[Paper Review] First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions

C. Cocuzza, Andreas Metz+4 more|arXiv (Cornell University)|Aug 28, 2023

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the first simultaneous global QCD analysis of dihadron fragmentation functions (DiFFs) and nucleon transversity parton distribution functions (PDFs), using data from e⁺e⁻ annihilation (Belle), semi-inclusive deep-inelastic scattering, and proton-proton collisions (STAR). It introduces a new number density interpretation for DiFFs, extracts π⁺π⁻ DiFFs and transversity distributions for up/down quarks and antiquarks, and finds consistency across multiple observables, including lattice QCD tensor charges and single-hadron fragmentation data, indicating a universal description of transversity and dihadron fragmentation.

ABSTRACT

We perform a comprehensive study within quantum chromodynamics (QCD) of dihadron observables in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, including recent cross section data from Belle and azimuthal asymmetries from STAR. We extract simultaneously for the first time $π^+π^-$ dihadron fragmentation functions (DiFFs) and the nucleon transversity distributions for up and down quarks as well as antiquarks. For the transversity distributions we impose their small-$x$ asymptotic behavior and the Soffer bound. In addition, we utilize a new definition of DiFFs that has a number density interpretation to then calculate expectation values for the dihadron invariant mass and momentum fraction. Furthermore, we investigate the compatibility of our transversity results with those from single-hadron fragmentation (from a transverse momentum dependent/collinear twist-3 framework) and the nucleon tensor charges computed in lattice QCD. We find a universal nature to all of this available information. Future measurements of dihadron production can significantly further this research, especially, as we show, those that are sensitive to the region of large parton momentum fractions.

Motivation & Objective

• To perform the first global QCD analysis that simultaneously extracts dihadron fragmentation functions (DiFFs) and nucleon transversity parton distribution functions (PDFs).
• To incorporate recent cross-section and azimuthal asymmetry data from Belle and STAR experiments into a unified QCD framework.
• To apply a new number density interpretation for DiFFs to enable meaningful calculation of dihadron invariant mass and momentum fraction expectation values.
• To test the compatibility of extracted transversity distributions with results from single-hadron fragmentation (TMD and twist-3 frameworks) and lattice QCD tensor charges.
• To assess the universality of transversity and DiFFs across multiple experimental observables and theoretical frameworks.

Proposed method

• Employ a simultaneous global fit to dihadron observables in e⁺e⁻ annihilation, semi-inclusive deep-inelastic scattering, and pp collisions using leading-twist collinear factorization.
• Use a new definition of DiFFs that preserves a number density interpretation, enabling physical expectation values for dihadron invariant mass $M_h$ and momentum fraction $z$.
• Implement constraints on transversity PDFs: small-$x$ asymptotic behavior and the Soffer bound, ensuring theoretical consistency.
• Extract $ar{u}$, $ar{d}$, $u$, and $d$ transversity distributions and $ar{u}$, $ar{d}$, $u$, $d$, $s$, $c$, $b$ DiFFs for $ar{ ho}^0$-like $ ho^0$-like states.
• Utilize PYTHIA-generated data at multiple center-of-mass energies ($ oot s o$ 10.58–91.19 GeV) to estimate systematic uncertainties in DiFF extraction.
• Compare results with lattice QCD tensor charges and single-hadron fragmentation data to test universality and consistency across frameworks.

Experimental results

Research questions

• RQ1 Can a simultaneous global QCD analysis of DiFFs and transversity PDFs be performed using diverse experimental data from e⁺e⁻, SIDIS, and pp collisions?
• RQ2 How does the new number density interpretation of DiFFs affect the physical interpretation and calculation of dihadron momentum fractions and invariant masses?
• RQ3 Are the extracted transversity distributions consistent with results from single-hadron TMD and twist-3 fragmentation frameworks?
• RQ4 To what extent do the extracted DiFFs and transversity PDFs agree with lattice QCD tensor charge calculations?
• RQ5 What is the universality of transversity and DiFFs across different observables and theoretical frameworks?

Key findings

• The first simultaneous extraction of $ar{u}$, $ar{d}$, $u$, and $d$ transversity PDFs and $ar{u}$, $ar{d}$, $u$, $d$, $s$, $c$, $b$ DiFFs for $ ho^0$-like $ar{ ho}^0$-like states is achieved using a global fit to Belle, STAR, and other data.
• The new DiFF definition allows for a physically meaningful number density interpretation, enabling calculation of expectation values for dihadron invariant mass $M_h$ and momentum fraction $z$.
• The extracted transversity distributions are consistent with the Soffer bound and exhibit the correct small-$x$ asymptotic behavior.
• The results for transversity are in good agreement with those from single-hadron fragmentation analyses in TMD and twist-3 frameworks.
• The extracted transversity distributions are compatible with lattice QCD tensor charges, supporting a universal description of transversity across different probes.
• Future dihadron measurements, especially in the large-parton-momentum-fraction region, are expected to significantly improve constraints on DiFFs and transversity.