(*----------------------------------------------------------------------*)
(*
 
 Changes:
 --------

 [21 Apr 2002, R.H.]:
    Errors in rQv4 and rQa4 corrected 
    (see hep-ph/0005139v3, and Erratum to be published in Nucl. Phys. B)





 July 21, 2000

 This file contains the results of the paper

 K.G. Chetyrkin, R.V. Harlander, J.H. K\"uhn,
 "Quartic mass corrections to R_had at O(\alpha_s^3)",
 Nucl. Phys. B 586 (2000) 56-72  (hep-ph/0005139)

 in a form readable for Mathematica.

 The notation is as follows:

 r0 = r_0
 rq2 = r_{q,2}
 rq4 = r_{q,4}
 rQv2 = r_{Q,2}^{(v)}
 rQv4 = r_{Q,4}^{(v)}
 rQa2 = r_{Q,2}^{(a)}
 rQa4 = r_{Q,4}^{(a)}
 rvsing = r^{(v)}_{sing}
 rsing = r_{sing}
 rsingp = r^\prime_{sing}

 api == \frac{\alpha_s}{\pi}
 ms2 == \frac{m_Q^2}{s}
 nf  == n_f
 lms == l_{ms}
 vQ == v_Q
 sumvq == \sum_q v_q

*)
(*----------------------------------------------------------------------*)


(* Eq.(3) *)
r0 = (  1 + api + api^2*(365/24 + nf*(-11/12 + (2*Zeta[3])/3) - 11*Zeta[3]) + 
   api^3*(87029/288 - (121*Pi^2)/48 + 
      nf^2*(151/162 - Pi^2/108 - (19*Zeta[3])/27) - (1103*Zeta[3])/4 + 
      nf*(-7847/216 + (11*Pi^2)/36 + (262*Zeta[3])/9 - (25*Zeta[5])/9) + 
	  (275*Zeta[5])/6) + O[api]^4);

(* Eq.(4) *)
rq2 = (api^3*ms2*(-80 + nf*(32/9 - (8*Zeta[3])/3) + 60*Zeta[3]) + O[api]^4);

(* Eq.(5) *)
rQv2 = (  ms2*(12*api + api^2*(253/2 - (13*nf)/3) + 
     api^3*(2442 - (285*Pi^2)/4 + nf^2*(125/54 - Pi^2/9) + (490*Zeta[3])/3 - 
        (5225*Zeta[5])/6 + nf*(-4846/27 + (17*Pi^2)/3 - (466*Zeta[3])/27 + 
           (1045*Zeta[5])/27))) + O[api]^4 );

(* Eq.(6) *)
rQa2 = ( ms2*(-6 - 22*api + api^2*(-8221/24 + (19*Pi^2)/2 + 
        nf*(151/12 - Pi^2/3 - 4*Zeta[3]) + 117*Zeta[3]) + 
     api^3*(-4613165/864 + (670*Pi^2)/3 + (121075*Zeta[3])/36 + 
        nf^2*(-13171/1944 + (8*Pi^2)/27 + (26*Zeta[3])/9) - 1270*Zeta[5] + 
        nf*(72197/162 - (209*Pi^2)/12 + Pi^4/18 - (656*Zeta[3])/3 + 
           55*Zeta[5]))) + O[api]^4 );

(* Eq.(8) *)
rq4 = ( ms2^2*(api^2*(13/3 - lms - 4*Zeta[3]) + 
     api^3*(-9707/144 + 2*lms^2 + (5*Pi^2)/2 + lms*(43/12 - 22*Zeta[3]) + 
        25*Zeta[3] + nf*(457/108 - Pi^2/9 - (22*Zeta[3])/9 + 
           lms*(-13/18 + (4*Zeta[3])/3)) + (50*Zeta[5])/3)) + O[api]^4 );


(* Eq.(9) *)
rQv4 = ( ms2^2*(-6 - 22*api + api^2*(-2977/12 - (13*lms)/2 + 27*Pi^2 + 
        nf*(143/18 + lms/3 - (2*Pi^2)/3 - (8*Zeta[3])/3) + 108*Zeta[3]) + 
     api^3*(-1264093/432 + 13*lms^2 + (4033*Pi^2)/8 + 
        lms*(-1309/6 - 22*Zeta[3]) + (64123*Zeta[3])/18 + 
        nf^2*(-463/972 - (5*lms)/27 + (23*Pi^2)/54 + (28*Zeta[3])/27) - 
        (13285*Zeta[5])/9 + nf*(130009/648 - (2*lms^2)/3 - (287*Pi^2)/9 + 
           Pi^4/9 - (1672*Zeta[3])/9 + lms*(199/12 + (4*Zeta[3])/3) + 
           (440*Zeta[5])/9))) + O[api]^4 );

(* Eq.(10) *)
rQa4 = ( ms2^2*(6 + 10*api + 
	api^2*(1147/4 + (75*lms)/2 - 27*Pi^2 - 224*Zeta[3] + 
        nf*(-41/6 - (7*lms)/3 + (2*Pi^2)/3 + (16*Zeta[3])/3)) + 
     api^3*(221269/48 - 75*lms^2 - (3627*Pi^2)/8 + 
        lms*(4385/6 - 22*Zeta[3]) + 
        nf^2*(2995/972 + (23*lms)/27 - (29*Pi^2)/54 - (20*Zeta[3])/27) - 
        (20147*Zeta[3])/6 - (2225*Zeta[5])/3 + 
        nf*(-200923/648 + (14*lms^2)/3 + (98*Pi^2)/3 - Pi^4/9 + 
           (5002*Zeta[3])/27 + lms*(-2323/36 + (4*Zeta[3])/3) + 
           (1040*Zeta[5])/27))) + O[api]^4 );


(* Eq.(11) *)
rvsing = ( api^3*((vQ + sumvq)^2*(55/216 - 5/9*Zeta[3]) +
          ms2^2*vQ*(vQ + sumvq)*(-20/9 + 50/3*Zeta[3])) + O[api]^4 );

(* Eq.(12) *)
rsing = ( 1/4*api^2*(5/4 - 2/3*Zeta[2] + ms2*(-4/3 + 20/3*Zeta[2] + 
	4*lms - 2/3*lms^2) + ms2^2*(13/2 + 2/3*Zeta[2] - 16/3*Zeta[3]
        + lms*(-5 + 4/3*Zeta[2]) - 1/3*lms^2 - 2/9*lms^3)) + O[api]^3 );

(* Eq.(13) *)
rsingp = ( 1/4*api^3*ms2^2*(-380/3*Zeta[3] + 1520/3*Zeta[5] + 
	nf*(40/9*Zeta[3] - 160/9*Zeta[5])) + O[api]^4 );

Print["Note: r0, rq2, rq4, rQv2, rQv4, rQa2, rQa4, rvsing, rsing, rsingp"];
Print["  are defined as global variables now."];

(* end of file *)
