We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

We present a determination of parton distribution functions (ABM11) and the strong coupling constant alpha_s at next-to-leading order and next-to-next-to-leading order (NNLO) in QCD based on world data for deep-inelastic scattering and fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for n_f=3,4,5 and uses the MSbar-scheme for alpha_s and the heavy-quark masses. At NNLO we obtain the value alpha_s(M_Z) = 0.1134 +- 0.0011. The fit results are used to compute benchmark cross sections at hadron colliders to NNLO accuracy and to compare to data from the LHC.

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Parton Distribution Functions and Benchmark Cross Sections at NNLO

We determine a new set of parton distribution functions (ABMP16), the strong coupling constant αs and the quark masses mc, mb and mt in a global fit to next-to-next-to-leading order (NNLO) in QCD. The analysis uses the MS¯ scheme for αs and all quark masses and is performed in the fixed-flavor number scheme for nf=3, 4, 5. Essential new elements of the fit are the combined data from HERA for inclusive deep-inelastic scattering (DIS), data from the fixed-target experiments NOMAD and CHORUS for neutrino-induced DIS, data from Tevatron and the LHC for the Drell-Yan process and the hadro-production of single-top and top-quark pairs. The theory predictions include new improved approximations at NNLO for the production of heavy quarks in DIS and for the hadro-production of single-top quarks. The description of higher twist effects relevant beyond the leading twist collinear factorization approximation is refined. At NNLO, we obtain the value αs(nf=5)(MZ)=0.1147±0.0008.

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Parton Distribution Functions, $\alpha_s$ and Heavy-Quark Masses for LHC Run II

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This article reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

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Scattering processes and resonances from lattice QCD

Baryons as relativistic three-quark bound states

We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1\text{ }\text{ }\mathrm{fm}$ and $L=2.8\text{ }\text{ }\mathrm{fm}$. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089\text{ }\text{ }\mathrm{fm}$, $a=0.070\text{ }\text{ }\mathrm{fm}$ and $a=0.056\text{ }\text{ }\mathrm{fm}$. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.

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Axial nucleon form factors from lattice QCD

We present results on the lower moments of the nucleon generalized parton distributions within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Our simulations are performed on lattices with three different values of the lattice spacings, namely, $a=0.089\text{ }\text{ }\mathrm{fm}$, $a=0.070\text{ }\text{ }\mathrm{fm}$, and $a=0.056\text{ }\text{ }\mathrm{fm}$, allowing the investigation of cutoff effects. The volume dependence is examined using simulations on two lattices of spatial length $L=2.1\text{ }\text{ }\mathrm{fm}$ and $L=2.8\text{ }\text{ }\mathrm{fm}$. The simulations span pion masses in the range of 260 to 470 MeV. Our results are renormalized nonperturbatively, and the values are given in the $\overline{\mathrm{MS}}$ scheme at a scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$. They are chirally extrapolated to the physical point in order to compare with the experiment. The consequences of these results on the spin carried by the quarks in the nucleon are investigated.

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Moments of nucleon generalized parton distributions from lattice QCD

We present results on the nucleon electromagnetic form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1\text{ }\text{ }\mathrm{fm}$ and $L=2.8\text{ }\text{ }\mathrm{fm}$. Cutoff effects are investigated using three different values of the lattice spacings, namely $a=0.089\text{ }\text{ }\mathrm{fm}$, $a=0.070\text{ }\text{ }\mathrm{fm}$ and $a=0.056\text{ }\text{ }\mathrm{fm}$. The nucleon magnetic moment, Dirac and Pauli radii are obtained in the continuum limit and chirally extrapolated to the physical pion mass allowing for a comparison with experiment.

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Nucleon electromagnetic form factors in twisted mass lattice QCD

The electromagnetic and axial form factors of the nucleon are evaluated in twisted mass QCD with two degenerate flavors of light, dynamical quarks. The axial charge g_A, magnetic moment and the Dirac and Pauli radii are determined for pion masses in the range 300 MeV to 500 MeV.

Nucleon form factors with dynamical twisted mass fermions

We present results on the electromagnetic and axial nucleon form factors using two degenerate flavors of twisted mass fermions on lattices of spatial size 2.1 fm and 2.7 fm and a lattice spacing of about 0.09 fm. We consider pion masses in the range of 260-470 MeV. We chirally extrapolate results on the nucleon axial ch arge, the isovector Dirac and Pauli root mean squared radii and magnetic moment to the physical point and co mpare to experiment.

P. A. Harraud

Papers

Axial nucleon form factors from lattice QCD

Moments of nucleon generalized parton distributions from lattice QCD

Nucleon electromagnetic form factors in twisted mass lattice QCD

Nucleon form factors with dynamical twisted mass fermions

Nucleon form factors with Nf=2 dynamical twisted mass fermions