2002 / 9 / 27 ( 15 : 42 : 15 ) /dfs/g/ce/ccs/tishika/1-loop-22/process/fsrc/zanalysis-genchk.f Revised 2002/09/24
these first 3 lines just give the history of when the file was created/revised.
Cuv alpha beta delta kappa esp. lamda 0.00E+00 .0 -2.0 1.0 .0 .0 1.00E-15 0.00E+00 .0 -1.0 1.0 .0 .0 1.00E-15 0.00E+00 .0 .0 1.0 .0 .0 1.00E-15 0.00E+00 .0 1.0 1.0 .0 .0 1.00E-15 0.00E+00 .0 2.0 1.0 .0 .0 1.00E-15
To make the test we set the all UV divergent factors, Cuv, to zero. The photon mass for IR divergence is set to lambda=10^-15GeV.
The test is made on beta with delta=1. We therefore generate data for the cross section and each one-loop matrix element of a diagram g times the full
tree-level amplitude. We need five values of beta in general, which are (-2,-1,0,1,2), as shown above.
-------------------------- <<selected graph>> 99 One should not pay too much attention to this entry. It is used by the program as a book-keeping device it does not always
correspond to the number of one-loop diagrams that are dependent on the gauge parameters. -------------------------- IU no. T : @ = ^2, # = ^3
For each one-loop diagram g that depends on the gauge parameter, we calculate the diffenrential cross section dsigmatest= Real (Tg *Ttree^dagger)
(see equation 6.6 of the paper). dsigmatest does not include the diagrams that do not depend on the gauge. The a^i (i=1,2,3,4) correspond to equation 6.7, that is the coefficient of the ith power in the gauge parameter.
a^0 for instance is the gauge independent part. The integer number appearing on the left is the number of the one-loop diagram g as it appears in gracefig.
RV | a^4 | a^3 | a^2 | a^1 | a^0 -------------------------- 1 @ | -.8926294E-05 | .4461238E-02 | .8411331E-02 4 @ | -.2310911E-06 | .1065293E-04 | .3052003E-05 9 @ | .4621823E-06 | .2631995E-06 | .3747113E-07 12 @ | -.2310911E-06 | .1065293E-04 | .3052003E-05 23 | .1162883E-03 | -.1162883E-03 25 | .1162883E-03 | -.1162883E-03 27 # | -.5804613E-04 | -.1248409E-02 | .6652586E-03 | .5170167E-02 28 | -.9911386E-03 | .1453175E-01 29 | -.1275262E-06 | -.6048228E-05 30 # | .1465954E-06 | -.6491296E-05 | -.3732261E-05 | -.5330459E-06 31 | .1997994E-03 | .5688999E-04 32 | .6376308E-07 | .1815562E-07 35 @ | .1048544E-06 | .5971158E-07 | .8501007E-08 37 | .6376308E-07 | .1815562E-07 38 # | .1465954E-06 | -.6491296E-05 | -.3732261E-05 | -.5330459E-06 39 | .1997994E-03 | .5688999E-04 42 | -.2284306E-05 | -.6504233E-06 43 | .2284306E-05 | -.2411574E-04 44 | .2284306E-05 | -.2411574E-04 45 | -.2284306E-05 | -.6504233E-06 58 @ | .7146101E-04 | .1998392E-34 | -.7146101E-04 59 | -.2057690E-04 | -.2057690E-04 60 @ | .7146101E-04 | .1998392E-34 | -.7146101E-04 61 | -.2057690E-04 | -.2057690E-04 63 @ | .5978400E-13 | -.4783845E-13 | -.1846826E-13 67 @ | -.2461771E-13 | -.1401908E-13 | -.1995865E-14 69 @ | .5978400E-13 | -.4783845E-13 | -.1846826E-13 72 @ | -.5348596E-12 | -.7049510E-12 | -.2510188E-11 75 | -.3978228E-13 | -.1132743E-13 77 | -.3978228E-13 | -.1132743E-13 78 @ | -.7079644E-12 | -.9691425E-12 | -.3213732E-11 79 @ | -.3642568E-14 | -.2074338E-14 | -.2953189E-15 91 | -.1386474E-12 | .1386474E-12 93 | -.1386474E-12 | .1386474E-12 95 | -.8893270E-13 | .8893270E-13 96 | -.8893270E-13 | .8893270E-13 123 | -.2240836E-02 | -.6724843E-02 126 | .5640279E-13 | .1605988E-13 129 | -.2823442E-02 | -.1221285E-01 130 | -.8012094E-15 | -.2281328E-15 132 | -.9970545E-02 | .1001987E-01 133 | -.4437841E-13 | -.1263611E-13 134 | -.4437841E-13 | -.1263611E-13 170 | -.4986578E-03 | -.1019782E+00 171 | .5271210E-03 | .1500901E-03 175 | -.4986578E-03 | -.1019782E+00 176 | .5271210E-03 | .1500901E-03 177 @ | -.3459754E-05 | .1168446E-03 | -.5246057E-03 178 @ | -.2681178E-05 | -.1526854E-05 | -.2173748E-06 179 | -.8856816E-16 | .8961233E-14 180 | .8856816E-16 | .2521851E-16 181 | .4313539E-14 | .1228218E-14 184 | .8856816E-16 | .2521851E-16 185 | -.8856816E-16 | .8961233E-14 190 | .4313539E-14 | .1228218E-14 194 @ | .1440046E-04 | -.1319089E-02 | .1061558E-01 197 @ | -.3827979E-13 | .9903911E-13 | .3130347E-13 201 @ | -.3827979E-13 | .9903911E-13 | .3130347E-13 205 @ | .1803263E-16 | .1026906E-16 | .1461984E-17 209 | -.6634029E-03 | .8113080E-01 210 | .8422653E-03 | .2398229E-03 214 | -.6634029E-03 | .8113080E-01 215 | .8422653E-03 | .2398229E-03 216 @ | -.2429701E-03 | .8639634E-03 | .2550019E-02 217 @ | -.3635518E-04 | -.2070323E-04 | -.2947473E-05 218 | -.5141143E-14 | -.1157094E-13 219 | .5141143E-14 | .1463866E-14 220 | -.8651686E-13 | -.2463443E-13 223 | .5141143E-14 | .1463866E-14 224 | -.5141143E-14 | -.1157094E-13 229 | -.8651686E-13 | -.2463443E-13 236 | -.1770349E-04 | -.1373286E-02 241 | -.1860966E-14 | -.5298833E-15 245 | -.1770349E-04 | -.1373286E-02 246 | -.1860966E-14 | -.5298833E-15 250 | -.2823442E-02 | -.1221285E-01 254 | -.2240836E-02 | -.6724843E-02 255 | .5640279E-13 | .1605988E-13 256 | -.8012094E-15 | -.2281328E-15 264 | -.1919137E-02 | -.5757411E-02 271 @ | .7116070E-12 | .0000000E+00 | .2275323E-11 273 | .5568653E-12 | .0000000E+00 274 | .5568653E-12 | .0000000E+00 277 | .6524269E-03 | -.2714769E-02 283 # | .2887647E-04 | .5564452E-03 | .4009333E-03 | -.1664247E-02 289 @ | .2390855E-12 | .1361523E-12 | .1938371E-13 294 | .6524269E-03 | -.2714769E-02 300 # | .2887647E-04 | .5564452E-03 | .4009333E-03 | -.1664247E-02 306 @ | .2390855E-12 | .1361523E-12 | .1938371E-13 316 @ | .2854663E-03 | .0000000E+00 | -.2854663E-03 319 | -.5192179E-02 | -.2317419E-01 320 | .8065584E-03 | -.1531387E-01 321 | .9563421E-12 | .8451992E-11 322 | .4395367E-02 | .3709453E-01 323 | .8348601E-02 | -.1168735E-01 326 | .4395367E-02 | .3709453E-01 327 | .1017475E-02 | .2576210E-03 329 | .1208937E-02 | -.3278990E-03 330 | .1721137E-03 | .4357856E-04 ---------------------------------------------------------------------- cnt 0 5 25 69
This counts the number of one-loop diagrams which are dependent on this specific combination of gauge parameters. The total number is arrived at
by adding all the entries. In this particular case :0+5+25+69=99. It means that there no diagram leads to a quartic dependence, 5 that have cubic dependence,
5+25 with a quartic and 5+25+69 that have a linear dependence.
tot -.21933E-01 -.21933E-01 -.21933E-01 -.21933E-01 -.21933E-01
This is just the value of dsigmatest
toto -.11507E-01 -.11507E-01 -.11507E-01 -.11507E-01 -.11507E-01
toto is just the contribution of all other diagrams that do not depend on the gauge parameter and which were not taken into account in the test above. Therefore
tot + toto=total correction. This value of total should be the same for any combination of parameters (all the tests for the same process are at the same point in phase space)
sum1 .94162E-31 .40068E-30 .17307E-27 .27802E-25 -.21933E-01
this is the sum on all coefficients for the quartic, cubic, quadratic, linear and constant term
sum2 .94595E-31 .39995E-30 .17307E-27 .27802E-25 -.21933E-01
this is the sum on all coefficients for the quartic, cubic, quadratic, linear and constant term, what's the difference
with sum1?? precision?
max .11273E-30 .58046E-04 .12484E-02 .99705E-02 .10198
For each term (quartic, cubic, quadratic, linear and constant) we give the maximum value of the coefficient.We display the absolute value.
s/m .83912 .68902E-26 .13863E-24 .27884E-23 -.21508
this gives the ratio of the sum over all coefficients (for quartic, cubic, quadratic, linear and constant) and the maximum, these values correspond to sum_i of the paper.
s/a0 -.43129E-29 -.18235E-28 -.78905E-26 -.12676E-23 1.0000
As with s/m but a0 stands here for tot.
b= 0 : -0.21933288997961144422646709524556334E-01 b= 1 : -0.21933288997961144422646681549115800E-01 b=-1 : -0.21933288997961144422646737153677301E-01 b= 2 : -0.21933288997961144422646653223820847E-01 b=-2 : -0.21933288997961144422646764437743266E-01
These are values of dsigmatest for the input parameters used to generate the data and to extract the coefficients.
Warning: these values are not the total one-loop corrections, since in dsigmatest we do not include the diagrams that do not depend on the gauge. Therefore
this values may be different depending on the combination of gauge parameters. Of course when all diagrams are included in any combination one should get the same
value (this will be givenn by tot+toto).
b=5 -> -0.21933288997961144422646566079406665E-01 This is the derived value of dsigmatest for beta=5. To machine precision it is given by the sum of
all gauge parameter independent entries (sum of all a^0).