Proton Structure


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Measurements related to the Quark Distributions of the Proton

    The analysis of deep inelastic lepton-proton scattering allows the structure of the proton to be determined. The lepton and a quark from the proton interact by exchanging a gauge boson of the electro-weak interactions. Cross sections were measured for neutral current events (photon, Z-boson exchange) and for charged current events (W-boson exchange). In these processes the relevant observables are the virtuality Q2 of the gauge bosons and the momentum x of the quark relative to the proton momentum. From the measured cross sections, structure functions are extracted which contain information on the quark distributions of the proton. 
The figure shows H1 measurements of the proton structure function (full symbols). The momentum region includes sea quarks at momenta x = 10^-5 up to the valence quark region. The virtuality Q2 spans five orders of magnitude up to Q2 = 30000 GeV^2. At these large Q2 values the scattering process is sensitive to structures of size 10^-3fm. 
    At small values of Q2 of about 10 GeV^2 the precision of the structure function measurement is about 4%. This precision is comparable with that of previous fixed target experiments (open symbols). For fixed values of x, the Q2 dependence of the data shows scaling violations that are predicted by perturbative QCD. The H1 measurements and the fixed target data are well compatible in most regions of the phase space. In the region below Q2=10000 GeV^2, the measured scaling violations are well described by a QCD fit (full curves).
At fixed Q^2 and small parton momenta x_Bj, the structure function F_2 rises according to (x_Bj)^-lambda which reflects the high gluon density in the proton. The figure shows the Q2 dependence of the fitted values of lambda.

The total photon--proton cross section sigma_gamma*p is directly related to this large gluon density: using the relation x_Bj s_gamma*p ~ Q^2 = const. gives an energy dependence of the cross section as sigma_gamma*p~ F_2~ (x_Bj)^-lambda~ (s_gamma*p)^lambda. 

    At large values of Q2 the cross sections were measured for neutral current events as well as charged current events. For these measurements the H1 liquid argon calorimeter was calibrated in situ. The new calibration improves the precision of the measurements significantly.
The figure shows the single differential cross section measurements dsigma/dQ2 for positron-proton scattering of the H1 and Zeus experiments. 
    In the region around Q2 = 10^3 GeV^2, the neutral current cross section is dominated by photon exchange. The cross section decreases essentially as the propagator term 1/Q^4. Owing to the dependence of photon-quark scattering on the quark charge, the lepton interacts preferentially with quarks of electric charge 2/3, for example u and anti-u quarks. The cross section is proportional to the square of the electro magnetic coupling constant, a term depending on the scattering angle theta^* in the lepton-quark center of mass system, y=0.5(1-cos(theta^*)), and to the quark distributions x f of the proton: 

    dsigma_NC / dQ^2 ~ alpha^2/x/Q^4 ((1+(1-y)^2) x ( 4/9 (f_u/p + f_anti-u/p) + 1/9 (f_d/p + f_anti-d/p) + ...)

    For charged current interactions in positron-proton scattering, the positrons interact only with quarks or anti-quarks of negative electric charge, for example d or anti-u quarks. Furthermore the helicity structure of the weak interactions imply specific distributions in the variable y which is related to the scattering angle in the lepton-quark center of mass system as explained above. The cross section for charged current events is proportional to the square of the Fermi coupling constant, to the propagator term which contains the mass of the W-boson, and to the quark and anti-quark distributions of the proton:

    dsigma_CC /dQ^2 ~ G_Fermi^2/(1+Q^2/M_W^2)^2 ((1-y)^2 f_d/p + f_anti-u/p)

    The figure above showing the Q2 dependencies of the cross sections demonstrates that at small Q2 charged current events are highly suppressed relative to neutral current events. This is caused by the W-boson mass in the propagator term.
     
     

At large values of Q2 > 10^4 GeV^2, the neutral current cross section is modified by Z-boson exchange. For the first time in lepton-proton scattering the interference between photons and Z-bosons is visible in the data. 
The figure shows the first measurement of the double differential charged current cross section as function of y in different regions of the quark momentum x. In this cross section the effect of the propagator term has been removed in order to reflect the quark distributions of the proton: sigma_CC ~ x [(1-y) f_d/p + f_anti-u/p]. In this measurement the contributions of quarks and anti-quarks from the proton can be separated owing to the different y distributions. 
    The curves reflect parameterizations of the quark and anti-quark contributions. The contribution of the anti-quarks is essentially flat and decreases with increasing quark momentum x. In contrast, the distribution of the quark scattering angle according to (1-y)^2 is well visible at large x and shows the dominance of the the d-valence quark contributions to the cross section measurement. 

Measurements related to the Gluon Distributions of the Proton

The gluon distributions of the proton can be determined from the scaling violations of the proton structure function. The scaling violations are predicted by perturbative QCD in form of the DGLAP evolution equations. The figure shows the gluon distribution for two values of the photon virtuality.

    Complementary information on the gluon of the proton comes from direct measurements that involve the photon-gluon-fusion processes or elastic vector meson production:

    D* Meson

    Jets

    Vector Meson


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last updated by
H1 webmaster on 19/05/98