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Polarisation fractions in $B\to V_1 V_2$: U-Spin constraints and new physics signatures

We investigate the decays of $B$ mesons, i.e., $B_d$, $B_s$, $B^+$, and their antiparticles, to two light vector mesons ($B \to V_1V_2$), focusing on the implications of SU(2) U-spin symmetry, which relates $ΔS = 0$ and $ΔS = 1$ decay amplitudes through the interchange $d \leftrightarrow s$. Performing a global fit, we find that the Standard Model (SM) yields only a very poor agreement with the data, both in the exact U-spin limit as well as when substantial U-spin breaking is allowed for. The tension is primarily driven by the unexpectedly small longitudinal polarisation fraction in almost all $ΔS = 1$ decays, especially for $B_s \to K^{*0} \overline{K^{*0}}$, for which the individual disagreement with U-spin based expectation is about $3.5σ$. Within the SM framework, the only effective resolution would be to disregard entirely the hierarchy between the longitudinal and transverse helicity amplitudes, in the heavy quark limit, as dictated by naive factorisation. An alternative would be to invoke new physics (NP) in the $b\to s$ sector that does not respect the hierarchy, and hence can reduce the tension for all the $ΔS=1$ modes. We demonstrate that certain colour suppressed NP operators can alleviate the tension significantly without adversely affecting the agreement for the other modes.