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Model-independent constraints on Delta F=2 operators and the scale of New Physics

UTfit Collaboration, M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. Silvestrini, V. Sordini, A. Stocchi, V. Vagnoni

TL;DR

The paper addresses constraining new physics in ΔF=2 transitions using a model-independent effective Hamiltonian. By mapping experimental data to the full operator basis with Wilson coefficients C_i(Λ) = F_i L_i / Λ^2 across four flavor structures (MFV small/large tanβ, NMFV, and general NP), it performs a UT-based NP analysis with NLO RG evolution and lattice matrix elements. The results yield stringent, sector-dependent lower bounds on the NP scale Λ, with the strongest constraints in the K sector (driven by chiral enhancement) and very high scales for generic tree-level or strongly interacting NP (e.g., Λ_GEN_tree > 2.4×10^5 TeV). For NMFV, Λ > 62 TeV (tree) or a few TeV when loop-suppressed, while MFV scenarios give Λ around 5 TeV, and heavy-Higgs bounds appear at large tanβ. Overall, the findings imply that NP contributing non-standard ΔF=2 operators is largely beyond direct LHC reach unless additional suppressions are present, underscoring flavor physics as a key probe of high-scale NP.

Abstract

We update the constraints on new-physics contributions to Delta F=2 processes from the generalized unitarity triangle analysis, including the most recent experimental developments. Based on these constraints, we derive upper bounds on the coefficients of the most general Delta F=2 effective Hamiltonian. These upper bounds can be translated into lower bounds on the scale of new physics that contributes to these low-energy effective interactions. We point out that, due to the enhancement in the renormalization group evolution and in the matrix elements, the coefficients of non-standard operators are much more constrained than the coefficient of the operator present in the Standard Model. Therefore, the scale of new physics in models that generate new Delta F=2 operators, such as next-to-minimal flavour violation, has to be much higher than the scale of minimal flavour violation, and it most probably lies beyond the reach of direct searches at the LHC.

Model-independent constraints on Delta F=2 operators and the scale of New Physics

TL;DR

The paper addresses constraining new physics in ΔF=2 transitions using a model-independent effective Hamiltonian. By mapping experimental data to the full operator basis with Wilson coefficients C_i(Λ) = F_i L_i / Λ^2 across four flavor structures (MFV small/large tanβ, NMFV, and general NP), it performs a UT-based NP analysis with NLO RG evolution and lattice matrix elements. The results yield stringent, sector-dependent lower bounds on the NP scale Λ, with the strongest constraints in the K sector (driven by chiral enhancement) and very high scales for generic tree-level or strongly interacting NP (e.g., Λ_GEN_tree > 2.4×10^5 TeV). For NMFV, Λ > 62 TeV (tree) or a few TeV when loop-suppressed, while MFV scenarios give Λ around 5 TeV, and heavy-Higgs bounds appear at large tanβ. Overall, the findings imply that NP contributing non-standard ΔF=2 operators is largely beyond direct LHC reach unless additional suppressions are present, underscoring flavor physics as a key probe of high-scale NP.

Abstract

We update the constraints on new-physics contributions to Delta F=2 processes from the generalized unitarity triangle analysis, including the most recent experimental developments. Based on these constraints, we derive upper bounds on the coefficients of the most general Delta F=2 effective Hamiltonian. These upper bounds can be translated into lower bounds on the scale of new physics that contributes to these low-energy effective interactions. We point out that, due to the enhancement in the renormalization group evolution and in the matrix elements, the coefficients of non-standard operators are much more constrained than the coefficient of the operator present in the Standard Model. Therefore, the scale of new physics in models that generate new Delta F=2 operators, such as next-to-minimal flavour violation, has to be much higher than the scale of minimal flavour violation, and it most probably lies beyond the reach of direct searches at the LHC.

Paper Structure

This paper contains 6 sections, 15 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Experimental input
  3. UT analysis and constraints on NP
  4. NP contributions to $\mathbf{\Delta F=2}$ processes
  5. Results
  6. Conclusions

Figures (7)

  • Figure 1: Determination of $\bar{\rho}$ and $\bar{\eta}$ from the NP generalized analysis. $68\%$ and $95\%$ probability regions for $\bar{\rho}$ and $\bar{\eta}$ are shown, together with the $2\,\sigma$ contours given by the tree-level determination of $\vert V_{ub}\vert$ and $\gamma$.
  • Figure 2: Constraints on $\phi_{B_d}$ vs. $C_{B_d}$, $\phi_{B_s}$ vs. $C_{B_s}$ and $C_{\epsilon_K}$ vs $C_{\Delta m_K}$ from the NP generalized analysis.
  • Figure 3: Allowed ranges in the Re$C^i_K$-Im$C^i_K$ planes in GeV$^{-2}$. Light (dark) regions correspond to $95\%$ ($68\%$) probability regions.
  • Figure 4: Allowed ranges in the Abs$C^i_D$-Arg$C^i_D$ planes in GeV$^{-2}$. Light (dark) regions correspond to $95\%$ ($68\%$) probability regions.
  • Figure 5: Allowed ranges in the Abs$C^i_{B_d}$-Arg$C^i_{B_d}$ planes in GeV$^{-2}$. Light (dark) regions correspond to $95\%$ ($68\%$) probability regions.
  • ...and 2 more figures