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pygfxx.f
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1 
2 C*********************************************************************
3 
4 C...PYGFXX
5 C...Auxiliary to PYRGHM.
6 
7  SUBROUTINE pygfxx(MA,TANB,MQ,MUR,MD,MTOP,AT,AB,XMU,XMGL,VH,
8  * stop1,stop2,sbot1,sbot2,deltamt,deltamb)
9  IMPLICIT DOUBLE PRECISION(a-h,m,o-z)
10  dimension vh(2,2),vh3t(2,2),vh3b(2,2),al(2,2)
11 C...Commonblocks.
12  INTEGER mstu,mstj,kchg
13  common/pydat1/mstu(200),paru(200),mstj(200),parj(200)
14  common/pydat2/kchg(500,4),pmas(500,4),parf(2000),vckm(4,4)
15  SAVE /pydat1/,/pydat2/
16 
17  g(x,y) = 2.d0 - (x+y)/(x-y)*dlog(x/y)
18 
19  t(x,y,z) = (x**2*y**2*log(x**2/y**2) + x**2*z**2*log(z**2/x**2)
20  * + y**2*z**2*log(y**2/z**2))/((x**2-y**2)*(y**2-z**2)*(x**2-z**2))
21 
22  IF(dabs(xmu).LT.0.000001d0) xmu = 0.000001d0
23  mq2 = mq**2
24  mur2 = mur**2
25  md2 = md**2
26  tanba = tanb
27  sinba = tanba/dsqrt(tanba**2+1d0)
28  cosba = sinba/tanba
29 
30  sinb = tanb/dsqrt(tanb**2+1d0)
31  cosb = sinb/tanb
32 
33  pi = paru(1)
34  mz = pmas(23,1)
35  mw = pmas(24,1)
36  sw = 1d0-mw**2/mz**2
37  v = 174.1d0
38 
39  alpha3 = 0.12d0/(1d0+23/12d0/pi*0.12d0*log(mtop**2/mz**2))
40  g2 = dsqrt(0.0336d0*4d0*pi)
41  g1 = dsqrt(0.0101d0*4d0*pi)
42 
43  IF(mq.GT.mur) mst = mq
44  IF(mur.GT.mq.OR.mur.EQ.mq) mst = mur
45 
46  msusyt = dsqrt(mst**2 + mtop**2)
47 
48  IF(mq.GT.md) msb = mq
49  IF(md.GT.mq.OR.md.EQ.mq) msb = md
50 
51  mb = pymrun(5,msb**2)
52  msusyb = dsqrt(msb**2 + mb**2)
53  tt = log(msusyt**2/mtop**2)
54  tb = log(msusyb**2/mtop**2)
55 
56  rmtop = mtop/(1d0+4d0*alpha3/3d0/pi)
57  ht = rmtop/(v*sinb)
58  htst = rmtop/v
59  hb = mb/v/cosb
60  g32 = alpha3*4d0*pi
61  bt2 = -(8d0*g32 - 9d0*ht**2/2d0 - hb**2/2d0)/(4d0*pi)**2
62  bb2 = -(8d0*g32 - 9d0*hb**2/2d0 - ht**2/2d0)/(4d0*pi)**2
63  al2 = 3d0/8d0/pi**2*ht**2
64 C BT2ST = -(8.*G32 - 9.*HTST**2/2.)/(4.*PI)**2
65 C ALST = 3./8./PI**2*HTST**2
66  al1 = 3d0/8d0/pi**2*hb**2
67 
68  al(1,1) = al1
69  al(1,2) = (al2+al1)/2d0
70  al(2,1) = (al2+al1)/2d0
71  al(2,2) = al2
72 
73  IF(ma.GT.mtop) THEN
74  vi = v*(1d0 + 3d0/32d0/pi**2*htst**2*
75  * log(mtop**2/ma**2))
76  h1i = vi* cosba
77  h2i = vi*sinba
78  h1t = h1i*(1d0+3d0/8d0/pi**2*hb**2*log(ma**2/msusyt**2))**.25d0
79  h2t = h2i*(1d0+3d0/8d0/pi**2*ht**2*log(ma**2/msusyt**2))**.25d0
80  h1b = h1i*(1d0+3d0/8d0/pi**2*hb**2*log(ma**2/msusyb**2))**.25d0
81  h2b = h2i*(1d0+3d0/8d0/pi**2*ht**2*log(ma**2/msusyb**2))**.25d0
82  ELSE
83  vi = v
84  h1i = vi*cosb
85  h2i = vi*sinb
86  h1t=h1i*(1d0+3d0/8d0/pi**2*hb**2*log(mtop**2/msusyt**2))**.25d0
87  h2t=h2i*(1d0+3d0/8d0/pi**2*ht**2*log(mtop**2/msusyt**2))**.25d0
88  h1b=h1i*(1d0+3d0/8d0/pi**2*hb**2*log(mtop**2/msusyb**2))**.25d0
89  h2b=h2i*(1d0+3d0/8d0/pi**2*ht**2*log(mtop**2/msusyb**2))**.25d0
90  ENDIF
91 
92  tanbst = h2t/h1t
93  sinbt = tanbst/dsqrt(1d0+tanbst**2)
94 
95  tanbsb = h2b/h1b
96  sinbb = tanbsb/dsqrt(1d0+tanbsb**2)
97  cosbb = sinbb/tanbsb
98 
99  deltamt = 0d0
100  deltamb = 0d0
101 
102  mtop4 = rmtop**4*(1d0+2d0*bt2*tt- al2*tt - 4d0*deltamt)
103  mtop2 = dsqrt(mtop4)
104  mbot4 = mb**4*(1d0+2d0*bb2*tb - al1*tb)
105  * /(1d0+deltamb)**4
106  mbot2 = dsqrt(mbot4)
107 
108  stop12 = (mq2 + mur2)*.5d0 + mtop2
109  * +1d0/8d0*(g2**2+g1**2)*(h1t**2-h2t**2)
110  * +sqrt(((g2**2-5d0*g1**2/3d0)/4d0*(h1t**2-h2t**2) +
111  * mq2 - mur2)**2*0.25d0 + mtop2*(at-xmu/tanbst)**2)
112  stop22 = (mq2 + mur2)*.5d0 + mtop2
113  * +1d0/8d0*(g2**2+g1**2)*(h1t**2-h2t**2)
114  * - sqrt(((g2**2-5d0*g1**2/3d0)/4d0*(h1t**2-h2t**2) +
115  * mq2 - mur2)**2*0.25d0
116  * + mtop2*(at-xmu/tanbst)**2)
117  IF(stop22.LT.0.) goto 120
118  sbot12 = (mq2 + md2)*.5d0
119  * - 1d0/8d0*(g2**2+g1**2)*(h1b**2-h2b**2)
120  * + sqrt(((g1**2/3d0-g2**2)/4d0*(h1b**2-h2b**2) +
121  * mq2 - md2)**2*0.25d0 + mbot2*(ab-xmu*tanbsb)**2)
122  sbot22 = (mq2 + md2)*.5d0
123  * - 1d0/8d0*(g2**2+g1**2)*(h1b**2-h2b**2)
124  * - sqrt(((g1**2/3d0-g2**2)/4d0*(h1b**2-h2b**2) +
125  * mq2 - md2)**2*0.25d0 + mbot2*(ab-xmu*tanbsb)**2)
126  IF(sbot22.LT.0.) sbot22 = 10000d0
127 
128  stop1 = dsqrt(stop12)
129  stop2 = dsqrt(stop22)
130  sbot1 = dsqrt(sbot12)
131  sbot2 = dsqrt(sbot22)
132 
133 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
134 C
135 C HERE IS THE DEFINITION OF DELTAMB AND DELTAMT, WHICH
136 C ARE THE VERTEX CORRECTIONS TO THE BOTTOM AND TOP QUARK
137 C MASS, KEEPING THE DOMINANT QCD AND TOP YUKAWA COUPLING
138 C INDUCED CORRECTIONS.
139 C
140 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
141 
142  x=sbot1
143  y=sbot2
144  z=xmgl
145  IF(x.EQ.y) x = x - 0.00001d0
146  IF(x.EQ.z) x = x - 0.00002d0
147  IF(y.EQ.z) y = y - 0.00003d0
148 
149  t1=t(x,y,z)
150  x=stop1
151  y=stop2
152  z=xmu
153  IF(x.EQ.y) x = x - 0.00001d0
154  IF(x.EQ.z) x = x - 0.00002d0
155  IF(y.EQ.z) y = y - 0.00003d0
156  t2=t(x,y,z)
157  deltamb = -2*alpha3/3d0/pi*xmgl*(ab-xmu*tanb)*t1
158  * + ht**2/(4d0*pi)**2*(at-xmu/tanb)*xmu*tanb*t2
159  x=stop1
160  y=stop2
161  z=xmgl
162  IF(x.EQ.y) x = x - 0.00001d0
163  IF(x.EQ.z) x = x - 0.00002d0
164  IF(y.EQ.z) y = y - 0.00003d0
165  t3=t(x,y,z)
166  deltamt = -2d0*alpha3/3d0/pi*(at-xmu/tanb)*xmgl*t3
167 
168 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
169 C
170 C HERE THE NEW VALUES OF THE TOP AND BOTTOM QUARK MASSES AT
171 C THE SCALE MS ARE DEFINED, TO BE USED IN THE EFFECTIVE
172 C POTENTIAL APPROXIMATION. THEY ARE JUST THE OLD ONES, BUT
173 C INCLUDING THE FINITE CORRECTIONS DELTAMT AND DELTAMB.
174 C THE DELTAMB CORRECTIONS CAN BECOME LARGE AND ARE RESUMMED
175 C TO ALL ORDERS, AS SUGGESTED IN THE TWO RECENT WORKS BY M. CARENA,
176 C S. MRENNA AND C.E.M. WAGNER, AS WELL AS IN THE WORK BY M. CARENA,
177 C D. GARCIA, U. NIERSTE AND C.E.M. WAGNER, TO APPEAR. THE TOP
178 C QUARK MASS CORRECTIONS ARE SMALL AND ARE KEPT IN THE PERTURBATIVE
179 C FORMULATION. THE FUNCTION T(X,Y,Z) IS NECESSARY FOR THE
180 C CALCULATION. THE ENTRIES ARE MASSES AND NOT THEIR SQUARES !
181 C
182 C
183 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
184 
185  mtop4 = rmtop**4*(1d0+2d0*bt2*tt- al2*tt - 4d0*deltamt)
186  mtop2 = dsqrt(mtop4)
187  mbot4 = mb**4*(1d0+2d0*bb2*tb - al1*tb)
188  * /(1d0+deltamb)**4
189  mbot2 = dsqrt(mbot4)
190 
191  stop12 = (mq2 + mur2)*.5d0 + mtop2
192  * +1d0/8d0*(g2**2+g1**2)*(h1t**2-h2t**2)
193  * +sqrt(((g2**2-5d0*g1**2/3d0)/4d0*(h1t**2-h2t**2) +
194  * mq2 - mur2)**2*0.25d0 + mtop2*(at-xmu/tanbst)**2)
195  stop22 = (mq2 + mur2)*.5d0 + mtop2
196  * +1d0/8d0*(g2**2+g1**2)*(h1t**2-h2t**2)
197  * - sqrt(((g2**2-5d0*g1**2/3d0)/4d0*(h1t**2-h2t**2) +
198  * mq2 - mur2)**2*0.25d0
199  * + mtop2*(at-xmu/tanbst)**2)
200 
201  IF(stop22.LT.0.) goto 120
202  sbot12 = (mq2 + md2)*.5d0
203  * - 1d0/8d0*(g2**2+g1**2)*(h1b**2-h2b**2)
204  * + sqrt(((g1**2/3d0-g2**2)/4d0*(h1b**2-h2b**2) +
205  * mq2 - md2)**2*0.25d0 + mbot2*(ab-xmu*tanbsb)**2)
206  sbot22 = (mq2 + md2)*.5d0
207  * - 1d0/8d0*(g2**2+g1**2)*(h1b**2-h2b**2)
208  * - sqrt(((g1**2/3d0-g2**2)/4d0*(h1b**2-h2b**2) +
209  * mq2 - md2)**2*0.25d0 + mbot2*(ab-xmu*tanbsb)**2)
210  IF(sbot22.LT.0.) goto 120
211 
212 
213  stop1 = dsqrt(stop12)
214  stop2 = dsqrt(stop22)
215  sbot1 = dsqrt(sbot12)
216  sbot2 = dsqrt(sbot22)
217 
218 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
219 CCC D-TERMS
220 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
221  stw=sw
222 
223  f1t=(mq2-mur2)/(stop12-stop22)*(.5d0-4d0/3d0*stw)*
224  * log(stop1/stop2)
225  * +(.5d0-2d0/3d0*stw)*log(stop1*stop2/(mq2+mtop2))
226  * + 2d0/3d0*stw*log(stop1*stop2/(mur2+mtop2))
227 
228  f1b=(mq2-md2)/(sbot12-sbot22)*(-.5d0+2d0/3d0*stw)*
229  * log(sbot1/sbot2)
230  * +(-.5d0+1d0/3d0*stw)*log(sbot1*sbot2/(mq2+mbot2))
231  * - 1d0/3d0*stw*log(sbot1*sbot2/(md2+mbot2))
232 
233  f2t=dsqrt(mtop2)*(at-xmu/tanbst)/(stop12-stop22)*
234  * (-.5d0*log(stop12/stop22)
235  * +(4d0/3d0*stw-.5d0)*(mq2-mur2)/(stop12-stop22)*
236  * g(stop12,stop22))
237 
238  f2b=dsqrt(mbot2)*(ab-xmu*tanbsb)/(sbot12-sbot22)*
239  * (.5d0*log(sbot12/sbot22)
240  * +(-2d0/3d0*stw+.5d0)*(mq2-md2)/(sbot12-sbot22)*
241  * g(sbot12,sbot22))
242 
243  vh3b(1,1) = mbot4/(cosbb**2)*(log(sbot1**2*sbot2**2/
244  * (mq2+mbot2)/(md2+mbot2))
245  * + 2d0*(ab*(ab-xmu*tanbsb)/(sbot1**2-sbot2**2))*
246  * log(sbot1**2/sbot2**2)) +
247  * mbot4/(cosbb**2)*(ab*(ab-xmu*tanbsb)/
248  * (sbot1**2-sbot2**2))**2*g(sbot12,sbot22)
249 
250  vh3t(1,1) =
251  * mtop4/(sinbt**2)*(xmu*(-at+xmu/tanbst)/(stop1**2
252  * -stop2**2))**2*g(stop12,stop22)
253 
254  vh3b(1,1)=vh3b(1,1)+
255  * mz**2*(2*mbot2*f1b-dsqrt(mbot2)*ab*f2b)
256 
257  vh3t(1,1) = vh3t(1,1) +
258  * mz**2*(dsqrt(mtop2)*xmu/tanbst*f2t)
259 
260  vh3t(2,2) = mtop4/(sinbt**2)*(log(stop1**2*stop2**2/
261  * (mq2+mtop2)/(mur2+mtop2))
262  * + 2d0*(at*(at-xmu/tanbst)/(stop1**2-stop2**2))*
263  * log(stop1**2/stop2**2)) +
264  * mtop4/(sinbt**2)*(at*(at-xmu/tanbst)/
265  * (stop1**2-stop2**2))**2*g(stop12,stop22)
266 
267  vh3b(2,2) =
268  * mbot4/(cosbb**2)*(xmu*(-ab+xmu*tanbsb)/(sbot1**2
269  * -sbot2**2))**2*g(sbot12,sbot22)
270 
271  vh3t(2,2)=vh3t(2,2)+
272  * mz**2*(-2*mtop2*f1t+dsqrt(mtop2)*at*f2t)
273  vh3b(2,2) = vh3b(2,2) -mz**2*dsqrt(mbot2)*xmu*tanbsb*f2b
274  vh3t(1,2) = -
275  * mtop4/(sinbt**2)*xmu*(at-xmu/tanbst)/
276  * (stop1**2-stop2**2)*(log(stop1**2/stop2**2) + at*
277  * (at - xmu/tanbst)/(stop1**2-stop2**2)*g(stop12,stop22))
278 
279  vh3b(1,2) =
280  * - mbot4/(cosbb**2)*xmu*(ab-xmu*tanbsb)/
281  * (sbot1**2-sbot2**2)*(log(sbot1**2/sbot2**2) + ab*
282  * (ab - xmu*tanbsb)/(sbot1**2-sbot2**2)*g(sbot12,sbot22))
283 
284 
285  vh3t(1,2)=vh3t(1,2) +
286  *mz**2*(mtop2/tanbst*f1t-dsqrt(mtop2)*(at/tanbst+xmu)/2d0*f2t)
287 
288  vh3b(1,2)=vh3b(1,2) +
289  *mz**2*(-mbot2*tanbsb*f1b+dsqrt(mbot2)*(ab*tanbsb+xmu)/2d0*f2b)
290 
291  vh3t(2,1) = vh3t(1,2)
292  vh3b(2,1) = vh3b(1,2)
293 
294 C TQ = LOG((MQ2 + MTOP2)/MTOP2)
295 C TU = LOG((MUR2+MTOP2)/MTOP2)
296 C TQD = LOG((MQ2 + MB**2)/MB**2)
297 C TD = LOG((MD2+MB**2)/MB**2)
298 
299  DO 110 i = 1,2
300  DO 100 j = 1,2
301  vh(i,j) =
302  * 6d0/(8d0*pi**2*(h1t**2+h2t**2))
303  * *vh3t(i,j)*0.5d0*(1d0-al(i,j)*tt/2d0) +
304  * 6d0/(8d0*pi**2*(h1b**2+h2b**2))
305  * *vh3b(i,j)*0.5d0*(1d0-al(i,j)*tb/2d0)
306  100 CONTINUE
307  110 CONTINUE
308 
309  goto 150
310  120 DO 140 i =1,2
311  DO 130 j = 1,2
312  vh(i,j) = -1d15
313  130 CONTINUE
314  140 CONTINUE
315 
316 
317  150 RETURN
318  END