There is no necessity for a formal group. Under US and UK law copyright as such arises (in an arrangement as well as a musical work) upon reduction to a material form (this is the UK language). It does not matter who makes the recording, the owner(s) of copyright is/are the arrangers (in the case of an extemporised arrangement, the performers)

When I last checked California had a common law copyright that did not depend on reduction to a material form and was not subject to federal pre-emption (won a bet with a US lawyer on that one at a satellite law symposium at UCLA back in the 70s - took him straight to hte page of Nimmer so asserting).

Recordings may have a copyright of their own. European purists would call it a neighbouring right. But it protects against reproduction of the recording, not of the song (etc) recorded. It lasts for 50 years. This is a UK hot potato at the moment as a lot of significant pop recordings are falling out of copyright as we speak, and Cliff Richard wants the right extended - and Tony Blair has been staying at his mansion - is this an issue of political embarrassment?

Performances do NOT have copyright. There is a different right which also lasts for 50 years. The right was first finally established in the UK under the old Performers Protection Acts 1958 to 1972 in Rickless -v- United Artists (the Pink Panther case) and was given statutory foundation in the Copyright Designs and Patents Act 1988. It keeps getting fine-tuned because our masters in Brussells are never happy.