English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

By using quark Yukawa matrices only, we can construct renormalizationinvariants that are exact at the one-loop level in the standard model. One ofthem $I^q$ is accidentally consistent with unity, even though quark masses arestrongly hierarchical. We calculate a lepton version of the invariant $I^l$ forDirac and Majorana neutrino cases and find that $I^l$ can also be close tounity. For the Dirac neutrino and inverted hierarchy case, if the lightestneutrino mass is 3.0 meV to 8.8 meV, an equality $I^q=I^l$ can be satisfied.These invariants are not changed even if new particles couple to the standardmodel particles, as long as those couplings are generation independent.

Renormalization group invariant of lepton Yukawa couplings