Correction terms and the non-orientable slice genus

By considering negative surgeries on a knot $K$ in $S^3$, we derive a lower bound to the non-orientable slice genus $\gamma_4(K)$ in terms of the signature $\sigma(K)$ and the concordance invariants $V_i(\overline{K})$, which strengthens a previous bound given by Batson, and which coincides with Ozsv\'ath-Stipsicz-Szab\'o's bound in terms of their $\upsilon$ invariant for L-space knots and quasi-alternating knots. A curious feature of our bound is superadditivity, implying, for instance, that the bound on the stable non-orientable genus is sometimes better than the one on $\gamma_4(K)$.