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