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

Margarita Gavrilova, Yuval Grossman, Guglielmo Papiri, Stefan Schacht

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.

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

Abstract

We show that within the Standard Model any system of hadronic weak charm decays related by -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 -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.
Paper Structure (35 sections, 121 equations, 1 figure, 8 tables)

This paper contains 35 sections, 121 equations, 1 figure, 8 tables.

Table of Contents

  1. Introduction
  2. Generalities of second order $SU(2)_F$ rate sum rules
  3. Symmetry argument for second order $SU(2)$ sum rules
  4. General symmetry argument.
  5. Recipe for second-order sum rules.
  6. Comments on applicability.
  7. The Shmushkevich method
  8. Shmushkevich's master equation.
  9. The Shmushkevich method in the presence of identical multiplets
  10. Second order master sum rules
  11. The Master Sum Rule for Charm Decays
  12. Charm Hamiltonian and the CKM-free rates
  13. The two generation approximation.
  14. Hamiltonian for charm decays.
  15. CKM-free rates.
  16. ...and 20 more sections

Figures (1)

  • Figure 1: Current experimental determinations of the NLO sum rules (red) Eqs. (\ref{['eq:master_DPP']}, \ref{['eq:RH-DPV']}, \ref{['eq:RH_DPPP_data']}) in comparison to the corresponding LO sum rules (blue) Eqs. (\ref{['eq:DPP-LO']}, \ref{['eq:RLO-DPV-1']}, \ref{['eq:RLO-DPV-2']}, \ref{['eq:DPPP-LO-1']}, \ref{['eq:DPPP-LO-2']}, \ref{['eq:DPPP-LO-3']}, \ref{['eq:DPPP-LO-4']}). The $U$-spin limit is illustrated by the dashed black line.