Measurement of CP Violation at the $\Upsilon(4S)$ without Time Ordering or $\Delta t$

TL;DR

This paper presents a method to measure CP violation in the Upsilon(4S) system without requiring the detection of decay time differences or ordering, simplifying experimental procedures.

Contribution

It derives new expressions for CP asymmetry that do not depend on decay time difference or ordering, enabling alternative measurement techniques for sin(2beta).

Findings

Derived CP asymmetry expressions independent of decay time difference.

Proposed a technique to measure sin(2beta) without time ordering.

Simplified experimental requirements for CP violation measurement.

Abstract

I derive the expressions for the CP-violating asymmetry arising from interference between mixed and direct decays in the Upsilon(4S) system, for the case in which only one of the B decay times is observed, integrating over the decay time of the other B. I observe that neither the difference of the decay times Delta t, nor even their time-ordering, need be detected. A technique for measurement of the CP-violating weak decay parameter sin(2beta) is described which exploits this observation.