One Sum To Rule Them All: A Second Order Master Rate Sum Rule for Charm Decays

TL;DR

The paper derives and tests a second-order U-spin sum rule for charm decay rates within the Standard Model, showing it holds well and can predict unmeasured decay rates.

Contribution

It introduces a new second-order U-spin sum rule for charm decays and demonstrates its validity and predictive power using experimental data.

Findings

The sum rule holds up to second order in U-spin breaking.

It accurately predicts unmeasured decay rates.

The sum rule is satisfied within experimental uncertainties.

Abstract

We show that within the Standard Model any system of hadronic weak charm decays related by $U$-spin satisfies the following rate sum rule: (sum of CF and DCS CKM-free rates) divided by (sum of SCS CKM-free rates) = 1, which holds up to second order in $U$-spin breaking. We test this sum rule against available data and find that it is well satisfied in all cases. For systems in which some decay rates have not yet been measured, we use this sum rule to predict the missing rates.