A possible solution of $B$ arrow ${\pi}{\pi}$ puzzle in Z' model

TL;DR

This paper investigates the $B \to \pi\pi$ puzzle involving discrepancies in decay measurements and CP asymmetries, proposing that a Z' boson in new physics models can resolve the issue by explaining lower C/T ratios.

Contribution

It demonstrates that the Z' model can successfully account for the lower C/T ratio in $B \to \pi\pi$ decays, offering a potential solution to the puzzle within new physics frameworks.

Findings

Larger C/T ratios are compatible with the SM.

Lower C/T ratios require new physics to explain.

Z' boson can resolve the $B \to \pi\pi$ puzzle.

Abstract

The discrepancies among the measurements of branching ratios and CP asymmetries of $B$ arrow ${\pi}{\pi}$ decays such as large direct CP asymmetry for $B^0 $ arrow ${\pi}^+ {\pi}^-$ mode and large branching ratio for $B^0$ arrow ${\pi}^0 {\pi}^0$ mode originate the $B$ arrow ${\pi}{\pi}$ puzzle. According to diagrammatic approach of this $b$ arrow $d$ transition the small ratio of color-suppressed amplitude (C) to color-allowed one (T) contradicts between the standard model (SM) approach and the experimental values. To make out the ambiguity we need to scrutinize the decays with different topological amplitudes. In this paper, the decays are studied in the SM by taking different values of C/T as constraints. We find that larger ratio of C/T is explained successfully in the SM but the lower ratio is not for which new physics (NP) is needed. The NP contribution can be included in $B$ arrow ${\pi}{\pi}$ decays at tree level by Z' boson. Here, we find that Z' model can explain the puzzle by providing a good solution for lower ratio of C/T.