQ*nf*tr*z5 + 5*cf*nf^2*tr^2*z5 - 
       (105*ca*cf^2*z7)/8 + (315*cf^3*z7)/4)
       );

(* CBJpolas4 = *)

 CNS=  (
      1 - (3*as*cf)/4 + (as^2*(-(ca*cf) + (21*cf^2)/2 - 
        11*ca*cf*(2 + LMQ)))/16 + (as^2*cf*(2 + LMQ)*nf*tr)/4 + 
     (as^3*nf^2*((-344*cf*tr^2)/27 - (16*cf*(2 + LMQ)^2*tr^2)/3))/64 + 
     (as^4*nf^3*((128*cf*tr^3)/243 + (1376*cf*(2 + LMQ)*tr^3)/27 + 
        (64*cf*(2 + LMQ)^3*tr^3)/9))/256 + 
     (as^3*((-4286*ca^2*cf)/27 - (145*ca*cf^2)/9 - (3*cf^3)/2 - 
        (124*ca^2*cf*(2 + LMQ))/3 + 77*ca*cf^2*(2 + LMQ) - 
        (121*ca^2*cf*(2 + LMQ)^2)/3 - (176*ca*cf^2*z3)/3 + 
        (440*ca^2*cf*z5)/3))/64 + 
     (as^3*nf*((2678*ca*cf*tr)/27 + (155*cf^2*tr)/9 + (68*ca*cf*(2 + LMQ)*tr)/
         3 - 16*cf^2*(2 + LMQ)*tr + (88*ca*cf*(2 + LMQ)^2*tr)/3 + 
        48*ca*cf*tr*z3 - (80*cf^2*tr*z3)/3 - (160*ca*cf*tr*z5)/3))/64 + 
     (as^4*nf^2*((-14119*ca*cf*tr^2)/81 - (44*cf^2*tr^2)/3 - 
        (4990*ca*cf*(2 + LMQ)*tr^2)/9 - (752*cf^2*(2 + LMQ)*tr^2)/9 - 
        72*ca*cf*(2 + LMQ)^2*tr^2 + 16*cf^2*(2 + LMQ)^2*tr^2 - 
        (176*ca*cf*(2 + LMQ)^3*tr^2)/3 + (2768*ca*cf*tr^2*z3)/9 + 
        96*cf^2*tr^2*z3 - 192*ca*cf*(2 + LMQ)*tr^2*z3 + 
        (320*cf^2*(2 + LMQ)*tr^2*z3)/3 - (128*ca*cf*tr^2*z3^2)/3 - 
        320*ca*cf*tr^2*z5 + (640*ca*cf*(2 + LMQ)*tr^2*z5)/3))/256 + 
     (as^4*((-1738585*ca^3*cf)/972 + (679481*ca^2*cf^2)/216 - 
        (3113*ca*cf^3)/18 - (4823*cf^4)/8 - 48*dFA4*dRinv - 
        (104087*ca^3*cf*(2 + LMQ))/54 + (547*ca^2*cf^2*(2 + LMQ))/9 - 
        (33*ca*cf^3*(2 + LMQ))/2 - 352*ca^3*cf*(2 + LMQ)^2 + 
        (847*ca^2*cf^2*(2 + LMQ)^2)/2 - (1331*ca^3*cf*(2 + LMQ)^3)/9 + 
        (4276*ca^3*cf*z3)/9 + (37072*ca^2*cf^2*z3)/9 - (7768*ca*cf^3*z3)/3 - 
        96*cf^4*z3 + 64*dFA4*dRinv*z3 - (1936*ca^2*cf^2*(2 + LMQ)*z3)/3 - 
        (968*ca^3*cf*z3^2)/3 - (3950*ca^3*cf*z5)/9 - (22000*ca^2*cf^2*z5)/9 + 
        (16720*ca*cf^3*z5)/3 + 320*dFA4*dRinv*z5 + 
        (4840*ca^3*cf*(2 + LMQ)*z5)/3 + 1540*ca^3*cf*z7 - 6160*ca^2*cf^2*z7))/
      256 + (as^4*nf*(208*dFF4*dRinv + (204007*ca^2*cf*tr)/162 - 
        (65179*ca*cf^2*tr)/54 + (2351*cf^3*tr)/9 + 
        (17069*ca^2*cf*(2 + LMQ)*tr)/9 + (1712*ca*cf^2*(2 + LMQ)*tr)/9 - 
        84*cf^3*(2 + LMQ)*tr + 326*ca^2*cf*(2 + LMQ)^2*tr - 
        198*ca*cf^2*(2 + LMQ)^2*tr + (484*ca^2*cf*(2 + LMQ)^3*tr)/3 + 
        256*dFF4*dRinv*z3 - 820*ca^2*cf*tr*z3 - (19568*ca*cf^2*tr*z3)/9 + 
        (3608*cf^3*tr*z3)/3 + 528*ca^2*cf*(2 + LMQ)*tr*z3 - 
        (176*ca*cf^2*(2 + LMQ)*tr*z3)/3 + (704*ca^2*cf*tr*z3^2)/3 - 
        640*dFF4*dRinv*z5 + (6280*ca^2*cf*tr*z5)/9 + (4400*ca*cf^2*tr*z5)/9 - 
        (4640*cf^3*tr*z5)/3 - (3520*ca^2*cf*(2 + LMQ)*tr*z5)/3 - 
        560*ca^2*cf*tr*z7 + 2240*ca*cf^2*tr*z7))/256
        ); 


ADNSas4 = dR*( 1 + (3*as*cf)/4 + (123*as^2*ca*cf)/32 + (90445*as^3*ca^2*cf)/
      3456 + (52207039*as^4*ca^3*cf)/248832 - (3*as^2*cf^2)/32 - 
     (127*as^3*ca*cf^2)/64 - (592141*as^4*ca^2*cf^2)/18432 - 
     (69*as^3*cf^3)/128 - (253*as^4*ca*cf^3)/32 + (4157*as^4*cf^4)/2048 + 
     (3*as^4*dFA4)/(16*dR) + (11*as^2*ca*cf*LMQ)/16 + 
     (485*as^3*ca^2*cf*LMQ)/64 + (539371*as^4*ca^3*cf*LMQ)/6912 - 
     (11*as^3*ca*cf^2*LMQ)/64 - (1431*as^4*ca^2*cf^2*LMQ)/256 - 
     (759*as^4*ca*cf^3*LMQ)/512 + (121*as^3*ca^2*cf*LMQ^2)/192 + 
     (16753*as^4*ca^3*cf*LMQ^2)/1536 - (121*as^4*ca^2*cf^2*LMQ^2)/512 + 
     (1331*as^4*ca^3*cf*LMQ^3)/2304 - (13*as^4*dFF4*nf)/(16*dR) - 
     (11*as^2*cf*nf*tr)/8 - (485*as^3*ca*cf*nf*tr)/27 - 
     (4379861*as^4*ca^2*cf*nf*tr)/20736 - (29*as^3*cf^2*nf*tr)/64 + 
     (32357*as^4*ca*cf^2*nf*tr)/13824 + (1001*as^4*cf^3*nf*tr)/384 - 
     (as^2*cf*LMQ*nf*tr)/4 - (259*as^3*ca*cf*LMQ*nf*tr)/48 - 
     (187393*as^4*ca^2*cf*LMQ*nf*tr)/2304 - (as^3*cf^2*LMQ*nf*tr)/8 - 
     (527*as^4*ca*cf^2*LMQ*nf*tr)/384 + (39*as^4*cf^3*LMQ*nf*tr)/64 - 
     (11*as^3*ca*cf*LMQ^2*nf*tr)/24 - (747*as^4*ca^2*cf*LMQ^2*nf*tr)/64 - 
     (33*as^4*ca*cf^2*LMQ^2*nf*tr)/128 - (121*as^4*ca^2*cf*LMQ^3*nf*tr)/192 + 
     (151*as^3*cf*nf^2*tr^2)/54 + (340843*as^4*ca*cf*nf^2*tr^2)/5184 + 
     (5713*as^4*cf^2*nf^2*tr^2)/1728 + (11*as^3*cf*LMQ*nf^2*tr^2)/12 + 
     (3439*as^4*ca*cf*LMQ*nf^2*tr^2)/128 + (115*as^4*cf^2*LMQ*nf^2*tr^2)/96 + 
     (as^3*cf*LMQ^2*nf^2*tr^2)/12 + (65*as^4*ca*cf*LMQ^2*nf^2*tr^2)/16 + 
     (as^4*cf^2*LMQ^2*nf^2*tr^2)/8 + (11*as^4*ca*cf*LMQ^3*nf^2*tr^2)/48 - 
     (6131*as^4*cf*nf^3*tr^3)/972 - (151*as^4*cf*LMQ*nf^3*tr^3)/54 - 
     (11*as^4*cf*LMQ^2*nf^3*tr^3)/24 - (as^4*cf*LMQ^3*nf^3*tr^3)/36 - 
     (11*as^2*ca*cf*z3)/4 - (2737*as^3*ca^2*cf*z3)/144 - 
     (456223*as^4*ca^3*cf*z3)/3456 - (143*as^3*ca*cf^2*z3)/16 - 
     (43925*as^4*ca^2*cf^2*z3)/384 - (139*as^4*ca*cf^3*z3)/128 + 
     (3*as^4*cf^4*z3)/8 - (as^4*dFA4*z3)/(4*dR) - (121*as^3*ca^2*cf*LMQ*z3)/
      24 - (32351*as^4*ca^3*cf*LMQ*z3)/576 - (1573*as^4*ca^2*cf^2*LMQ*z3)/
      64 - (1331*as^4*ca^3*cf*LMQ^2*z3)/192 - (as^4*dFF4*nf*z3)/dR + 
     as^2*cf*nf*tr*z3 + (112*as^3*ca*cf*nf*tr*z3)/9 + 
     (8609*as^4*ca^2*cf*nf*tr*z3)/72 + (19*as^3*cf^2*nf*tr*z3)/4 + 
     (10661*as^4*ca*cf^2*nf*tr*z3)/96 + (99*as^4*cf^3*nf*tr*z3)/32 + 
     (11*as^3*ca*cf*LMQ*nf*tr*z3)/3 + (911*as^4*ca^2*cf*LMQ*nf*tr*z3)/16 + 
     (187*as^4*ca*cf^2*LMQ*nf*tr*z3)/8 + (121*as^4*ca^2*cf*LMQ^2*nf*tr*z3)/
      16 - (19*as^3*cf*nf^2*tr^2*z3)/9 - (10453*as^4*ca*cf*nf^2*tr^2*z3)/
      288 - (581*as^4*cf^2*nf^2*tr^2*z3)/24 - (2*as^3*cf*LMQ*nf^2*tr^2*z3)/
      3 - (229*as^4*ca*cf*LMQ*nf^2*tr^2*z3)/12 - 
     (21*as^4*cf^2*LMQ*nf^2*tr^2*z3)/4 - (11*as^4*ca*cf*LMQ^2*nf^2*tr^2*z3)/
      4 + (203*as^4*cf*nf^3*tr^3*z3)/54 + (19*as^4*cf*LMQ*nf^3*tr^3*z3)/9 + 
     (as^4*cf*LMQ^2*nf^3*tr^3*z3)/3 + (605*as^4*ca^3*cf*z3^2)/32 - 
     (11*as^4*ca^2*cf*nf*tr*z3^2)/2 - (33*as^4*ca*cf^2*nf*tr*z3^2)/4 - 
     (as^4*ca*cf*nf^2*tr^2*z3^2)/2 + 3*as^4*cf^2*nf^2*tr^2*z3^2 - 
     (55*as^3*ca^2*cf*z5)/24 - (77995*as^4*ca^3*cf*z5)/1152 + 
     (55*as^3*ca*cf^2*z5)/4 + (6505*as^4*ca^2*cf^2*z5)/48 + 
     (2255*as^4*ca*cf^3*z5)/32 - (5*as^4*dFA4*z5)/(4*dR) - 
     (605*as^4*ca^3*cf*LMQ*z5)/96 + (605*as^4*ca^2*cf^2*LMQ*z5)/16 + 
     (5*as^4*dFF4*nf*z5)/(2*dR) + (5*as^3*ca*cf*nf*tr*z5)/6 + 
     (18805*as^4*ca^2*cf*nf*tr*z5)/288 - 5*as^3*cf^2*nf*tr*z5 - 
     (5155*as^4*ca*cf^2*nf*tr*z5)/48 - (125*as^4*cf^3*nf*tr*z5)/4 + 
     (55*as^4*ca^2*cf*LMQ*nf*tr*z5)/12 - (55*as^4*ca*cf^2*LMQ*nf*tr*z5)/2 - 
     (170*as^4*ca*cf*nf^2*tr^2*z5)/9 + (125*as^4*cf^2*nf^2*tr^2*z5)/6 - 
     (5*as^4*ca*cf*LMQ*nf^2*tr^2*z5)/6 + 5*as^4*cf^2*LMQ*nf^2*tr^2*z5 + 
     (5*as^4*cf*nf^3*tr^3*z5)/3 - (385*as^4*ca^3*cf*z7)/64 + 
     (1155*as^4*ca^2*cf^2*z7)/32 - (1155*as^4*ca*cf^3*z7)/16 + 
     (35*as^4*ca^2*cf*nf*tr*z7)/16 - (105*as^4*ca*cf^2*nf*tr*z7)/8 + 
     (105*as^4*cf^3*nf*tr*z7)/4
        ); 

RNSas4 = dR*(1 + (3*as*cf)/4 + (123*as^2*ca*cf)/32 + (90445*as^3*ca^2*cf)/3456 + 
     (52207039*as^4*ca^3*cf)/248832 - (3*as^2*cf^2)/32 - 
     (127*as^3*ca*cf^2)/64 - (592141*as^4*ca^2*cf^2)/18432 - 
     (69*as^3*cf^3)/128 - (253*as^4*ca*cf^3)/32 + (4157*as^4*cf^4)/2048 + 
     (3*as^4*dFA4)/(16*dR) + (11*as^2*ca*cf*LMS)/16 + 
     (485*as^3*ca^2*cf*LMS)/64 + (539371*as^4*ca^3*cf*LMS)/6912 - 
     (11*as^3*ca*cf^2*LMS)/64 - (1431*as^4*ca^2*cf^2*LMS)/256 - 
     (759*as^4*ca*cf^3*LMS)/512 + (121*as^3*ca^2*cf*LMS^2)/192 + 
     (16753*as^4*ca^3*cf*LMS^2)/1536 - (121*as^4*ca^2*cf^2*LMS^2)/512 + 
     (1331*as^4*ca^3*cf*LMS^3)/2304 - (13*as^4*dFF4*nf)/(16*dR) - 
     (121*as^3*ca^2*cf*Pi^2)/576 - (16753*as^4*ca^3*cf*Pi^2)/4608 + 
     (121*as^4*ca^2*cf^2*Pi^2)/1536 - (1331*as^4*ca^3*cf*LMS*Pi^2)/2304 - 
     (11*as^2*cf*nf*tr)/8 - (485*as^3*ca*cf*nf*tr)/27 - 
     (4379861*as^4*ca^2*cf*nf*tr)/20736 - (29*as^3*cf^2*nf*tr)/64 + 
     (32357*as^4*ca*cf^2*nf*tr)/13824 + (1001*as^4*cf^3*nf*tr)/384 - 
     (as^2*cf*LMS*nf*tr)/4 - (259*as^3*ca*cf*LMS*nf*tr)/48 - 
     (187393*as^4*ca^2*cf*LMS*nf*tr)/2304 - (as^3*cf^2*LMS*nf*tr)/8 - 
     (527*as^4*ca*cf^2*LMS*nf*tr)/384 + (39*as^4*cf^3*LMS*nf*tr)/64 - 
     (11*as^3*ca*cf*LMS^2*nf*tr)/24 - (747*as^4*ca^2*cf*LMS^2*nf*tr)/64 - 
     (33*as^4*ca*cf^2*LMS^2*nf*tr)/128 - (121*as^4*ca^2*cf*LMS^3*nf*tr)/192 + 
     (11*as^3*ca*cf*nf*Pi^2*tr)/72 + (249*as^4*ca^2*cf*nf*Pi^2*tr)/64 + 
     (11*as^4*ca*cf^2*nf*Pi^2*tr)/128 + (121*as^4*ca^2*cf*LMS*nf*Pi^2*tr)/
      192 + (151*as^3*cf*nf^2*tr^2)/54 + (340843*as^4*ca*cf*nf^2*tr^2)/5184 + 
     (5713*as^4*cf^2*nf^2*tr^2)/1728 + (11*as^3*cf*LMS*nf^2*tr^2)/12 + 
     (3439*as^4*ca*cf*LMS*nf^2*tr^2)/128 + (115*as^4*cf^2*LMS*nf^2*tr^2)/96 + 
     (as^3*cf*LMS^2*nf^2*tr^2)/12 + (65*as^4*ca*cf*LMS^2*nf^2*tr^2)/16 + 
     (as^4*cf^2*LMS^2*nf^2*tr^2)/8 + (11*as^4*ca*cf*LMS^3*nf^2*tr^2)/48 - 
     (as^3*cf*nf^2*Pi^2*tr^2)/36 - (65*as^4*ca*cf*nf^2*Pi^2*tr^2)/48 - 
     (as^4*cf^2*nf^2*Pi^2*tr^2)/24 - (11*as^4*ca*cf*LMS*nf^2*Pi^2*tr^2)/48 - 
     (6131*as^4*cf*nf^3*tr^3)/972 - (151*as^4*cf*LMS*nf^3*tr^3)/54 - 
     (11*as^4*cf*LMS^2*nf^3*tr^3)/24 - (as^4*cf*LMS^3*nf^3*tr^3)/36 + 
     (11*as^4*cf*nf^3*Pi^2*tr^3)/72 + (as^4*cf*LMS*nf^3*Pi^2*tr^3)/36 - 
     (11*as^2*ca*cf*z3)/4 - (2737*as^3*ca^2*cf*z3)/144 - 
     (456223*as^4*ca^3*cf*z3)/3456 - (143*as^3*ca*cf^2*z3)/16 - 
     (43925*as^4*ca^2*cf^2*z3)/384 - (139*as^4*ca*cf^3*z3)/128 + 
     (3*as^4*cf^4*z3)/8 - (as^4*dFA4*z3)/(4*dR) - (121*as^3*ca^2*cf*LMS*z3)/
      24 - (32351*as^4*ca^3*cf*LMS*z3)/576 - (1573*as^4*ca^2*cf^2*LMS*z3)/
      64 - (1331*as^4*ca^3*cf*LMS^2*z3)/192 - (as^4*dFF4*nf*z3)/dR + 
     (1331*as^4*ca^3*cf*Pi^2*z3)/576 + as^2*cf*nf*tr*z3 + 
     (112*as^3*ca*cf*nf*tr*z3)/9 + (8609*as^4*ca^2*cf*nf*tr*z3)/72 + 
     (19*as^3*cf^2*nf*tr*z3)/4 + (10661*as^4*ca*cf^2*nf*tr*z3)/96 + 
     (99*as^4*cf^3*nf*tr*z3)/32 + (11*as^3*ca*cf*LMS*nf*tr*z3)/3 + 
     (911*as^4*ca^2*cf*LMS*nf*tr*z3)/16 + (187*as^4*ca*cf^2*LMS*nf*tr*z3)/8 + 
     (121*as^4*ca^2*cf*LMS^2*nf*tr*z3)/16 - (121*as^4*ca^2*cf*nf*Pi^2*tr*z3)/
      48 - (19*as^3*cf*nf^2*tr^2*z3)/9 - (10453*as^4*ca*cf*nf^2*tr^2*z3)/
      288 - (581*as^4*cf^2*nf^2*tr^2*z3)/24 - (2*as^3*cf*LMS*nf^2*tr^2*z3)/
      3 - (229*as^4*ca*cf*LMS*nf^2*tr^2*z3)/12 - 
     (21*as^4*cf^2*LMS*nf^2*tr^2*z3)/4 - (11*as^4*ca*cf*LMS^2*nf^2*tr^2*z3)/
      4 + (11*as^4*ca*cf*nf^2*Pi^2*tr^2*z3)/12 + (203*as^4*cf*nf^3*tr^3*z3)/
      54 + (19*as^4*cf*LMS*nf^3*tr^3*z3)/9 + (as^4*cf*LMS^2*nf^3*tr^3*z3)/3 - 
     (as^4*cf*nf^3*Pi^2*tr^3*z3)/9 + (605*as^4*ca^3*cf*z3^2)/32 - 
     (11*as^4*ca^2*cf*nf*tr*z3^2)/2 - (33*as^4*ca*cf^2*nf*tr*z3^2)/4 - 
     (as^4*ca*cf*nf^2*tr^2*z3^2)/2 + 3*as^4*cf^2*nf^2*tr^2*z3^2 - 
     (55*as^3*ca^2*cf*z5)/24 - (77995*as^4*ca^3*cf*z5)/1152 + 
     (55*as^3*ca*cf^2*z5)/4 + (6505*as^4*ca^2*cf^2*z5)/48 + 
     (2255*as^4*ca*cf^3*z5)/32 - (5*as^4*dFA4*z5)/(4*dR) - 
     (605*as^4*ca^3*cf*LMS*z5)/96 + (605*as^4*ca^2*cf^2*LMS*z5)/16 + 
     (5*as^4*dFF4*nf*z5)/(2*dR) + (5*as^3*ca*cf*nf*tr*z5)/6 + 
     (18805*as^4*ca^2*cf*nf*tr*z5)/288 - 5*as^3*cf^2*nf*tr*z5 - 
     (5155*as^4*ca*cf^2*nf*tr*z5)/48 - (125*as^4*cf^3*nf*tr*z5)/4 + 
     (55*as^4*ca^2*cf*LMS*nf*tr*z5)/12 - (55*as^4*ca*cf^2*LMS*nf*tr*z5)/2 - 
     (170*as^4*ca*cf*nf^2*tr^2*z5)/9 + (125*as^4*cf^2*nf^2*tr^2*z5)/6 - 
     (5*as^4*ca*cf*LMS*nf^2*tr^2*z5)/6 + 5*as^4*cf^2*LMS*nf^2*tr^2*z5 + 
     (5*as^4*cf*nf^3*tr^3*z5)/3 - (385*as^4*ca^3*cf*z7)/64 + 
     (1155*as^4*ca^2*cf^2*z7)/32 - (1155*as^4*ca*cf^3*z7)/16 + 
     (35*as^4*ca^2*cf*nf*tr*z7)/16 - (105*as^4*ca*cf^2*nf*tr*z7)/8 + 
     (105*as^4*cf^3*nf*tr*z7)/4
     );

 (* from VVsi2.res with nl replaced by nf   *)

RSIas4 = (11*as^3*dabc^2)/192 + (3893*as^4*ca*dabc^2)/4608 - 
     (13*as^4*cf*dabc^2)/64 + (121*as^4*ca*dabc^2*LMS)/768 - 
     (149*as^4*dabc^2*nf*tr)/576 - (11*as^4*dabc^2*LMS*nf*tr)/192 - 
     (as^3*dabc^2*z3)/8 - (169*as^4*ca*dabc^2*z3)/128 - 
     (as^4*cf*dabc^2*z3)/4 - (11*as^4*ca*dabc^2*LMS*z3)/32 + 
     (13*as^4*dabc^2*nf*tr*z3)/32 + (as^4*dabc^2*LMS*nf*tr*z3)/8 - 
     (11*as^4*ca*dabc^2*z3^2)/32 + (as^4*dabc^2*nf*tr*z3^2)/8 + 
     (45*as^4*ca*dabc^2*z5)/64 + (5*as^4*cf*dabc^2*z5)/8 - 
     (5*as^4*dabc^2*nf*tr*z5)/16


QCD4 = {ca -> 3, cf -> 4/3, tr -> 1/2, dR -> 3, dRinv -> 1/3, dA -> 8, dAA4 -> 135, 

        dFF4 -> 5/12, dFA4 -> 15/2, ng -> 8, dabc^2 -> 40/3};
 

QED4 = {dRinv -> 1, dR -> 1, tr -> 1, cf -> 1, ca -> 0, dFF4 -> 1, dFA4 -> 0, dabc->4  };


(* /x1/chet/Ageficom4/gfc3/form/fin/mnc40/DIS/jvud/ABC.res *)

(* 

avsiMSbar = Ex[
getfold["/x1/chet/Ageficom4/gfc3/form/fin/mnc40/DIS/avsi/avsi4l.dt", "avsiMSbar"]
];

C["GLS_SI"]  = avsiMSbar/nl.->nf;

CSI           = C["GLS_SI"];

 *)

CSI = (
(-11*as^3*dabc^2*dRinv*nf)/192 - (481*as^4*ca*dabc^2*dRinv*nf)/1152 + 
 (37*as^4*cf*dabc^2*dRinv*nf)/128 - (121*as^4*ca*dabc^2*dRinv*LMQ*nf)/768 + 
 (119*as^4*dabc^2*dRinv*nf^2*tr)/1152 + (11*as^4*dabc^2*dRinv*LMQ*nf^2*tr)/
  192 + (as^3*dabc^2*dRinv*nf*z3)/8 + (971*as^4*ca*dabc^2*dRinv*nf*z3)/1152 + 
 (as^4*cf*dabc^2*dRinv*nf*z3)/16 + (11*as^4*ca*dabc^2*dRinv*LMQ*nf*z3)/32 - 
 (67*as^4*dabc^2*dRinv*nf^2*tr*z3)/288 - (as^4*dabc^2*dRinv*LMQ*nf^2*tr*z3)/
  8 + (11*as^4*ca*dabc^2*dRinv*nf*z3^2)/32 - (as^4*dabc^2*dRinv*nf^2*tr*z3^2)/
  8 - (295*as^4*ca*dabc^2*dRinv*nf*z5)/576 - (5*as^4*cf*dabc^2*dRinv*nf*z5)/
  8 + (35*as^4*dabc^2*dRinv*nf^2*tr*z5)/144
      );



(* now we start to check the Crewther relation *)


Block[{dR =1/dRinv},

zero1 = Ex[ADNSas4*CNS - dR*(1+ beta3/as*KNSas4)]//cut[as,{0,4}];

Print["zero1 = ", zero1]; 


(* now we check eqs. 3.17 -3.18 from the paper *)

(* cSI31= (-11/192 + z3/8);*)


cSI31 = Coef[CSI,  nf*dabc^2*   dRinv*   as^3];
cSI41 = Coef[CSI,  nf*dabc^2*   dRinv*cf*as^4];
cSI42 = Coef[CSI,  nf*dabc^2*   dRinv*ca*as^4];
cSI43 = Coef[CSI,  nf^2*dabc^2* dRinv*tr*as^4];

        

dSI31 = - cSI31;

dSI41=  -3/2*cSI31 - cSI41;
dSI42= -cSI42 - 11/12*kSI31;
dSI43= -cSI43 + 1/3*kSI31;



ADSIas4 = dR*dabc^2*dRinv(

 dSI31*as^3 

+dSI41*as^4*cf
+dSI42*as^4*ca
+dSI43*as^4*tr*nf
           );



zero2 = Ex[

(nf*ADNSas4 +  nf^2*ADSIas4)*(CNS+ CSI) 

- dR*nf*(1+ beta3/as*(KNSas4 + nf*dabc^2*dRinv*as^3*kSI31))

]//cut[as,{0,4}];

Print[ "zero2 = ", zero2 ];



(* now we add data about singlet Adler function, kSI31 and   check GCR *)

kSI31 = -179/384 + (25*z3)/48 - (5*z5)/24;

(* below from ~/tex/papers/12/VVfull/VVsi2.res  *)

ADSIas4 = (3*((11*as^3*dabc^2)/144 + (3893*as^4*ca*dabc^2)/3456 - 
       (13*as^4*cf*dabc^2)/48 + (121*as^4*ca*dabc^2*LMQ)/576 - 
       (149*as^4*dabc^2*nf*tr)/432 - (11*as^4*dabc^2*LMQ*nf*tr)/144 - 
       (as^3*dabc^2*z3)/6 - (169*as^4*ca*dabc^2*z3)/96 - 
       (as^4*cf*dabc^2*z3)/3 - (11*as^4*ca*dabc^2*LMQ*z3)/24 + 
       (13*as^4*dabc^2*nf*tr*z3)/24 + (as^4*dabc^2*LMQ*nf*tr*z3)/6 - 
       (11*as^4*ca*dabc^2*z3^2)/24 + (as^4*dabc^2*nf*tr*z3^2)/6 + 
       (15*as^4*ca*dabc^2*z5)/16 + (5*as^4*cf*dabc^2*z5)/6 - 
       (5*as^4*dabc^2*nf*tr*z5)/12))/4;



zero3 = Ex[

(nf*ADNSas4 +  nf^2*ADSIas4)*(CNS + CSI) 

- dR*nf*(1+ beta3/as*(KNSas4 + nf*dabc^2*dRinv*as^3*kSI31))

]//cut[as,{0,4}];

Print[ "zero3 = ", zero3 ];

 ]; (* <-- end of  Block[{dR =1/dRinv},....] *)




 (* 

getFold["Adler_GLS_Crewther_singlet.m_extended","test_all"]

*--#[ test_all :

Clear[dR,x,zer];
Clear[prz];

Get["Adler_GLS_Crewther_singlet.m"];
Get["PiVV_betaQED_5l.res"];

prz[n_Integer, e1_,e2_] := Module[{str,zer},

str = "zero" <> ToS[n];
ToE[ "Clear[" <>  str <> "];" ];

Evaluate[ToE[str]] = x*e1 -e2;
Print[ "zero",n," with x set to 1 = ", Ex[ToE[str]/.x->1] ];

];

prz[1,ADSI,ADSIas4];

prz[2,
Ex[(D[PiNS,LMQ]*12*Pi^2/.h->1/(16*Pi^2))] ,
 ADNSas4
];


RNS4=   Expand[(PiNS*LMQ*3/4)]/.{
LMQ^5 -> (4*LMS^3 -4*LMS*Pi^2),
LMQ^4 -> (3*LMS^2 - Pi^2),
LMQ^3 -> (2*LMS),
LMQ^2   -> (1),
LMQ    -> (0)
}/.h->1;
                     
RSI4=   Expand[(PiSI*LMQ*3/4)]/.{
LMQ^5 -> (4*LMS^3 -4*LMS*Pi^2),
LMQ^4 -> (3*LMS^2 - Pi^2),
LMQ^3 -> (2*LMS),
LMQ^2   -> (1),
LMQ    -> (0)
 }/.h->1;


prz[3,RNS4, RNSas4];

prz[4,RSI4, RSIas4];

*--#] test_all :

  *)
