(* [1] Hermann, Misiak and Steinhauser "B to Xs gamma in the Two Higgs Doublet Model up to Next-to-Next-to-Leading Order in QCD" *)
(* SFB/CPP-12-60, TTP12-29, IFT-5/2012 *)



Cl2[x_] := Im[PolyLog[2, E^(I*x)]];
MATADMasterIntegralRule = { D3 -> 6*Zeta[3] - 15/4*Zeta[4] - 6*(Cl2[Pi/3])^2,
	B4 -> -4*Zeta[2]*Log[2]^2 + 2/3*Log[2]^4 - 13/2*Zeta[4] + 16*PolyLog[4, 1/2],
	S2 -> 4/(9*Sqrt[3])*Cl2[Pi/3],
	T1ep -> ( -45/2 - Pi*Sqrt[3]*Log[3]^2/8 - 35*Pi^3*Sqrt[3]/216 - 9/2*Zeta[2]
	    + Zeta[3] + 6*Sqrt[3]*Cl2[Pi/3] - 6*Sqrt[3]*Im[PolyLog[3, E^(-I*Pi/6)/Sqrt[3]]] ),
	OepS2 -> ( -763/32 - 9*Pi*Sqrt[3]*Log[3]^2/16 - 35*Pi^3*Sqrt[3]/48 + 195/16*Zeta[2]
	    - 15/4*Zeta[3] + 57/16*Zeta[4] + 45*Sqrt[3]/2*Cl2[Pi/3]
	    - 27*Sqrt[3]*Im[PolyLog[3, Exp[(-I*Pi/6)]/Sqrt[3]]] ) };



(* Wilson coefficients SM *)
(* w = 1 - MW^2/mt^2 *)

c7t3LSM = ( 177503731/1749600
	- (17752346981*w)/195955200
	- (7043430599957*w^2)/54867456000
	- (1951275475739117*w^3)/10534551552000
	- (148920493184905249*w^4)/589934886912000
	- (6438305189823329749*w^5)/19467851268096000
	- (163550811694989761069*w^6)/389357025361920000
	- (21857253706055466513383*w^7)/41997161204180582400
	- (965966122450146404722571881*w^8)/1528696667832173199360000
	- (1259313234584087221721491652179*w^9)/1669336761272733133701120000
	- (3952617483756144402622251133699*w^10)/4451564696727288356536320000
	- (40005626386960868009742589462288913*w^11)/38746419120314317855292129280000
	- (18782523775742367026874088005867725041*w^12)/15808539001088241684959188746240000
	- (3689493098811965994577115222031005177*w^13)/2723284318587467767595636248018944
	- (3861802861511294337550591012221400867631*w^14)/2519922177913728291444014060666880000
	- (1145087777874152692175241503026036181513257*w^15)/665259454969224268941219712016056320000
	- (71568320898943316370141750115295293839395063*w^16)/37254529478276559060708303872899153920000
	- (2901893*Zeta[3])/38880
	+ (94143997*w*Zeta[3])/1244160
	+ (91942073*w^2*Zeta[3])/860160
	+ (137418234607*w^3*Zeta[3])/891813888
	+ (7490373009073*w^4*Zeta[3])/35672555520
	+ (467301421361*w^5*Zeta[3])/1698693120
	+ (329068267226885*w^6*Zeta[3])/941755465728
	+ (1164930029277053*w^7*Zeta[3])/2690729902080
	+ (32688338029429333*w^8*Zeta[3])/62185757736960
	+ (252163770914832607*w^9*Zeta[3])/401815665377280
	+ (30867491239401625609*w^10*Zeta[3])/41788829199237120
	+ (111379872064864887943*w^11*Zeta[3])/129672003333390336
	+ (37351912166183862346213*w^12*Zeta[3])/37790126685730897920
	+ (22934004324209673501271*w^13*Zeta[3])/20348529753855098880
	+ (140830032452197336709737*w^14*Zeta[3])/110463447235213393920
	+ (759244516114912056798329*w^15*Zeta[3])/530224546729024290816
	+ (237265169773150679549543747*w^16*Zeta[3])/148462873084126801428480 ) ;

c8t3LSM = ( 89806993/4665600
	- (2931320447*w)/81648000
	- (146044212721*w^2)/1828915200
	- (421986866464987*w^3)/3511517184000
	- (33829719303397841*w^4)/196644962304000
	- (6035867752125763991*w^5)/25957135024128000
	- (861220303899039573037*w^6)/2855284852654080000
	- (1858395150259947001404179*w^7)/4899668807154401280000
	- (72988951093099001774586401*w^8)/156789401828940840960000
	- (23983416129785324164871845847*w^9)/42803506699300849582080000
	- (3939115742005836548381661196639*w^10)/5935419595636384475381760000
	- (3338928508489605951153737393710181*w^11)/4305157680034924206143569920000
	- (4721585323526789026664864740658484797*w^12)/5269513000362747228319729582080000
	- (775398581949770146097750701068273030701*w^13)/756467866274296602109898957783040000
	- (6874829767129498901351455850735735476133*w^14)/5913417377504215723921952995698278400
	- (5513907558481664818215483644270449789725167*w^15)/4213309881471753703294391509435023360000
	- (125552424926986532135743097321123616718817039*w^16)/85798310313606620867085790737585930240000
	- (3426427*Zeta[3])/207360
	+ (377401*w*Zeta[3])/12960
	+ (257020361*w^2*Zeta[3])/3870720
	+ (148678249549*w^3*Zeta[3])/1486356480
	+ (48644809387*w^4*Zeta[3])/339738624
	+ (3067923823757*w^5*Zeta[3])/15854469120
	+ (787852603809259*w^6*Zeta[3])/3139184885760
	+ (113217484992547*w^7*Zeta[3])/358763986944
	+ (96339777793582171*w^8*Zeta[3])/248743030947840
	+ (811676013915491051*w^9*Zeta[3])/1741201216634880
	+ (2796711043890214519*w^10*Zeta[3])/5065312630210560
	+ (6640218640384678121*w^11*Zeta[3])/10291428835983360
	+ (13145813227214139738235*w^12*Zeta[3])/17635392453341085696
	+ (23136022137210640681529*w^13*Zeta[3])/27131373005140131840
	+ (33517559834958800208721*w^14*Zeta[3])/34655199132615966720
	+ (192421642408729551788101*w^15*Zeta[3])/176741515576341430272
	+ (240980147743902885729676147*w^16*Zeta[3])/197950497445502401904640 ) ;



(* Wilson coefficients 2HDM *)
(* r = mt^2/MH^2 *)
(* u = 1 - 1/r = 1 - MH^2/mt^2 *)
(* ubar = 1 - r = 1 - mt^2/MH^2 *)

(* LO *)
cH[0,1] = 0;
cH[0,2] = 0;
cH[0,3] = 0;
cH[0,4] = 0;
cH[0,5] = 0;
cH[0,6] = 0;
cHeff[0,7] = ( Ad*AuC * ( -r/(4*(-1 + r)^4) + (11*r^2)/(12*(-1 + r)^4) - (13*r^3)/(12*(-1 + r)^4)
	+ (5*r^4)/(12*(-1 + r)^4) - (r*Log[r])/(3*(-1 + r)^4) + (5*r^2*Log[r])/(6*(-1 + r)^4)
	- (r^3*Log[r])/(2*(-1 + r)^4) )
	+ Au*AuC * ( (-7*r)/(72*(-1 + r)^4) + r^2/(6*(-1 + r)^4) + r^3/(24*(-1 + r)^4)
	- r^4/(9*(-1 + r)^4) - (r^2*Log[r])/(6*(-1 + r)^4) + r^3*Log[r] /(4*(-1 + r)^4) ) );
cHeff[0,8] = ( Ad*AuC * ( (-3*r)/(4*(-1 + r)^4) + (7*r^2)/(4*(-1 + r)^4) - (5*r^3)/(4*(-1 + r)^4)
	+ r^4/(4*(-1 + r)^4) - (r*Log[r])/(2*(-1 + r)^4) + (r^2*Log[r])/(2*(-1 + r)^4) )
	+ Au*AuC * ( -r/(12*(-1 + r)^4) - r^2/(8*(-1 + r)^4) + r^3/(4*(-1 + r)^4)
	- r^4/(24*(-1 + r)^4) - (r^2*Log[r])/(4*(-1 + r)^4) )  );

(* NLO *)
cH[1,1] = 0;
cH[1,2] = 0;
cH[1,3] = 0;
cH[1,4] = ( Au*AuC * ( (-4*r)/(9*(-1 + r)^4) + (5*r^2)/(4*(-1 + r)^4) - r^3/(-1 + r)^4
	+ (7*r^4)/(36*(-1 + r)^4) - (r*Log[r])/(3*(-1 + r)^4) + (r^2*Log[r])/(2*(-1 + r)^4)) );
cH[1,5] = 0;
cH[1,6] = 0;
cH[2,7] = ( Ad*AuC * ( (28*r)/(3*(-1 + r)^5) - (36*r^2)/(-1 + r)^5 + (140*r^3)/(3*(-1 + r)^5)
	- (68*r^4)/(3*(-1 + r)^5) + (8*r^5)/(3*(-1 + r)^5) + (14*r*Log[mu^2/mt^2])/(3*(-1 + r)^5)
	- (178*r^2*Log[mu^2/mt^2])/(9*(-1 + r)^5) + (82*r^3*Log[mu^2/mt^2])/(3*(-1 + r)^5)
	- (14*r^4*Log[mu^2/mt^2])/(-1 + r)^5 + (16*r^5*Log[mu^2/mt^2])/(9*(-1 + r)^5) + (22*r*Log[r])/(3*(-1 + r)^5)
	- (194*r^2*Log[r])/(9*(-1 + r)^5) + (142*r^3*Log[r])/(9*(-1 + r)^5) - (14*r^4*Log[r])/(9*(-1 + r)^5)
	+ (32*r*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5) - (88*r^2*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5)
	+ (44*r^3*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5) + (4*r^4*Log[mu^2/mt^2]*Log[r])/(3*(-1 + r)^5)
	- (16*r*PolyLog[2, 1 - r^(-1)])/(3*(-1 + r)^5) + (208*r^2*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5)
	- (304*r^3*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) + (176*r^4*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5)
	- (32*r^5*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) )
	+ Au*AuC * ( (-797*r)/(486*(-1 + r)^5) + (6233*r^2)/(486*(-1 + r)^5) - (1445*r^3)/(54*(-1 + r)^5)
	+ (8771*r^4)/(486*(-1 + r)^5) - (601*r^5)/(243*(-1 + r)^5) + (31*r*Log[mu^2/mt^2])/(27*(-1 + r)^5)
	- (13*r^2*Log[mu^2/mt^2])/(27*(-1 + r)^5) - (17*r^3*Log[mu^2/mt^2])/(3*(-1 + r)^5)
	+ (149*r^4*Log[mu^2/mt^2])/(27*(-1 + r)^5) - (14*r^5*Log[mu^2/mt^2])/(27*(-1 + r)^5) - (7*r*Log[r])/(81*(-1 + r)^5)
	+ (463*r^2*Log[r])/(81*(-1 + r)^5) - (269*r^3*Log[r])/(27*(-1 + r)^5) + (7*r^4*Log[r])/(9*(-1 + r)^5)
	+ (28*r^2*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5) - (46*r^3*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5)
	- (2*r^4*Log[mu^2/mt^2]*Log[r])/(3*(-1 + r)^5) - (4*r^2*PolyLog[2, 1 - r^(-1)])/(-1 + r)^5
	+ (110*r^3*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) - (10*r^4*PolyLog[2, 1 - r^(-1)])/(-1 + r)^5
	+ (16*r^5*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) ) );
cH[2,8] = ( Ad*AuC * ((143*r)/(8*(-1 + r)^5) - (165*r^2)/(4*(-1 + r)^5) + (65*r^3)/(2*(-1 + r)^5)
	- (51*r^4)/(4*(-1 + r)^5) + (29*r^5)/(8*(-1 + r)^5) + (27*r*Log[mu^2/mt^2])/(2*(-1 + r)^5)
	- (89*r^2*Log[mu^2/mt^2])/(3*(-1 + r)^5) + (20*r^3*Log[mu^2/mt^2])/(-1 + r)^5 - (5*r^4*Log[mu^2/mt^2])/(-1 + r)^5
	+ (7*r^5*Log[mu^2/mt^2])/(6*(-1 + r)^5) + (55*r*Log[r])/(4*(-1 + r)^5) - (43*r^2*Log[r])/(3*(-1 + r)^5)
	+ (41*r^3*Log[r])/(12*(-1 + r)^5) - (17*r^4*Log[r])/(6*(-1 + r)^5) + (19*r*Log[mu^2/mt^2]*Log[r])/(3*(-1 + r)^5)
	- (2*r^2*Log[mu^2/mt^2]*Log[r])/(3*(-1 + r)^5) - (17*r^3*Log[mu^2/mt^2]*Log[r])/(3*(-1 + r)^5)
	- (6*r*PolyLog[2, 1 - r^(-1)])/(-1 + r)^5 + (97*r^2*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5)
	- (103*r^3*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5) + (59*r^4*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5)
	- (17*r^5*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5))
	+ Au*AuC * ( (-565*r)/(648*(-1 + r)^5) + (19283*r^2)/(1296*(-1 + r)^5) - (2867*r^3)/(144*(-1 + r)^5)
	+ (12101*r^4)/(1296*(-1 + r)^5) - (4451*r^5)/(1296*(-1 + r)^5) + (19*r*Log[mu^2/mt^2])/(18*(-1 + r)^5)
	+ (223*r^2*Log[mu^2/mt^2])/(36*(-1 + r)^5) - (31*r^3*Log[mu^2/mt^2])/(4*(-1 + r)^5)
	+ (25*r^4*Log[mu^2/mt^2])/(36*(-1 + r)^5) - (7*r^5*Log[mu^2/mt^2])/(36*(-1 + r)^5)
	+ (r*Log[r])/(108*(-1 + r)^5) + (2155*r^2*Log[r])/(216*(-1 + r)^5) - (107*r^3*Log[r])/(72*(-1 + r)^5)
	+ (13*r^4*Log[r])/(6*(-1 + r)^5) + (31*r^2*Log[mu^2/mt^2]*Log[r])/(6*(-1 + r)^5)
	+ (17*r^3*Log[mu^2/mt^2]*Log[r])/(6*(-1 + r)^5) - (5*r^2*PolyLog[2, 1 - r^(-1)])/(-1 + r)^5
	+ (47*r^3*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5) - (5*r^4*PolyLog[2, 1 - r^(-1)])/(-1 + r)^5
	+ (13*r^5*PolyLog[2, 1 - r^(-1)])/(6*(-1 + r)^5) ) ) ;
cHeff[1,7] = ( cH[2,7]  - 1/3*cH[1,3] - 4/9*cH[1,4] - 20/3*cH[1,5] - 80/9*cH[1,6] ) ;
cHeff[1,8] = ( cH[2,8]  + cH[1,3] - 1/6*cH[1,4] + 20*cH[1,5] - 10/3*cH[1,6] ) ;



(* NNLO *)
cH[2,1] = 0;
cH[2,2] = 0;
cH[2,3] = ( Au*AuC * ( (71*r)/(27*(-1 + r)^5) - (613*r^2)/(81*(-1 + r)^5) + (593*r^3)/(81*(-1 + r)^5)
	- (199*r^4)/(81*(-1 + r)^5) + (2*r^5)/(27*(-1 + r)^5) - (80*r*Log[mu^2/mt^2])/(81*(-1 + r)^5)
	+ (305*r^2*Log[mu^2/mt^2])/(81*(-1 + r)^5) - (5*r^3*Log[mu^2/mt^2])/(-1 + r)^5
	+ (215*r^4*Log[mu^2/mt^2])/(81*(-1 + r)^5) - (35*r^5*Log[mu^2/mt^2])/(81*(-1 + r)^5)
	+ (56*r*Log[r])/(81*(-1 + r)^5) + (10*r^2*Log[r])/(81*(-1 + r)^5) - (32*r^3*Log[r])/(27*(-1 + r)^5)
	+ (10*r^4*Log[r])/(27*(-1 + r)^5) - (20*r*Log[mu^2/mt^2]*Log[r])/(27*(-1 + r)^5)
	+ (50*r^2*Log[mu^2/mt^2]*Log[r])/(27*(-1 + r)^5) - (10*r^3*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5)
	+ (20*r*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5) - (50*r^2*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5)
	+ (10*r^3*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) - (10*r^4*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5)
	+ (10*r^5*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5) ) ) ;
cH[2,4] = ( Au*AuC * ( (9067*r)/(972*(-1 + r)^5) - (11417*r^2)/(1944*(-1 + r)^5)
	- (24953*r^3)/(648*(-1 + r)^5) + (97609*r^4)/(1944*(-1 + r)^5) - (29467*r^5)/(1944*(-1 + r)^5)
	+ (580*r*Log[mu^2/mt^2])/(81*(-1 + r)^5) - (6343*r^2*Log[mu^2/mt^2])/(324*(-1 + r)^5)
	+ (51*r^3*Log[mu^2/mt^2])/(4*(-1 + r)^5) - (241*r^4*Log[mu^2/mt^2])/(324*(-1 + r)^5)
	+ (133*r^5*Log[mu^2/mt^2])/(324*(-1 + r)^5) + (245*r*Log[r])/(27*(-1 + r)^5)
	- (5*r^2*Log[r])/(36*(-1 + r)^5) - (307*r^3*Log[r])/(12*(-1 + r)^5) + (515*r^4*Log[r])/(54*(-1 + r)^5)
	+ (91*r*Log[mu^2/mt^2]*Log[r])/(27*(-1 + r)^5) - (95*r^2*Log[mu^2/mt^2]*Log[r])/(54*(-1 + r)^5)
	- (125*r^3*Log[mu^2/mt^2]*Log[r])/(18*(-1 + r)^5) - (91*r*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5)
	+ (83*r^2*PolyLog[2, 1 - r^(-1)])/(54*(-1 + r)^5) + (335*r^3*PolyLog[2, 1 - r^(-1)])/(18*(-1 + r)^5)
	- (1421*r^4*PolyLog[2, 1 - r^(-1)])/(54*(-1 + r)^5) + (515*r^5*PolyLog[2, 1 - r^(-1)])/(54*(-1 + r)^5) ) ) ;
cH[2,5] = ( Au*AuC * ( (-11*r)/(54*(-1 + r)^5) + (43*r^2)/(81*(-1 + r)^5) - (35*r^3)/(81*(-1 + r)^5)
	+ (7*r^4)/(81*(-1 + r)^5) + r^5/(54*(-1 + r)^5) + (8*r*Log[mu^2/mt^2])/(81*(-1 + r)^5)
	- (61*r^2*Log[mu^2/mt^2])/(162*(-1 + r)^5) + (r^3*Log[mu^2/mt^2])/(2*(-1 + r)^5)
	- (43*r^4*Log[mu^2/mt^2])/(162*(-1 + r)^5) + (7*r^5*Log[mu^2/mt^2])/(162*(-1 + r)^5)
	- (2*r*Log[r])/(81*(-1 + r)^5) - (10*r^2*Log[r])/(81*(-1 + r)^5) + (5*r^3*Log[r])/(27*(-1 + r)^5)
	- (r^4*Log[r])/(27*(-1 + r)^5) + (2*r*Log[mu^2/mt^2]*Log[r])/(27*(-1 + r)^5)
	- (5*r^2*Log[mu^2/mt^2]*Log[r])/(27*(-1 + r)^5) + (r^3*Log[mu^2/mt^2]*Log[r])/(9*(-1 + r)^5)
	- (2*r*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5) + (5*r^2*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5)
	- (r^3*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^5) + (r^4*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5)
	- (r^5*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^5) ) ) ;
cH[2,6] = ( Au*AuC * ( (-55*r)/(144*(-1 + r)^5) + (215*r^2)/(216*(-1 + r)^5) - (175*r^3)/(216*(-1 + r)^5)
	+ (35*r^4)/(216*(-1 + r)^5) + (5*r^5)/(144*(-1 + r)^5) + (5*r*Log[mu^2/mt^2])/(27*(-1 + r)^5)
	- (305*r^2*Log[mu^2/mt^2])/(432*(-1 + r)^5) + (15*r^3*Log[mu^2/mt^2])/(16*(-1 + r)^5)
	- (215*r^4*Log[mu^2/mt^2])/(432*(-1 + r)^5) + (35*r^5*Log[mu^2/mt^2])/(432*(-1 + r)^5)
	- (5*r*Log[r])/(108*(-1 + r)^5) - (25*r^2*Log[r])/(108*(-1 + r)^5) + (25*r^3*Log[r])/(72*(-1 + r)^5)
	- (5*r^4*Log[r])/(72*(-1 + r)^5) + (5*r*Log[mu^2/mt^2]*Log[r])/(36*(-1 + r)^5)
	- (25*r^2*Log[mu^2/mt^2]*Log[r])/(72*(-1 + r)^5) + (5*r^3*Log[mu^2/mt^2]*Log[r])/(24*(-1 + r)^5)
	- (5*r*PolyLog[2, 1 - r^(-1)])/(36*(-1 + r)^5) + (25*r^2*PolyLog[2, 1 - r^(-1)])/(72*(-1 + r)^5)
	- (5*r^3*PolyLog[2, 1 - r^(-1)])/(24*(-1 + r)^5) + (5*r^4*PolyLog[2, 1 - r^(-1)])/(72*(-1 + r)^5)
	- (5*r^5*PolyLog[2, 1 - r^(-1)])/(72*(-1 + r)^5) ) ) ;



(* c7 and c8 to three loop order *)
(* exact log(mu^2/mt^2) part *)

(* equation (15) in [1] *)
cH3duL[7] = ( Log[mu^2/mt^2]^2 * ( (-475*r)/(9*(-1 + r)^6) + (7154*r^2)/(27*(-1 + r)^6)
	- (11468*r^3)/(27*(-1 + r)^6) + (2486*r^4)/(9*(-1 + r)^6) - (2003*r^5)/(27*(-1 + r)^6)
	+ (284*r^6)/(27*(-1 + r)^6) - (880*r*Log[r])/(27*(-1 + r)^6) + (940*r^2*Log[r])/(9*(-1 + r)^6)
	- (382*r^3*Log[r])/(9*(-1 + r)^6) - (920*r^4*Log[r])/(27*(-1 + r)^6) + (14*r^5*Log[r])/(3*(-1 + r)^6) )
	+ Log[mu^2/mt^2] * ( (-2341*r)/(9*(-1 + r)^6) + (95752*r^2)/(81*(-1 + r)^6)
	- (150808*r^3)/(81*(-1 + r)^6) + (34142*r^4)/(27*(-1 + r)^6) - (30091*r^5)/(81*(-1 + r)^6)
	+ (3790*r^6)/(81*(-1 + r)^6) - (16358*r*Log[r])/(81*(-1 + r)^6) + (732*r^2*Log[r])/(-1 + r)^6
	- (19406*r^3*Log[r])/(27*(-1 + r)^6) + (17816*r^4*Log[r])/(81*(-1 + r)^6) - (844*r^5*Log[r])/(27*(-1 + r)^6)
	+ (304*r*PolyLog[2, 1 - r^(-1)])/(3*(-1 + r)^6) - (14296*r^2*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6)
	+ (25280*r^3*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6) - (2192*r^4*PolyLog[2, 1 - r^(-1)])/(3*(-1 + r)^6)
	+ (7120*r^5*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6) - (1112*r^6*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6) ) ) ;

(* equation (14) in [1] *)
cH3uuL[7] = ( Log[mu^2/mt^2]^2 * ( (-1843*r)/(162*(-1 + r)^6) - (962*r^2)/(81*(-1 + r)^6) + (10582*r^3)/(81*(-1 + r)^6)
	- (10531*r^4)/(81*(-1 + r)^6) + (4183*r^5)/(162*(-1 + r)^6) - (259*r^6)/(81*(-1 + r)^6)
	- (1118*r^2*Log[r])/(27*(-1 + r)^6) + (2089*r^3*Log[r])/(27*(-1 + r)^6) + (532*r^4*Log[r])/(27*(-1 + r)^6)
	- (7*r^5*Log[r])/(3*(-1 + r)^6) )
	+ Log[mu^2/mt^2] * ( (54970*r)/(2187*(-1 + r)^6) - (755213*r^2)/(2187*(-1 + r)^6) + (2058721*r^3)/(2187*(-1 + r)^6)
	- (1828573*r^4)/(2187*(-1 + r)^6) + (538025*r^5)/(2187*(-1 + r)^6) - (67930*r^6)/(2187*(-1 + r)^6)
	+ (1435*r*Log[r])/(729*(-1 + r)^6) - (146588*r^2*Log[r])/(729*(-1 + r)^6) + (322801*r^3*Log[r])/(729*(-1 + r)^6)
	- (28130*r^4*Log[r])/(243*(-1 + r)^6) + (386*r^5*Log[r])/(27*(-1 + r)^6)
	+ (964*r^2*PolyLog[2, 1 - r^(-1)])/(9*(-1 + r)^6) - (10406*r^3*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6)
	+ (10544*r^4*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6) - (3550*r^5*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6)
	+ (520*r^6*PolyLog[2, 1 - r^(-1)])/(27*(-1 + r)^6) ) ) ;

(* equation (17) in [1] *)
cH3duL[8] = ( Log[mu^2/mt^2]^2 * ( (-1991*r)/(12*(-1 + r)^6) + (11695*r^2)/(36*(-1 + r)^6)
	- (3209*r^3)/(18*(-1 + r)^6) + (317*r^4)/(6*(-1 + r)^6) - (1465*r^5)/(36*(-1 + r)^6) + (259*r^6)/(36*(-1 + r)^6)
	- (1183*r*Log[r])/(18*(-1 + r)^6) - (317*r^2*Log[r])/(6*(-1 + r)^6) + (665*r^3*Log[r])/(6*(-1 + r)^6)
	+ (139*r^4*Log[r])/(18*(-1 + r)^6) )
	+ Log[mu^2/mt^2] * ( (-5012*r)/(9*(-1 + r)^6) + (35615*r^2)/(27*(-1 + r)^6) - (31916*r^3)/(27*(-1 + r)^6)
	+ (2066*r^4)/(3*(-1 + r)^6) - (8720*r^5)/(27*(-1 + r)^6) + (1463*r^6)/(27*(-1 + r)^6) - (19901*r*Log[r])/(54*(-1 + r)^6)
	+ (2897*r^2*Log[r])/(9*(-1 + r)^6) - (766*r^3*Log[r])/(9*(-1 + r)^6) + (4501*r^4*Log[r])/(27*(-1 + r)^6)
	- (629*r^5*Log[r])/(18*(-1 + r)^6) + (122*r*PolyLog[2, (-1 + r)/r])/(-1 + r)^6
	- (6121*r^2*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6) + (3916*r^3*PolyLog[2, (-1 + r)/r])/(9*(-1 + r)^6)
	- (373*r^4*PolyLog[2, (-1 + r)/r])/(-1 + r)^6 + (1718*r^5*PolyLog[2, (-1 + r)/r])/(9*(-1 + r)^6)
	- (629*r^6*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6) ) ) ;

(* equation (16) in [1] *)
cH3uuL[8] = ( Log[mu^2/mt^2]^2 * ( (-1183*r)/(108*(-1 + r)^6) - (26045*r^2)/(216*(-1 + r)^6) + (12743*r^3)/(108*(-1 + r)^6)
	+ (226*r^4)/(27*(-1 + r)^6) + (172*r^5)/(27*(-1 + r)^6) - (259*r^6)/(216*(-1 + r)^6)
	- (2683*r^2*Log[r])/(36*(-1 + r)^6) - (1469*r^3*Log[r])/(18*(-1 + r)^6) - (139*r^4*Log[r])/(36*(-1 + r)^6) )
	+ Log[mu^2/mt^2] * ( (18607*r)/(1458*(-1 + r)^6) - (6079465*r^2)/(11664*(-1 + r)^6) + (4318315*r^3)/(5832*(-1 + r)^6)
	- (1282319*r^4)/(2916*(-1 + r)^6) + (1472801*r^5)/(5832*(-1 + r)^6) - (522347*r^6)/(11664*(-1 + r)^6)
	+ (613*r*Log[r])/(486*(-1 + r)^6) - (698693*r^2*Log[r])/(1944*(-1 + r)^6) + (24317*r^3*Log[r])/(972*(-1 + r)^6)
	- (77927*r^4*Log[r])/(648*(-1 + r)^6) + (481*r^5*Log[r])/(18*(-1 + r)^6) + (425*r^2*PolyLog[2, (-1 + r)/r])/(3*(-1 + r)^6)
	- (4073*r^3*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6) + (3473*r^4*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6)
	- (2431*r^5*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6) + (481*r^6*PolyLog[2, (-1 + r)/r])/(18*(-1 + r)^6) ) ) ;



(* r -> 0, mu = mt *)

(* equation (22) in [1] *)
cH3dur0[7] = ( (-99253*r)/324 - (3335*Pi^2*r)/81 + (98*Pi^4*r)/135 - (1253*r^2)/18 - (587*Pi^2*r^2)/9
	+ (158*Pi^4*r^2)/135 + (76747*r^3)/486 - (839*Pi^2*r^3)/54 + (1594*Pi^4*r^3)/1215 + (209164516*r^4)/820125
	+ (1178032*Pi^2*r^4)/10935 + (266*Pi^4*r^4)/405 + (17943701963*r^5)/26244000 + (684379*Pi^2*r^5)/4374
	- (58*Pi^4*r^5)/45 + (16*Pi^2*r*Log[2]^2)/81 + (304*Pi^2*r^2*Log[2]^2)/81 + (176*Pi^2*r^3*Log[2]^2)/27
	+ (496*Pi^2*r^4*Log[2]^2)/81 + (16*Pi^2*r^5*Log[2]^2)/81 - (16*r*Log[2]^4)/81 - (304*r^2*Log[2]^4)/81
	- (176*r^3*Log[2]^4)/27 - (496*r^4*Log[2]^4)/81 - (16*r^5*Log[2]^4)/81 - (69241*r*Log[r])/243
	- (1696*Pi^2*r*Log[r])/81 - (66734*r^2*Log[r])/81 - (80*Pi^2*r^2*Log[r])/9 - (170689*r^3*Log[r])/162
	+ (1598*Pi^2*r^3*Log[r])/81 - (6773623*r^4*Log[r])/36450 + (26300*Pi^2*r^4*Log[r])/729
	+ (395739101*r^5*Log[r])/145800 - (48574*Pi^2*r^5*Log[r])/729 - (3335*r*Log[r]^2)/27 - (587*r^2*Log[r]^2)/3
	- (839*r^3*Log[r]^2)/18 + (1178032*r^4*Log[r]^2)/3645 + (684379*r^5*Log[r]^2)/1458 - (1696*r*Log[r]^3)/81
	- (80*r^2*Log[r]^3)/9 + (1598*r^3*Log[r]^3)/81 + (26300*r^4*Log[r]^3)/729 - (48574*r^5*Log[r]^3)/729
	- (128*r*PolyLog[4, 1/2])/27 - (2432*r^2*PolyLog[4, 1/2])/27 - (1408*r^3*PolyLog[4, 1/2])/9
	- (3968*r^4*PolyLog[4, 1/2])/27 - (128*r^5*PolyLog[4, 1/2])/27 + (178*r*Zeta[3])/3 + (2356*r^2*Zeta[3])/27
	+ (5788*r^3*Zeta[3])/81 + (29528*r^4*Zeta[3])/243 + (147008*r^5*Zeta[3])/243 + (856*r*Log[r]*Zeta[3])/27
	+ (928*r^2*Log[r]*Zeta[3])/27 + (736*r^3*Log[r]*Zeta[3])/27 - (8*r^4*Log[r]*Zeta[3])/27
	- (1592*r^5*Log[r]*Zeta[3])/27 ) ;

(* equation (18) in [1] *)
cH3uur0[7] = ( (-2320661*r)/52488 + (1345*Pi^2*r)/4374 - (7146973*r^2)/26244 - (163811*Pi^2*r^2)/4374
	+ (2993*Pi^4*r^2)/3645 - (8940387787*r^3)/26244000 - (1269332*Pi^2*r^3)/10935 + (1388*Pi^4*r^3)/729
	- (4679848193*r^4)/26244000 - (2631067*Pi^2*r^4)/14580 + (1271*Pi^4*r^4)/405 + (1872111923*r^5)/20575296
	- (12026329*Pi^2*r^5)/87480 + (14888*Pi^4*r^5)/3645 + (136*Pi^2*r^2*Log[2]^2)/243 + (992*Pi^2*r^3*Log[2]^2)/243
	+ (280*Pi^2*r^4*Log[2]^2)/27 + (4288*Pi^2*r^5*Log[2]^2)/243 - (136*r^2*Log[2]^4)/243 - (992*r^3*Log[2]^4)/243
	- (280*r^4*Log[2]^4)/27 - (4288*r^5*Log[2]^4)/243 + (9442*r*Log[r])/2187 - (1017379*r^2*Log[r])/4374
	- (5038*Pi^2*r^2*Log[r])/243 - (450929899*r^3*Log[r])/437400 - (8384*Pi^2*r^3*Log[r])/243 - (176403137*r^4*Log[r])/72900
	- (5651*Pi^2*r^4*Log[r])/243 - (1988905411*r^5*Log[r])/510300 + (30838*Pi^2*r^5*Log[r])/729 + (1345*r*Log[r]^2)/1458
	- (163811*r^2*Log[r]^2)/1458 - (1269332*r^3*Log[r]^2)/3645 - (2631067*r^4*Log[r]^2)/4860 - (12026329*r^5*Log[r]^2)/29160
	- (5038*r^2*Log[r]^3)/243 - (8384*r^3*Log[r]^3)/243 - (5651*r^4*Log[r]^3)/243 + (30838*r^5*Log[r]^3)/729
	- (1088*r^2*PolyLog[4, 1/2])/81 - (7936*r^3*PolyLog[4, 1/2])/81 - (2240*r^4*PolyLog[4, 1/2])/9
	- (34304*r^5*PolyLog[4, 1/2])/81 + (739*r*Zeta[3])/27 + (640*r^2*Zeta[3])/9 + (11788*r^3*Zeta[3])/81
	+ (16444*r^4*Zeta[3])/81 + (4144*r^5*Zeta[3])/27 + (308*r^2*Log[r]*Zeta[3])/9 + (592*r^3*Log[r]*Zeta[3])/9
	+ (272*r^4*Log[r]*Zeta[3])/3 + (880*r^5*Log[r]*Zeta[3])/9 ) ;

(* equation (30) in [1] *)
cH3dur0[8] = ( (-211327*r)/288 - (12575*Pi^2*r)/216 + (19*Pi^4*r)/9 - (1658933*r^2)/864
	- (4901*Pi^2*r^2)/24 + (1871*Pi^4*r^2)/270 - (60612743*r^3)/15552 - (34531*Pi^2*r^3)/72
	+ (6326*Pi^4*r^3)/405 - (54506788883*r^4)/8748000 - (26988989*Pi^2*r^4)/29160
	+ (8009*Pi^4*r^4)/270 - (333475905323*r^5)/34992000 - (51063637*Pi^2*r^5)/58320
	+ (6823*Pi^4*r^5)/135 + (56*Pi^2*r*Log[2]^2)/27 + (404*Pi^2*r^2*Log[2]^2)/27
	+ (400*Pi^2*r^3*Log[2]^2)/9 + (2636*Pi^2*r^4*Log[2]^2)/27 + (4904*Pi^2*r^5*Log[2]^2)/27
	- (56*r*Log[2]^4)/27 - (404*r^2*Log[2]^4)/27 - (400*r^3*Log[2]^4)/9 - (2636*r^4*Log[2]^4)/27
	- (4904*r^5*Log[2]^4)/27 - (732305*r*Log[r])/1296 - (1069*Pi^2*r*Log[r])/54
	- (394987*r^2*Log[r])/144 - (191*Pi^2*r^2*Log[r])/6 - (10483811*r^3*Log[r])/1296
	- (4393*Pi^2*r^3*Log[r])/108 - (3760061663*r^4*Log[r])/194400 + (13282*Pi^2*r^4*Log[r])/243
	- (8073505727*r^5*Log[r])/194400 + (243712*Pi^2*r^5*Log[r])/243 - (12575*r*Log[r]^2)/72
	- (4901*r^2*Log[r]^2)/8 - (34531*r^3*Log[r]^2)/24 - (26988989*r^4*Log[r]^2)/9720
	- (51063637*r^5*Log[r]^2)/19440 - (1069*r*Log[r]^3)/54 - (191*r^2*Log[r]^3)/6
	- (4393*r^3*Log[r]^3)/108 + (13282*r^4*Log[r]^3)/243 + (243712*r^5*Log[r]^3)/243
	- (448*r*PolyLog[4, 1/2])/9 - (3232*r^2*PolyLog[4, 1/2])/9 - (3200*r^3*PolyLog[4, 1/2])/3
	- (21088*r^4*PolyLog[4, 1/2])/9 - (39232*r^5*PolyLog[4, 1/2])/9 + (3779*r*Zeta[3])/24
	+ (26113*r^2*Zeta[3])/72 + (176131*r^3*Zeta[3])/216 + (843353*r^4*Zeta[3])/648
	- (688399*r^5*Zeta[3])/648 + (764*r*Log[r]*Zeta[3])/9 + (2150*r^2*Log[r]*Zeta[3])/9
	+ (4376*r^3*Log[r]*Zeta[3])/9 + (7730*r^4*Log[r]*Zeta[3])/9 + (12500*r^5*Log[r]*Zeta[3])/9 ) ;

(* equation (26) in [1] *)
cH3uur0[8] = ( (675233*r)/69984 + (1343*Pi^2*r)/5832 - (595840219*r^2)/1119744 - (2629925*Pi^2*r^2)/46656
	+ (6893*Pi^4*r^2)/3888 - (51577919389*r^3)/27993600 - (12124145*Pi^2*r^3)/46656
	+ (69781*Pi^4*r^3)/9720 - (60922946053*r^4)/13996800 - (726991*Pi^2*r^4)/972
	+ (40547*Pi^4*r^4)/2160 - (38586369054851*r^5)/4800902400 - (1429139171*Pi^2*r^5)/816480
	+ (38969*Pi^4*r^5)/972 + (253*Pi^2*r^2*Log[2]^2)/162 + (1009*Pi^2*r^3*Log[2]^2)/81
	+ (791*Pi^2*r^4*Log[2]^2)/18 + (9074*Pi^2*r^5*Log[2]^2)/81 - (253*r^2*Log[2]^4)/162
	- (1009*r^3*Log[2]^4)/81 - (791*r^4*Log[2]^4)/18 - (9074*r^5*Log[2]^4)/81
	+ (18883*r*Log[r])/5832 - (43166447*r^2*Log[r])/93312 - (29783*Pi^2*r^2*Log[r])/1296
	- (1277517793*r^3*Log[r])/466560 - (85951*Pi^2*r^3*Log[r])/1296 - (36720487*r^4*Log[r])/3888
	- (92939*Pi^2*r^4*Log[r])/648 - (483236767781*r^5*Log[r])/19051200
	- (220333*Pi^2*r^5*Log[r])/972 + (1343*r*Log[r]^2)/1944 - (2629925*r^2*Log[r]^2)/15552
	- (12124145*r^3*Log[r]^2)/15552 - (726991*r^4*Log[r]^2)/324 - (1429139171*r^5*Log[r]^2)/272160
	- (29783*r^2*Log[r]^3)/1296 - (85951*r^3*Log[r]^3)/1296 - (92939*r^4*Log[r]^3)/648
	- (220333*r^5*Log[r]^3)/972 - (1012*r^2*PolyLog[4, 1/2])/27 - (8072*r^3*PolyLog[4, 1/2])/27
	- (3164*r^4*PolyLog[4, 1/2])/3 - (72592*r^5*PolyLog[4, 1/2])/27 - (1339*r*Zeta[3])/144
	+ (3673*r^2*Zeta[3])/36 + (161513*r^3*Zeta[3])/432 + (222295*r^4*Zeta[3])/216
	+ (965759*r^5*Zeta[3])/432 + (433*r^2*Log[r]*Zeta[3])/6 + (787*r^3*Log[r]*Zeta[3])/3
	+ (1261*r^4*Log[r]*Zeta[3])/2 + 1258*r^5*Log[r]*Zeta[3] ) ;



(* r -> 1, MH >= mt, mu = mt  *)

(* equation (23) in [1] *)
cH3dur1m[7] = ( -341551/233280
	+ (142444807*ubar)/2332800
	- (1268318809*ubar^2)/108864000
	- (10161797509*ubar^3)/1097349120
	- (50054199662953*ubar^4)/49161240576000
	- (30558361039639*ubar^5)/36870930432000
	- (2345334590375537*ubar^6)/3244641878016000
	- (1402951540891649783*ubar^7)/2141463639490560000
	- (17860685977177410850673*ubar^8)/29398012842926407680000
	- (31216774492492157707889*ubar^9)/54596309565434757120000
	- (100834534952114244274394407*ubar^10)/185481862363637014855680000
	- (3477830304398932314252110263*ubar^11)/6677347045090932534804480000
	- (116714289769644239883794738847761*ubar^12)/232478514721885907131752775680000
	- (640782842699765165323208883562043*ubar^13)/1317378250090686807079932395520000
	- (1208589777331577294989743504823987243*ubar^14)/2553079048675751032120908982517760000
	- (142477425214746482828745996771426113*ubar^15)/307990488411677902287601718525952000
	- (1019736341022929318958490598403621219479*ubar^16)/2247098603451601975090342138365345792000
	+ (41075*Zeta[3])/3456
	- (5123249*ubar*Zeta[3])/103680
	+ (12863797*ubar^2*Zeta[3])/1244160
	+ (279252497*ubar^3*Zeta[3])/34836480
	+ (323209457*ubar^4*Zeta[3])/330301440
	+ (1593250823*ubar^5*Zeta[3])/2229534720
	+ (10003227043*ubar^6*Zeta[3])/17836277760
	+ (40369030787*ubar^7*Zeta[3])/87199580160
	+ (4270143343013*ubar^8*Zeta[3])/10762919608320
	+ (48974151637123*ubar^9*Zeta[3])/139917954908160
	+ (42330576802313*ubar^10*Zeta[3])/133938555125760
	+ (1215410268573835*ubar^11*Zeta[3])/4178882919923712
	+ (81378939166011247*ubar^12*Zeta[3])/299243084615516160
	+ (5681856619568691073*ubar^13*Zeta[3])/22044240566676357120
	+ (2514686477683520647*ubar^14*Zeta[3])/10174264876927549440
	+ (777938409039074273*ubar^15*Zeta[3])/3248924918682746880
	+ (551606956844739559733*ubar^16*Zeta[3])/2356553541017885736960 ) ; 

(* equation (19) in [1] *)
cH3uur1m[7] = ( -22842337/1166400 + (2092993999*ubar)/39191040
	- (865225948501*ubar^2)/18289152000
	+ (17765084205847*ubar^3)/1170505728000
	+ (23060519751481*ubar^4)/65548320768000
	+ (15146834307444139*ubar^5)/58403553804288000
	+ (246206693739199951*ubar^6)/1168071076085760000
	+ (1321247791446055147643*ubar^7)/7349503210731601920000
	+ (2955271009974545461333*ubar^8)/18872798368298434560000
	+ (76279148970390937314113827*ubar^9)/556445587090911044567040000
	+ (63720901886385872405419157*ubar^10)/534187763607274602784358400
	+ (2375152337378544614794089422749*ubar^11)/23247851472188590713175277568000
	+ (192269098602045175677978776306303*ubar^12)/2258362714441177383565598392320000
	+ (16492346240029297573106575020253319*ubar^13)/243150385588166764963896093573120000
	+ (17289881695712489316953196085317289*ubar^14)/345871671478354863531531341660160000
	+ (25532990001537193429825166303264497*ubar^15)/812282606800029632406861675233280000
	+ (118053091582139739700607684963938674709*ubar^16)/9831056390100758641020246855348387840000
	+ (899917*Zeta[3])/51840
	- (56016371*ubar*Zeta[3])/1244160
	+ (2724431963*ubar^2*Zeta[3])/69672960
	- (56875236793*ubar^3*Zeta[3])/4459069440
	- (13000037777*ubar^4*Zeta[3])/35672555520
	- (68046799*ubar^5*Zeta[3])/264241152
	- (314005890971*ubar^6*Zeta[3])/1569592442880
	- (617905546061*ubar^7*Zeta[3])/3767021862912
	- (77447594406313*ubar^8*Zeta[3])/559671819632640
	- (1850685520570171*ubar^9*Zeta[3])/15670810949713920
	- (841344474422761*ubar^10*Zeta[3])/8357765839847424
	- (164771804815671971*ubar^11*Zeta[3])/1945080050000855040
	- (18366125324181488219*ubar^12*Zeta[3])/264530886800116285440
	- (14367094538793465923*ubar^13*Zeta[3])/264530886800116285440
	- (10057792480765833071*ubar^14*Zeta[3])/257748043548831252480
	- (20606565075171854869*ubar^15*Zeta[3])/883707577881707151360
	- (130215677716585960859*ubar^16*Zeta[3])/18557859135515850178560 ) ;


(* equation (31) in [1] *)
cH3dur1m[8] = ( -4475339/77760
	+ (16077823*ubar)/388800
	+ (1961227291*ubar^2)/36288000
	- (182669607557*ubar^3)/5225472000
	- (978197515361*ubar^4)/2341011456000
	- (11251598841233*ubar^5)/49161240576000
	- (998923633913717*ubar^6)/8652378341376000
	- (242140503478140731*ubar^7)/5710569705308160000
	+ (28732170629802393947*ubar^8)/3919735045723521024000
	+ (21836243451098019153131*ubar^9)/509565555944057733120000
	+ (4290136131347157258039193*ubar^10)/61827287454545671618560000
	+ (401117529654797107970790701*ubar^11)/4451564696727288356536320000
	+ (637927997913831572686043344469*ubar^12)/5960987556971433516198789120000
	+ (440744289755914537933525536851*ubar^13)/3629141184822828669641687040000
	+ (914345863089596750571087051038082203*ubar^14)/6808210796468669418989090620047360000
	+ (163764839403086003645955858236963879*ubar^15)/1119965412406101462864006249185280000
	+ (118111255229392604613110752958654641613*ubar^16)/749032867817200658363447379455115264000
	+ (54571*Zeta[3])/1152
	- (144677*ubar*Zeta[3])/4320
	- (18422431*ubar^2*Zeta[3])/414720
	+ (1368551503*ubar^3*Zeta[3])/46448640
	+ (212894429*ubar^4*Zeta[3])/330301440
	+ (183674263*ubar^5*Zeta[3])/424673280
	+ (2030632153*ubar^6*Zeta[3])/6794772480
	+ (145045537093*ubar^7*Zeta[3])/697596641280
	+ (1021806393869*ubar^8*Zeta[3])/7175279738880
	+ (3470121255301*ubar^9*Zeta[3])/37311454642176
	+ (573122615539*ubar^10*Zeta[3])/10552734646272
	+ (64032916412407*ubar^11*Zeta[3])/2785921946615808
	- (582685651698373*ubar^12*Zeta[3])/185245719047700480
	- (5364838127801099*ubar^13*Zeta[3])/209945148254060544
	- (1228463269018338743*ubar^14*Zeta[3])/27131373005140131840
	- (546488329464973411*ubar^15*Zeta[3])/8663799783153991680
	- (62464802413509116983*ubar^16*Zeta[3])/785517847005961912320 ) ; 

(* equation (27) in [1] *)
cH3uur1m[8] = ( -10184003/1555200
	+ (920994491*ubar)/20412000
	- (5393419351*ubar^2)/95256000
	+ (975711240407*ubar^3)/55738368000
	+ (95100471101*ubar^4)/374561832960
	+ (14389675984771427*ubar^5)/77871405072384000
	+ (1308488106611424443*ubar^6)/8565854557962240000
	+ (681334961507200569347*ubar^7)/4899668807154401280000
	+ (7078536104003939357647*ubar^8)/52263133942980280320000
	+ (1967294021060859553599833*ubar^9)/14267835566433616527360000
	+ (366996679017406978794890443*ubar^10)/2543751255272736203735040000
	+ (5945373855027854480587932802351*ubar^11)/38746419120314317855292129280000
	+ (868005881834448259068053561908813*ubar^12)/5269513000362747228319729582080000
	+ (134442379553144848110758118715063003*ubar^13)/756467866274296602109898957783040000
	+ (4420617000920684623607197617219092879*ubar^14)/22996623134738616704140928316604416000
	+ (13918899608408719757686179264592472771*ubar^15)/66877934626535773068164944594206720000
	+ (70898459545299515656402878554435603563471*ubar^16)/314593804483224276512647899371148410880000
	+ (444857*Zeta[3])/69120
	- (3926893*ubar*Zeta[3])/103680
	+ (272479807*ubar^2*Zeta[3])/5806080
	- (622906981*ubar^3*Zeta[3])/42467328
	- (479903311*ubar^4*Zeta[3])/1698693120
	- (465069197*ubar^5*Zeta[3])/2264924160
	- (34758423745*ubar^6*Zeta[3])/209278992384
	- (1834069467289*ubar^7*Zeta[3])/12556739543040
	- (102129513797021*ubar^8*Zeta[3])/746229092843520
	- (701490192408749*ubar^9*Zeta[3])/5223603649904640
	- (1083332564482507*ubar^10*Zeta[3])/7959776990330880
	- (143657062046156297*ubar^11*Zeta[3])/1018851454762352640
	- (1867114275358119409*ubar^12*Zeta[3])/12596708895243632640
	- (55483170718248667363*ubar^13*Zeta[3])/352707849066821713920
	- (230897776946471029237*ubar^14*Zeta[3])/1374656232260433346560
	- (3119639607883112761*ubar^15*Zeta[3])/17327599566307983360
	- (38289404834703946447211*ubar^16*Zeta[3])/197950497445502401904640 ) ;



(* r -> 1, MH < mt, mu = mt  *)

(* equation (24) in [1] *)
cH3dur1p[7] = ( -341551/233280
	- (142444807*u)/2332800
	- (23747229407*u^2)/326592000
	- (2060338672331*u^3)/27433728000
	- (3404436524717161*u^4)/49161240576000
	- (510161538403817*u^5)/9217732608000
	- (36201056113172959*u^6)/1081547292672000
	- (7866025580826060097*u^7)/2141463639490560000
	+ (40007601558144896842759*u^8)/1175920513717056307200
	+ (30420314700154897994211247*u^9)/382174166958043299840000
	+ (4935392079648454270058044213*u^10)/37096372472727402971136000
	+ (1297727405862060158129804395423*u^11)/6677347045090932534804480000
	+ (4084002977571675938563055335995937*u^12)/15498567648125727142116851712000
	+ (149531377625972969156560617064315709*u^13)/439126083363562269026644131840000
	+ (177311074936202565870721931418254027*u^14)/416829232436857311366679017553920
	+ (287218476719551472877804996745426978997*u^15)/554382879141020224117683093346713600
	+ (110328491602704451446297256754475868775731*u^16)/178341159004095394848439852251217920000
	+ (41075*Zeta[3])/3456
	+ (5123249*u*Zeta[3])/103680
	+ (14868557*u^2*Zeta[3])/248832
	+ (240281311*u^3*Zeta[3])/3870720
	+ (34104347621*u^4*Zeta[3])/594542592
	+ (5113924453*u^5*Zeta[3])/111476736
	+ (494473257191*u^6*Zeta[3])/17836277760
	+ (36900029443*u^7*Zeta[3])/12457082880
	- (305427514622203*u^8*Zeta[3])/10762919608320
	- (1030400134191331*u^9*Zeta[3])/15546439434240
	- (38560501130154655*u^10*Zeta[3])/348240243326976
	- (307190230864791101*u^11*Zeta[3])/1899492236328960
	- (94769304438692045237*u^12*Zeta[3])/432240011111301120
	- (480417981707353184969*u^13*Zeta[3])/1695710812821258240
	- (514389923746996594637*u^14*Zeta[3])/1453466410989649920
	- (4761255330777562302781*u^15*Zeta[3])/11046344723521339392
	- (4756277326144986304693*u^16*Zeta[3])/9241386435364257792 ) ;

(* equation (20) in [1] *)
cH3uur1p[7] = ( -22842337/1166400
	- (2092993999*u)/39191040
	- (5525869444103*u^2)/54867456000
	- (22922971166093*u^3)/140460687360
	- (47294955764723101*u^4)/196644962304000
	- (19422291943029299503*u^5)/58403553804288000
	- (171039187096069624183*u^6)/389357025361920000
	- (4120734269198785007138051*u^7)/7349503210731601920000
	- (355026531244950833980300793*u^8)/509565555944057733120000
	- (31435506060829502746910411149*u^9)/37096372472727402971136000
	- (13524376139435234174710780497019*u^10)/13354694090181865069608960000
	- (2200487974647849458395039321325999*u^11)/1845067577157824659775815680000
	- (2436584036893018721351240229874764967*u^12)/1756504333454249076106576527360000
	- (1164450930428619262409033567024831199497*u^13)/729451156764500294891688280719360000
	- (3363463219746339343108642175197783031821*u^14)/1847942930470067413725610311155712000
	- (4610890924389119533341556314794405591627*u^15)/2239930824812202925728012498370560000
	- (17043305762896236433071354265132714937442773*u^16)/7373292292575568980765185141511290880000
	+ (899917*Zeta[3])/51840
	+ (56016371*u*Zeta[3])/1244160
	+ (651260971*u^2*Zeta[3])/7741440
	+ (202121733907*u^3*Zeta[3])/1486356480
	+ (476188968649*u^4*Zeta[3])/2378170368
	+ (9872935582357*u^5*Zeta[3])/35672555520
	+ (27320775160517*u^6*Zeta[3])/74742497280
	+ (1255237873400671*u^7*Zeta[3])/2690729902080
	+ (7209398902227043*u^8*Zeta[3])/12437151547392
	+ (81837214617410701*u^9*Zeta[3])/116080081108992
	+ (3200711388524595793*u^10*Zeta[3])/3798984472657920
	+ (71477699823216274457*u^11*Zeta[3])/72040001851883520
	+ (7827629718963804477323*u^12*Zeta[3])/6782843251285032960
	+ (45417653367264156361*u^13*Zeta[3])/34199209670344704
	+ (3716943201931867246939*u^14*Zeta[3])/2454743271893630976
	+ (100889939619724639441819*u^15*Zeta[3])/58913838525447143424
	+ (58310675611385886914609*u^16*Zeta[3])/30323299241038970880 ) ;

(* equation (32) in [1] *)
cH3dur1p[8] = ( -4475339/77760
	- (16077823*u)/388800
	+ (1381891433*u^2)/108864000
	+ (106283425249*u^3)/1045094400
	+ (527291338410463*u^4)/2341011456000
	+ (18835386860618813*u^5)/49161240576000
	+ (1659249617408808841*u^6)/2884126113792000
	+ (4578239566466278432931*u^7)/5710569705308160000
	+ (20820540175959196884886639*u^8)/19598675228617605120000
	+ (138315137182706625655523329*u^9)/101913111188811546624000
	+ (20851067320386655009040484329*u^10)/12365457490909134323712000
	+ (1303344868145632533977941018597*u^11)/635937813818184050933760000
	+ (63206610196586357347682253997058587*u^12)/25830946080209545236861419520000
	+ (421353150866226762744917680255075523*u^13)/146375361121187423008881377280000
	+ (3252789949299587159718898199938960786717*u^14)/972601542352667059855584374292480000
	+ (234854261062255638869516877282207997057*u^15)/61089022494878261610763977228288000
	+ (5466305976616020374395451952903463398568219*u^16)/1248388113028667763939078965758525440000
	+ (54571*Zeta[3])/1152
	+ (144677*u*Zeta[3])/4320
	- (4533439*u^2*Zeta[3])/414720
	- (437734327*u^3*Zeta[3])/5160960
	- (26545023823*u^4*Zeta[3])/141557760
	- (189559388905*u^5*Zeta[3])/594542592
	- (22767300693313*u^6*Zeta[3])/47563407360
	- (66471597646843*u^7*Zeta[3])/99656663040
	- (1268322931550399*u^8*Zeta[3])/1435055947776
	- (23404375547373377*u^9*Zeta[3])/20728585912320
	- (162839204757093563*u^10*Zeta[3])/116080081108992
	- (308441888893578959*u^11*Zeta[3])/180904022507520
	- (293294975214716208907*u^12*Zeta[3])/144080003703767040
	- (270717553391498682635*u^13*Zeta[3])/113047387521417216
	- (10783796417776167702113*u^14*Zeta[3])/3875910429305733120
	- (94210426870130963903341*u^15*Zeta[3])/29456919262723571712
	- (190759043833153082164009*u^16*Zeta[3])/52367856467064127488 ) ;

(* equation (28) in [1] *)
cH3uur1p[8] = ( -10184003/1555200
	- (920994491*u)/20412000
	- (29074180927*u^2)/285768000
	- (205852118110627*u^3)/1170505728000
	- (119165385988807*u^4)/445906944000
	- (29264204346957515891*u^5)/77871405072384000
	- (1431941732082266082509*u^6)/2855284852654080000
	- (3157033807695246877024691*u^7)/4899668807154401280000
	- (2802288140560876671525727*u^8)/3484208929532018688000
	- (103715366077903610299577687*u^9)/105687670862471233536000
	- (20931255769642901293673231400659*u^10)/17806258786909153426145280000
	- (1990079989061989304757208861982077*u^11)/1435052560011641402047856640000
	- (37826447881326487844152050138062011*u^12)/23420057779389987681421020364800
	- (1809618889897817475920921386836970941061*u^13)/972601542352667059855584374292480000
	- (20925232910744885359455879575644221923837*u^14)/9855695629173692873203254992830464000
	- (562435906125020361248077157079613639733243*u^15)/234072771192875205738577306079723520000
	- (849273201366933095648302829916633248510391169*u^16)/314593804483224276512647899371148410880000
	+ (444857*Zeta[3])/69120
	+ (3926893*u*Zeta[3])/103680
	+ (10941907*u^2*Zeta[3])/129024
	+ (72535781189*u^3*Zeta[3])/495452160
	+ (176291065297*u^4*Zeta[3])/792723456
	+ (14872040527937*u^5*Zeta[3])/47563407360
	+ (770013999151*u^6*Zeta[3])/1845493760
	+ (961583609378767*u^7*Zeta[3])/1793819934720
	+ (55478680447842859*u^8*Zeta[3])/82914343649280
	+ (3509910533614187*u^9*Zeta[3])/4299262263296
	+ (4953468973267359833*u^10*Zeta[3])/5065312630210560
	+ (27703462009436982311*u^11*Zeta[3])/24013333950627840
	+ (3037916662930036050103*u^12*Zeta[3])/2260947750428344320
	+ (5999331691405361969129*u^13*Zeta[3])/3875910429305733120
	+ (23124070131166316998379*u^14*Zeta[3])/13091964116766031872
	+ (19627468928096607606473*u^15*Zeta[3])/9818973087574523904
	+ (8716848547531576255624519*u^16*Zeta[3])/3881382302852988272640 ) ;



(* r -> infinity, mu = mt *)

(* equation (25) in [1] *)
cH3durinf[7] = ( 141788/945 - (8*B4)/3 + (4*D3)/3 - (959317*Pi^2)/51030 - (538*Pi^4)/3645
	+ 5427469961/(1180980*r^5) + (3848*B4)/(27*r^5) - (1924*D3)/(27*r^5)
	- (118484788*OepS2)/(295245*r^5) + (54743785919*Pi^2)/(41334300*r^5)
	+ (315545383*Pi^4)/(35429400*r^5) + 598067863/(314928*r^4) + (2168*B4)/(27*r^4) - (1084*D3)/(27*r^4)
	- (3235222*OepS2)/(19683*r^4) + (6574137083*Pi^2)/(11022480*r^4) + (11623793*Pi^4)/(4723920*r^4)
	+ 1371704/(2187*r^3) + (344*B4)/(9*r^3) - (172*D3)/(9*r^3) - (118814*OepS2)/(2187*r^3)
	+ (13662409*Pi^2)/(58320*r^3) + (40381*Pi^4)/(524880*r^3) + 99469/(486*r^2) + (344*B4)/(27*r^2)
	- (172*D3)/(27*r^2) - (3028*OepS2)/(243*r^2) + (2030239*Pi^2)/(29160*r^2) - (2285*Pi^4)/(5832*r^2)
	+ 21400913/(136080*r) + (8*B4)/(27*r) - (4*D3)/(27*r) - (38*OepS2)/(27*r) + (236477*Pi^2)/(136080*r)
	- (14383*Pi^4)/(58320*r) + (6663*S2)/70 + (27486237529*S2)/(1312200*r^5) + (55504361*S2)/(5832*r^4)
	+ (1238255*S2)/(324*r^3) + (3988*S2)/(3*r^2) + (57899*S2)/(140*r) + (59242394*T1ep)/(98415*r^5)
	+ (1617611*T1ep)/(6561*r^4) + (59407*T1ep)/(729*r^3) + (1514*T1ep)/(81*r^2) + (19*T1ep)/(9*r)
	- (41297605*Log[r])/(26244*r^5) - (163142*Pi^2*Log[r])/(3645*r^5) - (3757109*Log[r])/(8748*r^4)
	- (39725*Pi^2*Log[r])/(1458*r^4) - (11557*Log[r])/(324*r^3) - (21365*Pi^2*Log[r])/(1458*r^3)
	+ (16247*Log[r])/(486*r^2) - (1495*Pi^2*Log[r])/(243*r^2) + (1987*Log[r])/(162*r) - (163*Pi^2*Log[r])/(162*r)
	+ (29621197*S2*Log[r])/(3645*r^5) + (1617611*S2*Log[r])/(486*r^4) + (59407*S2*Log[r])/(54*r^3)
	+ (757*S2*Log[r])/(3*r^2) + (57*S2*Log[r])/(2*r) + (6572*Zeta[3])/243 - (494197567*Zeta[3])/(98415*r^5)
	- (35473265*Zeta[3])/(13122*r^4) - (1955389*Zeta[3])/(1458*r^3) - (140633*Zeta[3])/(243*r^2)
	- (9379*Zeta[3])/(54*r) ) ;

(* equation (21) in [1] *)
cH3uurinf[7] = ( -14758147/367416 + (124*B4)/81 - (62*D3)/81 + (1243481*Pi^2)/122472
	+ (185*Pi^4)/729 - 27856825919/(3149280*r^5) - (1744*B4)/(9*r^5) + (872*D3)/(9*r^5)
	+ (546103471*OepS2)/(885735*r^5) - (2084901614857*Pi^2)/(992023200*r^5)
	- (5148161149*Pi^4)/(425152800*r^5) - 11229480617/(3149280*r^4) - (7540*B4)/(81*r^4)
	+ (3770*D3)/(81*r^4) + (4344265*OepS2)/(19683*r^4) - (18516831397*Pi^2)/(22044960*r^4)
	- (3659663*Pi^4)/(1889568*r^4) - 1934929903/(1574640*r^3) - (2912*B4)/(81*r^3) + (1456*D3)/(81*r^3)
	+ (1204811*OepS2)/(19683*r^3) - (178231003*Pi^2)/(629856*r^3) + (9809263*Pi^4)/(9447840*r^3)
	- 204366253/(524880*r^2) - (76*B4)/(9*r^2) + (38*D3)/(9*r^2) + (290*OepS2)/(27*r^2) - (11817241*Pi^2)/(174960*r^2)
	+ (7661*Pi^4)/(6480*r^2) - 212243761/(1469664*r) + (80*B4)/(81*r) - (40*D3)/(81*r) + (47*OepS2)/(81*r)
	+ (119657*Pi^2)/(489888*r) + (15413*Pi^4)/(23328*r) - (5013*S2)/56 - (122725048463*S2)/(3936600*r^5)
	- (2203470119*S2)/(174960*r^4) - (14540233*S2)/(3240*r^3) - (765389*S2)/(540*r^2) - (23077*S2)/(56*r)
	- (546103471*T1ep)/(590490*r^5) - (4344265*T1ep)/(13122*r^4) - (1204811*T1ep)/(13122*r^3) - (145*T1ep)/(9*r^2)
	- (47*T1ep)/(54*r) + (201513655*Log[r])/(78732*r^5) + (101761*Pi^2*Log[r])/(1620*r^5) + (2990975*Log[r])/(4374*r^4)
	+ (30719*Pi^2*Log[r])/(972*r^4) + (522707*Log[r])/(5832*r^3) + (12743*Pi^2*Log[r])/(972*r^3)
	- (25667*Log[r])/(1458*r^2) + (593*Pi^2*Log[r])/(162*r^2) - (2407*Log[r])/(324*r) + (19*Pi^2*Log[r])/(108*r)
	- (546103471*S2*Log[r])/(43740*r^5) - (4344265*S2*Log[r])/(972*r^4) - (1204811*S2*Log[r])/(972*r^3)
	- (435*S2*Log[r])/(2*r^2) - (47*S2*Log[r])/(4*r) - (11542*Zeta[3])/243 + (11135269837*Zeta[3])/(1180980*r^5)
	+ (121778467*Zeta[3])/(26244*r^4) + (53621777*Zeta[3])/(26244*r^3) + (356021*Zeta[3])/(486*r^2)
	+ (141461*Zeta[3])/(972*r) ) ;

(* equation (33) in [1] *)
cH3durinf[8] = ( 2778187/30240 - 2*B4 + D3 - (356611*Pi^2)/34020 + (55*Pi^4)/486
	- 38473615657/(3149280*r^5) - (1688*B4)/(9*r^5) + (844*D3)/(9*r^5) + (36036736*OepS2)/(32805*r^5)
	- (62786900801*Pi^2)/(18370800*r^5) - (16386962*Pi^4)/(492075*r^5) - 4941833231/(1049760*r^4)
	- (842*B4)/(9*r^4) + (421*D3)/(9*r^4) + (2450327*OepS2)/(6561*r^4) - (109505017*Pi^2)/(91854*r^4)
	- (28921541*Pi^4)/(3149280*r^4) - 159734099/(116640*r^3) - (116*B4)/(3*r^3) + (58*D3)/(3*r^3)
	+ (66752*OepS2)/(729*r^3) - (171667*Pi^2)/(540*r^3) - (8629*Pi^4)/(10935*r^3) - 241511/(960*r^2)
	- (110*B4)/(9*r^2) + (55*D3)/(9*r^2) + (1879*OepS2)/(162*r^2) - (4442477*Pi^2)/(77760*r^2)
	+ (4645*Pi^4)/(5184*r^2) - 578281/(90720*r) - (32*B4)/(9*r) + (16*D3)/(9*r) - (426877*Pi^2)/(45360*r)
	+ (152*Pi^4)/(243*r) + (70299*S2)/280 - (17106060689*S2)/(437400*r^5) - (17849959*S2)/(1440*r^4)
	- (1344979*S2)/(540*r^3) + (6797*S2)/(80*r^2) + (197817*S2)/(560*r) - (18018368*T1ep)/(10935*r^5)
	- (2450327*T1ep)/(4374*r^4) - (33376*T1ep)/(243*r^3) - (1879*T1ep)/(108*r^2) + (5591201*Log[r])/(972*r^5)
	+ (63764*Pi^2*Log[r])/(1215*r^5) + (19125991*Log[r])/(11664*r^4) + (6358*Pi^2*Log[r])/(243*r^4)
	+ (12995*Log[r])/(48*r^3) + (9997*Pi^2*Log[r])/(972*r^3) + (2597*Log[r])/(1296*r^2) + (1559*Pi^2*Log[r])/(648*r^2)
	- (9009184*S2*Log[r])/(405*r^5) - (2450327*S2*Log[r])/(324*r^4) - (16688*S2*Log[r])/(9*r^3) - (1879*S2*Log[r])/(8*r^2)
	- (36925*Zeta[3])/648 + (714070349*Zeta[3])/(87480*r^5) + (56376187*Zeta[3])/(17496*r^4) + (2007193*Zeta[3])/(1944*r^3)
	+ (68585*Zeta[3])/(324*r^2) - (7847*Zeta[3])/(216*r) ) ;

(* equation (29) in [1] *)
cH3uurinf[8] = ( -112761457/2449440 + (203*B4)/108 - (203*D3)/216 + (836533*Pi^2)/102060
	- (2047*Pi^4)/19440 + 574498991309/(41990400*r^5) + (1381*B4)/(6*r^5) - (1381*D3)/(12*r^5)
	- (1899436931*OepS2)/(2361960*r^5) + (6582465573563*Pi^2)/(2645395200*r^5)
	+ (17310145049*Pi^4)/(1133740800*r^5) + 9698800789/(1866240*r^4) + (11335*B4)/(108*r^4)
	- (11335*D3)/(216*r^4) - (8557951*OepS2)/(34992*r^4) + (31814983087*Pi^2)/(39191040*r^4)
	+ (13790029*Pi^4)/(16796160*r^4) + 3465388063/(2099520*r^3) + (1127*B4)/(27*r^3)
	- (1127*D3)/(54*r^3) - (1401059*OepS2)/(26244*r^3) + (908762051*Pi^2)/(4199040*r^3)
	- (5771291*Pi^4)/(2519424*r^3) + 4051795607/(9797760*r^2) + (59*B4)/(4*r^2) - (59*D3)/(8*r^2)
	- (997*OepS2)/(162*r^2) + (161070269*Pi^2)/(3265920*r^2) - (134741*Pi^4)/(77760*r^2) + 22588795/(489888*r)
	+ (287*B4)/(54*r) - (287*D3)/(108*r) + (4844705*Pi^2)/(326592*r) - (6931*Pi^4)/(9720*r) - (170451*S2)/1120
	+ (639474719981*S2)/(20995200*r^5) + (2666174039*S2)/(311040*r^4) + (315161*S2)/(240*r^3) - (12478841*S2)/(40320*r^2)
	- (155625*S2)/(448*r) + (1899436931*T1ep)/(1574640*r^5) + (8557951*T1ep)/(23328*r^4) + (1401059*T1ep)/(17496*r^3)
	+ (997*T1ep)/(108*r^2) - (4230081307*Log[r])/(1049760*r^5) - (224177*Pi^2*Log[r])/(4320*r^5)
	- (11599679*Log[r])/(11664*r^4) - (35617*Pi^2*Log[r])/(1728*r^4) - (1121263*Log[r])/(7776*r^3)
	- (7717*Pi^2*Log[r])/(1296*r^3) - (1981*Log[r])/(486*r^2) - (61*Pi^2*Log[r])/(72*r^2)
	+ (1899436931*S2*Log[r])/(116640*r^5) + (8557951*S2*Log[r])/(1728*r^4) + (1401059*S2*Log[r])/(1296*r^3)
	+ (997*S2*Log[r])/(8*r^2) + (1198*Zeta[3])/81 - (29498529179*Zeta[3])/(3149280*r^5) - (178444285*Zeta[3])/(46656*r^4)
	- (5835145*Zeta[3])/(4374*r^3) - (111907*Zeta[3])/(324*r^2) - (39329*Zeta[3])/(1296*r) ) ;



(* equation (34) in [1] *)
cH[3,7] = ( Ad * AuC * Piecewise[ { { cH3duL[7] + cH3dur0[7], r < 0.16 },
			{ cH3duL[7] + cH3dur1m[7]/.{ubar -> 1 - r}, 0.16 <= r < 1 },
			{( (-45989*Log[mu^2/mt^2])/2430 + (7207*Log[mu^2/mt^2]^2)/810
				- 341551/233280 + (41075*Zeta[3])/3456 ), r == 1 },
			{ cH3duL[7] + cH3dur1p[7]/.{u -> 1 - 1/r}, 1 < r < 10.5 },
			{ cH3duL[7] + cH3durinf[7], 10.5 <= r } } ]
	+ Au * AuC * Piecewise[ { { cH3uuL[7] + cH3uur0[7], r < 0.097 },
			{ cH3uuL[7] + cH3uur1m[7]/.{ubar -> 1 - r}, 0.097 <= r < 1 },
			{( (30049*Log[mu^2/mt^2])/48600 - (3667*Log[mu^2/mt^2]^2)/1620
				- 22842337/1166400 + (899917*Zeta[3])/51840 ) , r == 1},
			{ cH3uuL[7] + cH3uur1p[7]/.{u -> 1 - 1/r}, 1 < r < 10.5 },
			{ cH3uuL[7] + cH3uurinf[7], 10.5 <= r } } ] ) ;



(* equation (35) in [1] *)
cH[3,8] = ( Ad * AuC * Piecewise[ { { cH3duL[8] + cH3dur0[8], r < 0.097 },
			{ cH3duL[8] + cH3dur1m[8]/.{ubar -> 1 - r}, 0.097 <= r < 1 },
			{( (-8959*Log[mu^2/mt^2])/3240 + (1009*Log[mu^2/mt^2]^2)/135
				-4475339/77760 + (54571*Zeta[3])/1152 ), r == 1 },
			{ cH3duL[8] + cH3dur1p[8]/.{u -> 1 - 1/r}, 1 < r < 10.5 },
			{ cH3duL[8] + cH3durinf[8], 10.5 <= r } } ]
	+ Au * AuC * Piecewise[ { { cH3uuL[8] + cH3uur0[8], r < 0.073 },
			{ cH3uuL[8] + cH3uur1m[8]/.{ubar -> 1 - r}, 0.073 <= r < 1 },
			{( (-45139*Log[mu^2/mt^2])/64800 - (2567*Log[mu^2/mt^2]^2)/2160
				-10184003/1555200 + (444857*Zeta[3])/69120 ) , r == 1},
			{ cH3uuL[8] + cH3uur1p[8]/.{u -> 1 - 1/r}, 1 < r < 10.5 },
			{ cH3uuL[8] + cH3uurinf[8], 10.5 <= r } } ] ) ;


cHeff[2,7] = ( cH[3,7] - 1/3*cH[2,3] - 4/9*cH[2,4] - 20/3*cH[2,5] - 80/9*cH[2,6] ) ;
cHeff[2,8] = ( cH[3,8]  + cH[2,3] - 1/6*cH[2,4] + 20*cH[2,5] - 10/3*cH[2,6] ) ;
