Abstract
In this Chapter we go back to the SoftDrop algorithm and we study two variables deeply connected to it: the angular separation of the two subjets that pass SoftDrop and their momentum sharing. We find that while the former can be described using the all-order techniques described so far, the latter one cannot be. It instead exhibits peculiar features. This observable is not collinear safe for all values of the angular exponent β but it belongs to the wider class of Sudakov-safe observables.
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Notes
- 1.
Note that we have used the same approach as for the rest of this book and included it in the double-logarithmic terms. In this specific case, this is less relevant as the endpoint of the distribution does not depend on it, so we could have left it explicitly as a separate correction.
- 2.
Here, the case of negative β can be seen as shifting a whole part of the distribution to θ g = 0.
- 3.
In practice, we have frozen the coupling at a scale μ NP = 1 GeV, cf. Appendix A.
- 4.
This is easy to understand from a physical viewpoint: both R′(θ g) and the denominator of Eq. (9.10) correspond to the probability for having a real emission passing the SoftDrop condition at a given θ g.
- 5.
Note that the assumptions used in this book slightly differ from the ones originally used in [51].
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Marzani, S., Soyez, G., Spannowsky, M. (2019). Curiosities: Sudakov Safety. In: Looking Inside Jets. Lecture Notes in Physics, vol 958. Springer, Cham. https://doi.org/10.1007/978-3-030-15709-8_9
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