Correlating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">/</mml:mo><mml:mi>ε</mml:mi></mml:mrow></mml:math> with hadronic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math> decays via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>U</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> flavor symmetry

Abstract

There are strong similarities between charge-parity ($CP$) violating observables in hadronic $B$ decays (in particular $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ in $B\ensuremath{\rightarrow}K\ensuremath{\pi}$) and direct $CP$ violation in kaon decays (${\ensuremath{\epsilon}}^{\ensuremath{'}}$): All these observables are very sensitive to new physics (NP) which is at the same time $CP$ and isospin violating (i.e., NP with complex couplings which are different for up quarks and down quarks). Intriguingly, both the measurements of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ and $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ show deviations from their Standard Model predictions, calling for a common explanation (the latter is known as the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle). For addressing this point, we parametrize NP using a gauge invariant effective field theory approach combined with a global $U(2{)}^{3}$ flavor symmetry in the quark sector (also known as less-minimal flavor violation). We first determine the operators which can provide a common explanation of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ and $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ and then perform a global fit of their Wilson coefficients to the data from hadronic $B$ decays. Here we also include e.g., the recently measured $CP$ asymmetry in ${B}_{s}\ensuremath{\rightarrow}KK$ as well as the purely isospin violating decay ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\rho}}^{0}$, finding a consistent NP pattern providing a very good fit to data. Furthermore, we can at the same time explain ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ for natural values of the free parameters within our $U(2{)}^{3}$ flavor approach, and this symmetry gives interesting predictions for hadronic decays involving $b\ensuremath{\rightarrow}d$ transitions.

Topics & Concepts