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I am reading some papers on particle phynomenology.

The mathematical derivation of Jacobian peak in some paper is wrong. However, it gives the right prediction.

If you have a W boson decaying in to an electron and a neutrion in the CM frame, then the electron transverse momentum and its 3-momentum must have the following relation as the figure indicated: enter image description here

The angle $\theta^ \star$ has the following relation: enter image description here

A basic QFT calculation gives the differential cross section in CM frame as: enter image description here

Now if we differentiate the cross section with the transverse monemtum, namely, using the chain rule: enter image description here

Many paper says the result is: enter image description here

However, if one really do the calculation, one should get exactly a minus sign in the front of the right hand side of the above eq, since there is a minus sign in front of the $4P_T^2/(m_w)^2$ in the expression for $\cos\theta^\star$.

I cannot figure out why.

The dirivation you can find in this paper: https://books.google.se/books?id=BipjDwAAQBAJ&pg=PA79&lpg=PA79&dq=polar+angle+of+the+electron+in+W+center&source=bl&ots=lONtgjxHP3&sig=ACfU3U3yqZFAwqCJJjlUa1vhlNhexsU8Rg&hl=zh-CN&sa=X&ved=2ahUKEwiO5Z-QycnkAhWMpYsKHZK0CYEQ6AEwAHoECAgQAQ#v=onepage&q=polar%20angle%20of%20the%20electron%20in%20W%20center&f=false

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  • $\begingroup$ Minor comment to the post (v1): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$ – Qmechanic Sep 11 at 22:27

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