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Constraining Models of New Physics in Light of Recent Experimental Results on $a_{ψK_S}$

We study extensions of the Standard Model where the charged current weak interactions are governed by the CKM matrix and where all tree-level decays are dominated by their Standard Model contribution. We constrain both analytically and numerically the ratio and the phase difference between the New Physics and the Standard Model contributions to the mixing amplitude of the neutral $B$ system using the experimental results on $R_u$, $Δm_{d,s}$, $ε_K$ and $a_{ψK_S}$. We present new results concerning models with minimal flavor violation and update the relevant parameter space. We also study the left-right symmetric model with spontaneously broken CP, probing the viability of this model in view of the recent results for $a_{ψK_S}$ and other observables.