Do spin correlations between $b$ and $b̄$ exist at all in $H → bb̄$, and can they survive parton showering?

Question

I'm studying the CP structure of $H → bb̄$. At generator level (with parton showering on), any spin correlation between the $b$ and $b̄$ branches seems completely washed out — even when tracing the final $B$-hadrons back to the original quarks.

Here's why I thought there might have been something:

In $H → gg$, spin correlations between the two gluons do manifest, even after showering, as azimuthal correlations between subsequent splittings (e.g., when each gluon splits into q q̄, the angle between planes shows correlation — see Richardson/Webster, Spin Correlations in Parton Shower Simulations arXiv:1807.01955 and PanScales paper arXiv:2103.16526). I understand that this effect arises from the gluon's polarization state being preserved and transmitted into the angular distribution of subsequent splittings during showering.

However, PanScales explicitly footnotes that $H → qq̄$ does not manifest spin correlations:

That particular case, with a $qq̄$ hard process, would have zero correlation, but the correlation is non-zero for a $gg$ hard process.

Later PanScales work ("Soft spin correlations" arXiv:2111.01161) extends spin correlations beyond collinear limits (soft-wide-angle effects), but here, no mention of H → qq̄.

Thus: Is there any setup where spin correlations survive between the b and b̄ splittings of H → bb̄? Could going beyond the collinear limit help? Or are correlations inevitably lost during showering for a quark hard process?

I am also aware that parton showers like Herwig aim to resum soft and collinear emissions to all orders at leading-log (and sometimes next-to-leading-log) accuracy, and propagate spin correlations using algorithms like Collins-Knowles. However, these methods rely on collinear factorization and don't capture full spin entanglement beyond the soft/collinear limits. Is it conceivable that treating the decay as a full 3-body process (e.g., H → bb̄g), or employing a more complete spin-correlation algorithm, could restore any meaningful correlation between the b and b̄ branches?

To be clear:

I’m asking whether anything from the b branch could in principle remain correlated with anything from the b̄ branch at generator level. I'm an undergraduate and tried working through spin density matrix calculations manually, but I'm unsure if I'm missing some key principle here. Any references, clarifications, or intuition would be really helpful.

This post imported from StackExchange Physics at 2025-04-27 19:32 (UTC), posted by SE-user CallmeIshmael