Next to Minimal Flavor Violation

TL;DR

Next-to Minimal Flavor Violation (NMFV) extends MFV by allowing TeV-scale flavor-violating physics that dominantly couples to the third generation and is quasi-aligned with the Yukawa matrices, with a characteristic scale $\Lambda_{\rm NMFV}\sim 2-3\,{\rm TeV}$. It shows that $\Delta F=2$ amplitudes can be as large as $\sim 30-40\%$ of the SM, with arbitrary CP phases, while kaon constraints remain suppressed by small mixings; tree-level CKM inputs from $B$ decays and $A_{DK}$ or $S_{\rho\rho}$ measurements now constrain the NP more tightly, leaving room for substantial but testable NP at the TeV scale. For $\Delta F=1$ processes, the framework (under LH-only operators and $Z$-penguin alignment) can accommodate anomalies in $B\to \phi K_S$, $\eta^{\prime} K_S$ and constrain $B\to K\pi$ via SU(3) symmetry and hadronic modeling with two hadronic approaches. The paper also analyzes correlations among observables and discusses realizations in SUSY (non-abelian/alignment) and RS1 models, arguing that flavor physics will play a crucial role in probing NP before direct collider discoveries.

Abstract

The flavor structure of a wide class of models, denoted as next to minimal flavor violation (NMFV), is considered. In the NMFV framework, new physics (NP), which is required for stabilization of the electroweak symmetry breaking (EWSB) scale, naturally couples (dominantly) to the third generation quarks and is quasi-aligned with the Yukawa matrices. Consequently, new sources of flavor and CP violation are present in the theory, mediated by a low scale of few TeV. However, in spite of the low flavor scale, the most severe bounds on the scale of NP are evaded since these are related to flavor violation in the first two generations. Instead, one typically finds that the NP contributions are comparable in size to SM loop processes. We argue that, in spite of the successful SM unitary triangle fit and contrary to the common lore, such a sizable contribution to Delta F=2 processes of ~ 40% (with arbitrary phase) compared to SM is presently allowed since B-factories are only beginning to constrain these models. Thus, it is very interesting that in the NMFV models one is not forced to separate the scale of NP related to EWSB and the scale of flavor violation. We show briefly that this simple setup includes a wide class of supersymmetric and non-supersymmetric models all of which solve the hierarchy problem. We further discuss tests related to Delta F=1 processes, in particular the ones related to b -> s transition. The b -> s processes are computed using two different hadronic models to estimate the uncertainties involved. In addition, we derive constraints on the NP from B -> Kpi data using only SU(3) flavor symmetry and minimal dynamical assumptions. Finally we argue that in many cases correlating Delta F=2 and Delta F=1 processes is a powerful tool to probe our framework.

Figures (12)

• Figure 1: The constraint on the $\rho$ and $\eta$ Wolfenstein parameters before 2004. Left: allowing for NP in $\Delta F=2$Ligeti04. Right: within the SM.
• Figure 2: Left: The allowed range for $h_d$ and $\sigma_d$ before 2004 from $V_{ub},\Delta m_d$ and $S_{\psi K}$. Right: The allowed range for $h_K$ and $\sigma_K$ before 2004 from $V_{ub}$ and $\varepsilon_K$.
• Figure 3: Left: The allowed range for $h_s-\sigma_s$ using the data on $\Delta m_s$. Right: the future projection for a measured $\Delta m_s=(18.3\pm 0.3) ps^{-1}$.
• Figure 4: The constraint on the $\rho$ and $\eta$ Wolfenstein parameters after summer 2005. Left: allowing for NP in $\Delta F=2$Ligeti04. Right: within the SM.
• Figure 5: Left: The allowed range for $h_d$ and $\sigma_d$ after summer 2005. Right: The same for $h_K$ and $\sigma_K$.