Investigating Tensor Meson Decays through pQCD Analysis

In this research, we look at a specific type of decay of particles known as Tensor Mesons. These particles are involved in two-body Decays, which means they disintegrate into two other particles. We calculate various characteristics of these decays using a method called perturbative Quantum Chromodynamics (pQCD).

#Key Findings

1. For the decay purely based on annihilation, we observe that the main form of polarization is longitudinal, while transverse Polarizations are considerably less.
2. The asymmetry seen in these decays relates to the interference between two types of contributions called tree and penguin contributions. In many cases, the direct asymmetry we find is small.
3. There are limited types of diagrams contributing to these decays. This limitation arises because tensor mesons cannot be generated through certain currents or densities. Thus, the nonfactorizable and annihilation contributions become essential in these decay processes.
4. The Branching Ratios we calculate are of a size that can be checked in experiments at facilities like LHCb and Belle II. For our particular case, we have also analyzed mixing, noting that the mixing angle is very small, leading to minimal changes in the decay branching ratio.

#Introduction

The study of how mesons decay into two particles has gained traction over the years, with significant theoretical and experimental work. In light of a recent increase in interest surrounding tensor mesons, we utilize the flavor SU(3) symmetry to examine nine different mesons in this research. Previous research has already reported some charmless hadronic decays involving light tensor mesons, indicating a larger number of decay modes related to these particles.

Historically, studies using pQCD have shown to provide good predictions that match experimental results. Initial findings have indicated similarities in behavior between certain decays, though differences still exist.

#Perturbative QCD Approach

In the pQCD method, we essentially separate the hard parts of decay processes from the softer, nonperturbative aspects. This allows us to calculate the hard decay parts directly while absorbing the nonperturbative aspects into wave functions representing the particles involved.

For tensor mesons, we found that their decay characteristics involve three main helicity components, which describe how the particles are oriented in relation to their momentum. This method offers a generalized way to express the decay amplitudes.

#Diagrams and Contributions

In our examination, we categorize Feynman diagrams into different types that contribute to the decay process. The first set relates to annihilation diagrams, while others serve as nonfactorizable emission diagrams. Each diagram contributes differently based on the polarization states of the tensor mesons involved.

The contributions from these diagrams result in distinct outcomes for longitudinal and transverse polarization amplitudes, which are crucial for understanding the overall decay process.

#Input Parameters and Numerical Results

We gather various input parameters that define our calculations, including decay constants and masses of the involved mesons. These parameters are essential for estimating branching ratios, direct violations, and polarization fractions.

Through our calculations, we outline numerical results for various decay processes, noting errors arising from uncertainties in parameters like the shape parameter for meson distribution amplitudes and decay constants.

#Branching Ratios and Polarization

In the results, we observe that certain decays primarily stem from specific types of diagrams, with some contributing significantly more than others. Our findings indicate branching ratios for different decay channels and highlight the dominance of longitudinal polarization contributions in the overall decay process.

For many decays, the contributions predominantly come from longitudinal polarization, particularly in pure annihilation cases. This behavior suggests that while transverse contributions exist, they play a lesser role in most decay scenarios.

#Direct Violations and Asymmetries

The decay processes also exhibit direct violations, which relate to how the decay behavior deviates from what is normally expected. These violations often arise due to the interplay between tree and penguin contributions in the decay process.

In many cases, the magnitude of direct violations is small. However, in certain special channels, we observe larger direct violations, particularly where tree contributions become more comparable to penguin contributions.

#Summary of Findings

To summarize, our research into tensor meson decays through the pQCD approach has led to several noteworthy conclusions:

1. The tensor meson decays analyzed are significantly influenced by nonfactorizable emission and annihilation contributions.
2. In cases of pure annihilation decay, the branching ratios fall into a category easily testable by experiments.
3. Polarization fractions reveal that longitidinal contributions are the main driving force behind these decays, particularly in pure annihilation scenarios.
4. Direct violations in the decay processes tend to be small, with only a few channels displaying significant direct violation due to specific conditions.

#Future Prospects

We believe that our findings can provide fruitful insights into the behavior of tensor mesons. These results can be scrutinized within experimental setups like LHCb and Belle II, paving the way for a better understanding of decays in the realm of Quantum Chromodynamics.

Considering the complexity and scope of particle decays, ongoing research will be vital in confirming our predictions and further unraveling the intricate dynamics of tensor mesons in particle physics.