(* ::Package:: *)

(*******************************************************************************************************************************************)

(************* Perturbative results for the coefficient X defined in Eq. (1) *************)

(* Definitions: *)
(* a5, a6 = (alpha_s (mu)/(4*Pi)) with 5,6 flavors *)
(* LmuMW = Log[mu^2/MW^2], Lmumb = Log[mu^2/mb^2], Lmumc = Log[mu^2/mc^2] *)
(* mc, mb = mc (mu), mb (mu) *)
(* zx = Zeta[x] *)


(* Non-anomalous diagrams *)

XNApert = mc^2/MW^2*1/(32*a5)*(8*a5*(3 - Lmumc + LmuMW) + (32*a5^2*(29 + Lmumc + 23*LmuMW - 6*Lmumc*LmuMW + 6*LmuMW^2 + 12*z2))/3 - 
 (8*a5^3*(-39265 + 72*B4 - 72*Lmumb^2 + 1773*Lmumc - 270*Lmumc^2 - 324*Lmumc^3 + 48*Lmumb*(5 + 3*Lmumc) - 30225*LmuMW + 2868*Lmumc*LmuMW + 
    972*Lmumc^2*LmuMW - 10302*LmuMW^2 + 720*Lmumc*LmuMW^2 - 1368*LmuMW^3 - 20604*z2 + 1440*Lmumc*z2 - 8208*LmuMW*z2 + 7560*z3 - 
    2808*Lmumc*z3 + 2808*LmuMW*z3 + 5616*z4))/27);


(* Anomalous top diagrams *)

XAtpert = mc^2/MW^2*1/(32*a6)*(16*a6^3*(-1 + 4*Lmumt)*(-1 + Lmumc - LmuMW));


(*Anomalous bottom diagrams *)

XAbpert = mc^2/MW^2*1/(32*a6)*((16*a6^3*(36 + 6*Lmumb^2 + 3*Lmumc - 12*Lmumb*Lmumc + 9*LmuMW + 6*LmuMW^2 + 2*Pi^2))/3);


(* Anomalous phi boson diagrams *)

XAphipert = mc^2/MW^2*1/(32*a6)*((-4*a6^3*(75 + 6*Lmumt^2 + 36*LmuMW + 6*LmuMW^2 - 12*Lmumt*(3 + LmuMW) + 2*Pi^2))/3);



(*******************************************************************************************************************************************)

(************* RG-improved results for the coefficient X defined in Eq. (1) *************)

(* Definitions: *)
(* mu = mu_W *)
(* a6mut, a5mu, a5mub, a4muc = (alpha_s (mu_t,mu_W,mu_b,mu_c)/(4*Pi)) with 6,5,4 flavors *)
(* Lmutmt = Log[mu_t^2/mt^2], LmuMW = Log[mu_W^2/MW^2], Lmubmb = Log[mu_b^2/mb^2], Lmucmc = Log[mu_c^2/mc^2] *)
(* mc, mb, mt = mc (mc), mb (mb), mt (mt) *)
(* x = order parameter that counts the powers of a *)

(* Kc = (a4muc/a4mc) *)
(* Ln = (a4muc/a4mub)^(n/25) *)
(* iLn = (a4muc/a4mub)^(-n/25) *)
(* Mn = (a5mub/a5mu)^(n/23) *)
(* iMn = (a5mub/a5mu)^(-n/23) *)



(* Non-anomalous diagrams *)

XNAres = mc^2/MW^2*1/(32*a4muc)*(Kc^(24/25)*((48*iL6*iM6)/7 + L1*((-744*iM1)/65 + (96*iM6)/35 - (48*M12)/143) + (24*L12*M12)/11 + 
  (a5mub*((-2609808*iL6*iM6)/2314375 + L1*((317527296*iM1)/21490625 - (598688792*iM6)/34715625 + 
        Lmubmb*((496*iM1)/65 - (32*iM6)/5 - (16*M12)/13) - (212453104*M12)/141838125) + (3769008*L12*M12)/3636875) + 
    a4muc*((-966244*iL6*iM6)/13125 - (57302*L12*M12)/6875 + L1*((3772576*iM1)/40625 - (486784*iM6)/21875 + (243392*M12)/89375) + 
      Lmucmc*(-16*iL6*iM6 + 8*L12*M12)) + a5mu*((51784*iL6*iM6)/3703 - (74968*L12*M12)/5819 + LmuMW*((96*iL6*iM6)/7 - (96*L12*M12)/11) + 
      L1*((2888594*iM1)/103155 + (103568*iM6)/18515 + (149936*M12)/75647 + LmuMW*((-248*iM1)/65 + (192*iM6)/35 + (192*M12)/143))))*x + 
  x^2*(a4muc*a5mub*((52535652524*iL6*iM6)/4339453125 - (8998820684*L12*M12)/2273046875 + 
      Lmucmc*((869936*iL6*iM6)/330625 + (1256336*L12*M12)/330625) + L1*((-1610075075584*iM1)/13431640625 + (9107253903904*iM6)/65091796875 + 
        (3231836618048*M12)/265946484375 + Lmubmb*((-7545152*iM1)/121875 + (486784*iM6)/9375 + (243392*M12)/24375))) + 
    a5mu*(a4muc*((-3127248706*iL6*iM6)/20829375 + L1*((-43941291928*iM1)/193415625 - (1575476416*iM6)/34715625 + 
          LmuMW*((3772576*iM1)/121875 - (973568*iM6)/21875 - (973568*M12)/89375) - (2280826432*M12)/141838125) + 
        (536977042*L12*M12)/10910625 + LmuMW*((-1932488*iL6*iM6)/13125 + (229208*L12*M12)/6875) + 
        Lmucmc*((-51784*iL6*iM6)/1587 - (74968*L12*M12)/1587 + LmuMW*(-32*iL6*iM6 - 32*L12*M12))) + 
      a5mub*((-2815547864*iL6*iM6)/1224304375 - (11773124656*L12*M12)/1923906875 + 
        LmuMW*((-5219616*iL6*iM6)/2314375 - (15076032*L12*M12)/3636875) + L1*((-1232805701696*iM1)/34105621875 - 
          (1937656275308*iM6)/55093696875 + (1990898037584*M12)/225097104375 + Lmubmb*((-5777188*iM1)/309465 - (103568*iM6)/7935 + 
            (149936*M12)/20631) + LmuMW*((105842432*iM1)/21490625 - (1197377584*iM6)/34715625 + (849812416*M12)/141838125 + 
            Lmubmb*((496*iM1)/195 - (64*iM6)/5 + (64*M12)/13))))) + a5mu^2*((4547225582*iL6*iM6)/17629983 - (4408255988*L12*M12)/27704259 + 
      LmuMW*((2270120*iL6*iM6)/11109 - (1593032*L12*M12)/17457) + LmuMW^2*((464*iL6*iM6)/7 - 16*L12*M12) + (928*iL6*iM6*z2)/7 - 
      32*L12*M12*z2 - (33792*iL6*iM6*z3)/161 + (21696*L12*M12*z3)/253 + L1*((186258655106476*iM1)/396007196715 + (9094451164*iM6)/88149915 + 
        (8816511976*M12)/360155367 + LmuMW^2*((-992*iM1)/65 + (928*iM6)/35 + (32*M12)/13) + 
        LmuMW*((4224752*iM1)/20631 + (908048*iM6)/11109 + (3186064*M12)/226941) - (1984*iM1*z2)/65 + (1856*iM6*z2)/35 + (64*M12*z2)/13 + 
        (11292096*iM1*z3)/61295 - (67584*iM6*z3)/805 - (43392*M12*z3)/3289)) + 
    a4muc^2*((-154908593762*iL6*iM6)/1058203125 - (92425094048*L12*M12)/2358984375 + Lmucmc^2*(-48*iL6*iM6 + 48*L12*M12) + 
      Lmucmc*((1052824*iL6*iM6)/4375 + (409032*L12*M12)/6875 - (3416512*iL6*iM6*nc)/13125 - (68896*L12*M12*nc)/1875) + 
      (41472*iL6*iM6*z3)/175 + (497664*L12*M12*z3)/16775 + L1*((67642386632*iM1)/228515625 - (8728049888*iM6)/123046875 + 
        (4364024944*M12)/502734375 + Lmucmc*((-30180608*iM1)/121875 + (3894272*iM6)/65625 - (1947136*M12)/268125 + (41498336*iM1*nc)/121875 - 
          (5354624*iM6*nc)/65625 + (243392*M12*nc)/24375) - (95232*iM1*z3)/325 + (12288*iM6*z3)/175 - (6144*M12*z3)/715)) + 
    a5mub^2*((-131103395957144*iL6*iM6)/6886712109375 + (145141698310112*L12*M12)/10821976171875 + 
      Lmubmb*((29168*iL6*iM6)/4375 - (12368*L12*M12)/6875) + Lmubmb^2*((-32*iL6*iM6)/7 + (32*L12*M12)/11) + (111744*iL6*iM6*z3)/4025 - 
      (87552*L12*M12*z3)/6325 + L1*((8979765189244912*iM1)/63948041015625 - (7571838885537535304*iM6)/60706367244140625 + 
        Lmubmb^2*((992*iM1)/39 - (352*iM6)/21 - (3008*M12)/429) - (12963405793382801804*M12)/506327799153515625 + 
        Lmubmb*((1259000272*iM1)/21490625 - (5396295872*iM6)/104146875 - (3800287936*M12)/425514375 + (43648*iM1*nc)/1495 - 
          (2816*iM6*nc)/115 - (1408*M12*nc)/299) - (785664*iM1*z3)/7475 + (11452416*iM6*z3)/165025 + (23665152*M12*z3)/1003145)))));
          
          
          
(* Anomalous top diagrams *)

XAtres = mc^2/MW^2*1/(32*a4muc)*Kc^(24/25)*a6mut^2*(2-8*Lmutmt)*((48*iL6*iM6)/7 + L1*((-744*iM1)/65 + (96*iM6)/35 - (48*M12)/143) + (24*L12*M12)/11);
  


(* Anomalous bottom diagrams *)

(* XAbres = XAb5res + XAbSres *)


(* Contribution from A^b(mu_W)^(5) *)

XAb5res = mc^2/MW^2*1/(32*a4muc)*(Kc^(24/25)*((a5mu*((-1152*iL6*iM6)/161 + L1*((912*iM1)/65 - (2304*iM6)/805 + (1152*M12)/3289) - (576*L12*M12)/253) + 
    a5mub*((1152*iL6*iM6)/161 + L1*((-1600*iM6)/161 - (400*M12)/253) + (576*L12*M12)/253))*x + 
  (a4muc*a5mub*((-6654752*iL6*iM6)/100625 - (1797648*L12*M12)/158125 + L1*((973568*iM6)/12075 + (243392*M12)/18975) + 
      Lmucmc*((-384*iL6*iM6)/23 + (192*L12*M12)/23)) + a5mub^2*((1519543808*iL6*iM6)/53230625 + 
      L1*((-3691289184*iM6)/87298225 + Lmubmb*((-25600*iM6)/483 - (13600*M12)/759) - (287431504*M12)/197409575) + 
      (881545792*L12*M12)/83648125 + Lmubmb*((384*iL6*iM6)/7 + (192*L12*M12)/11)) + 
    a5mu^2*((-5781728*iL6*iM6)/85169 - (2304*iL6*iM6*LmuMW)/161 - (470224*L12*M12)/133837 + (2304*L12*LmuMW*M12)/253 + 
      L1*((9464071312*iM1)/83177315 - (11563456*iM6)/425845 + (1344*iM1*LmuMW)/65 - (4608*iM6*LmuMW)/805 + 
        (940448*M12)/1739881 - (4608*LmuMW*M12)/3289)) + 
    a5mu*(a4muc*((6654752*iL6*iM6)/100625 + L1*((-4624448*iM1)/40625 + (11682816*iM6)/503125 - (5841408*M12)/2055625) + 
        (1797648*L12*M12)/158125 + Lmucmc*((384*iL6*iM6)/23 - (192*L12*M12)/23)) + 
      a5mub*((194859456*iL6*iM6)/7604375 + (2304*iL6*iM6*LmuMW)/161 - (952665792*L12*M12)/83648125 - 
        (2304*L12*LmuMW*M12)/253 + L1*((-389227008*iM1)/21490625 - (1820509856*iM6)/114065625 - (3200*iM6*LmuMW)/161 + 
          (28450384496*M12)/3262276875 + (1600*LmuMW*M12)/253 + Lmubmb*((-608*iM1)/65 + (768*iM6)/115 + 
            (384*M12)/299)))))*x^2));
          
          
          
(* Contribution from A^S(mu_W)^(5) *)

XAbSres = mc^2/MW^2*1/(32*a4muc)*(Kc^(24/25)*((a5mu - a5mut)*((1152*iL6*iM6)/161 - (17856*iM1*L1)/1495 + (2304*iM6*L1)/805 - (1152*L1*M12)/3289 + (576*L12*M12)/253)*x + 
  (a5mu - a5mut)*((28192*a5mut*iL6*iM6)/529 - (3058832*a5mut*iM1*L1)/34385 + (56384*a5mut*iM6*L1)/2645 - (197344*a5mut*L1*M12)/75647 + 
    (98672*a5mut*L12*M12)/5819 + a5mub*((-587256192*iL6*iM6)/53230625 + (7620655104*iM1*L1)/494284375 - (1146310336*iM6*L1)/266153125 + 
      (11904*iM1*L1*Lmubmb)/1495 - (768*iM6*L1*Lmubmb)/115 + (668455168*L1*M12)/1087425625 - (171854208*L12*M12)/83648125 - 
      (384*L1*Lmubmb*M12)/299) + a4muc*((-6654752*iL6*iM6)/100625 + (90541824*iM1*L1)/934375 - (11682816*iM6*L1)/503125 - 
      (384*iL6*iM6*Lmucmc)/23 + (5841408*L1*M12)/2055625 - (1797648*L12*M12)/158125 + (192*L12*Lmucmc*M12)/23) + 
    a5mu*((5781728*iL6*iM6)/85169 - (69059424*iM1*L1)/790855 + (11563456*iM6*L1)/425845 + (2304*iL6*iM6*LmuMW)/161 - 
      (5952*iM1*L1*LmuMW)/1495 + (4608*iM6*L1*LmuMW)/805 - (940448*L1*M12)/1739881 + (470224*L12*M12)/133837 + (4608*L1*LmuMW*M12)/3289 - 
      (2304*L12*LmuMW*M12)/253))*x^2));
      



(*******************************************************************************************************************************************)

(************* Decoupling coefficients *************)

(* a = alpha_s (mu)/(4*Pi) *)
(* Lmutmt = Log[mu_t^2/mt^2], LmuMW = Log[mu_W^2/MW^2], Lmubmb = Log[mu_b^2/mb^2], Lmucmc = Log[mu_c^2/mc^2] *)


(* C^{NA}_ {nu} *)

CNAnu = (8*a*(2 + LmuMW) + (2*a^2*(-1 + nc^2)*(33 + 34*LmuMW + 12*LmuMW^2 + 24*z2))/nc + 
 (a^3*(-1 + nc^2)*(100*LmuMW^2*(-117 + 652*nc^2 - 64*nc*nf) + 600*LmuMW^3*(-9 + 17*nc^2 - 2*nc*nf) + 
    25*LmuMW*(-4*nc*nf*(161 + 72*z2) + nc^2*(7313 + 2448*z2 - 864*z3) - 3*(859 + 432*z2 - 720*z3)) - 400*nc*nf*(49 + 32*z2 - 12*z3) + 
    nc^2*(232331 + 130400*z2 - 61800*z3 - 10800*z4) + 8*(-11524 - 2925*z2 + 6975*z3 + 3375*z4)))/(150*nc^2));


(* C_ {+} *)

Cp = (1 + a*(11/3 + 2*LmuMW) + a^2*(21709/1800 + LmuMW^2*(13 - (2*nf)/3) - (5*LmuMW*(-159 + 8*nf))/18 + 26*z2 - (nf*(55 + 24*z2))/18));


(* C_ {-} *)

Cm = (1 + a*(-22/3 - 4*LmuMW) + a^2*(-92443/900 + LmuMW^2*(-14 + (4*nf)/3) + (5*LmuMW*(-105 + 8*nf))/9 - 28*z2 + (nf*(55 + 24*z2))/9));
   

(* B_ {nu} *)

Bnu = (1 - (2*a*Lmubmb)/3 - (2*a^2*(56 + 39*Lmubmb + 30*Lmubmb^2))/27);


(* B_ {+} *)

Bp = (1 + (a^2*(-59 - 12*Lmubmb - 36*Lmubmb^2))/54);


(* B_ {-} *)

Bm = (1 + (a^2*(59 + 12*Lmubmb + 36*Lmubmb^2))/27);


(* B^{NA}_ {+,nu} *)

BNApnu = ((8*a^3*(-1279 + 783*Lmubmb - 288*Lmubmb^2 + 36*Lmubmb^3 + 288*z3))/27);


(* B^{NA}_ {-,nu} *)

BNAmnu = ((-8*a^3*(-1231 + 723*Lmubmb - 288*Lmubmb^2 + 36*Lmubmb^3 + 288*z3))/27);


(* C^{NA}_ {+,nu} *)

CNApnu = (-16*a*(-1 + Lmucmc) + a^2*(44 + 80 Lmucmc - 48 Lmucmc^2));


(* C^{NA}_ {-,nu} *)

CNAmnu = (8*a*(-1 + Lmucmc) + a^2*(-28 + 48 Lmucmc + 48 Lmucmc^2));


(* C_ {t} *)

Ct = (-2*a^2*(-1 + 4*Lmutmt));


(* C^{S}_ {nu} *)

CSnu = (-a*8*(3 + LmuMW));


(* C^{S}_ {+,nu} *)

CSpnu = (16*a*(2 + Lmucmc) + a^2*(-(524/3) - 80*Lmucmc + 48*Lmucmc^2));


(* C^{S}_ {-,nu} *)

CSmnu = (-8*a*(2 + Lmucmc) - 4/3*a^2*(17 + 36*Lmucmc + 36*Lmucmc^2));


(* C^b_{nu} *)

Cbnu = (a^3*8/3*( 55 + 18*LmuMW + 12*LmuMW^2+ 4*\[Pi]^2));


(* C_b *)

Cb = (-2*a^2*(-1 + 4*Lmubmb));


(* B^{b}_ {+,nu} *)

Bbpnu = (a^3*(-(368/3) - 64*Lmubmb - 64*Lmubmb^2));


(* B^{b}_ {-,nu} *)

Bbmnu = (a^3*(328/3 - 64*Lmubmb + 32*Lmubmb^2));


(* B^{(c+u)}_ {+,nu} *)

Bcupnu = (a^3*(-8/9)*(12*Lmubmb^3 + 12*Lmubmb^2 + 107*Lmubmb + 96*z3 - 3616/27));


(* B^{(c+u)}_ {-,nu} *)

Bcumnu = (a^3*(8/9)*(12*Lmubmb^3 + 12*Lmubmb^2 + 95*Lmubmb + 96*z3 - 3020/27));




(*******************************************************************************************************************************************)

(************* Anomalous dimensions *************)

(* g = a*g0 + a^2*g1 + a^3*g2 *)
(* a = alpha_s/(4*Pi) *)
(* zx = Zeta[x] *)


(* g_ {nu} *)

gnu0 = (3 - (2*nf)/3);
gnu1 = -(2/9)*(147 + 37*nf);
gnu2 = 1/162*(-173259 - 18705*nf + 1535*nf^2 + 17280*nf*z3);


(* g_ {+} *)

gp0 = -2;
gp1 = (7/2 - (2*nf)/9);
gp2 = (-7432209 + 317346*nf + 13000*nf^2 + 2721600*z3 + 216000*nf*z3)/8100;


(* g_ {-} *)

gm0 = 4;
gm1 = (7 + (4*nf)/9);
gm2 =  (-996057 + 188058*nf - 13000*nf^2 - 1360800*z3 - 216000*nf*z3)/4050;


(* g^{NA}_ {+,nu} *)

gNApnd0 = -16;
gNApnd1 = -144;
gNApnd2 = -(1060082/225 - 144*nf - 896*z3);


(* g^{NA}_ {-,nu} *)

gNAmnd0 = 8;
gNAmnd1 = 208;
gNAmnd2 = -(-(879586/225) + 144*nf + 64*z3);


(* g^{S} *)

gS0 = 0;
gS1 = -8*nf;
gS2 = (-((340*nf)/3) - (8*nf^2)/9);


(* g^{S}_ {+,nu} *)

gSpnd0 = 16;
gSpnd1 = (-144);
gSpnd2 = (800/9*nf + 67682/225  - 896*z3);


(* g^{S}_ {-,nu} *)

gSmnd0 = (-8);
gSmnd1 = 80;
gSmnd2 = (560/9*nf + 147614/225  + 64*z3);


(* g^{NS}_ {+,nu} *)

gNSpnd0 = -16;
gNSpnd1 = 144;
gNSpnd2 = -(67682/225) + (64*nf)/9 + 896*z3;



(* g^{NS}_ {-,nu} *)

gNSmnd0 = 8;
gNSmnd1 = -80;
gNSmnd2 = -(147614/225 + (128*nf)/9 + 64*z3);


(*******************************************************************************************************************************************)

