[Paper Review] Minimal flavour violation and beyond: Towards a flavour code for short distance dynamics

Andrzej J. Buras|arXiv (Cornell University)|Dec 7, 2010

Particle physics theoretical and experimental studies55 citations

TL;DR

This paper proposes a 3×3 flavour code matrix to classify New Physics models based on their patterns of flavour and CP violation, particularly focusing on short-distance dynamics. By analyzing correlations in B-meson and kaon decays, it distinguishes between Minimal Flavour Violation (MFV) and non-MFV scenarios, including models with right-handed currents and scalar interactions, offering a systematic framework to identify the underlying dynamics of flavour violation beyond the Standard Model.

ABSTRACT

This decade should provide the first definitive signals of New Physics (NP) beyond the Standard Model (SM) and the goal of these lectures is a review of flavour physics in various extensions of the SM that have been popular in the last ten years. After an overture, two pilot sections and a brief summary of the structure of flavour violation and CP violation in the SM, we will present the theoretical framework for weak decays that will allow us to distinguish between different NP scenarios. Subsequently we will present twelve concrete BSM models summarizing the patterns of flavour violation characteristic for each model. In addition to models with minimal flavour violation (MFV) accompanied by flavour blind phases we will discuss a number of extensions containing non-MFV sources of flavour and CP violation and, in particular, new local operators originating in right-handed charged currents and scalar currents. Next we will address various anomalies in the data as seen from the point of view of the SM that appear very natural in certain extensions of the SM. In this presentation selected superstars of this field will play a very important role. These are processes that are very sensitive to NP effects and which are theoretically clean. Particular emphasis will be put on correlations between various observables that could allow us to distinguish between various NP scenarios. Armed with this knowledge we will propose a coding system in a form of a 3*3 matrix which helps to distinguish between various extensions of the SM. Finding which flavour code is chosen by nature would be an important step towards the fundamental theory of flavour. We give several examples of flavour codes representing specific models.

Motivation & Objective

• To develop a systematic classification framework for New Physics models based on their flavour and CP violation patterns, especially in the context of short-distance dynamics.
• To distinguish between Minimal Flavour Violation (MFV) and non-MFV scenarios, including models with right-handed currents, scalar interactions, and flavour-blind or non-blind phases.
• To identify observable correlations in rare B-meson and kaon decays that can discriminate between competing New Physics models.
• To propose a 3×3 matrix-based coding system that encodes the structure of flavour violation, aiming to guide experimental searches and theory development.
• To assess the potential of future experiments (LHC, Belle II, SFF, EDMs) in resolving tensions in flavour data and identifying the correct dynamics of flavour.

Proposed method

• Constructs a 3×3 flavour code matrix (FCM) to encode the structure of flavour violation in various BSM models, based on the presence of left-handed, right-handed, and scalar currents.
• Analyzes twelve specific BSM models, including MFV models, supersymmetric extensions, and models with non-MFV sources such as right-handed charged currents and scalar interactions.
• Uses theoretical predictions and experimental constraints from rare decays (e.g., $B_{s,d} o au^+ au^-$, $K^+ o u ar{ u}$, $K_L o u ar{ u}$) to map out characteristic flavour patterns.
• Evaluates correlations between observables such as $S_{ ext{ψK}_S}$, $S_{ ext{ψφ}}$, $S_{ ext{η'K}_S}$, and $Br(B_{s,d} o au^+ au^-)$ to distinguish between models.
• Compares the FCMs of specific models (e.g., RVV2, $SSU(5)_{RN}$) and identifies key differences in their flavour violation patterns, especially in $S_{ ext{ψK}_S}$ and related observables.
• Leaves entries for flavour-blind phases (FBPs) and non-MFV phases incomplete where further study is needed, acknowledging limitations of the current coding approach.

Experimental results

Research questions

• RQ1 Can a 3×3 flavour code matrix effectively distinguish between different New Physics models based on their flavour and CP violation patterns?
• RQ2 How do correlations between rare decay observables (e.g., $S_{ ext{ψK}_S}$, $Br(B_{s,d} o au^+ au^-)$) help discriminate between MFV and non-MFV models?
• RQ3 To what extent do models with right-handed currents or scalar interactions lead to deviations from MFV predictions in B-meson and kaon decays?
• RQ4 Can the flavour code matrix capture the differences between models like RVV2 and $SSU(5)_{RN}$, especially in $S_{ ext{ψK}_S}$ and its correlations?
• RQ5 What role will future experiments (Belle II, LHC, SFF, EDMs) play in validating or refining the proposed flavour coding system?

Key findings

• The 3×3 flavour code matrix provides a systematic way to classify BSM models by their flavour structure, with entries encoding the presence of left-handed, right-handed, and scalar currents.
• Models with right-handed currents (e.g., RVV2) show distinct patterns in $S_{ ext{ψK}_S}$ and its correlations with $S_{ ext{ψφ}}$ and $S_{ ext{η'K}_S}$, differing from MFV and other non-MFV models.
• The $SSU(5)_{RN}$ model exhibits similarities to the RVV2 model but also key differences in flavour violation patterns, particularly in $S_{ ext{ψK}_S}$ correlations.
• The entry (MFV, RH) is always empty, as MFV implies suppression of right-handed currents by mass ratios ($m_s/m_b$, $m_d/m_b$, etc.).
• The flavour code matrix cannot yet fully capture all model features, especially in cases with non-flavour-blind phases (e.g., RSc model), indicating the need for refinement.
• Correlations between observables such as $S_{ ext{ψK}_S}$, $Br(B_{s,d} o au^+ au^-)$, and $K^+ o u ar{ u}$ are crucial for distinguishing models and will be key in future LHC and Belle II data.