Entropic Screening of BSM Physics: Environment-Dependent Wilson Coefficients in b to s ll Transitions

We propose a Beyond Standard Model scenario in which the effective field theory Wilson coefficients for rare b to s lepton–lepton transitions are not universal constants but are dynamically modulated by the local effective temperature, or entropy, of the parton collision medium. The framework is realised via a dimension‑eight operator that couples Standard Model semileptonic currents to an ultra‑light hidden‑sector scalar field protected by a discrete symmetry. A dimension‑six gluon portal term couples this scalar to the QCD gluon condensate, so that its vacuum expectation value becomes an environment‑dependent order parameter that tracks the initial state saturation scale and the resulting charged‑particle multiplicity. Using the correspondence between parton entanglement and final‑state multiplicity developed in the QCD saturation and Color Glass Condensate literature, we argue that low‑multiplicity events represent a coherent, low‑entropy regime in which hidden‑sector symmetry breaking is maximised, while high‑multiplicity events undergo effective symmetry restoration. In this “entropic screening” picture, new‑physics contributions to the Wilson coefficient C9 are largest in quiet events and are strongly suppressed in high‑multiplicity collisions. From a simple finite‑temperature Ginzburg–Landau treatment of the hidden scalar, we derive a scaling law for the new‑physics shift in C9 as a function of charged‑track multiplicity: the contribution decreases with multiplicity and vanishes above a critical value, providing a concrete target for LHCb Run 3 analyses that stratify b to s lepton–lepton observables (such as angular observables and branching ratios) by event activity. This mechanism offers a possible reconciliation between earlier tensions in lepton flavour universality ratios measured at LHCb and null results from high‑luminosity ATLAS and CMS searches, and it remains compatible with existing constraints from B–Bbar mixing, Bs to mu mu branching ratios, and current cosmological bounds on ultra‑light scalar fields.