bibkey: lesterhaddadingripaios2022parity
authors: Christopher G. Lester; Ward Haddadin; Ben Gripaios
year: 2022
title: "Lorentz and permutation invariants of particles III: constraining non-standard sources of parity violation"
doi: 10.1142/S0217751X22500932
url: "https://arxiv.org/abs/2008.05206v6"
claim: "The paper defines chirality of collider events under Lorentz and permutation symmetries, constructs sets of continuous Lorentz- and permutation-invariant parity-odd event variables that are nonzero on every chiral event of several event classes, and conjectures that its three-variable sets for events with two pairs of interchangeable momenta are minimal."
strata_touched:
  - D5/S3/Geometry/Lorentz/ChiralEventParityMinimality
license: citation-only
triage: anchor

Lester, Haddadin and Gripaios, Lorentz and permutation invariants of particles III

C. G. Lester, W. Haddadin and B. Gripaios, International Journal of Modern Physics A 37(16) (2022) 2250093, DOI 10.1142/S0217751X22500932; arXiv:2008.05206v6. Quotations are from the arXiv v6 TeX source.

Events are tuples of forward-time-directed non-spacelike four-vectors with a symmetry group $S{O}^{+}(1,3)$ times permutation groups of interchangeable momenta. An event is chiral if no element of the group maps it to its parity image. The paper seeks sets of event variables that are real, parity odd, continuous, invariant under the group, and sufficient (at least one variable is nonzero on every chiral event). For events $(p,q,a,b)$ with interchangeable pairs $(pq)$ and $(ab)$ it constructs three-element sets $S$ and $\hat{S}$ with these properties and writes:

No claim is made that either set $S$ or $\hat{S}$ is globally \textbf{minimal} for the class of events with which it is concerned. That is to say: it has not been proved that there does not exist some other set $S_{?}$ containing only one or two event variables but which retains all the stated properties. Nonetheless, we \textit{conjecture} that there is indeed no smaller set $S_{?}$ and that $S$ and $\hat{S}$ are therefore examples of \textbf{minimal} sets.

Verified locator

Source: https://arxiv.org/abs/2008.05206v6

• DOI: https://doi.org/10.1142/S0217751X22500932 (journal version; title, authors, journal, volume, issue and article number from Crossref; the journal text was not read).
• URL: https://arxiv.org/abs/2008.05206v6. The e-print members introduction.tex (md5 2b21a1456fcb7bb5df295f300f8b61ae), goals.tex (md5 ea160376a3657575029f0097aa1a1465) and prelims.tex (md5 04a02e231b8adc28fe6cfda2b77d734d). Locations:
  • the conjecture, introduction.tex l. 103–104;
  • the required properties of event variables, goals.tex l. 1–17;
  • the set $\mathbb{V}$, prelims.tex l. 25–27; the symmetry group, l. 191; parity, l. 228–238; chirality, l. 240–243 and 265–268; collision events, l. 433–441; the two event classes, l. 656–666.