The UTfit Collaboration Report on the Status of the Unitarity Triangle beyond the Standard Model I. Model-independent Analysis and Minimal Flavour Violation

TL;DR

The paper develops a model-independent framework to analyze the Unitarity Triangle when new physics enters loop-level flavor transitions, using tree-level inputs to determine a NP-insensitive region in the CKM plane and then constraining NP in $|\\Delta F|=2$ and $|\\Delta F|=1$ processes. It introduces a parameterization with $C_{B_q}$, $\phi_{B_q}$, and $C_{\epsilon_K}$ (and, for $|\\Delta F|=1$, $C_{Pen}$ and $\phi_{Pen}$) to quantify NP effects, and performs global fits with current data to bound NP amplitudes and phases. Special attention is given to MFV, where the Universal Unitarity Triangle can be determined independently of NP, and NP contributions are mapped to shifts in the top-box function $S_0(x_t)$, allowing extraction of lower bounds on the NP scale $\Lambda$ (typically a few TeV). The work also provides a plausible 2010 scenario with projected experimental and lattice improvements, showing potential NP sensitivity up to around 7–9 TeV in MFV and highlighting the continuing power of flavor data to probe physics beyond the SM. The results collectively indicate a preference for MFV-like structures, while demonstrating the UT’s resilience as a precise CKM probe even in the presence of NP.

Abstract

Starting from a (new physics independent) tree level determination of rhobar and etabar, we perform the Unitarity Triangle analysis in general extensions of the Standard Model with arbitrary new physics contributions to loop-mediated processes. Using a simple parameterization, we determine the allowed ranges of non-standard contributions to |Delta F|=2 processes. Remarkably, the recent measurements from B factories allow us to determine with good precision the shape of the Unitarity Triangle even in the presence of new physics, and to derive stringent constraints on non-standard contributions to |Delta F|=2 processes. Since the present experimental constraints favour models with Minimal Flavour Violation, we present the determination of the Universal Unitarity Triangle that can be defined in this class of extensions of the Standard Model. Finally, we perform a combined fit of the Unitarity Triangle and of new physics contributions in Minimal Flavour Violation, reaching a sensitivity to a new physics scale of about 5 TeV. We also extrapolate all these analyses into a "year 2010" scenario for experimental and theoretical inputs in the flavour sector. All the results presented in this paper are also available at the URL http://www.utfit.org, where they are continuously updated.

Figures (18)

• Figure 1: The selected region on $\bar{\rho}$-$\bar{\eta}$ plane obtained from the determination of $\vert V_{ub}/V_{cb}\vert$ and $\gamma$ (using $DK$ final states). Selected regions corresponding to $68\%$ and $95\%$ probability are shown, together with $95\%$ probability regions for $\gamma$ and $\vert V_{ub}/V_{cb}\vert$.
• Figure 2: P.d.f. of $\alpha$ from the combination of isospin analyses of $\pi \pi$, $\rho \pi$ and $\rho \rho$ decay modes, including NP effects in the $|\Delta F| = 1$ Hamiltonian.
• Figure 3: Output P.d.f.'s for $C_{\epsilon_K}$ (top-left),$C_{B_d}$ (top-center), $\phi_{B_d}$ (top-right), and 2D distributions of $\phi_{B_d}\,vs.\,C_{B_d}$ (bottom-left) and $\phi_{B_d}\,vs.\,\gamma$. Dark (light) areas correspond to the $68\%$ ($95\%$) probability region.
• Figure 4: The selected region on $\bar{\rho}$-$\bar{\eta}$ plane obtained from the NP generalized analysis. Selected regions corresponding to $68\%$ and $95\%$ probability are shown, together with $95\%$ probability regions for $\gamma$ (from $DK$ final states) and $\vert V_{ub}/V_{cb}\vert$.
• Figure 5: 2D distributions of $\phi_{B_d}$ vs. $C_{B_d}$ (left) and $\phi_{B_d}$vs. $\gamma$ (right) using the following constraints: i) $|V_{ub}/V_{cb}|$, $\Delta m_d$, $\varepsilon_K$ and $\sin 2 \beta$ (first row); ii) the constraints in i) plus $\gamma$ (second row); iii) the constraints in ii) plus $\cos 2 \beta$ from $B_d \to J/\psi K^*$ and $\beta$ from $B \to D h^0$ (third row); iv) the constraints in ii) plus $\alpha$ (fourth row).