Gluon Form Factor Research Articles

Quark and Gluon Form Factors in Four-Loop QCD.

We compute the photon-quark and Higgs-gluon form factors to four-loop order within massless perturbative quantum chromodynamics. Our results constitute ready-to-use building blocks for N^{4}LO cross sections for Drell-Yan processes and gluon-fusion Higgs boson production at the LHC. We present complete analytic expressions for both form factors and show several of the most complicated master integrals.

Fermionic corrections to quark and gluon form factors in four-loop QCD

We analytically compute all four-loop QCD corrections to the photon-quark and Higgs-gluon form factors involving a closed massless fermion loop. Our calculation of non-planar vertex integrals confirms a previous conjecture for the analytical form of the non-fermionic contributions to the collinear anomalous dimensions of quarks and gluons.

Gluon parton densities in soft-wall AdS/QCD

We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton distributions are defined in terms of the unpolarized and polarized gluon PDFs and profile functions. The latter are related to gluon PDFs via differential equations.

Approximate four-loop QCD corrections to the Higgs-boson production cross section

We study the soft and collinear contributions to inclusive Higgs-boson production in gluon-gluon fusion at four loops. Using recent progress for the quark and gluon form factors and Mellin moments of splitting functions, we are able to complete the soft-gluon enhanced contributions exactly in the limit of a large number of colours, and to a sufficiently accurate numerical accuracy for QCD. The four-loop soft and virtual contributions increase the QCD cross section at 14 TeV by 2.7% and 0.2% for the standard choices μR=mH and μR=mH/2 of the renormalization scale, and reduce the scale uncertainty to below ±3%. As by-products, we derive the complete δ(1−x) term for the gluon-gluon splitting function at four loops and its purely Abelian contributions at five loops, and provide a numerical result for the single pole of the four-loop gluon form factor in dimensional regularization. Finally we present the closely related fourth-order coefficients D4 for the soft-gluon exponentiation of Higgs-boson and Drell-Yan lepton-pair production.

Quark and gluon form factors in four loop QCD: The Nf2 and NqγNf contributions

We calculate the four-loop massless QCD corrections with two closed quark lines to quark and gluon form factors. The results for the gluon form factor and the singlet part of the quark form factor are given for the first time. From our analytic expressions for the form factors, we determine the corresponding cusp anomalous dimensions. The relevant Feynman integrals are obtained with novel integral reduction techniques and direct integration methods.

Resummation improved rapidity spectrum for gluon fusion Higgs production

Gluon-induced processes such as Higgs production typically exhibit large perturbative corrections. These partially arise from large virtual corrections to the gluon form factor, which at timelike momentum transfer contains Sudakov logarithms evaluated at negative arguments ln2(−1) = −π2. It has been observed that resumming these terms in the timelike form factor leads to a much improved perturbative convergence for the total cross section. We discuss how to consistently incorporate the resummed form factor into the perturbative predictions for generic cross sections differential in the Born kinematics, including in particular the Higgs rapidity spectrum. We verify that this indeed improves the perturbative convergence, leading to smaller and more reliable perturbative uncertainties, and that this is not affected by cancellations between resummed and unresummed contributions. Combining both fixed-order and resummation uncertainties, the perturbative uncertainty for the total cross section at N3LO + N3LLφ′ is about a factor of two smaller than at N3LO. The perturbative uncertainty of the rapidity spectrum at NNLO + NNLLφ′ is similarly reduced compared to NNLO. We also study the analogous resummation for quark-induced processes, namely Higgs production through bottom quark annihilation and the Drell-Yan rapidity spectrum. For the former the resummation leads to a small improvement, while for the latter it confirms the already small uncertainties of the fixed-order predictions.

Quark and gluon form factors to four-loop order in QCD: TheNf3contributions

We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for arbitrary values of the space-time dimension. This is the first calculation of a gluon form factor at this perturbative order in QCD.

Further evidence for zero crossing on the three gluon vertex

The three gluon one particle irreducible function is investigated using lattice QCD simulations over a large region of momentum in the Landau gauge for four dimensional pure Yang-Mills equations and the SU(3) gauge group. The results favor a zero crossing of the gluon form factor for momenta in the range $220 - 260$ MeV. This zero crossing is required to happen in order to have a properly defined set of Dyson-Schwinger equations. It is also shown that in the high momentum region the lattice results are compatible with the predictions of renormalisation group improved perturbation theory.

Gluon dynamics, center symmetry, and the deconfinement phase transition in SU(3) pure Yang-Mills theory

The correlations between the modulus of the Polyakov loop, its phase $\ensuremath{\theta}$, and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to $\ensuremath{\theta}=0$, $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$. We find that the gluon propagator form factors associated with $\ensuremath{\theta}\ensuremath{\approx}0$ differ quantitatively and qualitatively from those associated to $\ensuremath{\theta}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$. This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature ${T}_{c}$, the difference between the propagators associated to $\ensuremath{\theta}\ensuremath{\approx}0$ and $\ensuremath{\theta}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/3$ allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.

Masses of tetraquarks with open charm and bottom

The masses of the heavy tetraquarks with open charm and bottom are calculated within the diquark–antidiquark picture in the framework of the relativistic quark model. The dynamics of the light quarks and diquarks is treated completely relativistically. The diquark structure is taken into account by calculating the diquark–gluon form factor. New experimental data on charmed and charmed-strange mesons are discussed. Our results indicate that the anomalous scalar Ds0⁎(2317) and axial vector Ds1(2460) mesons could not be considered as diquark–antidiquark bound states. On the other hand, Ds(2632) and DsJ⁎(2860) could be interpreted as scalar and tensor tetraquarks, respectively. The predictions for masses of the corresponding bottom counterparts of the charmed tetraquarks are given.

The quark and gluon form factors to three loops in QCD through to $ \mathcal{O}\left( {{\epsilon^2}} \right) $

We give explicit formulae for the O(eps) and O(eps^2) contributions to the unrenormalised three loop QCD corrections to quark and gluon form factors. These contributions have at most transcendentality weight eight. The O(eps) terms of the three-loop form factors are required for the extraction of the four-loop quark and gluon collinear anomalous dimensions. The O(eps^2) terms represent an irreducible contribution to the finite part of the form factors at four-loops. For the sake of completeness, we also give the contributions to the one and two loop form factors to the same transcendentality weight eight.

Calculation of the quark and gluon form factors to three loops in QCD

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al.\ for the three-loop form factors. In addition, we derive the subleading ${\cal O}(\e)$ terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.

Quark and Gluon Form Factors to Three Loops

We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs-boson and two gluons to three-loop order within massless perturbative quantum chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.

Renormalization-group improved prediction for Higgs production at hadron colliders

We use renormalization-group methods in effective field theory to improve the theoretical prediction for the cross section for Higgs-boson production at hadron colliders. In addition to soft-gluon resummation at N3LL, we also resum enhanced contributions of the form (C A π α s ) n , which arise in the analytic continuation of the gluon form factor to time-like momentum transfer. This resummation is achieved by evaluating the matching corrections arising at the Higgs-boson mass scale at a time-like renormalization point μ 2<0, followed by renormalization-group evolution to μ 2>0. We match our resummed result to NNLO fixed-order perturbation theory and give numerical predictions for the total production cross section as a function of the Higgs-boson mass. Resummation effects are significant even at NNLO, where our improved predictions for the cross sections at the Tevatron and the LHC exceed the fixed-order predictions by about 13% and 8%, respectively, for m H =120 GeV. We also discuss the application of our technique to other time-like processes such as Drell–Yan production, e + e −→hadrons, and hadronic decays of the Higgs boson.

Origin of the large perturbative corrections to Higgs production at hadron colliders

The very large $K$ factor for Higgs-boson production at hadron colliders is shown to result from enhanced perturbative corrections of the form $({C}_{A}\ensuremath{\pi}{\ensuremath{\alpha}}_{s}{)}^{n}$, which arise in the analytic continuation of the gluon form factor to timelike momentum transfer. These terms are resummed to all orders in perturbation theory using the renormalization group. After the resummation, the $K$ factor for the production of a light Higgs boson at the LHC is reduced to a value close to 1.3.

Masses of heavy tetraquarks in the relativistic quark model

The masses of heavy tetraquarks with hidden charm and bottom are calculated in the framework of the relativistic quark model. The tetraquark is considered as the bound state of a heavy–light diquark and antidiquark. The light quark in a heavy–light diquark is treated completely relativistically. The internal structure of the diquark is taken into account by calculating the diquark–gluon form factor in terms of the diquark wave functions. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that the X(3872) can be the tetraquark state with hidden charm. The masses of ground state tetraquarks with hidden bottom are found to be below the open bottom threshold.

Three-loop results for quark and gluon form factors

We study the photon–quark–quark and Higgs–gluon–gluon form factors for on-shell massless quarks and gluons in perturbative QCD. Previous third-order results for the quark case are extended by calculating the fermion-loop contributions up to the finite terms in dimensional regularization. For the gluon case the complete set of infrared poles at three loops is derived. Using the exponentiation of the form factor, the latter results are employed to extract a function entering the infrared factorization of general third-order amplitudes. We evaluate the infrared finite absolute ratio of the time-like and space-like gluon form factors up to the fourth order in the strong coupling constant. The result supports previous indications that the perturbative expansion of the Higgs boson production rate at the LHC is under control.

Two-loop quark and gluon form factors in dimensional regularisation

We compute the two-loop corrections to the massless quark form factor γ∗→qq¯ and gluon form factor H→gg to all orders in the dimensional regularisation parameter ε=(4−d)/2. The two-loop contributions to the form factors are reduced to linear combinations of master integrals, which are computed in a closed form, expressed as Γ-functions and generalised hypergeometric functions of unit argument. Using the newly developed HypExp-package, these can be expanded to any desired order, yielding Laurent expansions in ε. We provide expansions of the form factors to order ε2, as required for ultraviolet renormalisation and infrared factorisation of the three-loop form factors.

Signals of Confinement in Green Functions of SU(2) Yang-Mills Theory

It has been well established that the removal of center vortices from SU(2) lattice configurations results in the loss of confinement. The running coupling constant, gluon form factor, and ghost form factor are studied in the Landau gauge for the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed, and the IR singularity of the ghost form factor disappears. Hence, the removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.

Propagators and running coupling from SU(2) lattice gauge theory

We perform numerical studies of the running coupling constant α R ( p 2) and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used, respectively, for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost–ghost–gluon vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gluon form factor is suppressed while the ghost form factor is divergent. Correspondingly, the ghost propagator diverges faster than 1/ p 2 and the gluon propagator appears to be finite. Precision data for the running coupling α R ( p 2) are obtained. These data are consistent with an IR fixed point given by lim p→0 α R ( p 2)=5(1).