{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"f0544ac292eeec680e1a34b662100943d97a629fcef72545a9f57662def912ff","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a947ae6beec6754800efd4e6af82e1fd4c7a65e44462525ecc0cc50af278eb2c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.gravity-positivity.allowed-negativity","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Without gravity, a certain coefficient in the scattering of two particles must be positive. With gravity it may be slightly negative, and the size of the allowed negative value is not known.","posed_since":"","precise":"For a weakly coupled 4D effective field theory of a massless scalar coupled to Einstein gravity, with $2\\to 2$ amplitude $M(s,t) = 8\\pi G s^2/(-t) + c_2 s^2/\\Lambda^4 + ...$, determine the lowest value of $c_2$ consistent with unitarity, analyticity, crossing and a UV completion whose amplitude Reggeizes (grows as $s^{2 + \\alpha' t}$) above a scale $M_*$. Under this Regge assumption proposals give $c_2 \\ge -\\operatorname{O}(\\Lambda^4/(M_{\\mathrm{pl}}^2 M_*^2))$; smeared impact-parameter sum rules in $D = 4$ instead give $c_2 \\ge -\\operatorname{O}(G \\Lambda^4/M^2)\\operatorname{log}(M b_{\\mathrm{IR}})$, where $M$ is the EFT cutoff and $b_{\\mathrm{IR}}$ an infrared impact-parameter cutoff. An answer is the optimal bound in $D = 4$ with its assumptions stated, saying which form is optimal, or an explicit consistent UV completion that violates it.","problem_ref":null,"references":"","settled_by":"A derivation from stated axioms of the optimal lower bound on $c_{2}$, checked against explicit string-theory amplitudes.","status_note":"Bounds allowing Planck-suppressed negativity have been derived since 2020, but their size depends on the assumed Regge behavior of the UV completion or on an infrared cutoff.","title":"How negative can forward-limit coefficients be once gravity is included","topic_ref":"c287e09ddd295934e0940296a3c2ccaa657a88b499d8136c31f6e679a27a272a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"df45c1fff56a5577cac4689c0fc8e4aec93697163d7d850de81b3992b7b593c7","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"865cdcf979366473d6211e28b04b36b7581919a63b50973f8579ee2ae4065a02","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"aoArJhZxVhLBfvI2kDCKvcfURkOgnfS-KrEI0ASHBuqkyukio2dOOZiiY2qdny9hePR1zS4Z9NJ36fqPnbnwCg"},"schema":"pubphys.envelope/1"},"record_hash":"df45c1fff56a5577cac4689c0fc8e4aec93697163d7d850de81b3992b7b593c7","leaf_index":1914}