Data for Polarization in Charmless B -> phi K^*: A Signal for New Physics?

The recent observations of sizable transverse fractions of B-> phi K* are strongly contrary to the Standard Model expectation. We analyze all possible new-physics four-quark operators. We find that two classes of new-physics operators could offer resolutions to the B-> phi K* polarization anomaly. The (1-\gamma_5)\otimes (1-\gamma_5) and \sigma(1-\gamma_5)\otimes \sigma(1-\gamma_5) operators in the first class contribute to different helicity amplitudes as H{00}: H{--}: H{++} ~ O(1/mb):O(1):O(1/mb^2), while the contributions arising from (1+\gamma_5)\otimes (1+\gamma_5) and \sigma(1+\gamma_5)\otimes \sigma(1+\gamma_5) operators in the second class to various helicity amplitudes are given as H{00}: H{--}: H{++} ~ O(1/mb):O(1/mb^2):O(1). For each class of new physics, we find that all new physics effects can be lumped into a single parameter. Two possible experimental results of polarization phases, \arg(A_\perp)- \arg(A_\parallel) ~ \pi or 0, originating from the phase ambiguity in data, could be separately accounted for by our two new-physics scenarios: (i) the first scenario with the first class new-physics operators, and (ii) the second scenario with the second class new-physics operators. The consistency between the data and the new physics analysis, suggests a small new-physics weak phase, together with a large strong phase. We obtain sizable transversely polarized amplitudes \Lambda_{\parallel\parallel} + \Lambda_{\perp\perp} = \Lambda_{00}. In the second scenario, we find \Lambda_{\parallel\parallel} ~ \Lambda_{\perp\perp}, while, in the first scenario, we obtain \Lambda_{\parallel\parallel} ~ \Lambda_{\perp\perp}/2. We discuss the impact of the new-physics weak phase on observations.