The interference between the K+K- S-wave and P-wave amplitudes in B_s ->
J/psi K+K- decays with the K+K- pairs in the region around the phi(1020
resonance is used to determine the variation of the difference of the strong
phase between these amplitudes as a function of K+K- invariant mass. Combined
with the results from the CP asymmetry measurements in our B_s -> J/psi phi
decays, we conclude that the B_s mass eigenstate that is almost CP =+1 is
lighter and decays faster than the mass eigenstate that is almost CP =-1. This
determines the sign of the decay width difference DeltaGamma_s == Gamma_L
-Gamma_H to be positive. Our result also resolves the ambiguity in the past
measurements of the CP violating phase phi_s to be close to zero rather than
pi. These conclusions are in agreement with the Standard Model expectations.
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