RevModPhys.84.1307

Incoming neutrino ux improved hadro production

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Unformatted text preview: ple, in the form of model-independent differential cross sections. Neutrino deep inelastic scattering has long been used to validate the standard model and probe nucleon structure. Over the years, experiments have measured cross sections, electroweak parameters, coupling constants, nucleon structure functions, and scaling variables using such processes. In deep inelastic scattering (Fig. 27), the neutrino scatters off a quark in the nucleon via the exchange of a virtual W or Z boson producing a lepton and a hadronic system in the final state.11 Both CC and NC processes are possible VI. HIGH-ENERGY CROSS SECTIONS: E $ 20–500 GeV Up to now, we have largely discussed neutrino scattering from composite entities such as nucleons or nuclei. Given enough energy, the neutrino can actually begin to resolve the Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012  N ! À X;  N ! þ X; " (80)  N !  X;  N !  X: " " (81) Here we restrict ourselves to the case of  scattering, as an example, though e and  DIS interactions are also possible. Following the formalism introduced in Sec. II, DIS processes can be completely described in terms of three dimensionless kinematic invariants. The first two, the inelasticity ðyÞ and the four-momentum transfer (Q2 ¼ Àq2 ), have already been defined. We now define the Bjorken scaling variable x, x¼ Q2 2pe Á q ðBjorken scaling variableÞ: (82) The Bjorken scaling variable plays a prominent role in deep inelastic neutrino scattering, where the target can carry a portion of the incoming energy momentum of the struck nucleus. 11 Quarks cannot be individually detected; they quickly recombine and thus appear as a hadronic shower. Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . . 1334 On a practical level, these Lorentz-invariant parameters cannot be readily determined from four-vectors, but they can be reconstructed using readily measured observables in a given experiment, x¼ Q2 Q2 ¼ ; 2M 2ME y where the sum is over all quark species. The struck quark carries a fraction x of the nucleon’s momentum, such that xq " (xq) is the probability of finding the quark (antiquark) with a given momentum fraction. These probabilities are known as parton distribution functions (PDFs). In this way, F2 ðx; Q2 Þ measures the sum of the quark and antiquark PDFs in the nucleon, while xF3 ðx; Q2 Þ measures their difference and is therefore sensitive to the valence quark PDFs. The third structure function 2xF1 ðx; Q2 Þ is commonly related to F2 ðx; Q2 Þ via a longitudinal structure function, RL ðx; Q2 Þ, (83) y ¼ Ehad =E ; (84) Q2 ¼ Àm2 þ 2E ðE À p cos Þ;  (85) F2 ðx; Q2 Þ ¼ where E is the incident neutrino energy, MN is the nucleon mass,  ¼ Ehad is the energy of the hadronic system, and E , p , and cos are the energy, momentum, and scattering angle of the outgoing muon in the laboratory frame. In the case of NC scattering, th...
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This document was uploaded on 09/28/2013.

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