[Paper Review] Measurement of Azimuthal Modulations in the Cross-Section of Di-Pion Pairs in Di-Jet Production from Electron-Positron Annihilation

P. H. Hansen, I. Adachi+419 more|arXiv (Cornell University)|May 29, 2015

Muon and positron interactions and applications9 citations

TL;DR

This study presents the first measurement of azimuthal modulations in di-pion pair production from electron-positron annihilation using the Belle experiment. The amplitude of the $\cos[2(\Phi_{R_1}-\Phi_{R_2})] $ modulation, sensitive to the helicity-dependent fragmentation function $G_1^\perp$, is found to be consistent with zero within statistical and systematic uncertainties, with a systematic uncertainty ranging from $2 \times 10^{-3}$ at low mass and low $z$ to $5 \times 10^{-3}$ at high mass and high $z$. The di-pion sample purity exceeds 90%, with a 18% average contribution from charm quarks, and detector effects were simulated using Pythia, EvtGen, and GEANT3.

ABSTRACT

We present an extraction of azimuthal correlations between two pairs of charged pions detected in opposite jets from electron-positron annihilation. These correlations may arise from the dependence of the di-pion fragmentation on the polarization of the parent quark in the process $e^+e^- ightarrow q \bar{q}$. Due to the correlation of the quark polarizations, the cross-section of di-pion pair production, in which the pion pairs are detected in opposite jets in a dijet event, exhibits a modulation in the azimuthal angles of the planes containing the hadron pairs with respect to the production plane. The measurement of this modulation allows access to combinations of fragmentation functions that are sensitive to the quark's transverse polarization and helicity. Within our uncertainties we do not observe a significant signal from the previously unmeasured helicity dependent fragmentation function $G_1^\perp$. This measurement uses a dataset of 938~fb$^{-1}$ collected by the Belle experiment at or near $\sqrt{s}\approx10.58$ GeV.

Motivation & Objective

• To measure azimuthal angular correlations in di-jet events from electron-positron annihilation involving di-pion pairs.
• To probe the helicity-dependent fragmentation function $G_1^\perp$ via the $\cos[2(\Phi_{R_1}-\Phi_{R_2})]$ modulation in the di-pion cross-section.
• To assess contributions from light quarks and charm quarks in the fragmentation process.
• To quantify systematic uncertainties from detector smearing and fiducial cut edge effects in the asymmetry measurement.
• To test theoretical predictions regarding $G_1^\perp$ arising from $p$-wave interference in partial-wave expansions.

Proposed method

• The analysis uses data from the Belle experiment at the KEK $e^+e^-$ collider, collected at $\sqrt{s} \approx 10.5$ GeV.
• Events are selected with two jets containing pion pairs, using kinematic and topological constraints to isolate di-jet configurations.
• The azimuthal angle difference $\Phi_{R_1} - \Phi_{R_2}$ between the two pion pairs is measured in the event's rest frame to extract the $\cos[2(\Phi_{R_1}-\Phi_{R_2})]$ modulation.
• Systematic uncertainties are estimated using Monte Carlo simulations with Pythia for parton showering, EvtGen for decays, and GEANT3 for detector response.
• The di-pion sample purity is above 90%, with the remainder attributed to kaon contamination, and charm contributions are measured to be 18% on average.
• The asymmetry $A^{\cos[2(\Phi_{R_1}-\Phi_{R_2})]}$ is extracted as a function of di-pion invariant mass $M$ and momentum fraction $z$, with statistical and systematic uncertainties evaluated.

Experimental results

Research questions

• RQ1 Does the $\cos[2(\Phi_{R_1}-\Phi_{R_2})]$ modulation in di-pion pair production exhibit a non-zero signal, indicating a non-vanishing $G_1^\perp$ fragmentation function?
• RQ2 How do contributions from charm quark fragmentation affect the measured azimuthal asymmetry?
• RQ3 To what extent do detector smearing and fiducial cut effects bias the asymmetry measurement?
• RQ4 Is there evidence for a non-zero $G_1^\perp$ amplitude when restricting the decay angle $\theta_{\text{decay}}$ to regions where $\cos(\theta_{\text{decay}}) > 0$?
• RQ5 Does the $p$-wave interference in the partial-wave expansion of $G_1^\perp$ lead to a measurable enhancement in the asymmetry?

Key findings

• The amplitude of the $\cos[2(\Phi_{R_1}-\Phi_{R_2})]$ modulation is consistent with zero within statistical uncertainties, which are symmetric and on the order of $10^{-3}$ in magnitude.
• The systematic uncertainty on the asymmetry is asymmetric and ranges from $2 \times 10^{-3}$ at low $M$ and low $z$ to $5 \times 10^{-3}$ at high $M$ and high $z$, with the dominant contributions from detector smearing and fiducial cut edge effects.
• The di-pion sample purity exceeds 90%, with the remaining 10% attributed to kaon contamination, and the charm quark contribution is 18% on average, decreasing monotonically from 21% to 5% in $z$.
• Restricting the decay angle $\theta_{\text{decay}}$ to positive $\cos(\theta_{\text{decay}})$ values does not yield a significantly non-zero amplitude for $G_1^\perp$, supporting the null result.
• The measured asymmetry shows no significant deviation from zero across the entire $M$ and $z$ phase space, indicating no evidence for a non-zero $G_1^\perp$ fragmentation function in this kinematic regime.