Determination of $α_s$ and $m_c$ in deep-inelastic scattering

TL;DR

The paper addresses determining the strong coupling constant $α_s(M_Z^2)$ and the charm-quark mass $m_c(m_c)$ from unpolarized world DIS data. It employs a fixed-flavor-number (FFN) QCD analysis with NNLO Wilson coefficients and running-mass definitions, incorporating twist-4 corrections and Drell-Yan constraints to fit PDFs and $α_s$ simultaneously. The NNLO results are $α_s(M_Z^2) = 0.1134 obreak\pm\nobreak 0.0011$ (exp) and $m_c(m_c) = 1.24 obreak\pm\nobreak 0.03\,(exp)^{+0.03}_{-0.02}\,(scale)^{+0.00}_{-0.07}\,(th)$, with ~30 MeV experimental precision for the charm mass and a ~70 MeV theoretical uncertainty from missing NNLO massive terms. The work also contrasts FFN with various VFN schemes, concluding that FFN offers more precise extractions for $α_s(M_Z^2)$ and $m_c(m_c)$ and quantifies the scheme-related uncertainties in heavy-quark PDFs and matching.

Abstract

We describe the determination of the strong coupling constant $α_s(M_Z^2)$ and of the charm-quark mass $m_c(m_c)$ in the $\bar{\rm MS}$-scheme, based on the QCD analysis of the unpolarized World deep-inelastic scattering data. At NNLO the values of $α_s(M_Z^2)=0.1134\pm 0.0011(\text{exp})$ and $m_c(m_c)=1.24 \pm 0.03 (\text{exp})\,^{+0.03}_{-0.02} (\text{scale})\,^{+0.00}_{-0.07} (\text{th})$ are obtained and are compared with other determinations, also clarifying discrepancies.

Figures (5)

• Figure 1: The $\chi^2$-profile versus the value of $\alpha_s(M_Z^2)$, for the separate data subsets, all obtained in variants of the ABM11 analysis with the value of $\alpha_s$ fixed and all other parameters fitted (solid lines: NNLO fit, dashes: NLO fit); from Ref. Alekhin:2012ig.
• Figure 2: The values of $\alpha_s(M_Z^2)$ obtained in the ABM fit Alekhin:2012ig in comparison to the ones obtained by JR JRnew, CTEQ Gao:2013xoa, MSTW Martin:2009bu, and NNPDF Ball:2011us from the analysis of the DIS data (squares) and from the combination of the DIS and jet Tevatron data Abulencia:2007ezAbazov:2008hua (circles).
• Figure 3: The combined HERA data on the reduced cross section for the open charm production Abramowicz:1900rp versus $x$ at different values of $Q^2$ in comparison with the analysis of Alekhin:2012vu at NLO (dashed line) and NNLO (solid line) together with a fit variant based on the option (A+B)/2 of the NNLO Wilson coefficients of Ref. Kawamura:2012cr, cf. Eq. (\ref{['eq:inter']}) (dotted line); from Ref. Alekhin:2012vu.
• Figure 4: The values of $m_c(m_c)$ obtained in the NLO and NNLO variants of our analysis with the value of $\alpha_s(M_Z^2)$ fixed. The position of the star displays the result with the value of $\alpha_s(M_Z^2)$ fitted Alekhin:2012ig; from Ref. Alekhin:2012vu.
• Figure 5: The difference between the $c$-quark PDFs derivatives $\dot{c}(x,\mu^2)\equiv \frac{dc(x,\mu^2)}{d\ln\mu^2}$ calculated with the FOPT matching condition and with the massless 4-flavor evolution starting at the matching point $\mu_0=m_c=1.4~{\rm GeV}$ versus the factorization scale $\mu^2$ at different values of $x$ in the LO, NLO, and NNLO* approximations. The arrows display upper margin of the HERA collider kinematics with the collision c.m.s. energy squared $s=10^5~{\rm GeV}^2$ and the vertical lines correspond to the matching point position $\mu_0$.