[Paper Review] Simultaneous extraction of $α_s$ and $m_t$ from LHC $t\bar{t}$ differential distributions

A. M. Cooper-Sarkar, M. Czakon+3 more|arXiv (Cornell University)|Oct 8, 2020

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a simultaneous extraction of the strong coupling constant $\alpha_s$ and top-quark pole mass $m_t$ from 8 TeV LHC $t\bar{t}$ differential distributions using next-to-next-to-leading order (NNLO) QCD predictions. By combining ATLAS and CMS single-differential measurements—specifically for $p_T^\text{avg}$, $y_\text{avg}$, $m_{t\bar{t}}$, and $y_{t\bar{t}}$—and employing fastNLO tables for efficient theory evaluation, the authors achieve a precise joint determination: $\alpha_s = 0.1159^{+0.0013}_{-0.0014}$ and $m_t = 173.8^{+0.8}_{-0.8}$ GeV, consistent with world averages and previous extractions.

ABSTRACT

We present a joint extraction of the strong coupling $α_s$ and the top-quark pole mass $m_t$ from measurements of top-quark pair production performed by the ATLAS and CMS experiments at the 8 TeV LHC. For the first time, differential NNLO theory predictions for different values of the top-quark mass are utilised for four kinematic distributions: the average transverse momentum of the top-quark, its average rapidity and the pair invariant mass and rapidity. The use of fastNLO tables for these distributions allows rapid evaluation of the differential theory predictions for different PDF sets. We consider the single differential distributions from the experiments both separately and in combination in order to obtain the best fit to theory. Our final values are $α_s=0.1159^{+0.0013}_{-0.0014}$ and $m_t=173.8^{+0.8}_{-0.8}$ GeV which are compatible with previous extractions using top-quark measurements. In the case of $m_t$, our value is also compatible with the world average value collated by the Particle Data Group.

Motivation & Objective

• To perform a simultaneous determination of $\alpha_s$ and $m_t$ using differential $t\bar{t}$ distributions from the LHC, overcoming the degeneracy between these parameters when using total cross sections alone.
• To utilize next-to-next-to-leading order (NNLO) QCD predictions with flexible $m_t$ dependence for four kinematic distributions: $p_T^\text{avg}$, $y_\text{avg}$, $m_{t\bar{t}}$, and $y_{t\bar{t}}$.
• To improve precision by combining ATLAS and CMS 8 TeV measurements and evaluating theory predictions rapidly via fastNLO tables for multiple PDF sets.
• To assess the impact of underflow events in the $m_{t\bar{t}}$ distribution on the extracted parameters, revealing discrepancies between ATLAS and CMS treatments.

Proposed method

• The analysis uses single-differential $t\bar{t}$ cross-section measurements from ATLAS and CMS at 8 TeV, including distributions in average transverse momentum, rapidity, and pair invariant mass and rapidity.
• NNLO QCD predictions are computed for various $m_t$ values and implemented via fastNLO tables, enabling rapid evaluation across multiple parton distribution function (PDF) sets (CT14, NNPDF30, NNPDF31).
• A global $\chi^2$ minimization is performed to fit the theoretical predictions to the experimental data, with uncertainties propagated through a p-value-based weighting scheme for averaging.
• The extraction accounts for both statistical and systematic uncertainties, with a combined averaging procedure that includes both $p$-value weights and systematic shifts across different PDF sets.
• The impact of underflow events in the $m_{t\bar{t}}$ distribution is evaluated by comparing fits with and without these events, revealing significant shifts in CMS results but minimal effects in ATLAS.

Experimental results

Research questions

• RQ1 Can a simultaneous extraction of $\alpha_s$ and $m_t$ be achieved using differential $t\bar{t}$ distributions at NNLO accuracy, overcoming the degeneracy present in total cross-section measurements?
• RQ2 How do the shapes of differential distributions—specifically $p_T^\text{avg}$, $y_\text{avg}$, $m_{t\bar{t}}$, and $y_{t\bar{t}}$—constrain both $\alpha_s$ and $m_t$ simultaneously?
• RQ3 What is the impact of underflow events in the $m_{t\bar{t}}$ distribution on the extracted values of $\alpha_s$ and $m_t$, and why do ATLAS and CMS show different sensitivities?
• RQ4 How do the results compare to world averages and previous extractions, and what does this imply about the consistency of LHC $t\bar{t}$ measurements?
• RQ5 To what extent do different PDF sets affect the final values of $\alpha_s$ and $m_t$ in the simultaneous fit?

Key findings

• The simultaneous extraction yields $\alpha_s = 0.1159^{+0.0013}_{-0.0014}$ and $m_t = 173.8^{+0.8}_{-0.8}$ GeV, representing a precise joint determination at NNLO accuracy.
• The value of $m_t$ is consistent with the world average value compiled by the Particle Data Group and with previous extractions using top-quark measurements.
• The inclusion of underflow events in the $m_{t\bar{t}}$ distribution causes a significant upward shift in $m_t$ for CMS data (by ~0.3 GeV) but has negligible effect on ATLAS results, suggesting differing experimental treatments.
• The $\chi^2_{\text{min}}$ values are low for ATLAS data (0.13–0.21) and moderate for CMS (2.02–5.03), indicating good agreement with theory across PDF sets.
• The results demonstrate that differential distributions at NNLO provide sufficient sensitivity to break the degeneracy between $\alpha_s$ and $m_t$, enabling a robust simultaneous fit.
• The study highlights the importance of consistent treatment of underflow events in $m_{t\bar{t}}$ distributions, as discrepancies between experiments may affect parameter extraction.