In[]:=
<<X`
Package-X v2.1.1, by Hiren H. PatelFor more information, see the
guide
In[]:=
eps=0.5
-2
10
​​mpi=0.139​​mi=10.86(*+0.005I*)​​mf=10.3552​​x=0.4650000000000001​​4*mpi*mpi​​(*mz=1/2((mi+Ieps)^2+mf^2)-mpi^2*)​​sa[mz_]=2*mpi^2+mf^2+(mi+Ieps)^2-2mz^2​​spl=
1
2
2
mz
-
2
mf
2
(mi+Ieps)
+
2
mf
2
mpi
+
2
(mi+Ieps)
2
mpi
-
4
mpi
+
2
mf
2
mz
+
2
(mi+Ieps)
2
mz
+2
2
mpi
2
mz
-
4
mz
+
4
mf
-2
2
mf
2
mpi
+
4
mpi
-2
2
mf
2
mz
-2
2
mpi
2
mz
+
4
mz
4
(mi+Ieps)
-2
2
(mi+Ieps)
2
mpi
+
4
mpi
-2
2
(mi+Ieps)
2
mz
-2
2
mpi
2
mz
+
4
mz
HeavisideTheta[mz-Re@mi]​​ +
1
2
2
mz
-
2
mf
2
(mi+Ieps)
+
2
mf
2
mpi
+
2
(mi+Ieps)
2
mpi
-
4
mpi
+
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mf
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mz
+
2
(mi+Ieps)
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mz
+2
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mpi
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-
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mz
-
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mf
-2
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mf
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mpi
+
4
mpi
-2
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mf
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mz
-2
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mpi
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mz
+
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mz
4
(mi+Ieps)
-2
2
(mi+Ieps)
2
mpi
+
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mpi
-2
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(mi+Ieps)
2
mz
-2
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mpi
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+
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mz
HeavisideTheta[Re@mi-mz]​​Y[s_,mz_]=s+2*mz^2-mf^2-(mi+Ieps)^2-2*mpi^2​​sigma[s_]=Sqrt[1-(4*mpi^2/s)]​​κ[s_]=Expand[Sqrt[KallenExpand[Kallenλ[s,(mi+Ieps)^2,mf^2]]]*sigma[s]]​​(*l[s_,mz_]=(-sigma[s]/κ[s])Log[(Y[s,mz]+κ[s])/(Y[s,mz]-κ[s])]*)(*+2PiIHeavisideTheta[Re[sa[mz]]-s]*)(*+2PiHeavisideTheta[sa-s]*)(*+2PiIHeavisideTheta[sa-s]HeavisideTheta[s-Re[spl]]*)​​log[s_,mz_]=Log[(Y[s,mz]+κ[s])/(Y[s,mz]-κ[s])]*+2IPiHeavisideTheta[Re[sa[mz]]-s]​​discC0[s_,mz_]=(-sigma[s]/κ[s])log[s,mz]​​(*Plot[Im[log[s,10.42]]​​,{s,8.055584040000014`-0.1,8.055584040000014`+0.1}]*)​​​​Czero[s_,mz_]=Integrate[discC0[s,mz]/(s-x),{s,0.07728400000000002,0.2}]​​
Out[]=
0.005
Out[]=
0.139
Out[]=
10.86
Out[]=
10.3552
Out[]=
0.465
Out[]=
0.077284
Out[]=
(225.208+0.1086)-2
2
mz
Out[]=
(-12642.3-11.6431)+(225.208+0.1086)
2
mz
-
4
mz
-
(13905.2+25.6123)-(235.918+0.2172)
2
mz
+
4
mz
11494.2-214.499
2
mz
+
4
mz
HeavisideTheta[10.86-mz]
2
2
mz
+
(-12642.3-11.6431)+(225.208+0.1086)
2
mz
-
4
mz
+
(13905.2+25.6123)-(235.918+0.2172)
2
mz
+
4
mz
11494.2-214.499
2
mz
+
4
mz
HeavisideTheta[-10.86+mz]
2
2
mz
Out[]=
(-225.208-0.1086)+2
2
mz
+s
Out[]=
1-
0.077284
s
Out[]=
1-
0.077284
s
(114.68+2.32608)-(450.339+0.2172)s+
2
s
Out[]=
2πHeavisideTheta[225.208-s-2Re[
2
mz
]]Log
(-225.208-0.1086)+2
2
mz
+s+
1-
0.077284
s
(114.68+2.32608)-(450.339+0.2172)s+
2
s
(-225.208-0.1086)+2
2
mz
+s-
1-
0.077284
s
(114.68+2.32608)-(450.339+0.2172)s+
2
s

Out[]=
-
2πHeavisideTheta[225.208-s-2Re[
2
mz
]]Log
(-225.208-0.1086)+2
2
mz
+s+
1-
0.077284
s
(114.68+2.32608)-(450.339+0.2172)s+
2
s
(-225.208-0.1086)+2
2
mz
+s-
1-
0.077284
s
(114.68+2.32608)-(450.339+0.2172)s+
2
s

(114.68+2.32608)-(450.339+0.2172)s+
2
s
Out[]=
ConditionalExpression[0.+0.,Re[
2
mz
]>112.566]
In[]:=
(*X=Integrate[(l[s,mz]/(s-x)),{s,4*mpi*mpi+0.01,0.2}]*)​​
In[]:=
(*Plot[Im[x],{mz,10.22,10.92}]*)