Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ) (1006.3080v2)

Abstract: We give a factorization formula for the e+e- thrust distribution dsigma/dtau with tau=1-T based on soft-collinear effective theory. The result is applicable for all tau, i.e. in the peak, tail, and far-tail regions. The formula includes O(alphas^3) fixed-order QCD results, resummation of singular partonic alphas^j ln^k(tau)/tau terms with N^3LL accuracy, hadronization effects from fitting a universal nonperturbative soft function defined in field theory, bottom quark mass effects, QED corrections, and the dominant top mass dependent terms from the axial anomaly. We do not rely on Monte Carlo generators to determine nonperturbative effects since they are not compatible with higher order perturbative analyses. Instead our treatment is based on fitting nonperturbative matrix elements in field theory, which are moments Omega_i of a nonperturbative soft function. We present a global analysis of all available thrust data measured at center-of-mass energies Q=35 to 207 GeV in the tail region, where a two parameter fit to $\alpha_s(m_Z)$ and the first moment Omega_1 suffices. We use a short distance scheme to define Omega_1, called the R-gap scheme, thus ensuring that the perturbative dsigma/dtau does not suffer from an O(Lambda_QCD) renormalon ambiguity. We find alphas(mZ)=0.1135 \pm (0.0002){expt} \pm (0.0005){hadr} \pm (0.0009)_{pert}, with chi^2/dof=0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. The hadronization uncertainty in alphas is significantly decreased compared to earlier analyses by our two parameter fit, which determines Omega_1=0.323 GeV with 16% uncertainty.

• The paper develops a novel SCET factorization of the thrust distribution with N³LL resummation to enhance theoretical predictions.
• It incorporates universal power corrections via the soft function, significantly reducing hadronization uncertainties with parameter Ω₁.
• The global analysis yields a precise αₛ(mZ) = 0.1135 ± 0.0009, validated by independent numerical implementations.

Summary of "Thrust at N³LL with Power Corrections and a Precision Global Fit for αₛ(mZ)"

This paper reports on a comprehensive analysis of the thrust distribution in $e^+e^-$ annihilation events. The authors have developed a factorization formula for the differential cross-section $d\sigma/d\tau$ for thrust, defined as $\tau=1-T$, using soft-collinear effective theory (SCET). The factorization formula is applicable across all regions of thrust: peak, tail, and far-tail. This is achieved by including both fixed-order QCD calculations at ${\cal O}(\alpha_s^3)$ and resummation of singular partonic terms at next-to-next-to-next-to-leading logarithmic (N³LL) accuracy.

Key Components and Results

1. Factorization and Resummation: The thrust distribution is factorized into hard, jet, and soft functions using SCET. The resummation at N³LL order ensures that logarithms of the thrust variable $\tau$ are summed to all orders, improving the perturbative accuracy of the predictions. The analysis incorporates renormalization group evolution to manage scale dependencies across different kinematic regimes.
2. Power Corrections: Nonperturbative effects are encapsulated within a universal soft function, allowing for power corrections that significantly reduce the hadronization uncertainty. The parameter $\Omega_1$ is extracted as a measure of these nonperturbative effects, representing the first moment of the soft function.
3. Precision Fit for $\alpha_s(m_Z)$: The authors perform a precise global fit of the strong coupling constant $\alpha_s(m_Z)$ by analyzing thrust data from experiments at various center-of-mass energies ranging from 35 to 207 GeV. The thrust data is fitted in the tail region, where $\Omega_1$ suffices to capture nonperturbative effects. The analysis yields $\alpha_s(m_Z) = 0.1135 \pm 0.0009$ with separated experimental, hadronization, and perturbative uncertainties.
4. Renormalon Subtractions and Scheme Dependence: The analysis employs an R-gap scheme to define $\Omega_1$ and remove renormalon ambiguities in the perturbative series. This step is crucial for reducing theoretical uncertainties in $\alpha_s(m_Z)$ by enhancing the stability of the perturbative series against higher-order corrections.
5. Numerical Validation: Two independent codes were developed for cross-verifying the numerical results: one in Mathematica implementing the theoretical expressions directly, and a second code in Fortran optimized for cluster computations.

Implications and Future Directions

The work presents a rigorous treatment of the thrust distribution with implications for precise extractions of QCD parameters. It underscores the importance of combining perturbative calculations with nonperturbative corrections for accurate event-shape predictions. The findings further suggest that the inclusion of renormalon subtractions and power corrections is critical in reducing uncertainties in $\alpha_s(m_Z)$ measurements from high-energy collider data.

Future research could extend these techniques to other event shapes, with the potential to provide a more comprehensive understanding of QCD dynamics and improve the precision of the extracted QCD parameters from multiple observables. Additionally, further developments could aim at completing the summation of logarithms for the nonsingular contributions and refining the treatment of subleading power corrections beyond leading order.