One finds experimentally that at ,suggesting that about half of the momentum is carried by gluons. This shows the important role of gluons in the proton structure. Although the naive quark model works very well in many cases, it is a too gross simplification as a model of hadrons, at least at large. There are other sum rules Gross-Llewellyn Smith sum rule,the Adler sum rule… could be studied and used by particle physicists to figure out different PDFs 3.
The obvious first QCD corrections will be due to real gluon emission by either the initial or final quark. To get rid of infrared divergences, the one-loop virtual gluon contribution should also be taken into account. One can easily understand the main qualitative features of gluon emission, with a few kinematical considerations.
At very low values of momentum transfer, the proton behaves as a single object, either point-like at , or with a finite size. At higher energies, the photon is sensitive to shorter distances and scatters with the constituent partons. Thus, a parton with momentum fraction can be resolved into a parton and a gluon of smaller momentum fractions, and , , respectively.
In a similar way, a gluon with momentum fraction can be resolved into a quark and an antiquark. This simple picture implies that increasing the , the photon will notice some qualitative changes in the parton distributions: — Gluon bremsstrahlung will shift the valence and sea distributions to smaller values.
Thus, without any detailed calculation, one can expect to find a definite dependence in the parton distributions; i. Let us consider a quark with momentum fraction. At lowest order, its contribution to the proton structure function can be written as If the quark emits a gluon before being struck by the photon, its momentum fraction will be degraded to , , Assuming that the quark remains approximately on- shell implying that Therefore, gets contributions from quarks with initial momentum fractions.
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The explicit calculation of the DIS diagrams gives the result: Where is called the quark splitting function. The important feature in eq. The divergence shows up when one tries to resolve the original quark with momentum fraction y into a quark with momentum fraction yz and a gluon.
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Physical observables should not depend on any cut-off, however, our definition of a parton distribution obviously depends on the power resolution of our photon probe. Thus, given its value at some reference point , one can compute the quark distribution at any other value of high-enough for perturbation theory to be valid. Including the leading higher-order logarithmic corrections into the running coupling, the of the parton distribution Altarelli-Parisi equation is given by Thus, the change in the distribution for a quark with momentum fraction , which interacts with the virtual photon, is given by the integral over of the corresponding distribution for a quark with momentum fraction which, having radiated a gluon, is left with a fraction of its original momentum.
The splitting function has then a very intuitive physical interpretation: is the probability associated with the splitting process. This probability is high for large momentum fractions;i. Therefore, increasing , the quark distribution function will decrease at large and will increase at small. Then we will look at the parton level calculation at lowest order.
The larger filled circle represents the hadron. The smaller filled circle represents a sum of subdiagrams in which the particles have virtualities of order Q2. All of these interactions are effectively instantaneous on the time scale of the intra-hadron interactions that form the wave function. The Parton distribution in eq.
The hard scattering cross sections are calcalated in perturbation theory. Now,we change variables in this eq. The variable y is identical to the parton level version of because appears in both the numerator and denominator: Eq. We have seen, in the case of deeply inelastic scattering of a lepton from a single hadron, that the dependence on these long time scales can be factored into a parton distribution function.
We need then in the hadron-hadron collision two parton distribution functions. Here, however, there are two parton distribution functions: The meaning of this formula is intuitive: gives the probability to find a parton in hadron A; gives the probability to find a parton in hadron B; and gives the cross section for these partons to produce the observed boson created. The hard scattering cross section can be calculated perturbatively. The observation of scaling violation and the identification of partons as quarks and gluons has confirmed the field theory of quarks and gluons and their strong interactions QCD.
At sufficiently large four-momentum transfer squared , when the strong coupling is small, a perturbative technique is applicable for QCD calculations of the coefficient and splitting functions. The latter represent the probability of a parton to emit another parton. In this chapter, using the QPM presented in chapter. Expressions for structure functions are determined by convolution integrals of appropriate sums over the densities of quarks of different flavours and gluons, which predict a logarithmic dependence evolution of the structure functions.
Partons quarks and gluons enter differently into different structure functions. In deep inelastic scattering the cross section of the neutral or charged current NC or CC process can be expressed in terms of three structure functions. The structure function depends on the valence quarks and is sizable only at large , when is comparable with the mass squared.
The longitudinal structure function , vanishing in the quark-parton model QPM , is directly sensitive to the gluon momentum distribution in the proton. So, The dominant contribution to the cross section is due to the proton structure function , which, in the framework of QPM, is related to the sum of the proton momentum fractions carried by the quarks and antiquarks in the proton weighted by the quark charges squared.
In these experiments H1 and ZEUS the target is always a proton entring in a collision with an electron or a positron many collisions to have accepted results physically -statistic point of view- ,the analysis take care about the important difference between charged current or neutre current processes. We compare the results with the standard model predictions. At high the cross section measurements are approaching each other demonstrating the unification of the weak and electromagnetic forces.
The double differential NC cross section measurements at high are shown in Figure8.
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At low the cross sections of the and interactions are essentially indistinguishable. At high they depart from each other due to the different sign of the contribution to the cross section see eq. It is dominated by the term and depends on the valence quark density only. Double differential CC cross sections are shown in Figure 9 as a function of for different. They are sensitive to individual flavours in the proton, the data to d and the data to u quarks. At high , the contribution from the valence quarks dominates the cross section and allows a local extraction of u and d densities. With increasing ,the structure function increases at small and decreases at large.
In the ZEUS fit their jet data are used as well. Its behaviour in is a reflection of the gluon density dynamics in the associated kinematic range. The derivative measurements are shown in Figure 14 as a function of for different. They show a continuous growth towards low without an indication of a change in the dynamics.
The derivatives are well described by the pQCD calculations for. We observed also the independence of the local derivatives in at fixed suggests that can be parameterised in a very simple form. Hazel, A. Peskin ,D. Derrick et al. Adloff et al. C 21 ZEUS Collab. Chekanov et al.
H1 Collab. C 30 1. D 70 Unlike our previous works, where the parton densities inside the nucleon have been computed at the hadronic scale of energy, i. Thus, at the first step, the extracted partonic distributions have been considered to calculate the nucleons and the nuclei structure functions and then the ratios of the neutron to the proton and He 3 to H 3 nuclei structure functions as well as the European Muon Collaboration ratios for the valence quark distributions, He 3 and H 3 nuclei, are calculated. The results are in a good agreement with both theoretical and available experimental data.
Library subscriptions will be modified accordingly. This arrangement will initially last for two years, up to the end of The PL valence-up quarks u val x the heavy full curve , Eq. The same as the Fig. The PL valence-down quarks d val x the heavy full curve , Eq. The PL sea quarks q sea x the full curve , Eq. The dashed curve is our previous results from Ref.
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The PL gluons g x the full curve , Eq. I also added to the present figure our previous results from Ref. The EMC ratios of the bound PL valence-up and -down quarks to the free valence quark in the helium-3 nucleus. The filled squares are the experimental data [ 78 ].
The small dashed curve is the theoretical result [ 16 ] for helium-3 and tritium, which is presented for comparison. The dashed curves are the same ratio, but only the U -type and D -type constituent quarks are included [ 22 ]. Text is free of markings. Foxing page edges. Ships with Tracking Number! May not contain Access Codes or Supplements.
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An Introduction to Quarks and Partons
View basket. Continue shopping. Title: introduction quarks partons. Results 1 - 27 of United Kingdom. Search Within These Results:. Introduction to Quarks and Partons F. An Introduction to Quarks and Partons F. An Introduction to Quarks and Partons. London, Academic Some figs.