def fZmInvM(nl):
return (8481925./93312. +
(137.*nl)/216. + (652841.*pi*pi)/38880. - (nl*pi*pi)/27. -
(695.*pi*pi*pi*pi)/7776. - (575.*pi*pi*log(2))/162. -
(22.*pi*pi*log(2)*log(2))/81. -
(55.*log(2)*log(2)*log(2)*log(2))/162. - (220.*A4)/27. -
nl*nl*(-2353./23328. - (13.*pi*pi)/324. - (7.*zeta(3))/54.) +
(58.*zeta(3))/27. -
(1439.*pi*pi*zeta(3))/432. - nl*(246643./23328. + (967.*pi*pi)/648. -
(61.*pi*pi*pi*pi)/1944. + (11.*pi*pi*log(2))/81. -
(2.*pi*pi*log(2)*log(2))/81. -
log(2)*log(2)*log(2)*log(2)/81. - (8.*A4)/27. +
(241.*zeta(3))/72.) +
(1975.*zeta(5))/216.)
def gamma3_qcd(nf):
return (
(4603055. / 162. + 135680. * zeta(3) / 27. - 8800. * zeta(5) +
(-91723. / 27. - 34192. * zeta(3) / 9. + 880. * zeta(4) +
18400. * zeta(5) / 9.) * nf +
(5242. / 243. + 800. * zeta(3) / 9. - 160. * zeta(4) / 3.) * nf**2 +
(-332. / 243. + 64. * zeta(3) / 27.) * nf**3) / 256.)
def fKsFromMs3(Mu, M, Nf):
b0 = 11 - 2 * Nf / 3.
return -(b0 / 2.)**2 * (
2353 / 2592. + 13 / 36. * pi**2 + 7 / 6. * zeta(3) - 16 / 9. * Mu / M *
((log(M / (2 * Mu)) + 8 / 3.)**2 + 67 / 36. - pi**2 / 6.) -
2 / 3. * Mu**2 / M**2 *
((log(M / (2 * Mu)) + 13 / 6.)**2 + 10 / 9. - pi**2 / 6.))
def fKsFromMs2(Mu, M, Nf):
b0 = 11 - 2*Nf/3.
return ((((1/3.)*log(M/(2*Mu))+13/18.)*b0 - pi**2/3. + 23/18.)*Mu**2/M**2
+ (((8/9.)*log(M/(2*Mu))+64/27.)*b0 - 8*pi**2/9. + 92/27.) * Mu/M
- (pi**2/12. + 71/96.)*b0
+ zeta(3)/6. - pi**2/9. * log(2) + 7*pi**2/12. + 23/72.
)
def fKsFromMs2(Mu, M, Nf):
b0 = 11 - 2 * Nf / 3.
return (((
(1 / 3.) * log(M /
(2 * Mu)) + 13 / 18.) * b0 - pi**2 / 3. + 23 / 18.) *
Mu**2 / M**2 + (((8 / 9.) * log(M / (2 * Mu)) + 64 / 27.) * b0 -
8 * pi**2 / 9. + 92 / 27.) * Mu / M -
(pi**2 / 12. + 71 / 96.) * b0 + zeta(3) / 6. -
pi**2 / 9. * log(2) + 7 * pi**2 / 12. + 23 / 72.)
def fOsFromMs2(mu, M, nl):
lmM=log((mu*mu)/(M*M))
return ((1111.*ca*cf)/384. - (71.*cf*cf)/128. -
(143.*cf*tr)/96. - (71.*cf*nl*tr)/96. +
lmM*((185.*ca*cf)/96. - (9.*cf*cf)/32. - (13.*cf*tr)/24. -
(13.*cf*nl*tr)/24.) +
lmM*lmM*((11.*ca*cf)/32. + (9.*cf*cf)/32. - (cf*tr)/8. - (cf*nl*tr)/8.) -
(ca*cf*zeta(2))/2. + (15.*cf*cf*zeta(2))/8. + (3.*ca*cf*log(2)*zeta(2))/2.
- 3.*cf*cf*log(2)*zeta(2) +
cf*tr*zeta(2) - (cf*nl*tr*zeta(2))/2. - (3.*ca*cf*zeta(3))/8. +
(3.*cf*cf*zeta(3))/4.)
def fMsFromOs2(mu, M, nl):
lmM=log((mu*mu)/(M*M))
erg= ((-1111.*ca*cf)/384. + (7.*cf*cf)/128. -
(185.*ca*cf*lmM)/96. + (21.*cf*cf*lmM)/32. - (11.*ca*cf*lmM*lmM)/32. +
(9.*cf*cf*lmM*lmM)/32. + (143.*cf*tr)/96. + (13.*cf*lmM*tr)/24. +
(cf*lmM*lmM*tr)/8. +
(71.*cf*nl*tr)/96. + (13.*cf*lmM*nl*tr)/24. + (cf*lmM*lmM*nl*tr)/8. +
(ca*cf*zeta(2))/2 - (15.*cf*cf*zeta(2))/8. - (3.*ca*cf*log(2)*zeta(2))/2. +
3.*cf*cf*log(2)*zeta(2) -
cf*tr*zeta(2) + (cf*nl*tr*zeta(2))/2. + (3.*ca*cf*zeta(3))/8. -
(3.*cf*cf*zeta(3))/4.)
return erg
def gamma2_16_9(f):
if f != 5:
raise ValueError('Only implemented for 5 flavours')
return np.array([
-1359190 / 19683. + (6976 * zeta(3)) / 243.,
-229696 / 6561. - (3584 * zeta(3)) / 81.,
-1290092 / 6561. + (3200 * zeta(3)) / 81.,
-819971 / 19683. - (19936 * zeta(3)) / 243.,
-16821944 / 6561. + (30464 * zeta(3)) / 81.,
-17787368 / 19683. - (286720 * zeta(3)) / 243.
])
def gamma2_16_9(f):
if f != 5:
raise ValueError('Only implemented for 5 flavours')
return np.array([-1359190/19683. + (6976*zeta(3))/243., -229696/6561. - (3584*zeta(3))/81.,
-1290092/6561. + (3200*zeta(3))/81., -819971/19683. - (19936*zeta(3))/243.,
-16821944/6561. + (30464*zeta(3))/81., -17787368/19683. - (286720*zeta(3))/243.])
def gamma2_qcd(nf):
return (1249. + (-2216. / 27. - 160. * zeta(3) / 3.) * nf -
140. * nf * nf / 81.) / 64.
def fZmM(nl):
return (-9478333. / 93312. +
55. * log(2) * log(2) * log(2) * log(2) / 162. +
(-644201. / 6480. + 587. * log(2) / 27. +
44. * log(2) * log(2) / 27.) * zeta(2) - 61. * zeta(3) / 27. +
3475 * zeta(4) / 432. + 1439. * zeta(2) * zeta(3) / 72. -
1975. * zeta(5) / 216. + 220. * A4 / 27. + nl *
(246643. / 23328. - log(2) * log(2) * log(2) * log(2) / 81. +
(967. / 108. + 22. * log(2) / 27. - 4. * log(2) * log(2) / 27.) *
zeta(2) + 241. * zeta(3) / 72. - 305. * zeta(4) / 108. -
8. * A4 / 27.) + nl * nl *
(-2353. / 23328. - 13. * zeta(2) / 54 - 7. * zeta(3) / 54.))
def fOsFromMs3(mu, M, nl):
lmM = log((mu * mu) / (M * M))
return (lmM * lmM * lmM *
((121. * ca * ca * cf) / 576. + (33. * ca * cf * cf) / 128. +
(9. * cf * cf * cf) / 128. - (11. * ca * cf * tr) / 72. -
(3. * cf * cf * tr) / 32. - (11. * ca * cf * nl * tr) / 72. -
(3. * cf * cf * nl * tr) / 32. + (cf * tr * tr) / 36. +
(cf * nl * tr * tr) / 18. + (cf * nl * nl * tr * tr) / 36.) +
lmM * lmM *
((2341. * ca * ca * cf) / 1152. + (21. * ca * cf * cf) / 64. -
(63. * cf * cf * cf) / 128. - (373. * ca * cf * tr) / 288. -
(3. * cf * cf * tr) / 32. - (373. * ca * cf * nl * tr) / 288. -
(3. * cf * cf * nl * tr) / 32. + (13. * cf * tr * tr) / 72. +
(13. * cf * nl * tr * tr) / 36. +
(13. * cf * nl * nl * tr * tr) / 72.) + lmM *
((13243. * ca * ca * cf) / 1728. - (4219. * ca * cf * cf) / 1536. +
(495. * cf * cf * cf) / 512. - (583. * ca * cf * tr) / 108. -
(307. * cf * cf * tr) / 384. - (869. * ca * cf * nl * tr) / 216. -
(91. * cf * cf * nl * tr) / 384. + (197. * cf * tr * tr) / 216. +
(143. * cf * nl * tr * tr) / 108. +
(89. * cf * nl * nl * tr * tr) / 216. -
(11. * ca * ca * cf * zeta(2)) / 12. +
(49. * ca * cf * cf * zeta(2)) / 16. +
(45. * cf * cf * cf * zeta(2)) / 32. +
(11. * ca * ca * cf * log(2) * zeta(2)) / 4. -
(35. * ca * cf * cf * log(2) * zeta(2)) / 8. -
(9. * cf * cf * cf * log(2) * zeta(2)) / 4. +
(13. * ca * cf * tr * zeta(2)) / 6. -
(cf * cf * tr * zeta(2)) / 2. - ca * cf * log(2) * tr * zeta(2) +
2. * cf * cf * log(2) * tr * zeta(2) -
(7. * ca * cf * nl * tr * zeta(2)) / 12. -
(13. * cf * cf * nl * tr * zeta(2)) / 8. - ca * cf * log(2) * nl *
tr * zeta(2) + 2. * cf * cf * log(2) * nl * tr * zeta(2) -
(2. * cf * tr * tr * zeta(2)) / 3. -
(cf * nl * tr * tr * zeta(2)) / 3. +
(cf * nl * nl * tr * tr * zeta(2)) / 3. -
(11. * ca * ca * cf * zeta(3)) / 16. +
(35. * ca * cf * cf * zeta(3)) / 32. +
(9. * cf * cf * cf * zeta(3)) / 16. -
(ca * cf * tr * zeta(3)) / 2. + (cf * cf * tr * zeta(3)) / 4. -
(ca * cf * nl * tr * zeta(3)) / 2. +
(cf * cf * nl * tr * zeta(3)) / 4.))
def SeidelC(q2, mb, mu):
"""Function $A(s\equiv q^2)$ defined in eq. (31) of hep-ph/0403185v2.
"""
return (-(16)/(81) * log((q2)/(mu**2)) + (428)/(243)
- (64)/(27) * zeta(3) + (16)/(81) * pi * 1j)
def gamma2_16(f):
return np.array([
[
-1927 / 2. + (257 * f) / 9. + (40 * f**2) / 9. +
(224 + (160 * f) / 3.) * zeta(3), 475 / 9. + (362 * f) / 27. -
(40 * f**2) / 27. - (896 / 3. + (320 * f) / 9.) * zeta(3),
269107 / 13122. - (2288 * f) / 729. - (1360 * zeta(3)) / 81.,
-2425817 / 13122. + (30815 * f) / 4374. - (776 * zeta(3)) / 81.,
-343783 / 52488. + (392 * f) / 729. + (124 * zeta(3)) / 81.,
-37573 / 69984. + (35 * f) / 972. + (100 * zeta(3)) / 27.
],
[
307 / 2. + (361 * f) / 3. - (20 * f**2) / 3. -
(1344 + 160 * f) * zeta(3),
1298 / 3. - (76 * f) / 3. - 224 * zeta(3),
69797 / 2187. + (904 * f) / 243. + (2720 * zeta(3)) / 27.,
1457549 / 8748. - (22067 * f) / 729. - (2768 * zeta(3)) / 27.,
-37889 / 8748. - (28 * f) / 243. - (248 * zeta(3)) / 27.,
366919 / 11664. - (35 * f) / 162. - (110 * zeta(3)) / 9.
],
[
0, 0,
-4203068 / 2187. + (14012 * f) / 243. - (608 * zeta(3)) / 27.,
-18422762 / 2187. + (888605 * f) / 2916. + (272 * f**2) / 27. +
(39824 / 27. + 160 * f) * zeta(3),
674281 / 4374. - (1352 * f) / 243. - (496 * zeta(3)) / 27.,
9284531 / 11664. - (2798 * f) / 81. - (26 * f**2) / 27. -
(1921 / 9. + 20 * f) * zeta(3)
],
[
0, 0, -5875184 / 6561. + (217892 * f) / 2187. +
(472 * f**2) / 81. + (27520 / 81. + (1360 * f) / 9.) * zeta(3),
-70274587 / 13122. + (8860733 * f) / 17496. -
(4010 * f**2) / 729. + (16592 / 81. + (2512 * f) / 27.) * zeta(3),
2951809 / 52488. - (31175 * f) / 8748. - (52 * f**2) / 81. -
(3154 / 81. + (136 * f) / 9.) * zeta(3),
3227801 / 8748. - (105293 * f) / 11664. - (65 * f**2) / 54. +
(200 / 27. - (220 * f) / 9.) * zeta(3)
],
[
0, 0, -194951552 / 2187. + (358672 * f) / 81. -
(2144 * f**2) / 81. + (87040 * zeta(3)) / 27.,
-130500332 / 2187. - (2949616 * f) / 729. + (3088 * f**2) / 27. +
(238016 / 27. + 640 * f) * zeta(3), 14732222 / 2187. -
(27428 * f) / 81. + (272 * f**2) / 81. - (13984 * zeta(3)) / 27.,
16521659 / 2916. + (8081 * f) / 54. - (316 * f**2) / 27. -
(22420 / 9. + 200 * f) * zeta(3)
],
[
0, 0,
162733912 / 6561. - (2535466 * f) / 2187. + (17920 * f**2) / 243. +
(174208 / 81. + (12160 * f) / 9.) * zeta(3),
13286236 / 6561. - (1826023 * f) / 4374. - (159548 * f**2) / 729. -
(24832 / 81. + (9440 * f) / 27.) * zeta(3),
-22191107 / 13122. + (395783 * f) / 4374. - (1720 * f**2) / 243. -
(33832 / 81. + (1360 * f) / 9.) * zeta(3),
-32043361 / 8748. + (3353393 * f) / 5832. - (533 * f**2) / 81. +
(9248 / 27. - (1120 * f) / 9.) * zeta(3)
]
])
def SeidelC(q2, mb, mu):
"""Function $A(s\equiv q^2)$ defined in eq. (31) of hep-ph/0403185v2.
"""
flavio.citations.register("Seidel:2004jh")
return (-(16) / (81) * log((q2) / (mu**2)) + (428) / (243) - (64) /
(27) * zeta(3) + (16) / (81) * pi * 1j)
def fKsFromMs3(Mu, M, Nf):
b0 = 11 - 2*Nf/3.
return -(b0/2.)**2*(2353/2592.+13/36.*pi**2+7/6.*zeta(3)
-16/9.*Mu/M*((log(M/(2*Mu))+8/3.)**2+67/36.-pi**2/6.)
-2/3.*Mu**2/M**2*((log(M/(2*Mu))+13/6.)**2+10/9.-pi**2/6.))
def gamma2_16(f):
return np.array([[-1927/2. + (257*f)/9. + (40*f**2)/9. + (224 + (160*f)/3.)*zeta(3),
475/9. + (362*f)/27. - (40*f**2)/27. - (896/3. + (320*f)/9.)*zeta(3),
269107/13122. - (2288*f)/729. - (1360*zeta(3))/81., -2425817/13122. + (30815*f)/4374. -
(776*zeta(3))/81., -343783/52488. + (392*f)/729. + (124*zeta(3))/81.,
-37573/69984. + (35*f)/972. + (100*zeta(3))/27.],
[307/2. + (361*f)/3. - (20*f**2)/3. - (1344 + 160*f)*zeta(3),
1298/3. - (76*f)/3. - 224*zeta(3), 69797/2187. + (904*f)/243. + (2720*zeta(3))/27.,
1457549/8748. - (22067*f)/729. - (2768*zeta(3))/27., -37889/8748. - (28*f)/243. -
(248*zeta(3))/27., 366919/11664. - (35*f)/162. - (110*zeta(3))/9.],
[0, 0, -4203068/2187. + (14012*f)/243. - (608*zeta(3))/27.,
-18422762/2187. + (888605*f)/2916. + (272*f**2)/27. + (39824/27. + 160*f)*zeta(3),
674281/4374. - (1352*f)/243. - (496*zeta(3))/27., 9284531/11664. - (2798*f)/81. -
(26*f**2)/27. - (1921/9. + 20*f)*zeta(3)],
[0, 0, -5875184/6561. + (217892*f)/2187. + (472*f**2)/81. +
(27520/81. + (1360*f)/9.)*zeta(3), -70274587/13122. + (8860733*f)/17496. -
(4010*f**2)/729. + (16592/81. + (2512*f)/27.)*zeta(3),
2951809/52488. - (31175*f)/8748. - (52*f**2)/81. - (3154/81. + (136*f)/9.)*zeta(3),
3227801/8748. - (105293*f)/11664. - (65*f**2)/54. + (200/27. - (220*f)/9.)*zeta(3)],
[0, 0, -194951552/2187. + (358672*f)/81. - (2144*f**2)/81. + (87040*zeta(3))/27.,
-130500332/2187. - (2949616*f)/729. + (3088*f**2)/27. + (238016/27. + 640*f)*zeta(3),
14732222/2187. - (27428*f)/81. + (272*f**2)/81. - (13984*zeta(3))/27.,
16521659/2916. + (8081*f)/54. - (316*f**2)/27. - (22420/9. + 200*f)*zeta(3)],
[0, 0, 162733912/6561. - (2535466*f)/2187. + (17920*f**2)/243. +
(174208/81. + (12160*f)/9.)*zeta(3), 13286236/6561. - (1826023*f)/4374. -
(159548*f**2)/729. - (24832/81. + (9440*f)/27.)*zeta(3),
-22191107/13122. + (395783*f)/4374. - (1720*f**2)/243. - (33832/81. + (1360*f)/9.)*zeta(3),
-32043361/8748. + (3353393*f)/5832. - (533*f**2)/81. + (9248/27. - (1120*f)/9.)*zeta(3)]])
def gamma3_qcd(nf):
return ((4603055./162. + 135680.*zeta(3)/27. - 8800.*zeta(5) +
(-91723./27. - 34192.*zeta(3)/9. +
880.*zeta(4) + 18400.*zeta(5)/9.)*nf +
(5242./243. + 800.*zeta(3)/9. - 160.*zeta(4)/3.)*nf**2 +
(-332./243. + 64.*zeta(3)/27.)*nf**3)/256.)
def fZmM(nl):
return (-9478333./93312. + 55.*log(2)*log(2)*log(2)*log(2)/162. +
(-644201./6480. + 587.*log(2)/27. + 44.*log(2)*log(2)/27.)*zeta(2) -
61.*zeta(3)/27. + 3475*zeta(4)/432. + 1439.*zeta(2)*zeta(3)/72. -
1975.*zeta(5)/216. + 220.*A4/27. + nl*(246643./23328. -
log(2)*log(2)*log(2)*log(2)/81. +(967./108. + 22.*log(2)/27. -
4.*log(2)*log(2)/27.)*zeta(2) + 241.*zeta(3)/72. - 305.*zeta(4)/108. -
8.*A4/27.) + nl*nl*(-2353./23328. - 13.*zeta(2)/54 - 7.*zeta(3)/54.))
def gamma2_qcd(nf):
return (1249. + (-2216./27. - 160.*zeta(3)/3.)*nf-140.*nf*nf/81.)/64.
def fOsFromMs3(mu, M, nl):
lmM=log((mu*mu)/(M*M))
return (lmM*lmM*lmM*((121.*ca*ca*cf)/576. + (33.*ca*cf*cf)/128. +
(9.*cf*cf*cf)/128. - (11.*ca*cf*tr)/72. - (3.*cf*cf*tr)/32. -
(11.*ca*cf*nl*tr)/72. -
(3.*cf*cf*nl*tr)/32. + (cf*tr*tr)/36. + (cf*nl*tr*tr)/18. +
(cf*nl*nl*tr*tr)/36.) + lmM*lmM*((2341.*ca*ca*cf)/1152.
+ (21.*ca*cf*cf)/64. -
(63.*cf*cf*cf)/128. - (373.*ca*cf*tr)/288. - (3.*cf*cf*tr)/32. -
(373.*ca*cf*nl*tr)/288. - (3.*cf*cf*nl*tr)/32. + (13.*cf*tr*tr)/72. +
(13.*cf*nl*tr*tr)/36. + (13.*cf*nl*nl*tr*tr)/72.) +
lmM*((13243.*ca*ca*cf)/1728. - (4219.*ca*cf*cf)/1536. +
(495.*cf*cf*cf)/512. -
(583.*ca*cf*tr)/108. - (307.*cf*cf*tr)/384. - (869.*ca*cf*nl*tr)/216. -
(91.*cf*cf*nl*tr)/384. + (197.*cf*tr*tr)/216. + (143.*cf*nl*tr*tr)/108. +
(89.*cf*nl*nl*tr*tr)/216. - (11.*ca*ca*cf*zeta(2))/12. +
(49.*ca*cf*cf*zeta(2))/16. +
(45.*cf*cf*cf*zeta(2))/32. + (11.*ca*ca*cf*log(2)*zeta(2))/4. -
(35.*ca*cf*cf*log(2)*zeta(2))/8. -
(9.*cf*cf*cf*log(2)*zeta(2))/4. + (13.*ca*cf*tr*zeta(2))/6. -
(cf*cf*tr*zeta(2))/2. -
ca*cf*log(2)*tr*zeta(2) + 2.*cf*cf*log(2)*tr*zeta(2) -
(7.*ca*cf*nl*tr*zeta(2))/12. -
(13.*cf*cf*nl*tr*zeta(2))/8. - ca*cf*log(2)*nl*tr*zeta(2) +
2.*cf*cf*log(2)*nl*tr*zeta(2) -
(2.*cf*tr*tr*zeta(2))/3. - (cf*nl*tr*tr*zeta(2))/3. +
(cf*nl*nl*tr*tr*zeta(2))/3. -
(11.*ca*ca*cf*zeta(3))/16. + (35.*ca*cf*cf*zeta(3))/32. +
(9.*cf*cf*cf*zeta(3))/16. -
(ca*cf*tr*zeta(3))/2. + (cf*cf*tr*zeta(3))/4. - (ca*cf*nl*tr*zeta(3))/2. +
(cf*cf*nl*tr*zeta(3))/4.))
def fMsFromOs3(mu, M, nl):
lmM = log((mu * mu) / (M * M))
erg = (
(lmM * lmM *
(-2341. * ca * ca * cf + 1962. * ca * cf * cf - 243. * cf * cf * cf +
1492. * ca * cf * tr - 468. * cf * cf * tr + 1492. * ca * cf * nl *
tr - 468. * cf * cf * nl * tr - 208. * cf * tr * tr -
416. * cf * nl * tr * tr - 208. * cf * nl * nl * tr * tr)) / 1152. +
(lmM * lmM * lmM *
(-242. * ca * ca * cf + 297. * ca * cf * cf - 81. * cf * cf * cf +
176. * ca * cf * tr - 108. * cf * cf * tr + 176. * ca * cf * nl * tr
- 108. * cf * cf * nl * tr - 32. * cf * tr * tr -
64. * cf * nl * tr * tr - 32. * cf * nl * nl * tr * tr)) / 1152. +
(lmM *
(-105944. * ca * ca * cf + 52317. * ca * cf * cf -
13203. * cf * cf * cf + 74624. * ca * cf * tr - 5436. * cf * cf * tr
+ 55616. * ca * cf * nl * tr + 2340. * cf * cf * nl * tr -
12608. * cf * tr * tr - 18304. * cf * nl * tr * tr -
5696. * cf * nl * nl * tr * tr + 12672. * ca * ca * cf * zeta(2) -
52704. * ca * cf * cf * zeta(2) + 19440. * cf * cf * cf * zeta(2) -
38016. * ca * ca * cf * log(2) * zeta(2) + 91584. * ca * cf * cf *
log(2) * zeta(2) - 31104. * cf * cf * cf * log(2) * zeta(2) -
29952. * ca * cf * tr * zeta(2) + 27648. * cf * cf * tr * zeta(2) +
13824. * ca * cf * log(2) * tr * zeta(2) - 27648. * cf * cf *
log(2) * tr * zeta(2) + 8064. * ca * cf * nl * tr * zeta(2) +
12096. * cf * cf * nl * tr * zeta(2) + 13824. * ca * cf * log(2) *
nl * tr * zeta(2) - 27648. * cf * cf * log(2) * nl * tr * zeta(2) +
9216. * cf * tr * tr * zeta(2) + 4608. * cf * nl * tr * tr * zeta(2)
- 4608. * cf * nl * nl * tr * tr * zeta(2) +
9504. * ca * ca * cf * zeta(3) - 22896. * ca * cf * cf * zeta(3) +
7776. * cf * cf * cf * zeta(3) + 6912. * ca * cf * tr * zeta(3) -
3456. * cf * cf * tr * zeta(3) + 6912. * ca * cf * nl * tr * zeta(3)
- 3456. * cf * cf * nl * tr * zeta(3))) / 13824.)
return erg
def fMsFromOs3(mu, M, nl):
lmM=log((mu*mu)/(M*M))
erg= ((lmM*lmM*(-2341.*ca*ca*cf + 1962.*ca*cf*cf - 243.*cf*cf*cf
+ 1492.*ca*cf*tr -
468.*cf*cf*tr + 1492.*ca*cf*nl*tr - 468.*cf*cf*nl*tr - 208.*cf*tr*tr -
416.*cf*nl*tr*tr - 208.*cf*nl*nl*tr*tr))/1152. +
(lmM*lmM*lmM*(-242.*ca*ca*cf + 297.*ca*cf*cf - 81.*cf*cf*cf +
176.*ca*cf*tr - 108.*cf*cf*tr + 176.*ca*cf*nl*tr - 108.*cf*cf*nl*tr -
32.*cf*tr*tr - 64.*cf*nl*tr*tr - 32.*cf*nl*nl*tr*tr))/1152. +
(lmM*(-105944.*ca*ca*cf + 52317.*ca*cf*cf - 13203.*cf*cf*cf +
74624.*ca*cf*tr -
5436.*cf*cf*tr + 55616.*ca*cf*nl*tr + 2340.*cf*cf*nl*tr -
12608.*cf*tr*tr -
18304.*cf*nl*tr*tr - 5696.*cf*nl*nl*tr*tr + 12672.*ca*ca*cf*zeta(2) -
52704.*ca*cf*cf*zeta(2) + 19440.*cf*cf*cf*zeta(2) -
38016.*ca*ca*cf*log(2)*zeta(2) +
91584.*ca*cf*cf*log(2)*zeta(2) - 31104.*cf*cf*cf*log(2)*zeta(2) -
29952.*ca*cf*tr*zeta(2) +
27648.*cf*cf*tr*zeta(2) + 13824.*ca*cf*log(2)*tr*zeta(2) -
27648.*cf*cf*log(2)*tr*zeta(2) +
8064.*ca*cf*nl*tr*zeta(2) + 12096.*cf*cf*nl*tr*zeta(2) +
13824.*ca*cf*log(2)*nl*tr*zeta(2) -
27648.*cf*cf*log(2)*nl*tr*zeta(2) + 9216.*cf*tr*tr*zeta(2) +
4608.*cf*nl*tr*tr*zeta(2) -
4608.*cf*nl*nl*tr*tr*zeta(2) + 9504.*ca*ca*cf*zeta(3) -
22896.*ca*cf*cf*zeta(3) +
7776.*cf*cf*cf*zeta(3) + 6912.*ca*cf*tr*zeta(3) - 3456.*cf*cf*tr*zeta(3) +
6912.*ca*cf*nl*tr*zeta(3) - 3456.*cf*cf*nl*tr*zeta(3)))/13824.)
return erg
