Testing the standard model with D(s) → K1(→Kππ)γ decays

The photon polarization in D-((s)) -> K-1(-> K pi pi)gamma decays can be extracted from an up-down asymmetry in the law system, along the lines of the method known to B -> K-1(-> K pi pi)gamma decays. Charm physics is advantageous as partner decays exist: D+ -> K-1(+)(-> K pi pi)gamma, which is standard model-like, and D-s -> K-1(+)(-> K pi pi)gamma, which is sensitive to physics beyond the standard model in vertical bar Delta c vertical bar = vertical bar Delta u vertical bar= 1 transitions. The standard model predicts their photon polarizations to be equal up to U-spin breaking corrections, while new physics in the dipole operators can split them apart at order one level. We estimate the proportionality factor in the asymmetry multiplying the polarization parameter from axial vectors K-1(1270) and K-1(1400), and find it to be sizable, up to the few O(10)% range. The actual value of the hadronic factor matters for the experimental sensitivity but is not needed as an input to perform the null test.