Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions (1512.02830v3)

Abstract: New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the $SU(3)_C \times SU(2)_L \times U(1)_Y$ gauge invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for $b \to s$ and $b\to c$ transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, $W$, $Z$ and the Higgs particle. We first carry out the matching of the dim-6 operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter $b \to s$ transitions already at tree level, but can give relevant one-loop matching effects.

• The paper presents a comprehensive matching analysis of gauge invariant dimension‐6 operators, translating high-energy formulations into measurable B decay predictions.
• It evaluates both tree‐level and one‐loop contributions, highlighting the roles of top quark effects and Higgs interactions in b→s and b→c transitions.
• The study provides quantitative constraints on Wilson coefficients using experimental data, guiding future searches for new physics in flavor processes.

Overview of "Matching of Gauge Invariant Dimension-Six Operators for $b\to s$ and $b\to c$ Transitions"

This paper presents a rigorous analysis of dimension-six operators in the context of B physics, specifically examining their impact on transitions such as $b\to s$ and $b\to c$. The research leverages an effective field theory (EFT) approach that allows for a model-independent paper of potential new physics (NP) effects that manifest above the electroweak (EW) scale. By integrating out heavy particles—top quarks, W and Z bosons, and the Higgs boson—the authors derive how these high-energy interactions affect low-energy B physics processes.

The Standard Model (SM) serves as the prevailing theory of particle physics, having undergone intense scrutiny and verification, particularly following the observation of the Higgs boson. Nonetheless, it is widely conjectured to be an effective low-energy manifestation of a more comprehensive theory incorporating NP. The authors employ the concept of dimension-six operators, which complement the SM via Wilson coefficients. These operators facilitate predictions of NP effects without committing to specific high-energy models.

Key Contributions and Findings

1. Operator Basis and Dimension Matching: The authors conduct a detailed matching analysis of dimension-six operators, which are gauge invariant under the symmetry group $SU(3)_C \times SU(2)_L \times U(1)_Y$. They translate high-energy theoretical formulations into tangible predictions relevant for B physics transitions, after EW symmetry breaking.
2. Tree-Level Contributions: The authors categorize and evaluate contributions from various dimension-six operators to $b\to s$ and $b \to c$ transitions at tree level. This includes both current-current (four-fermion) operators and those involving Higgs interactions, which notably affect processes such as $B_s$ meson mixing.
3. One-Loop Effects: Crucial one-loop corrections are explored, focusing on operators that involve the top quark. The EFT framework allows the team to address scenarios where tree-level contributions are subdominant or null.
4. Quantitative Constraints: The researchers provide a systematic method to impose constraints on Wilson coefficients, using existing experimental data, particularly from flavor-changing neutral current processes and rare B decays. The strong constraints derived from such data have significant implications for the phenomenological validity of candidate NP models.
5. Numerical and Analytical Insights: The paper offers numerical results, identifying which operators contribute significantly at one-loop order. These insights could steer future experiments and theoretical work to focus on particularly promising contributions that influence observable quantities.

Implications and Future Directions

The research accentuates the role of B physics as a critical testing ground for NP theories beyond the SM. The dimension-six operators addressed provide a robust methodology for elucidating how deviations in flavor observables might arise from underlying NP dynamics. The findings suggest careful scrutinizing of the $b \to s$ and $b \to c$ transition sectors for experimental discrepancies when compared to SM predictions.

The results in this paper highlight the precision required in both theoretical calculations and experimental measurements to make definitive interpretations about the presence of NP. Future directions include extending the analysis to higher-dimension operators or incorporating specific NP models to concretely link observed phenomena with theoretical descriptions at high energies.

In sum, the paper by Aebischer et al. enriches the understanding of effective theories in particle physics, offering a detailed map for how high-energy interactions can manifest at scales accessible by experiments, thus providing a critical stepping-stone for future discoveries in the particle physics landscape.