In the HERA collider an electron beam of energy E_e = 30 GeV hits a proton beam with energy E_p = 820 GeV. The energy and the direction of the scattered electron are measured in order to study the proton structure. Calculate the centre of mass energy √s and the energy E_e,f an electron beam must have to reach the same √s at a fixed target. Calculate the maximum four-momentum transfer of the electron Q²_max for  x = 0.4, 0.01 and 0.0001. Compare with Fig. 6.13.

 

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x=6.3E-05 ZEUS 96/97 x=0.000102 A Fixed Target x=0.000161 Fit QCD x=0.000253 x=0.0004 x=0.0005 x=0.000632 x=0.0008 x=0.00102 x=0.0013 x=0.00161 x=0.0021 x=0.00253 x=0.0032 x=0.005 x=0.008 oaestst** x=0.013 x=0.021 paantiot |४4* अं 2 itsdata ttleplizzi rtaaydapte ree i x=0.05 x=0.032 padsolzzljij x=0.08 x=0.13 x=0.18 x=0.25 x=0.4 x=0.65 102 10 103 105 ợ (GeV2) 104 The F2 parton structure function as a function of Q' at different values of x as measured by the ZEUS experiment at HERA and by several fixed-target experiments. Lines are the DGLAP theoretical predictions (adapted from Chekanov et al. 2001). Fig. 6.13. **..**