proton charge
In[14]:= quarkcharges = �2 � 3, -1 � 3, -1 � 3, 2 � 3, -1 � 3, 2 � 3�;protoncharge[xi_] := NIntegrate�Sum�quarkcharges[[i]]
�cteq5pdf[1, i, x, 10] - cteq5pdf[1, -i, x, 10]�, {i, 1, 6}�, {x, xi, 1}�;LogLinearPlot�protoncharge[xi], �xi, 10^�-6�, 1��
Out[15]=
10-5 10-4 0.001 0.010 0.100 1
0.2
0.4
0.6
0.8
1.0
zoom on interesting region, 3 x 10-5 seems like a good cuto� to get charge
correct
In[16]:= LogLinearPlot�{1, protoncharge[xi]}, �xi, 5 × 10-6, 5 × 10-5��
Out[16]=
1.×10-5 2.×10-5 5.×10-5
0.985
0.990
0.995
1.000
4 hw4_solution.nb
total momentum fraction of all quarks as function of Q
In[20]:= quarkmomfrac[q_] := NIntegrate�Sum�x �cteq5pdf[1, i, x, q] + cteq5pdf[1, -i, x, q]�, {i, 1, 6}�, �x, 3 × 10-5, 1��;
gluonmomfrac[q_] := NIntegrate�x cteq5pdf[1, 0, x, q], �x, 3 × 10-5, 1��;LogLinearPlot[{quarkmomfrac[q]}, {q, 2, 2000}, PlotLegends � {"quarks"}]
LogLinearPlot[{quarkmomfrac[q], gluonmomfrac[q], quarkmomfrac[q] + gluonmomfrac[q]},
{q, 2, 2000}, PlotLegends � {"quarks", "gluon", "quarks+gluon"}]
Out[22]=
5 10 50 100 500 1000
0.52
0.53
0.54
0.55
0.56
0.57
quarks
Out[23]=
5 10 50 100 500 1000
0.5
0.6
0.7
0.8
0.9
1.0
quarks
gluon
quarks+gluon
hw4_solution.nb 5
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