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Many well studied knots can be realized as positive braid knots where thebraid word contains a positive full twist; we say that such knots are twistpositive. Some important families of knots are twist positive, including torusknots, 1-bridge braids, algebraic knots, and Lorenz knots. We prove that if aknot is twist positive, the braid index appears as the third exponent in itsAlexander polynomial. We provide a few applications of this result. Afterobserving that most known examples of L-space knots are twist positive, weprove: if $K$ is a twist positive L-space knot, the braid index and bridgeindex of $K$ agree. This allows us to provide evidence for Baker'sreinterpretation of the slice-ribbon conjecture: that every smooth concordanceclass contains at most one fibered, strongly quasipositive knot. In particular,we provide the first example of an infinite family of positive braid knotswhich are distinct in concordance, and where, as $g \to \infty$, the number ofhyperbolic knots of genus g gets arbitrarily large. Finally, we collect someevidence for a few new conjectures, including the following: the braid andbridge indices agree for any L-space knot.

Twist positivity, L-space knots, and concordance