Convince yourself that the interaction time is much shorter...

Name: Problem 2, Chapter 9: Quarks And Leptons. An Introductory Course In Modern Particle Physics
Uploaded: 2020-10-12T15:00:28-08:00
Duration: 24 s
Channel: Sarah Mccrumb
Description: Convince yourself that the interaction time is much shorter than the time scale over which the partons inside the target interact with one another. Read the explicit derivation in J. D. Bjorken and E. A. Paschos, Phys. Rev. 185,1975 (1969); see also Perl (1974).

Convince yourself that the interaction time is much shorter than the time scale over which the partons inside the target interact with one another. Read the explicit derivation in J. D. Bjorken and E. A. Paschos, Phys. Rev. 185,1975 (1969); see also Perl (1974).

Key Concepts

Time Scale Separation

This concept refers to the idea that different processes occur on very different time scales, allowing for a clear distinction between the short-duration interaction (such as a high-energy collision event) and the longer-duration internal dynamics (like interactions among constituents within a composite particle). By establishing that the interaction time is much shorter than the target’s internal interaction time, one can treat the internal structure as effectively static during the scattering event.

Parton Model

The parton model depicts hadrons (such as protons) as being composed of more fundamental constituents called partons, which behave quasi-independently during high-energy interactions. This theoretical framework is crucial because it allows the simplification of complex internal dynamics by assuming that, during the very short interaction time, partons do not have time to interact with each other.

Lorentz Contraction and Time Dilation

In high-energy physics, Lorentz contraction and time dilation are relativistic effects experienced by particles moving at speeds close to the speed of light. These effects imply that in the frame in which the scattering occurs, the internal structure of the fast-moving target appears ‘frozen’ due to the severely contracted time scale. This underlies the validity of treating the high-energy interaction as a snapshot of the target’s internal state.

Factorization

Factorization is a theoretical framework used to separate a complex process into a short-distance (perturbative) part and a long-distance (non-perturbative) part. The justification for factorization in high-energy processes relies on the separation of time scales, allowing one to compute the short interaction independently of the long-term internal dynamics of the target.

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