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calculate 3L MSSM beta-function of BMu parameter
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Alexander Voigt authored and Alexander Voigt committed Dec 3, 2015
1 parent feb9583 commit 4d73d25
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242 changes: 242 additions & 0 deletions meta/ThreeLoopMSSM/beta_BMu.m
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{6*Mu*trace[Adj[Yb], hb] + 2*Mu*trace[Adj[Ye], he] +
(6*Mu*(g1^2*M1 + 5*g2^2*M2 + 5*trace[Adj[Yt], ht]))/5 +
BMu*((-3*g1^2)/5 - 3*g2^2 + 3*trace[Adj[Yb], Yb] + trace[Adj[Ye], Ye] +
3*trace[Adj[Yt], Yt]),
(-2*Mu*(207*g1^4*M1 + 45*g1^2*g2^2*M1 + 45*g1^2*g2^2*M2 + 375*g2^4*M2 +
10*(g1^2 - 40*g3^2)*trace[Adj[Yb], hb] - 10*(g1^2*M1 - 40*g3^2*M3)*
trace[Adj[Yb], Yb] - 30*g1^2*trace[Adj[Ye], he] +
30*g1^2*M1*trace[Adj[Ye], Ye] - 20*g1^2*trace[Adj[Yt], ht] -
400*g3^2*trace[Adj[Yt], ht] + 20*g1^2*M1*trace[Adj[Yt], Yt] +
400*g3^2*M3*trace[Adj[Yt], Yt] + 225*trace[Adj[Yb], hb, Adj[Yb], Yb] +
225*trace[Adj[Yb], Yb, Adj[Yb], hb] +
75*trace[Adj[Ye], he, Adj[Ye], Ye] +
75*trace[Adj[Ye], Ye, Adj[Ye], he] +
150*trace[Adj[Yt], ht, Adj[Yb], Yb] +
225*trace[Adj[Yt], ht, Adj[Yt], Yt] +
150*trace[Adj[Yt], Yt, Adj[Yb], hb] +
225*trace[Adj[Yt], Yt, Adj[Yt], ht]))/25 +
BMu*((207*g1^4)/50 + (9*g1^2*g2^2)/5 + (15*g2^4)/2 -
(2*g1^2*trace[Adj[Yb], Yb])/5 + 16*g3^2*trace[Adj[Yb], Yb] +
(6*g1^2*trace[Adj[Ye], Ye])/5 + (4*g1^2*trace[Adj[Yt], Yt])/5 +
16*g3^2*trace[Adj[Yt], Yt] - 9*trace[Adj[Yb], Yb, Adj[Yb], Yb] -
3*trace[Adj[Ye], Ye, Adj[Ye], Ye] - 6*trace[Adj[Yt], Yt, Adj[Yb], Yb] -
9*trace[Adj[Yt], Yt, Adj[Yt], Yt]),
BMu*((-1001*g1^4*trace[Adj[Yb], Yb])/60 - (3*g1^2*g2^2*trace[Adj[Yb], Yb])/
10 - (315*g2^4*trace[Adj[Yb], Yb])/4 -
(284*g1^2*g3^2*trace[Adj[Yb], Yb])/15 - 132*g2^2*g3^2*
trace[Adj[Yb], Yb] - (160*g3^4*trace[Adj[Yb], Yb])/3 -
(657*g1^4*trace[Adj[Ye], Ye])/20 - (81*g1^2*g2^2*trace[Adj[Ye], Ye])/10 -
(105*g2^4*trace[Adj[Ye], Ye])/4 - (2357*g1^4*trace[Adj[Yt], Yt])/60 -
(57*g1^2*g2^2*trace[Adj[Yt], Yt])/10 - (315*g2^4*trace[Adj[Yt], Yt])/4 -
(124*g1^2*g3^2*trace[Adj[Yt], Yt])/3 - 132*g2^2*g3^2*trace[Adj[Yt], Yt] -
(160*g3^4*trace[Adj[Yt], Yt])/3 + 3*g1^2*trace[Adj[Yb], Yb, Adj[Yb],
Yb] + 9*g2^2*trace[Adj[Yb], Yb, Adj[Yb], Yb] +
72*g3^2*trace[Adj[Yb], Yb, Adj[Yb], Yb] + 54*trace[Adj[Yb], Yb]*
trace[Adj[Yb], Yb, Adj[Yb], Yb] + 18*trace[Adj[Ye], Ye]*
trace[Adj[Yb], Yb, Adj[Yb], Yb] + 9*g1^2*trace[Adj[Ye], Ye, Adj[Ye],
Ye] + 3*g2^2*trace[Adj[Ye], Ye, Adj[Ye], Ye] +
18*trace[Adj[Yb], Yb]*trace[Adj[Ye], Ye, Adj[Ye], Ye] +
6*trace[Adj[Ye], Ye]*trace[Adj[Ye], Ye, Adj[Ye], Ye] -
(6*g1^2*trace[Adj[Yt], Yt, Adj[Yb], Yb])/5 +
36*g2^2*trace[Adj[Yt], Yt, Adj[Yb], Yb] +
48*g3^2*trace[Adj[Yt], Yt, Adj[Yb], Yb] + 18*trace[Adj[Yb], Yb]*
trace[Adj[Yt], Yt, Adj[Yb], Yb] + 6*trace[Adj[Ye], Ye]*
trace[Adj[Yt], Yt, Adj[Yb], Yb] + 18*trace[Adj[Yt], Yt]*
trace[Adj[Yt], Yt, Adj[Yb], Yb] +
(57*g1^2*trace[Adj[Yt], Yt, Adj[Yt], Yt])/5 +
9*g2^2*trace[Adj[Yt], Yt, Adj[Yt], Yt] +
72*g3^2*trace[Adj[Yt], Yt, Adj[Yt], Yt] + 54*trace[Adj[Yt], Yt]*
trace[Adj[Yt], Yt, Adj[Yt], Yt] + 3*trace[Adj[Yb], Yb, Adj[Yb], Yb,
Adj[Yb], Yb] + 9*trace[Adj[Yb], Yb, Adj[Yt], Yt, Adj[Yb], Yb] +
trace[Adj[Ye], Ye, Adj[Ye], Ye, Adj[Ye], Ye] +
9*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yb], Yb] +
3*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yt], Yt] -
(77*g1^4*trace[Adj[Yb], Yb]*Zeta[3])/50 - 9*g1^2*g2^2*trace[Adj[Yb], Yb]*
Zeta[3] - (189*g2^4*trace[Adj[Yb], Yb]*Zeta[3])/2 +
(112*g1^2*g3^2*trace[Adj[Yb], Yb]*Zeta[3])/5 +
144*g2^2*g3^2*trace[Adj[Yb], Yb]*Zeta[3] - 16*g3^4*trace[Adj[Yb], Yb]*
Zeta[3] + (81*g1^4*trace[Adj[Ye], Ye]*Zeta[3])/50 +
(81*g1^2*g2^2*trace[Adj[Ye], Ye]*Zeta[3])/5 -
(63*g2^4*trace[Adj[Ye], Ye]*Zeta[3])/2 -
(13*g1^4*trace[Adj[Yt], Yt]*Zeta[3])/10 +
(63*g1^2*g2^2*trace[Adj[Yt], Yt]*Zeta[3])/5 -
(189*g2^4*trace[Adj[Yt], Yt]*Zeta[3])/2 +
(208*g1^2*g3^2*trace[Adj[Yt], Yt]*Zeta[3])/5 +
144*g2^2*g3^2*trace[Adj[Yt], Yt]*Zeta[3] - 16*g3^4*trace[Adj[Yt], Yt]*
Zeta[3] + (54*g1^2*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3])/5 +
54*g2^2*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] -
144*g3^2*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] -
(54*g1^2*trace[Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3])/5 +
18*g2^2*trace[Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3] +
(48*g1^2*trace[Adj[Yt], Yt, Adj[Yb], Yb]*Zeta[3])/5 -
96*g3^2*trace[Adj[Yt], Yt, Adj[Yb], Yb]*Zeta[3] -
(18*g1^2*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3])/5 +
54*g2^2*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] -
144*g3^2*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] +
18*trace[Adj[Yb], Yb, Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] +
6*trace[Adj[Ye], Ye, Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3] +
18*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] +
2*((1839*g1^6)/100 - (1791*g1^6*Zeta[3])/250) +
2*((27*g1^4*g2^2)/100 - (243*g1^4*g2^2*Zeta[3])/50) +
2*((9*g1^2*g2^4)/4 - (81*g1^2*g2^4*Zeta[3])/10) +
2*((345*g2^6)/4 + (315*g2^6*Zeta[3])/2) +
2*((66*g1^4*g3^2)/5 - (396*g1^4*g3^2*Zeta[3])/25) +
2*(90*g2^4*g3^2 - 108*g2^4*g3^2*Zeta[3])) -
2*Mu*((5517*g1^6*M1)/50 + (27*g1^4*g2^2*M1)/25 + (9*g1^2*g2^4*M1)/2 +
(264*g1^4*g3^2*M1)/5 + (27*g1^4*g2^2*M2)/50 + 9*g1^2*g2^4*M2 +
(1035*g2^6*M2)/2 + 360*g2^4*g3^2*M2 + (132*g1^4*g3^2*M3)/5 +
180*g2^4*g3^2*M3 + (657*g1^4*trace[Adj[Ye], he])/20 +
(81*g1^2*g2^2*trace[Adj[Ye], he])/10 + (105*g2^4*trace[Adj[Ye], he])/4 -
(657*g1^4*M1*trace[Adj[Ye], Ye])/10 -
(81*g1^2*g2^2*M1*trace[Adj[Ye], Ye])/10 -
(81*g1^2*g2^2*M2*trace[Adj[Ye], Ye])/10 -
(105*g2^4*M2*trace[Adj[Ye], Ye])/2 + (2357*g1^4*trace[Adj[Yt], ht])/60 +
(57*g1^2*g2^2*trace[Adj[Yt], ht])/10 + (315*g2^4*trace[Adj[Yt], ht])/4 +
(124*g1^2*g3^2*trace[Adj[Yt], ht])/3 + 132*g2^2*g3^2*trace[Adj[Yt], ht] +
(160*g3^4*trace[Adj[Yt], ht])/3 - (2357*g1^4*M1*trace[Adj[Yt], Yt])/30 -
(57*g1^2*g2^2*M1*trace[Adj[Yt], Yt])/10 -
(124*g1^2*g3^2*M1*trace[Adj[Yt], Yt])/3 -
(57*g1^2*g2^2*M2*trace[Adj[Yt], Yt])/10 -
(315*g2^4*M2*trace[Adj[Yt], Yt])/2 - 132*g2^2*g3^2*M2*
trace[Adj[Yt], Yt] - (124*g1^2*g3^2*M3*trace[Adj[Yt], Yt])/3 -
132*g2^2*g3^2*M3*trace[Adj[Yt], Yt] - (320*g3^4*M3*trace[Adj[Yt], Yt])/
3 - 3*g1^2*trace[Adj[Yb], hb, Adj[Yb], Yb] -
9*g2^2*trace[Adj[Yb], hb, Adj[Yb], Yb] -
72*g3^2*trace[Adj[Yb], hb, Adj[Yb], Yb] - 18*trace[Adj[Ye], Ye]*
trace[Adj[Yb], hb, Adj[Yb], Yb] - 3*g1^2*trace[Adj[Yb], Yb, Adj[Yb],
hb] - 9*g2^2*trace[Adj[Yb], Yb, Adj[Yb], hb] -
72*g3^2*trace[Adj[Yb], Yb, Adj[Yb], hb] - 18*trace[Adj[Ye], Ye]*
trace[Adj[Yb], Yb, Adj[Yb], hb] + 3*g1^2*M1*trace[Adj[Yb], Yb, Adj[Yb],
Yb] + 9*g2^2*M2*trace[Adj[Yb], Yb, Adj[Yb], Yb] +
72*g3^2*M3*trace[Adj[Yb], Yb, Adj[Yb], Yb] - 18*trace[Adj[Ye], he]*
trace[Adj[Yb], Yb, Adj[Yb], Yb] - 9*g1^2*trace[Adj[Ye], he, Adj[Ye],
Ye] - 3*g2^2*trace[Adj[Ye], he, Adj[Ye], Ye] -
6*trace[Adj[Ye], Ye]*trace[Adj[Ye], he, Adj[Ye], Ye] -
9*g1^2*trace[Adj[Ye], Ye, Adj[Ye], he] -
3*g2^2*trace[Adj[Ye], Ye, Adj[Ye], he] - 6*trace[Adj[Ye], Ye]*
trace[Adj[Ye], Ye, Adj[Ye], he] + 9*g1^2*M1*trace[Adj[Ye], Ye, Adj[Ye],
Ye] + 3*g2^2*M2*trace[Adj[Ye], Ye, Adj[Ye], Ye] -
6*trace[Adj[Ye], he]*trace[Adj[Ye], Ye, Adj[Ye], Ye] +
(6*g1^2*trace[Adj[Yt], ht, Adj[Yb], Yb])/5 -
36*g2^2*trace[Adj[Yt], ht, Adj[Yb], Yb] -
48*g3^2*trace[Adj[Yt], ht, Adj[Yb], Yb] - 6*trace[Adj[Ye], Ye]*
trace[Adj[Yt], ht, Adj[Yb], Yb] - 18*trace[Adj[Yt], Yt]*
trace[Adj[Yt], ht, Adj[Yb], Yb] -
(57*g1^2*trace[Adj[Yt], ht, Adj[Yt], Yt])/5 -
9*g2^2*trace[Adj[Yt], ht, Adj[Yt], Yt] -
72*g3^2*trace[Adj[Yt], ht, Adj[Yt], Yt] - 54*trace[Adj[Yt], Yt]*
trace[Adj[Yt], ht, Adj[Yt], Yt] +
(6*g1^2*trace[Adj[Yt], Yt, Adj[Yb], hb])/5 -
36*g2^2*trace[Adj[Yt], Yt, Adj[Yb], hb] -
48*g3^2*trace[Adj[Yt], Yt, Adj[Yb], hb] - 6*trace[Adj[Ye], Ye]*
trace[Adj[Yt], Yt, Adj[Yb], hb] - 18*trace[Adj[Yt], Yt]*
trace[Adj[Yt], Yt, Adj[Yb], hb] -
(6*g1^2*M1*trace[Adj[Yt], Yt, Adj[Yb], Yb])/5 +
36*g2^2*M2*trace[Adj[Yt], Yt, Adj[Yb], Yb] +
48*g3^2*M3*trace[Adj[Yt], Yt, Adj[Yb], Yb] - 6*trace[Adj[Ye], he]*
trace[Adj[Yt], Yt, Adj[Yb], Yb] - 18*trace[Adj[Yt], ht]*
trace[Adj[Yt], Yt, Adj[Yb], Yb] -
(57*g1^2*trace[Adj[Yt], Yt, Adj[Yt], ht])/5 -
9*g2^2*trace[Adj[Yt], Yt, Adj[Yt], ht] -
72*g3^2*trace[Adj[Yt], Yt, Adj[Yt], ht] - 54*trace[Adj[Yt], Yt]*
trace[Adj[Yt], Yt, Adj[Yt], ht] +
(57*g1^2*M1*trace[Adj[Yt], Yt, Adj[Yt], Yt])/5 +
9*g2^2*M2*trace[Adj[Yt], Yt, Adj[Yt], Yt] +
72*g3^2*M3*trace[Adj[Yt], Yt, Adj[Yt], Yt] - 54*trace[Adj[Yt], ht]*
trace[Adj[Yt], Yt, Adj[Yt], Yt] - 3*trace[Adj[Yb], hb, Adj[Yb], Yb,
Adj[Yb], Yb] - 9*trace[Adj[Yb], hb, Adj[Yt], Yt, Adj[Yb], Yb] -
3*trace[Adj[Yb], Yb, Adj[Yb], hb, Adj[Yb], Yb] -
3*trace[Adj[Yb], Yb, Adj[Yb], Yb, Adj[Yb], hb] -
9*trace[Adj[Yb], Yb, Adj[Yt], ht, Adj[Yb], Yb] -
9*trace[Adj[Yb], Yb, Adj[Yt], Yt, Adj[Yb], hb] -
trace[Adj[Ye], he, Adj[Ye], Ye, Adj[Ye], Ye] -
trace[Adj[Ye], Ye, Adj[Ye], he, Adj[Ye], Ye] -
trace[Adj[Ye], Ye, Adj[Ye], Ye, Adj[Ye], he] -
9*trace[Adj[Yt], ht, Adj[Yt], Yt, Adj[Yb], Yb] -
3*trace[Adj[Yt], ht, Adj[Yt], Yt, Adj[Yt], Yt] -
9*trace[Adj[Yt], Yt, Adj[Yt], ht, Adj[Yb], Yb] -
3*trace[Adj[Yt], Yt, Adj[Yt], ht, Adj[Yt], Yt] -
9*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yb], hb] -
3*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yt], ht] -
(5373*g1^6*M1*Zeta[3])/125 - (486*g1^4*g2^2*M1*Zeta[3])/25 -
(81*g1^2*g2^4*M1*Zeta[3])/5 - (1584*g1^4*g3^2*M1*Zeta[3])/25 -
(243*g1^4*g2^2*M2*Zeta[3])/25 - (162*g1^2*g2^4*M2*Zeta[3])/5 +
945*g2^6*M2*Zeta[3] - 432*g2^4*g3^2*M2*Zeta[3] -
(792*g1^4*g3^2*M3*Zeta[3])/25 - 216*g2^4*g3^2*M3*Zeta[3] -
(81*g1^4*trace[Adj[Ye], he]*Zeta[3])/50 -
(81*g1^2*g2^2*trace[Adj[Ye], he]*Zeta[3])/5 +
(63*g2^4*trace[Adj[Ye], he]*Zeta[3])/2 +
(81*g1^4*M1*trace[Adj[Ye], Ye]*Zeta[3])/25 +
(81*g1^2*g2^2*M1*trace[Adj[Ye], Ye]*Zeta[3])/5 +
(81*g1^2*g2^2*M2*trace[Adj[Ye], Ye]*Zeta[3])/5 -
63*g2^4*M2*trace[Adj[Ye], Ye]*Zeta[3] +
(13*g1^4*trace[Adj[Yt], ht]*Zeta[3])/10 -
(63*g1^2*g2^2*trace[Adj[Yt], ht]*Zeta[3])/5 +
(189*g2^4*trace[Adj[Yt], ht]*Zeta[3])/2 -
(208*g1^2*g3^2*trace[Adj[Yt], ht]*Zeta[3])/5 -
144*g2^2*g3^2*trace[Adj[Yt], ht]*Zeta[3] + 16*g3^4*trace[Adj[Yt], ht]*
Zeta[3] - (13*g1^4*M1*trace[Adj[Yt], Yt]*Zeta[3])/5 +
(63*g1^2*g2^2*M1*trace[Adj[Yt], Yt]*Zeta[3])/5 +
(208*g1^2*g3^2*M1*trace[Adj[Yt], Yt]*Zeta[3])/5 +
(63*g1^2*g2^2*M2*trace[Adj[Yt], Yt]*Zeta[3])/5 -
189*g2^4*M2*trace[Adj[Yt], Yt]*Zeta[3] + 144*g2^2*g3^2*M2*
trace[Adj[Yt], Yt]*Zeta[3] + (208*g1^2*g3^2*M3*trace[Adj[Yt], Yt]*
Zeta[3])/5 + 144*g2^2*g3^2*M3*trace[Adj[Yt], Yt]*Zeta[3] -
32*g3^4*M3*trace[Adj[Yt], Yt]*Zeta[3] -
(54*g1^2*trace[Adj[Yb], hb, Adj[Yb], Yb]*Zeta[3])/5 -
54*g2^2*trace[Adj[Yb], hb, Adj[Yb], Yb]*Zeta[3] +
144*g3^2*trace[Adj[Yb], hb, Adj[Yb], Yb]*Zeta[3] -
(54*g1^2*trace[Adj[Yb], Yb, Adj[Yb], hb]*Zeta[3])/5 -
54*g2^2*trace[Adj[Yb], Yb, Adj[Yb], hb]*Zeta[3] +
144*g3^2*trace[Adj[Yb], Yb, Adj[Yb], hb]*Zeta[3] +
(54*g1^2*M1*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3])/5 +
54*g2^2*M2*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] -
144*g3^2*M3*trace[Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] +
(54*g1^2*trace[Adj[Ye], he, Adj[Ye], Ye]*Zeta[3])/5 -
18*g2^2*trace[Adj[Ye], he, Adj[Ye], Ye]*Zeta[3] +
(54*g1^2*trace[Adj[Ye], Ye, Adj[Ye], he]*Zeta[3])/5 -
18*g2^2*trace[Adj[Ye], Ye, Adj[Ye], he]*Zeta[3] -
(54*g1^2*M1*trace[Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3])/5 +
18*g2^2*M2*trace[Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3] -
(48*g1^2*trace[Adj[Yt], ht, Adj[Yb], Yb]*Zeta[3])/5 +
96*g3^2*trace[Adj[Yt], ht, Adj[Yb], Yb]*Zeta[3] +
(18*g1^2*trace[Adj[Yt], ht, Adj[Yt], Yt]*Zeta[3])/5 -
54*g2^2*trace[Adj[Yt], ht, Adj[Yt], Yt]*Zeta[3] +
144*g3^2*trace[Adj[Yt], ht, Adj[Yt], Yt]*Zeta[3] -
(48*g1^2*trace[Adj[Yt], Yt, Adj[Yb], hb]*Zeta[3])/5 +
96*g3^2*trace[Adj[Yt], Yt, Adj[Yb], hb]*Zeta[3] +
(48*g1^2*M1*trace[Adj[Yt], Yt, Adj[Yb], Yb]*Zeta[3])/5 -
96*g3^2*M3*trace[Adj[Yt], Yt, Adj[Yb], Yb]*Zeta[3] +
(18*g1^2*trace[Adj[Yt], Yt, Adj[Yt], ht]*Zeta[3])/5 -
54*g2^2*trace[Adj[Yt], Yt, Adj[Yt], ht]*Zeta[3] +
144*g3^2*trace[Adj[Yt], Yt, Adj[Yt], ht]*Zeta[3] -
(18*g1^2*M1*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3])/5 +
54*g2^2*M2*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] -
144*g3^2*M3*trace[Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] -
18*trace[Adj[Yb], hb, Adj[Yb], Yb, Adj[Yb], Yb]*Zeta[3] -
18*trace[Adj[Yb], Yb, Adj[Yb], hb, Adj[Yb], Yb]*Zeta[3] -
18*trace[Adj[Yb], Yb, Adj[Yb], Yb, Adj[Yb], hb]*Zeta[3] -
6*trace[Adj[Ye], he, Adj[Ye], Ye, Adj[Ye], Ye]*Zeta[3] -
6*trace[Adj[Ye], Ye, Adj[Ye], he, Adj[Ye], Ye]*Zeta[3] -
6*trace[Adj[Ye], Ye, Adj[Ye], Ye, Adj[Ye], he]*Zeta[3] -
18*trace[Adj[Yt], ht, Adj[Yt], Yt, Adj[Yt], Yt]*Zeta[3] -
18*trace[Adj[Yt], Yt, Adj[Yt], ht, Adj[Yt], Yt]*Zeta[3] -
18*trace[Adj[Yt], Yt, Adj[Yt], Yt, Adj[Yt], ht]*Zeta[3] +
trace[Adj[Yb], hb]*((1001*g1^4)/60 + (3*g1^2*g2^2)/10 + (315*g2^4)/4 +
(284*g1^2*g3^2)/15 + 132*g2^2*g3^2 + (160*g3^4)/3 -
54*trace[Adj[Yb], Yb, Adj[Yb], Yb] - 18*trace[Adj[Ye], Ye, Adj[Ye],
Ye] - 18*trace[Adj[Yt], Yt, Adj[Yb], Yb] + (77*g1^4*Zeta[3])/50 +
9*g1^2*g2^2*Zeta[3] + (189*g2^4*Zeta[3])/2 - (112*g1^2*g3^2*Zeta[3])/
5 - 144*g2^2*g3^2*Zeta[3] + 16*g3^4*Zeta[3]) +
trace[Adj[Yb], Yb]*((-1001*g1^4*M1)/30 - (3*g1^2*g2^2*M1)/10 -
(284*g1^2*g3^2*M1)/15 - (3*g1^2*g2^2*M2)/10 - (315*g2^4*M2)/2 -
132*g2^2*g3^2*M2 - (284*g1^2*g3^2*M3)/15 - 132*g2^2*g3^2*M3 -
(320*g3^4*M3)/3 - 54*trace[Adj[Yb], hb, Adj[Yb], Yb] -
54*trace[Adj[Yb], Yb, Adj[Yb], hb] - 18*trace[Adj[Ye], he, Adj[Ye],
Ye] - 18*trace[Adj[Ye], Ye, Adj[Ye], he] -
18*trace[Adj[Yt], ht, Adj[Yb], Yb] - 18*trace[Adj[Yt], Yt, Adj[Yb],
hb] - (77*g1^4*M1*Zeta[3])/25 - 9*g1^2*g2^2*M1*Zeta[3] +
(112*g1^2*g3^2*M1*Zeta[3])/5 - 9*g1^2*g2^2*M2*Zeta[3] -
189*g2^4*M2*Zeta[3] + 144*g2^2*g3^2*M2*Zeta[3] +
(112*g1^2*g3^2*M3*Zeta[3])/5 + 144*g2^2*g3^2*M3*Zeta[3] -
32*g3^4*M3*Zeta[3]))}
56 changes: 56 additions & 0 deletions meta/ThreeLoopMSSM/extract_MSSM_beta_functions_from_hep-ph-0308231.m
View file
Expand Up @@ -75,6 +75,61 @@
betaMu2 = Mu * (gammaH12 + gammaH22);
betaMu3 = Mu * (gammaH13 + gammaH23);

(* calculates gamma_1, Eq. (2.4b) arxiv:hep-ph/0408128 *)
Gamma1[gamma_] :=
Module[{gp = gamma //. repl},
DYuk[yuk_, tri_] := {
Derivative[1, 0][trace][yuk, p_] :> trace[tri, p],
Derivative[0, 1][trace][p_, yuk] :> trace[p, tri],
Derivative[1, 0][trace][Adj[yuk], p_] -> 0,
Derivative[0, 1][trace][p_, Adj[yuk]] -> 0,
Derivative[1, 0, 0, 0][trace][yuk, p__ ] :> trace[tri, p],
Derivative[0, 1, 0, 0][trace][p_, yuk, q__] :> trace[p, tri, q],
Derivative[0, 0, 1, 0][trace][p__, yuk, q_] :> trace[p, tri, q],
Derivative[0, 0, 0, 1][trace][p__, yuk ] :> trace[p, tri],
Derivative[1, 0, 0, 0][trace][Adj[yuk], p__ ] -> 0,
Derivative[0, 1, 0, 0][trace][p_, Adj[yuk], q__] -> 0,
Derivative[0, 0, 1, 0][trace][p__, Adj[yuk], q_] -> 0,
Derivative[0, 0, 0, 1][trace][p__, Adj[yuk] ] -> 0,
Derivative[1, 0, 0, 0, 0, 0][trace][yuk, p__ ] :> trace[tri, p],
Derivative[0, 1, 0, 0, 0, 0][trace][p_, yuk, q__ ] :> trace[p, tri, q],
Derivative[0, 0, 1, 0, 0, 0][trace][p_, q_, yuk, r__] :> trace[p, q, tri, r],
Derivative[0, 0, 0, 1, 0, 0][trace][p__, yuk, q_, r_] :> trace[p, tri, q, r],
Derivative[0, 0, 0, 0, 1, 0][trace][p__, yuk, q_ ] :> trace[p, tri, q],
Derivative[0, 0, 0, 0, 0, 1][trace][p__, yuk ] :> trace[p, tri],
Derivative[1, 0, 0, 0, 0, 0][trace][Adj[yuk], p__ ] -> 0,
Derivative[0, 1, 0, 0, 0, 0][trace][p_, Adj[yuk], q__ ] -> 0,
Derivative[0, 0, 1, 0, 0, 0][trace][p_, q_, Adj[yuk], r__] -> 0,
Derivative[0, 0, 0, 1, 0, 0][trace][p__, Adj[yuk], q_, r_] -> 0,
Derivative[0, 0, 0, 0, 1, 0][trace][p__, Adj[yuk], q_ ] -> 0,
Derivative[0, 0, 0, 0, 0, 1][trace][p__, Adj[yuk] ] -> 0
};
(
+ M1 g1/2 D[gp, g1]
+ M2 g2/2 D[gp, g2]
+ M3 g3/2 D[gp, g3]
- (D[gp, Yt] /. DYuk[Yt, ht])
- (D[gp, Yb] /. DYuk[Yb, hb])
- (D[gp, Ye] /. DYuk[Ye, he])
)
];

gamma1H11 = Gamma1[gammaH11];
gamma1H21 = Gamma1[gammaH21];
gamma1H12 = Gamma1[gammaH12];
gamma1H22 = Gamma1[gammaH22];
gamma1H13 = Gamma1[gammaH13];
gamma1H23 = Gamma1[gammaH23];

On[Assert];
Assert[FreeQ[gamma1H13, Derivative[__][__][__]]];
Assert[FreeQ[gamma1H23, Derivative[__][__][__]]];

(* calculate beta-functions of BMu, Eq. (2.3), arxiv:hep-ph/0408128 *)
betaBMu1 = Simplify[BMu (gammaH11 + gammaH21) - 2 Mu (gamma1H11 + gamma1H21)];
betaBMu2 = Simplify[BMu (gammaH12 + gammaH22) - 2 Mu (gamma1H12 + gamma1H22)];
betaBMu3 = Simplify[BMu (gammaH13 + gammaH23) - 2 Mu (gamma1H13 + gamma1H23)];

{g1 bg11 , g1 bg12 , g1 bg13 } //. repl >> "beta_g1.m";
{g2 bg21 , g2 bg22 , g2 bg23 } //. repl >> "beta_g2.m";
{g3 bg31 , g3 bg32 , g3 bg33 } //. repl >> "beta_g3.m";
Expand All @@ -95,6 +150,7 @@
{betaM21 , betaM22 , betaM23 } //. repl >> "beta_M2.m";
{betaM31 , betaM32 , betaM33 } //. repl >> "beta_M3.m";
{betaMu1 , betaMu2 , betaMu3 } //. repl >> "beta_Mu.m";
{betaBMu1 , betaBMu2 , betaBMu3 } //. repl >> "beta_BMu.m";

{gammaQ1 , gammaQ2 , gammaQ3 } //. repl >> "gamma_SqL.m";
{gammat1 , gammat2 , gammat3 } //. repl >> "gamma_SuR.m";
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