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twoloophiggs.f
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c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c subroutines for the dominant two-loop radiative corrections to the
c Higgs masses, consitently in DRbar scheme, for SuSpect v2.3 interface
c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subroutine su_DSZHiggs(t,mg,T1,T2,st,ct,q,mu,tanb,v2,gs,
$ OS,S11,S22,S12)
c Two-loop O(a_t a_s) corrections to the CP-even Higgs mass matrix.
c Routine written by P. Slavich (e-mail: [email protected]).
c Based on G. Degrassi, P. Slavich and F. Zwirner,
c Nucl. Phys. B611 (2001) 403 [hep-ph/0105096].
c
c Last update: 24/02/2004: mg is given as input instead of mg^2;
c value of pi corrected (10th digit);
c unused variables cleaned up.
c 22/10/2002: gs is given as input.
c
c
c I/O PARAMETERS:
c t = m_top^2, mg = m_gluino, T1 = m_stop1^2, T2 = m_stop2^2,
c st = sin(theta_stop), ct = cos(theta_stop), q = Q^2 (ren. scale),
c mu = Higgs mixing parameter, tanb = tan(beta), v2 = v^2,
c gs = strong coupling constant,
c OS = renormalization scheme for 1-loop (0 = DRbar, 1 = On-Shell),
c Sij = 2-loop corrections to the CP-even Higgs mass matrix elements.
implicit none
integer OS
real*8 ht,gs,k,mt,pi,v2
real*8 t,mg,T1,T2,st,ct,q,A,X,mu,tanb,sb,s2t,c2t
real*8 F1,F2,F3,sF2,sF3
real*8 DF1,DF2,DF3,DsF2,DsF3
real*8 F2_s,sF2_A,sF3_A
real*8 S11,S22,S12,osdr
c$$$ pi = 3.14159265897d0
pi = 3.1415926535898d0
mt = dsqrt(t)
s2t = 2d0*ct*st
c2t = ct**2 - st**2
X = (T1-T2)*s2t/2d0/mt ! eq. (19) of DSZ
A = X - mu/tanb ! notice the sign convention for mu
sb = dsin(datan(tanb))
ht = dsqrt(2d0/v2)*mt/sb
k = 4d0*gs**2/(16d0*Pi**2)**2 ! gs^2/(16 Pi^2)^2 CF Nc
call strfuncs(t,mg,T1,T2,s2t,c2t,q,F1,F2,F3)
call strsfuncs(mg,T1,T2,q,A,sF2,sF3)
call strdfuncs(t,mg,T1,T2,s2t,c2t,q,A,X,
$ DF1,DF2,DF3,DsF2,DsF3)
osdr = 1d0*OS
if(s2t.ne.0.and.A.ne.0) then
S11 = .5d0 * ht**2 * mu**2 * s2t**2 * (F3 + osdr*DF3) ! eq. (25)
S12 = .5d0 * ht**2 * mu * A * s2t**2 * (F3 + sF3 + ! eq. (26)
$ osdr*(DF3 + DsF3)) +
$ ht**2 * mt * mu * s2t * (F2 + osdr*DF2)
S22 = .5d0 * ht**2 * A**2 * s2t**2 * (F3 + 2d0*sF3 + ! eq. (27)
$ osdr*(DF3 + 2d0*DsF3)) +
$ 2d0 * ht**2 * mt * A * s2t * (F2 + sF2 +
$ osdr*(DF2 + DsF2)) +
$ 2d0 * ht**2 * mt**2 * (F1 + osdr*DF1)
c some of the functions have poles in s2t=0 or in A=0.
c when necessary we consider the residues:
elseif(s2t.eq.0.and.A.eq.0) then
S11 = 0d0
S12 = 0d0
S22 = 2 * ht**2 * mt**2 * (F1 + osdr*DF1)
elseif(s2t.eq.0.and.A.ne.0) then
call strresfuncs(t,mg,T1,T2,q,F2_s,sF2_A,sF3_A)
S11 = 0d0
S12 = ht**2 * mt * mu * (F2_s + osdr*DF2)
S22 = 2d0 * ht**2 * mt**2 * (F1 + osdr*DF1) +
$ 2d0 * ht**2 * mt * A * (F2_s + osdr*DF2)
elseif(s2t.ne.0.and.A.eq.0) then
call strresfuncs(t,mg,T1,T2,q,F2_s,sF2_A,sF3_A)
S11 = .5d0 * ht**2 * mu**2 * s2t**2 * (F3 + osdr*DF3)
S12 = .5d0 * ht**2 * mu * s2t**2 * (sF3_A + osdr*DsF3) +
$ ht**2 * mt * mu * s2t * (F2 + osdr*DF2)
S22 = 2d0 * ht**2 * mt**2 * (F1 + osdr*DF1) +
$ 2d0 * ht**2 * mt * s2t * (sF2_A + osdr*DsF2)
endif
S11 = k*S11
S12 = k*S12
S22 = k*S22
return
end
*
***********************************************************************
*
subroutine strfuncs(t,mg,T1,T2,s2t,c2t,q,F1,F2,F3)
implicit none
real*8 t,mg,T1,T2,s2t,c2t,q,F1,F2,F3
real*8 strF1ab,strF1c,strF2ab,strF2c,strF3ab,strF3c
F1 = strF1ab(t,T1,T2,s2t,c2t,q)
$ + strF1c(t,mg,T1,s2t,q)
$ + strF1c(t,mg,T2,-s2t,q)
F2 = strF2ab(T1,T2,s2t,c2t,q)
$ + strF2c(t,mg,T1,T2,s2t,q)
$ - strF2c(t,mg,T2,T1,-s2t,q)
F3 = strF3ab(T1,T2,s2t,c2t,q)
$ + strF3c(t,mg,T1,T2,s2t,q)
$ + strF3c(t,mg,T2,T1,-s2t,q)
return
end
*
*********************************************************************
*
function strF1ab(t,T1,T2,s2t,c2t,q)
implicit none
real*8 t,T1,T2,s2t,c2t,q
real*8 strF1ab
strF1ab = ! eq. (32)
$ -6*(1d0-dLog(t/q))+5*dLog(T1*T2/t**2)+dLog(T1*T2/t**2)**2
$ +8*dLog(t/q)**2-4*dLog(T1/q)**2-4*dLog(T2/q)**2
$ -c2t**2*(2d0-dLog(T1/q)-dLog(T2/q)-dLog(T1/T2)**2)
$ -s2t**2*(T1/T2*(1d0-dLog(T1/q))+T2/T1*(1d0-dLog(T2/q)))
return
end
*
*********************************************************************
*
function strF1c(t,mg,T1,s2t,q)
implicit none
real*8 t,g,mt,mg,T1,s2t,q
real*8 strF1c,phi,del
mt = dsqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strF1c = ! eq. (A1)
$ +4*(t+g-mg*mt*s2t)/T1*(1d0-dLog(g/q))
$ +4*dLog(t/g) - 2*dLog(T1/g)
$ +2d0/del*(4*g**2*dLog(T1/g)
$ +(g**2-T1**2+t*(10*g+3*t+2*t*g/T1-2*t**2/T1))*dLog(t/g))
$ +2*mg/mt*s2t*(dLog(T1/q)**2+2*dLog(t/q)*dLog(T1/q))
$ +4*mg/mt*s2t/del*(g*(T1-t-g)
$ *Log(T1/g)+t*(T1-3*g-2*t-(t*g-t**2)/T1)*dLog(t/g))
$ +(4*g*(t+g-T1-2*mg*mt*s2t)/del
$ -4*mg/mt*s2t)*phi(t,T1,g)
return
end
*
*********************************************************************
*
function strF2ab(T1,T2,s2t,c2t,q)
implicit none
real*8 T1,T2,s2t,c2t,q
real*8 strF2ab
strF2ab = ! eq. (33)
$ 5*dLog(T1/T2)-3*(dLog(T1/q)**2-dLog(T2/q)**2)
$ +c2t**2*(5*dLog(T1/T2)
$ -(T1+T2)/(T1-T2)*dLog(T1/T2)**2
$ -2/(T1-T2)*(T1*dLog(T1/q)-T2*dLog(T2/q))*dLog(T1/T2))
$ +s2t**2*(T1/T2*(1d0-dLog(T1/q))-T2/T1*(1d0-dLog(T2/q)))
return
end
*
*********************************************************************
*
function strF2c(t,mg,T1,T2,s2t,q)
implicit none
real*8 t,g,mg,mt,T1,T2,s2t,q
real*8 strF2c,phi,del
mt = dsqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strF2c = ! eq. (A2)
$ 4*(t+g)/T1-4*mg/mt*s2t/(T1-T2)*(3*T1-t*T2/T1)
$ +2*mg/mt*s2t/(T1-T2)*(
$ (4*t+5*T1+T2)*dLog(T1/q)-2*t*T2/T1*dLog(g/q))
$ -4*(g+t)/T1*dLog(g/q) - 2*dLog(T1/g)
$ +2.d0/del*(2*g*(g+t-T1)*dLog(T1/g)
$ +2*t*(3*g+2*t-T1+(g*t-t**2)/T1)*dLog(t/g))
$ -4*mg*mt*s2t/del/T1*(2*g*T1*dLog(T1/g)-
$ ((t-T1)**2-g*(t+T1))*dLog(t/g))
$ -8*mg*mt/s2t/(T1-T2)*(dLog(T1/q)-dLog(t/q)*dLog(T1/q))
$ -mg/mt*s2t/(T1-T2)*((T1+T2)*dLog(T1/q)**2
$ +(10*t-2*g+T1+T2)*dLog(t/q)*dLog(T1/q)
$ +(2*g-2*t+T1+T2)*dLog(T1/q)*dLog(g/q))
$ +(8*g*t/del-8*mg*mt/s2t/(T1-T2)
$ +2*s2t/mg/mt/(T1-T2)*(4*g*t-del)
$ +s2t/mg/mt/del*(T1-g-t)**3)*phi(t,T1,g)
return
end
*
*********************************************************************
*
function strF3ab(T1,T2,s2t,c2t,q)
implicit none
real*8 T1,T2,s2t,c2t,q
real*8 strF3ab
strF3ab = ! eq. (34)
$ (3+9*c2t**2)*(2d0-(T1+T2)/(T1-T2)*dLog(T1/T2))
$ +4d0-(3d0+13*c2t**2)/(T1-T2)*(T1*dLog(T1/q)-T2*dLog(T2/q))
$ +3*(T1+T2)/(T1-T2)*(dLog(T1/q)**2-dLog(T2/q)**2)
$ -c2t**2*(4d0-((T1+T2)/(T1-T2))**2*dLog(T1/T2)**2
$ -6*(T1+T2)/(T1-T2)**2
$ *(T1*dLog(T1/q)-T2*dLog(T2/q))*dLog(T1/T2))
$ -s2t**2*(T1/T2+T2/T1 + 2*dLog(T1*T2/q**2)
$ -T1**2/T2/(T1-T2)*dLog(T1/q)
$ +T2**2/T1/(T1-T2)*dLog(T2/q))
return
end
*
*********************************************************************
*
function strF3c(t,mg,T1,T2,s2t,q)
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,q
real*8 strF3c,phi,del
mt = dsqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strF3c = ! eq. (A3)
$ -4*T2/T1/(T1-T2)*(g+t)
$ +4*mg*mt*s2t/(T1-T2)**2*(21*T1-T2**2/T1)
$ +4d0/(T1-T2)*(g*T2/T1*dLog(g/q)-2*(t+g)*dLog(T1/q))
$ -24*mg*mt*s2t/(T1-T2)**2*(3*T1+T2)*dLog(T1/q)
$ +4*t/T1/del*(2*g*T1*dLog(T1/q)-g*(g-t+T1)*dLog(g/q)+
$ (g*(T+T1)-(t-T1)**2)*dLog(t/q))
$ -4*mg*mt*s2t/T1/del*(t*(g-t+T1)*dLog(t/q)
$ -g*(g-t-T1)*dLog(g/q)+T1*(g+t-T1)*dLog(T1/q))
$ +2*(2*g+2*t-T1-T2)/(T1-T2)*dLog(g*t/q**2)*dLog(T1/q)
$ +12*mg*mt*s2t/(T1-T2)**2*(2*(g-t)*dLog(g/t)*dLog(T1/q)
$ +(T1+T2)*dLog(t*g/q**2)*dLog(T1/q))
$ +8*mg*mt/s2t/(T1-T2)**2*
$ (-8*T1+2*(3*T1+T2)*dLog(T1/q)-2*(g-t)*dLog(g/t)*dLog(T1/q)
$ -(T1+T2)*dLog(t*g/q**2)*dLog(T1/q))
$ -((8/s2t-12*s2t)*mt/mg/(T1-T2)**2
$ *(2*del+(g+t-T1)*(T1-T2))
$ +(4*del+8*g*t)/g/(T1-T2)+2*(g+t-T1)/g
$ -4*t*(g+t-T1- 2*mg*mt*s2t)/del)*phi(t,T1,g)
return
end
*
*********************************************************************
*
subroutine strsfuncs(mg,T1,T2,q,A,sF2,sF3)
c shift to the Fi functions due to the renormalization of A
implicit none
real*8 mg,T1,T2,q,A,sF2,sF3
sF2 = mg/A * ! eq. (35)
$ 2d0*(dlog(T2/q)**2 - dlog(T1/q)**2)
sF3 = mg/A * ! eq. (36)
$ (8d0 - 2d0*(T1+T2)/(T1-T2)*(dlog(T2/q)**2 - dlog(T1/q)**2)
$ + 8d0/(T1-T2)*(T2*dlog(T2/q) - T1*dlog(T1/q)))
return
end
*
*********************************************************************
*
subroutine strresfuncs(t,mg,T1,T2,q,F2_s,sF2_A,sF3_A)
c residues of some singular functions for s2t=0 and for A=0
implicit none
real*8 t,g,mt,mg,T1,T2,q,sF2_A,sF3_A,F2_s,phi
mt = dsqrt(t)
g = mg**2
F2_s = -8*mg*mt/(T1-T2)*(
$ (dLog(T1/q)-dLog(t/q)*dLog(T1/q)+phi(t,T1,g))-
$ (dLog(T2/q)-dLog(t/q)*dLog(T2/q)+phi(t,T2,g)))
sF2_A = mg*
$ 2d0*(dlog(T2/q)**2 - dlog(T1/q)**2)
sF3_A = mg*
$ (8d0 - 2d0*(T1+T2)/(T1-T2)*(dlog(T2/q)**2 - dlog(T1/q)**2)
$ + 8d0/(T1-T2)*(T2*dlog(T2/q) - T1*dlog(T1/q)))
return
end
*
***********************************************************************
*
subroutine strdfuncs(t,mg,T1,T2,s2t,c2t,q,At,X,
$ DF1,DF2,DF3,DsF2,DsF3)
c shift of the parameters from DRbar to On-Shell scheme
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,c2t,q,At,X,myB0
real*8 DF1,DF2,DF3,DsF2,DsF3
real*8 msdr
real*8 F1o,F2o,F3o,dm1,dm2,dmt,dAt,dth,ds2t
msdr = -5d0
mt = dSqrt(t)
g = mg**2
F1o = dLog(T1/q) + dLog(T2/q) - 2d0*dLog(t/q) ! eq. (31)
F2o = dLog(T1/q) - dLog(T2/q)
F3o = 2d0 - (T1+T2)/(T1-T2)*(dLog(T1/q) - dLog(T2/q))
dmt = ! eq. (B2)
$ mt*(3*Log(t/q) + msdr + .5d0*(2*g/t*(dLog(g/q)-1d0)
$ -T1/t*(dLog(T1/q)-1d0) - T2/t*(dLog(T2/q)-1d0)
$ +(g+t-T1 - 2*s2t*mg*mt)/t*myB0(t,g,T1,q)
$ +(g+t-T2 + 2*s2t*mg*mt)/t*myB0(t,g,T2,q)))
dm1 = ! eq. (B3)
$ T1*(3*dLog(T1/q) - 7d0 - c2t**2*(dLog(T1/q)-1d0)
$ -s2t**2*T2/T1*(dLog(T2/q)-1d0) + 2*(
$ g/T1*(dLog(g/q)-1d0) + t/T1*(dLog(t/q)-1d0)
$ +(T1-g-t + 2*s2t*mg*mt)/T1*myB0(T1,t,g,q)))
dm2 = ! eq. (B4)
$ T2*(3*dLog(T2/q) - 7d0 - c2t**2*(dLog(T2/q)-1d0)
$ -s2t**2*T1/T2*(dLog(T1/q)-1d0) + 2*(
$ g/T2*(dLog(g/q)-1d0) + t/T2*(dLog(t/q)-1d0)
$ +(T2-g-t - 2*s2t*mg*mt)/T2*myB0(T2,t,g,q)))
c$$$c On-Shell theta-stop: asymmetric definition used in FeynHiggs
c$$$ dth = (4d0*mg*mt*c2t*myB0(T1,t,g,q) +
c$$$ $ c2t*s2t*(T2*(1d0-Log(T2/q))-T1*(1d0-Log(T1/q))))/(T1-T2)
c On-Shell theta-stop: eq. (B6)-(B7) of DSZ
dth = (4d0*mg*mt*c2t*(myB0(T1,t,g,q)+myB0(T2,t,g,q)) +
$ 2d0*c2t*s2t*(T2*(1d0-dLog(T2/q))-T1*(1d0-dLog(T1/q))))/
$ 2d0/(T1-T2)
ds2t = 2d0*c2t*dth
dAt = ((dm1-dm2)/(T1-T2) + ds2t/s2t - dmt/mt)*X ! eq. (B8)
DF1 = dm1/T1 + dm2/T2 - 4d0*dmt/mt + 4d0*dmt/mt*F1o ! eq. (37)
DF2 = dm1/T1 - dm2/T2 + (3d0*dmt/mt + ds2t/s2t)*F2o ! eq. (38)
DF3 = (2d0*T1*T2/(T1-T2)**2*dLog(T1/T2) - (T1+T2)/(T1-T2))
$ *(dm1/T1-dm2/T2) + (2d0*dmt/mt + 2d0*ds2t/s2t)*F3o ! eq. (39)
DsF2 = dAt/At * F2o ! eq. (40)
DsF3 = dAt/At * F3o ! eq. (41)
c residues of some singular functions for s2t=0 and for A=0
if(s2t.eq.0d0) then
DF2 = ds2t*F2o
DsF2 = ds2t*X/At * F2o
endif
if(At.eq.0d0) then
DsF2 = dAt * F2o
DsF3 = dAt * F3o
endif
return
end
*
**************************************************************************
**************************************************************************
*
subroutine su_DSZodd(t,mg,T1,T2,st,ct,q,mu,tanb,v2,gs,DMA)
c Two-loop O(a_t a_s) corrections to the CP-odd Higgs mass in the
c DRbar scheme. Written by P. Slavich (e-mail: [email protected]).
c Based on G. Degrassi, P. Slavich and F. Zwirner,
c Nucl. Phys. B611 (2001) 403 [hep-ph/0105096].
c
c Last update: 24/02/2004: mg is given as input instead of mg^2;
c value of pi corrected (10th digit);
c unused variables cleaned up;
c some formulae simplified.
c 22/10/2002: gs is given as input.
c
c
c I/O PARAMETERS:
c t = m_top^2, mg = m_gluino, T1 = m_stop1^2, T2 = m_stop2^2,
c st = sin(theta_stop), ct = cos(theta_stop), q = Q^2 (ren. scale),
c mu = Higgs mixing parameter, tanb = tan(beta), v2 = v^2,
c gs = strong coupling constant,
c DMA = 2-loop corrections to the CP-odd Higgs mass.
implicit none
real*8 ht,gs,k,mt,pi,v2
real*8 t,mg,T1,T2,st,ct,q,A,X,mu,tanb,sb,cb,s2t
real*8 FA,FA_A,DMA
c$$$ pi = 3.14159265897d0
pi = 3.1415926535898d0
mt = dsqrt(t)
s2t = 2d0*ct*st
X = (T1-T2)*s2t/2d0/mt ! eq. (19) of DSZ
A = X - mu/tanb ! notice the sign convention for mu
sb = dsin(datan(tanb))
cb = dcos(datan(tanb))
ht = dsqrt(2d0/v2)*mt/sb
k = 4d0*gs**2/(16d0*Pi**2)**2 ! gs^2/(16 Pi^2)^2 CF Nc
call strfuncsodd(t,mg,T1,T2,s2t,q,A,FA,FA_A)
if(A.ne.0d0) then
DMA = ht**2*mu*A/(T1-T2)/sb/cb * FA ! eq. (C1)
else
c the function FA has poles in A=0.
c when necessary we consider the residues:
DMA = ht**2*mu/(T1-T2)/sb/cb * FA_A
endif
DMA = k*DMA
return
end
*
***********************************************************************
*
subroutine strfuncsodd(t,mg,T1,T2,s2t,q,A,FA,FA_A)
implicit none
real*8 t,mg,T1,T2,s2t,q,A,FA,FA_A
real*8 strFAab,strFAc,strresFAc
FA = strFAab(T1,T2,s2t,q)
$ + strFAc(t,mg,T1,T2,s2t,A,q)
$ - strFAc(t,mg,T2,T1,-s2t,A,q)
FA_A = strresFAc(t,mg,T1,q) - strresFAc(t,mg,T2,q)
return
end
*
*********************************************************************
*
function strFAab(T1,T2,s2t,q)
implicit none
real*8 T1,T2,s2t,q
real*8 strFAab
strFAab = ! eq. (C4)
$ (8d0 - s2t**2*(2d0 - (T1+T2)/(T1-T2)*dLog(T1/T2)))
$ *(T1*(1d0 - dLog(T1/q)) - T2*(1d0 - dLog(T2/q)))
$ + 2d0*(T1*dLog(T1/q)**2 - T2*dLog(T2/q)**2)
$ + 2d0/(T1-T2)*(T1*dLog(T1/q) - T2*dLog(T2/q))**2
return
end
*
*********************************************************************
*
function strFAc(t,mg,T1,T2,s2t,A,q)
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,A,q
real*8 strFAc,phi,del
mt = dSqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strFAc = ! eq. (C5)
$ 16d0*T1/(T1-T2)*mg*mt*s2t
$ -4d0*(g+t)*dLog(T1/q)
$ - 2d0*mg/A*T1*(5d0- 4d0*dLog(T1/q))
$ - 4d0*mg*mt*s2t*(3d0* T1 + T2)/(T1-T2)*dLog(T1/q)
$ + 2d0*(g+t-T1)*dLog(t*g/q**2)*dLog(T1/q)
$ + 2d0*T1*(1d0+mg/A)*dLog(g/q)*dLog(t/q)
$ - 2d0*mg/A*((g-t)*dLog(g/t)+ T1*dLog(t*g/q**2))*dLog(T1/q)
$ + 2d0*mg*mt*s2t/(T1-T2)*
$ (2d0*(g-t)*dLog(g/t) + (T1+T2)*dLog(t*g/q**2))*dLog(T1/q)
$ - (4d0* t + 2d0* del/g*(1d0 + mg/A)
$ - 2d0*mt/mg*s2t/(T1-T2)*
$ (2d0*del + (g+t-T1)*(T1-T2)))*phi(t,T1,g)
return
end
*
*********************************************************************
*
function strresFAc(t,mg,T1,q)
c residue of FA for A=0
implicit none
real*8 t,g,mg,T1,q
real*8 strresFAc,phi,del
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strresFAc =
$ - 2d0*mg*T1*(5d0- 4d0*dLog(T1/q))
$ + 2d0*mg*T1*dLog(g/q)*dLog(t/q)
$ - 2d0*mg*((g-t)*dLog(g/t)+ T1*dLog(t*g/q**2))*dLog(T1/q)
$ - 2*del/mg*phi(t, T1, g)
return
end
*
*********************************************************************
*********************************************************************
*
subroutine su_ewsb2loop(t,mg,T1,T2,st,ct,q,mu,tanb,vv,gs,
$ S1,S2)
c Two-loop O(a_t a_s) corrections to the Higgs tadpoles.
c Written by P. Slavich (e-mail: [email protected]).
c Based on A. Dedes and P. Slavich,
c Nucl. Phys. B657 (2003) 333 [hep-ph/0212132].
c
c Last update: 24/02/2004: mg is given as input instead of mg^2;
c value of pi corrected (10th digit);
c unused variables cleaned up.
c Last update: 12/12/2002.
c
c I/O PARAMETERS:
c t = m_top^2, g = m_gluino^2, T1 = m_stop1^2, T2 = m_stop2^2,
c st = sin(theta_stop), ct = cos(theta_stop), q = Q^2 (ren. scale),
c mu = Higgs mixing parameter, tanb = tan(beta), vv = v^2,
c gs = strong coupling constant
c Si = 1/vi*dVeff/dvi = 2-loop corrections to the Higgs tadpoles.
c
c Notice: we assume that the 1-loop part is computed in terms of
c running (DRbar) parameters, evaluated at the scale Q.
implicit none
real*8 gs,k,mt,vv
real*8 t,mg,T1,T2,st,ct,q,A,X,mu,tanb,sb,cb,s2t,c2t,v1,v2
real*8 F2l,G2l,S1,S2,pi
c$$$ pi = 3.14159265897d0
pi = 3.1415926535898d0
mt = dsqrt(t)
s2t = 2d0*ct*st
c2t = ct**2 - st**2
X = (T1-T2)*s2t/2d0/mt
A = X - mu/tanb ! notice the sign convention for mu
sb = dsin(datan(tanb))
cb = dcos(datan(tanb))
v1 = sqrt(vv)*cb
v2 = sqrt(vv)*sb
k = 4d0*gs**2/(16d0*Pi**2)**2 ! gs^2/(16 Pi^2)^2 CF Nc
call strfuncstad(t,mg,T1,T2,s2t,c2t,q,F2l,G2l)
S1 = mt * mu/tanB * s2t * F2l
S1 = S1/v1**2
S2 = mt * A * s2t * F2l + 2d0 * mt**2 * G2l
S2 = S2/v2**2
S1 = k*S1
S2 = k*S2
return
end
*
***********************************************************************
*
subroutine strfuncstad(t,mg,T1,T2,s2t,c2t,q,F2l,G2l)
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,c2t,q
real*8 F2l,G2l,strF2lc,strG2lc
mt = sqrt(t)
g = mg**2
F2l = 4*mg*mt*(1+4*c2t**2)/s2t
$ -(2*(T1-T2)+4*mg*mt/s2t)*dLog(g/q)*dLog(t/q)
$ -2*(4-s2t**2)*(T1-T2)
$ +(4*T1*T2-s2t**2*(T1+T2)**2)/(T1-T2)*dLog(T1/q)*dLog(T2/q)
$ + strF2lc(t,mg,T1,T2,s2t,c2t,q)
$ - strF2lc(t,mg,T2,T1,-s2t,c2t,q)
G2l = 5*mg/mt*s2t*(T1-T2)-10*(T1+T2-2*t)-4*g
$ + 12*t*(dLog(t/q)**2-2*dLog(t/q))
$ +(4*g-s2t*mg/mt*(T1-T2))*dLog(g/q)*dLog(t/q)
$ +s2t**2*(T1+T2)*dLog(T1/q)*dLog(T2/q)
$ + strG2lc(t,mg,T1,T2,s2t,q)
$ + strG2lc(t,mg,T2,T1,-s2t,q)
return
end
*
*********************************************************************
*
function strF2lc(t,mg,T1,T2,s2t,c2t,q)
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,c2t,q
real*8 strF2lc,phi,del
mt = dsqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strF2lc = (4*(g+t+2*T1)-s2t**2*(3*T1+T2)-4*s2t*mg*mt
$ -16*mg*mt*T1*c2t**2/s2t/(T1-T2))*dLog(T1/q)
$ +T1/(T1-T2)*(s2t**2*(T1+T2)-2*(2*T1-T2))*dLog(T1/q)**2
$ +2*(T1-g-t+mg*mt*s2t
$ +2*c2t**2*mg*mt*T1/s2t/(T1-T2))*dLog(g*t/q**2)*dLog(T1/q)
$ +4*mg*mt*c2t**2*(t-g)/s2t/(T1-T2)*dLog(t/g)*dLog(T1/q)
$ +((2*del+4*g*t)/T1-2*mg*mt*s2t/T1*(g+t-T1)
$ +4*c2t**2*mg*mt/T1/(T1-T2)/s2t*del)*phi(g,t,T1)
return
end
*
*********************************************************************
*
function strG2lc(t,mg,T1,T2,s2t,q)
implicit none
real*8 t,g,mt,mg,T1,T2,s2t,q
real*8 strG2lc,phi,del
mt = sqrt(t)
g = mg**2
del = g**2 + t**2 + T1**2 - 2*(g*t + g*T1 + t*T1)
strG2lc = (4*(g+t+2*T1)+s2t**2*(T1-T2)
$ -4*mg/mt*s2t*(t+T1))*dLog(T1/q)
$ +(mg/mt*s2t*(5*t-g+T1)-2*(g+2*t))*dLog(t/q)*dLog(T1/q)
$ +(mg/mt*s2t*(g-t+T1)-2*g)*dLog(g/q)*dLog(T1/q)
$ -(2+s2t**2)*T1*dLog(T1/q)**2
$ +(2*g/T1*(g+t-T1-2*mg*mt*s2t)
$ +mg/mt*s2t*del/T1)*phi(g,t,T1)
return
end
*
**********************************************************************
**********************************************************************
*
c
c Two-loop O(a_t^2 + at ab + ab^2) corrections to the Higgs masses
c and to the minimization conditions of the effective potential.
c Written by P. Slavich (e-mail: [email protected]).
c Based on A. Dedes, G. Degrassi and P. Slavich, hep-ph/0305127.
c
c Last update: 25/09/2003: numerical value of Pi corrected (10th digit)
c 17/09/2003: error corrected in F1q, F6q and FAq;
c optimization: calls to makederiv reduced to 2
c 20/07/2003: routines optimized, bug for mu<0 corrected
c
c I/O PARAMETERS:
c t = m_top^2, b = m_bot^2, A0 = m_A^2, T1 = m_stop1^2, T2 = m_stop2^2,
c B1 = m_sbot1^2, B2 = m_sbot2^2, st = sin(theta_stop),
c ct = cos(theta_stop), sb = sin(theta_sbot), cb = cos(theta_sbot),
c q = Q^2 (ren. scale), mu = Higgs mixing parameter, tanb = tan(beta),
c vv = v^2,
c Sij = 2-loop corrections to the CP-even Higgs mass matrix elements,
c Si = 1/vi*dVeff/dvi = 2-loop corrections to the Higgs tadpoles,
c DMA = 2-loop corrections to the CP-odd Higgs mass.
c
c Notice: we assume that the 1-loop part is computed in terms of
c running (DRbar) parameters, evaluated at the scale Q. The
c parameters in the bottom/sbottom sector should be computed
c in term of the "resummed" bottom Yukawa coupling.
c
c
subroutine su_DDSHiggs(t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,
$ vv,S11,S12,S22)
implicit none
real*8 t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,vv,S11,S12,S22
real*8 c2t,s2t,c2b,s2b,At,Ab,Xt,Xb,mt,mb,cbe,sbe,ht,hb,pi,k
real*8 F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp
pi = 3.14159265358979d0
mt = dsqrt(t)
mb = dsqrt(b)
s2t = 2d0*ct*st
s2b = 2d0*cb*sb
c2t = ct**2 - st**2
c2b = cb**2 - sb**2
Xt = (T1-T2)*s2t/2d0/mt
Xb = (B1-B2)*s2b/2d0/mb
At = Xt - mu/tanb
Ab = Xb - mu*tanb
sbe = dsin(datan(tanb))
cbe = dcos(datan(tanb))
ht = dsqrt(2d0/vv)*mt/sbe
hb = dsqrt(2d0/vv)*mb/cbe
k = 3d0/(16d0*Pi**2)**2
call makefuncs(t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,q,mu,vv,tanb,
$ F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp)
S11 = .5d0*ht**2*mu**2*s2t**2*F3t
$ + 2d0*hb**2*mb**2*F1b + 2d0*hb**2*Ab*mb*s2b*F2b
$ + .5d0*hb**2*Ab**2*s2b**2*F3b
$ + 2d0*hb*ht*mb*mu*s2t*F4t + ht*hb*mu*Ab*s2t*s2b*F5
S12 = ht**2*mu*mt*s2t*F2t + .5d0*ht**2*At*mu*s2t**2*F3t
$ +hb**2*mu*mb*s2b*F2b + .5d0*hb**2*Ab*mu*s2b**2*F3b
$ +ht*hb*mb*At*s2t*F4t + hb*ht*mt*Ab*s2b*F4b
$ +.5d0*ht*hb*s2t*s2b*(At*Ab+mu**2)*F5
$ +2d0*ht*hb*mt*mb*F6
S22 = .5d0*hb**2*mu**2*s2b**2*F3b
$ + 2d0*ht**2*mt**2*F1t + 2d0*ht**2*At*mt*s2t*F2t
$ + .5d0*ht**2*At**2*s2t**2*F3t
$ + 2d0*ht*hb*mt*mu*s2b*F4b + hb*ht*mu*At*s2b*s2t*F5
S11 = k*S11
S12 = k*S12
S22 = k*S22
return
end
*
***********************************************************************
*
subroutine su_DDSodd(t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,vv,
$ DMA)
implicit none
real*8 t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,vv,DMA
real*8 c2t,s2t,c2b,s2b,At,Ab,Xt,Xb,mt,mb,cbe,sbe,ht,hb,pi,k
real*8 F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp
pi = 3.14159265358979d0
mt = dsqrt(t)
mb = dsqrt(b)
s2t = 2d0*ct*st
s2b = 2d0*cb*sb
c2t = ct**2 - st**2
c2b = cb**2 - sb**2
Xt = (T1-T2)*s2t/2d0/mt
Xb = (B1-B2)*s2b/2d0/mb
At = Xt - mu/tanb
Ab = Xb - mu*tanb
sbe = dsin(datan(tanb))
cbe = dcos(datan(tanb))
ht = dsqrt(2d0/vv)*mt/sbe
hb = dsqrt(2d0/vv)*mb/cbe
k = 3d0/(16d0*Pi**2)**2
call makefuncs(t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,q,mu,vv,tanb,
$ F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp)
DMA = -(ht**2*mu*At/(T1-T2)*Ft + hb**2*mu*Ab/(B1-B2)*Fb
$ + 2d0*ht*hb*FAp)/sbe/cbe
DMA = k*DMA
return
end
*
***********************************************************************
*
subroutine su_DDStad(t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,vv,
$ S1,S2)
implicit none
real*8 t,b,A0,T1,T2,B1,B2,st,ct,sb,cb,q,mu,tanb,vv
real*8 c2t,s2t,c2b,s2b,At,Ab,Xt,Xb,mt,mb,cbe,sbe,pi,k
real*8 F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp
real*8 v1,v2,S1,S2
pi = 3.14159265358979d0
mt = dsqrt(t)
mb = dsqrt(b)
s2t = 2d0*ct*st
s2b = 2d0*cb*sb
c2t = ct**2 - st**2
c2b = cb**2 - sb**2
Xt = (T1-T2)*s2t/2d0/mt
Xb = (B1-B2)*s2b/2d0/mb
At = Xt - mu/tanb
Ab = Xb - mu*tanb
sbe = dsin(datan(tanb))
cbe = dcos(datan(tanb))
k = 3d0/(16d0*Pi**2)**2
call makefuncs(t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,q,mu,vv,tanb,
$ F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp)
v1 = Sqrt(vv)*cbe
v2 = Sqrt(vv)*sbe
S1 = mt*mu/tanb*s2t*Ft + mb*Ab*s2b*Fb + 2d0*mb**2*Gb
S2 = mb*mu*tanb*s2b*Fb + mt*At*s2t*Ft + 2d0*mt**2*Gt
S1 = k*S1/v1**2
S2 = k*S2/v2**2
return
end
*
***********************************************************************
*
subroutine makefuncs(t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,
$ q,mu,vv,tanb,F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,
$ Ft,Fb,Gt,Gb,FAp)
implicit none
real*8 t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,q,mu,vv,tanb,
$ F1t,F2t,F3t,F4t,F1b,F2b,F3b,F4b,F5,F6,Ft,Fb,Gt,Gb,FAp
real*8 D1t,DT1,DT2,Dc2t,DT1T1,DT2T2,Dtt,Dc2tc2t,DT1t,DT2t,DT1T2,
$ Dtc2t,DT1c2t,DT2c2t,Dtb,DT1b,DT2b,DB1t,DB2t,DT1B1,DT2B1,
$ DT1B2,DT2B2,Dbc2t,DB1c2t,DB2c2t,DT1c2b,DT2c2b,Dc2tc2b,
$ Dcptpb,Dcpttptb,Dcpbptt,Dcptptb,Dcptmptt,Dcpbmptb,
$ Dspbmptbspbptt,Dsptmpttsptptb,Dsptmpttspbmptb
common/listderiv/D1t,DT1,DT2,Dc2t,DT1T1,DT2T2,
$ Dtt,Dc2tc2t,DT1t,DT2t,DT1T2,
$ Dtc2t,DT1c2t,DT2c2t,Dtb,DT1b,DT2b,DB1t,DB2t,DT1B1,DT2B1,
$ DT1B2,DT2B2,Dbc2t,DB1c2t,DB2c2t,DT1c2b,DT2c2b,Dc2tc2b,
$ Dcptpb,Dcpttptb,Dcpbptt,Dcptptb,Dcptmptt,Dcpbmptb,
$ Dspbmptbspbptt,Dsptmpttsptptb,Dsptmpttspbmptb
real*8 D1b,DB1,DB2,Dc2b,DB1B1,DB2B2,Dbb,Dc2bc2b,DB1b,DB2b,DB1B2,
$ Dbc2b,DB1c2b,DB2c2b,Dtc2b
real*8 Xt,Xb,At,Ab
call makederiv(b,t,A0,B1,B2,T1,T2,s2b,c2b,s2t,c2t,
$ q,mu,vv,1d0/tanb)
D1b = D1t
DB1 = DT1
DB2 = DT2
Dc2b = Dc2t
DB1B1 = DT1T1
DB2B2 = DT2T2
Dbb = Dtt
Dc2bc2b = Dc2tc2t
DB1b = DT1t
DB2b = DT2t
DB1B2 = DT1T2
Dbc2b = Dtc2t
DB1c2b = DT1c2t
DB2c2b = DT2c2t
Dtc2b = Dbc2t
call makederiv(t,b,A0,T1,T2,B1,B2,s2t,c2t,s2b,c2b,q,mu,vv,tanb)
F1t = Dtt + DT1T1 + DT2T2 + 2d0*(DT1t + DT2t + DT1T2)
$ +(Dcptpb + Dcptmptt + Dcptptb - 2d0*Dsptmpttsptptb)
$ /4d0/t**2
F2t = DT1T1 - DT2T2 + DT1t - DT2t
$ -4d0*c2t**2/(T1-T2)*(Dtc2t + DT1c2t + DT2c2t)
$ -(Dcptmptt - Dsptmpttsptptb)/s2t**2/t/(T1-T2)
F3t = DT1T1 + DT2T2 - 2d0*DT1T2
$ - 2d0/(T1-T2)*(DT1-DT2)
$ + 16d0*c2t**2/(T1-T2)**2*(c2t**2*Dc2tc2t + 2d0*Dc2t)
$ -8d0*c2t**2/(T1-T2)*(DT1c2t-DT2c2t)
$ + 4d0/s2t**4/(T1-T2)**2*(Dcptmptt + Dcpbptt + Dcpttptb)
F4t = DT1b + DT1B1 + DT1B2 - DT2b - DT2B1 - DT2B2
$ -4d0*c2t**2/(T1-T2)*(DB1c2t + DB2c2t + Dbc2t)
$ -(Dcpbptt + Dsptmpttspbmptb - Dspbmptbspbptt)
$ /b/s2t**2/(T1-T2)