MASSIVE LEPTON PAIR PRODUCTION IN HADRON-HADRON COLLISIONS AT HIGH ENERGIES

MASSIVE LEPTON PAIR PRODUCTION IN HADRON-HADRON COLLISIONS AT HIGH ENERGIES

June 1970 | Sidney D. Drell and Tung-Mow Yan
This paper discusses the production of massive lepton pairs in high-energy hadron-hadron collisions, focusing on the limiting region where $ s \to \infty $ and $ Q^2/s $ is finite. The authors use a parton model to analyze the process, connecting it to deep inelastic electron scattering. They predict a rapidly decreasing cross section as $ Q^2/s \to 1 $, due to the observed rapid fall-off of the inelastic scattering structure function $ \nu W_2 $ near threshold. The parton model, based on Feynman's impulse approximation, treats hadrons as composed of partons, which are treated as free particles during collisions. In the Bjorken limit, partons are strongly bound but can be viewed as long-lived in an infinite momentum frame. The ratio $ x = Q^2/2M\nu $ measures the fraction of the longitudinal momentum of the parton from which the electron scatters, and is finite in the Bjorken limit. The paper also discusses the application of the impulse approximation to electron-positron annihilation into hadrons and to the production of massive lepton pairs in hadron-hadron collisions. It shows that such processes can be described in an infinite momentum frame as the creation of a free parton-antiparton pair and its decay into final states. The authors analyze the kinematics of the process in the center-of-mass frame, showing that a massive state with $ Q^2 \sim s $ emerging from a colliding proton is impossible to satisfy both energy and momentum conservation without exchanging "wee" partons. In contrast, the dominant amplitude in the production of a massive lepton pair is the annihilation of an anti-parton-parton pair, resulting in a very massive system due to the addition of energies and subtraction of momenta. The paper derives the cross section for the process in the deep inelastic region, showing that it simplifies in the scaling limit. The result is expressed in terms of invariant structure functions and the momentum fraction $ x $. The authors conclude that the observed rapid decrease of the inelastic structure function $ F_2(x) $ as $ x \to 1 $ leads to a prediction of a very rapid falloff in $ \mathcal{F}(\tau) $ with increasing $ \tau = Q^2/s $. The paper also discusses the angular distribution of the vector $ q $, the total momentum of the muon pair, and the polarization of the virtual photon. It concludes that the parton and anti-parton structures of different hadrons can be compared, and that the impulse approximation applies to processes with hard partons, independent of the total cross section for hadrons at high energies.This paper discusses the production of massive lepton pairs in high-energy hadron-hadron collisions, focusing on the limiting region where $ s \to \infty $ and $ Q^2/s $ is finite. The authors use a parton model to analyze the process, connecting it to deep inelastic electron scattering. They predict a rapidly decreasing cross section as $ Q^2/s \to 1 $, due to the observed rapid fall-off of the inelastic scattering structure function $ \nu W_2 $ near threshold. The parton model, based on Feynman's impulse approximation, treats hadrons as composed of partons, which are treated as free particles during collisions. In the Bjorken limit, partons are strongly bound but can be viewed as long-lived in an infinite momentum frame. The ratio $ x = Q^2/2M\nu $ measures the fraction of the longitudinal momentum of the parton from which the electron scatters, and is finite in the Bjorken limit. The paper also discusses the application of the impulse approximation to electron-positron annihilation into hadrons and to the production of massive lepton pairs in hadron-hadron collisions. It shows that such processes can be described in an infinite momentum frame as the creation of a free parton-antiparton pair and its decay into final states. The authors analyze the kinematics of the process in the center-of-mass frame, showing that a massive state with $ Q^2 \sim s $ emerging from a colliding proton is impossible to satisfy both energy and momentum conservation without exchanging "wee" partons. In contrast, the dominant amplitude in the production of a massive lepton pair is the annihilation of an anti-parton-parton pair, resulting in a very massive system due to the addition of energies and subtraction of momenta. The paper derives the cross section for the process in the deep inelastic region, showing that it simplifies in the scaling limit. The result is expressed in terms of invariant structure functions and the momentum fraction $ x $. The authors conclude that the observed rapid decrease of the inelastic structure function $ F_2(x) $ as $ x \to 1 $ leads to a prediction of a very rapid falloff in $ \mathcal{F}(\tau) $ with increasing $ \tau = Q^2/s $. The paper also discusses the angular distribution of the vector $ q $, the total momentum of the muon pair, and the polarization of the virtual photon. It concludes that the parton and anti-parton structures of different hadrons can be compared, and that the impulse approximation applies to processes with hard partons, independent of the total cross section for hadrons at high energies.
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[slides and audio] Massive Lepton-Pair Production in Hadron-Hadron Collisions at High Energies