What is the energy dependence of the Equivalent photon approximation?

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Discussion Overview

The discussion revolves around the energy dependence of the Equivalent Photon Approximation (EPA) and its validity at high center of mass energies, specifically questioning its application at 100 TeV. Participants explore the conditions under which the EPA is applicable and the potential limitations or corrections needed for accurate physical descriptions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the maximum center of mass energy for the EPA to be valid, specifically asking if it can be applied at 100 TeV.
  • Another participant suggests that the validity of the EPA depends on the type of process being considered, such as elastic or inelastic scattering, and emphasizes the role of the probe energy and exchange energy Q².
  • A follow-up question is posed regarding the validity of the EPA for the gg->e-e+ process at 100 TeV, indicating a specific application of the approximation.
  • One participant expresses skepticism about the EPA being a good approximation at high energies, noting that the cross-section may be influenced by low-Q values, which could lead to significant power corrections that the EPA neglects.
  • Concerns are raised about the photon flux distributions potentially peaking at small Q values, which could affect the applicability of the EPA in certain scenarios.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the EPA at high energies. There are competing views regarding the conditions under which the approximation holds, and the discussion remains unresolved regarding its applicability in specific processes.

Contextual Notes

Participants highlight the dependence of the EPA's validity on various energy scales and the nature of the scattering process, indicating that assumptions about these factors are crucial for determining the approximation's applicability.

ribella
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Hi,
What is the energy dependence of the Equivalent photon approximation? For this approach to be valid, what is the maximum center of mass-energy. As know, this approach is an energy-dependent approach. Can this approach be used to calculate, for example, at a center of mass energy of 100 TeV? Is there any problem with the approach in terms of physics?
 
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For what type of process do you have in mind?

A probe of the elastic form factor of a nucleon/nucleus? Or something like the inelastic photon pdf of a nucleus?

Typically this is governed by the probe energy / exchange energy Q^2 through the photon its self. If this energy scale is sufficiently small compared to other scales in the scattering process, then it is a decent approximation. If there are other energy scales such as a fermion mass that is mf~Q, then the EPA (assuming the photon is essentially on shell) neglects power corrections of the form Q/mf which can be important for a precision theory description.
 
Thank you for your answer. For example, let's assume that the center of mass energy for the gg->e-e+ process (Here, g is EPA photon) is 100 TeV. In this case, is the EPA approximation valid for the incoming photons at these energies?
 
I would not be confident that the EPA is a good approximation in this case.

(Do you mean the photon photon CoM or the hadronic one? That wasnt clear to me)

Even if the CoM is high, I think it is possible that the cross-section may still be dominated by low-Q (corresponding the virtuality probe of the nucleus/nucleon that is giving you these EPA photons).

Depending if you are considering a nucleus or a nucleon form factor (im not sure what you have in mind exactly) these distributions-the photon flux-may peak at small Q (eg at values below the electron mass). If that were the case, terms like Q/m_electron power corrections are absent in the EPA approach.

Note that a form factor like woods-saxon peaks as Q tends to zero (ie when you resolve the whole photon field of the nucleus).
 

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