An Exploration of Higher Order Flavor Sum Rules

TL;DR

This paper investigates higher-order flavor sum rules in B meson decays, demonstrating their existence at arbitrary orders and discussing the challenges in applying them for understanding flavor symmetry breaking.

Contribution

It introduces the concept of higher-order flavor sum rules in B decays and shows they can be constructed for arbitrary orders, expanding the theoretical framework.

Findings

Higher-order sum rules exist for B decay modes with increasing meson numbers.

Sum rules can be formulated for isospin and U-spin symmetries at higher orders.

Practical and theoretical issues need addressing for effective use of these sum rules.

Abstract

We explore the idea of higher-order flavor sum rules, i.e. sum rules that hold to higher orders in the flavor symmetry-breaking parameters. In particular, we consider isospin sum rules based on $B \to n\pi$ decays, and U-spin sum rules based on $B_d$ and $B_s$ decays to $n$ charged pions and/or kaons. We also demonstrate that sum rules exist to arbitrary orders by considering decay modes with increasing number of final state mesons $n$. Finally, we identify various theoretical and practical issues that need to be addressed in utilizing these sum rules.