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Flavor constraints for a Vector-like quark of Nelson-Barr type

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 Publication date 2021
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and research's language is English




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The Nelson-Barr (NB) mechanism to solve the strong CP problem assumes CP conservation, arranges vanishing $bar{theta}$ at tree-level and requires vector-like quarks (VLQs) to transmit the CP breaking to the SM. We analyze the flavor constraints coming from the presence of one such down type VLQ of NB type by performing a global fit on the relevant flavor observables. A comparison is made to the case of one generic VLQ. We find that the allowed parameter space for the VLQ Yukawa couplings and the mixing to the SM are confined to a region much smaller than in the generic case, making the NB case falsifiable in principle.



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We analyze the Nelson-Barr approach to the Strong CP Problem. We derive the necessary conditions in order to simultaneously reproduce the CKM phase and the quark masses. Then we quantify the irreducible contributions to the QCD topological angle, namely the corrections arising from loops of the colored fermion mediators that characterize these models. Corrections analytic in the couplings first arise at 3-loop order and are safely below current bounds; non-analytic effects are 2-loop order and decouple as the mediators exceed a few TeV. We discuss collider, electroweak, and flavor bounds and argue that most of the parameter space above the TeV scale is still allowed in models with down-type mediators, whereas other scenarios are more severely constrained. With two or more families of mediators the dominant experimental bound is due to the neutron electric dipole moment.
We present a supersymmetric solution to the strong CP problem based on spontaneous CP violation which simultaneously addresses the affects coming from supersymmetry breaking. The generated CP violating phase is communicated to the quark sector by interacting with a heavy quark a la Nelson-Barr. The Majorana mass of the right handed neutrinos is generated by interactions with the CP violating sector and so does not conserve CP. This gives the neutrino sector a non-trivial CP violating phase which can then generate the baryon asymmetry of the universe through leptogeneis. The problematic phase in the supersymmetry breaking parameters are suppressed by appealing to a particular gauge mediation model which naturally suppresses the phases of the tree-level gluino mass. This suppression plus the fact that in gauge mediation all loop generated flavor and CP violation is of the minimal flavor violation variety allows for a complete and consistent solution to the strong CP problem.
We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor changing neutral currents (FCNCs) arise at tree level and the unitarity of the $3times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from $brightarrow s$ transitions, especially $B_srightarrow mu^+mu^-$ and $bar{B}rightarrow X_sgamma$ processes. In order to analyze these processes, we derive an effective Lagrangian which is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for $brightarrow sgamma^{(*)}$. It includes the effects of the SM quarks and the violation of the CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on $Delta M_{B_s}$, $mathrm{Br}[B_srightarrowmu^+mu^-]$, $mathrm{Br}[bar{B}rightarrow X_sgamma]$ and CKM matrix elements as well as theoretical uncertainties. We find that the constraint from the $mathrm{Br}[B_srightarrowmu^+mu^-]$ is more stringent than that from the $mathrm{Br}[bar{B}rightarrow X_sgamma$]. We also obtain the bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of $brightarrow s$ transition. Using the CKM elements which satisfy above constraints, we show how the unitarity is violated on the complex plane.
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