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...
Assuming a stable tau, the calculations are equivalent up to corrections of order (mtau/mw)^2, and therefore almost numerically equivalent.
As the others alluded to, since this particle is not stable, the experimental (and theoretical) reality is more complicated.
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...
I would recommend that you implement this boost into your code.
1) generate the momenta in the CoM frame as you are doing.
2) apply the resultant boost to both p1 and p2
3) print the boosted (Lab frame momenta) and compare them to what you expect (i.e. p1_Lab = x1 Ehadron (1, 0, 0, 1), p2_Lab )...
The answers should be equivalent.
If you use the same set if inputs to both calculations, there should be a “correct” answer (up to numerical uncertainties of the numerical integration procedure).
If the integration without the pdf convolution agrees (i.e. you get the same exact answer for a...
I am instead suggesting to perform the phase-space sum with i = eL, eR meaning that you will have an integrals over the momenta of those out-going particles only (and not also the Higgs).
This will mean that the manipulations you did to deal with the delta functions before can be applied in the...
Is this a process of the form (1->2)? Cannot one immediately consider the 2body final state phase space of eL and eR evaluated in h CoM frame? Then apply the same procedure as you did and just deal with the dOmega integral.
You write the relation for ##C_L## there, which depends also on the hadronic variable ##x## (in addition to ##y## and ##Q^2##).
Maybe it would make sense to write: ##C_L(x,Q,y)##
This is not always true, and often bugs (which are sometimes, but not always) can lead to incorrect results being published.
This is true of experimental and theoretical work.
In some fortunate cases, mistakes are found. For example, someone repeats a calculation and does not find agreement...
Hi Caf,
Glad I was of help. In this case, the `double real' (since two emissions) would contribute to the matrix element at level $\mathcal{O}(\alpha_s)$ as you say. However, it won't contribute to the cross section until $\mathcal{O}(\alpha_s^2)$,
since the specific distinct final state:
e-e+...
At the end of the day, this is all speculation.
In the standard model, the Higgs mechanism is responsible for the top quark mass, and a yukawa coupling close to one is actually natural.
The fact that the other yukawa couplings are so small, and have a hierarchical structure is strange.
Of...
Hi again,
It is correct that you should consider all diagrams which occurs at a given fixed-order in the expansion. So, as you say at alpha^3 alpha_s you would consider:
real-real (so a QED and QCD emission of a photon and gluon respectively)
virtual-real (either a virtual QED + real QCD or...
Hi CAF,
These are important questions.
1) For the first. The KLN theorem in this case is telling us that we should not consider the real photon corrections without the corresponding virtual corrections.
In this case, one would consider photon emissions from the electron lines, and also the...