Gluon Field Strength Research Articles

Amplitude’s positivity vs. subluminality: causality and unitarity constraints on dimension 6 & 8 gluonic operators in the SMEFT

We derive the causality and unitarity constraints on dimension 6 and dimension 8 Gluon field strength operators in the Standard Model Effective Field Theory (SMEFT). In the first part of the paper, we use the ‘amplitude analysis’ i.e. dispersion relation for 2 → 2 scattering in the forward limit, to put bounds on the Wilson coefficients. We show that the dimension 6 operators can exist only in the presence of certain dimension 8 operators. It is interesting that the square of the dimension 6 Wilson coefficients can be constrained in this case even at the tree level. In the second part of this work, we successfully rederive all these bounds using the classical causality argument that demands that the speed of fluctuations about any non-trivial background should not exceed the speed of light. We also point out some subtleties in the superluminality analysis regarding whether the low-frequency phase velocity can always be used as the relevant quantity for Causality violation: as an example, we show that, due to these subtleties, if a small pion mass is added in the chiral Lagrangian, it is unclear if any strict positivity bound can be derived on the dimension 8 Wilson coefficient. Finally, we mention an interesting non-relativistic example where the subluminality requirement produces a stronger bound than the ‘amplitude analysis’.

Nonlocal gluon condensates in QCD sum rules

Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. Short-distance expansions of two-, three-, and four-gluon condensates are presented up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators as examples. Methodological aspects of the background field approach are discussed in relation to glueball studies within QCD sum rules. We confirm the results for Operator Product Expansion (OPE) of the two-gluon $0^{\pm +}$ glueball current correlators and calculate additional contributions coming from dimension-6 four-quark condensate and dimension-8 mixed quark-gluon condensates. The OPEs used in QCD sum rules for three-gluon $0^{\pm +}$ glueballs are revisited up to dimension-6 order.

Hadron collider probes of the quartic couplings of gluons to the photon and Z boson

We explore the experimental sensitivities of measuring the gg → Zγ process at the LHC to the dimension-8 quartic couplings of gluon pairs to the Z boson and photon, in addition to comparing them with the analogous sensitivities in the gg → γγ process. These processes can both receive contributions from 4 different CP-conserving dimension-8 operators with distinct Lorentz structures that contain a pair of gluon field strengths, {hat{G}}_{mu v}^a , and a pair of electroweak SU(2) gauge field strengths, {W}_{mu v}^i , as well as 4 similar operators containing a pair of {hat{G}}_{mu v}^a and a pair of U(1) gauge field strengths, Bμν. We calculate the scattering angular distributions for gg → Zγ and the Z → overline{f}f decay angular distributions for these 4 Lorentz structures, as well as the Standard Model background. We analyze the sensitivity of ATLAS measurements of the Z(→ ℓ+ℓ−, overline{nu}nu , overline{q}q )γ final states with integrated luminosities up to 139 fb−1 at sqrt{s} = 13 TeV, showing that they exclude values ≲ 2 TeV for the dimension-8 operator scales, and compare the Zγ sensitivity with that of an ATLAS measurement of the γγ final state. We present combined Zγ and γγ constraints on the scales of dimension-8 SMEFT operators and γγ constraints on the nonlinearity scale of the Born-Infeld extension of the Standard Model. We also estimate the sensitivities to dimension-8 operators of experiments at possible future proton-proton colliders with centre-of-mass energies of 25, 50 and 100 TeV, and discuss possible measurements of the Z spin and angular correlations.

Top-pair production via gluon fusion in the Standard Model effective field theory

We compute the leading corrections to the differential cross section for top-pair production via gluon fusion due to dimension-six operators at leading order in QCD. The Standard Model fields are assumed to couple only weakly to the hypothetical new sector. A systematic approach then suggests treating single insertions of the operator class containing gluon field strength tensors on the same footing as expli\-citly loop suppressed contributions from four-fermion operators. This is in particular the case for the chromomagnetic operator $Q_{(uG)}$ and the purely bosonic operators $Q_{(G)}$ and $Q_{(\varphi G)}$. All leading order dimension-six contributions are consequently suppressed with a loop factor $1/16\pi^2$.

Operator product expansion of the non-local gluon condensate

We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

Contribution of the Darwin operator to non-leptonic decays of heavy quarks

We compute the Darwin operator contribution ( 1/{m}_b^3 correction) to the width of the inclusive non-leptonic decay of a B meson (B+, Bd or Bs), stemming from the quark flavour-changing transition b → {q}_1{overline{q}}_2{q}_3 , where q1, q2 = u, c and q3 = d, s. The key ideas of the computation are the local expansion of the quark propagator in the external gluon field including terms with a covariant derivative of the gluon field strength tensor and the standard technique of the Heavy Quark Expansion (HQE). We confirm the previously known expressions of the 1/{m}_b^3 contributions to the semi-leptonic decay b → {q}_1mathrm{ell}{overline{nu}}_{mathrm{ell}} , with ℓ = e, μ, τ and of the 1/{m}_b^2 contributions to the non-leptonic modes. We find that this new term can give a sizeable correction of about −4 % to the non-leptonic decay width of a B meson. For Bd and Bs mesons this turns out to be the dominant correction to the free b-quark decay, while for the B+ meson the Darwin term gives the second most important correction — roughly 1/2 to 1/3 of the phase space enhanced Pauli interference contribution. Due to the tiny experimental uncertainties in lifetime measurements the incorporation of the Darwin term contribution is crucial for precision tests of the Standard Model.

Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions

We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form $\mathrm{Tr}\, F^n$ where $F$ is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalised unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a generalisation of dimensional reconstruction to any number of loops, both for amplitudes and form factors. Several novel results for one-loop minimal and non-minimal form factors of $\mathrm{Tr}\, F^n$ with $n>2$ are presented. Finally, we describe the \texttt{Mathematica} package \texttt{SpinorHelicity6D}, which is tailored to handle six-dimensional quantities written in the spinor-helicity formalism.

Constraining anomalous gluon self-interactions at the LHC: a reappraisal

Anomalous self-interactions of non-abelian gauge fields can be described by higher dimensional operators featuring gauge-invariant combinations of the field strengths. In the case of QCD, the gluon self-interactions start to be modified at dimension six by operators of the type GGG, with G the gluon field strength tensor, possibly leading to deviations in all observables and measurements that probe strong interactions at very small distances. In this work we consider the sensitivity to the triple gluon operator of a series of observables at the LHC in di-jet, three- and multi-jet final states and heavy-quark production. We critically re-examine the robustness of long-standing as well as more recent proposals addressing issues such as the validity of the EFT expansion and the impact of higher order QCD corrections. Our results support the conclusion that multi-jet observables can reliably bound these anomalous interactions to the level that their impact on other key observables at the LHC, involving for example top quark and Higgs production, can be safely neglected. We also highlight the potential of using previously suggested angular observables in three-jet events at the LHC to further constrain these interactions.

Scale-chiral symmetry, ω meson, and dense baryonic matter

It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension ($\gamma_{G^2}$) of the gluon field strength tensor squared ($G^2$) that represents the quantum trace anomaly should be $0 <\gamma_{G^2} <3$.

Higher-twist effects in light-cone sum rule for the Brightarrow pi form factor

We calculate the higher-twist corrections to the QCD light-cone sum rule for the B rightarrow pi transition form factor. The light-cone expansion of the massive quark propagator in the external gluonic field is extended to include new terms containing the derivatives of the gluon-field strength. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function are obtained in a factorized approximation, expressed via the product of the lower-twist pion distribution amplitudes and the quark-condensate density. The numerical analysis reveals that new higher-twist effects for the B rightarrow pi form factor are strongly suppressed. This result justifies the conventional truncation of the operator product expansion in the light-cone sum rules up to twist-4 terms.

Dimension-six triple gluon operator inHiggs+jetobservables

Recently a lot of progress has been made towards a full classification of new physics effects in Higgs observables by means of effective dimension-six operators. Specifically, Higgs production in association with a high transverse momentum jet has been suggested as a way to discriminate between operators that modify the Higgs-top coupling (${O}_{t}$) and operators that induce an effective Higgs-gluon coupling (${O}_{g}$)---a distinction that is hard to achieve with signal strength measurements alone. With this article we would like to draw attention to another source of new physics in $\mathrm{Higgs}+\mathrm{jet}$ observables: the triple gluon operator ${O}_{3g}$ (consisting of three factors of the gluon field strength tensor). We compute the distortions of kinematic distributions in $\mathrm{Higgs}+\mathrm{jet}$ production at a 14 TeV LHC due to ${O}_{3g}$ and compare them with the distortions due to ${O}_{t}$ and ${O}_{g}$. We find that the transverse momentum distributions alone cannot discriminate between ${O}_{3g}$ and ${O}_{g}$ if the coefficient of the operator ${O}_{t}$ treated as an unknown parameter. We further show that the jet rapidity and the difference between the Higgs and jet rapidity are well suited to remove this new degeneracy. Using rough estimates for the expected bounds we find that allowed distortions in kinematic distributions due to ${O}_{g}$ are of similar size as those due to ${O}_{3g}$. We conclude that a full analysis of new physics in $\mathrm{Higgs}+\mathrm{jet}$ observables must take the contributions from ${O}_{3g}$ into account.

Scaling dimensions in AdS/QCD and the gluon field strength propagator

We derive the scaling dimension of antisymmetric tensor operators in the boundary theory of the AdS/CFT correspondence using a functional integral representation of the boundary-to-boundary propagators of their dual fields in the bulk. We then apply this technique to AdS/QCD in which the bulk metric is warped, resulting in non-constant scaling dimensions. In particular, we compute the two-point correlation function of gluon field strength operators, for which it is prerequisite to know the ow of the anomalous scaling dimension under rescaling. The results are in very good agreement with quenched lattice QCD data, thus confirming the functional form of the scaling dimension.

Universal structure of subleading infrared poles in gauge theory amplitudes

We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G(alpha_s), depending on both the spin and gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix elements involving the gluon field strength. We then show that G(alpha_s) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B_delta (alpha_s) of delta(1 - z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B_delta (alpha_s). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.

One-loop ϕ-MHV amplitudes using the unitarity bootstrap: the general helicity case

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν. We treat H as the real part of a complex field that couples to the selfdual gluon field strengths and compute the one-loop corrections to the -MHV amplitudes involving , two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work where the two negative helicity gluons were constrained to be colour adjacent. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

One-loop phi-MHV amplitudes using the unitarity bootstrap

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν produced by considering the heavy top quark limit of the one-loop coupling of Higgs and gluons in the standard model. We treat H as the real part of a complex field that couples to the selfdual gluon field strengths and compute the one-loop corrections to amplitudes involving , two colour adjacent negative helicity gluons and an arbitrary number of positive helicity gluons - the so-called -MHV amplitudes. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

Disentangling dimension six operators through di-Higgs boson production

New physics near the TeV scale can generate dimension-six operators that modify the production rate and branching ratios of the Higgs boson. Here, we show how Higgs boson pair production can yield complementary information on dimension-six operators involving the gluon field strength. For example, the invariant mass distribution of the Higgs boson pair can show the extent to which the masses of exotic TeV-scale quarks come from electroweak symmetry breaking. We discuss both the current Tevatron bounds on these operators and the most promising LHC measurement channels for two different Higgs masses: 120 GeV and 180 GeV. We argue that the operators considered in this paper are the ones most likely to yield interesting Higgs pair physics at the LHC.

The QCD partition function in the external field in the covariant gauge

The QCD partition function in the external stationary gluomagnetic field is computed in the third order in external field invariants in arbitrary dimension and arbitrary covariant gauge. The contributions proportional to third order invariants in gluon field strength are shown to be dependent on covariant quantum gauge fixing parameter \alpha

Vacuum expectation value of a Wegner–Wilson loop near the light-cone

Vacuum expectation values for one Wegner–Wilson loop representing a moving quark–antiquark pair are calculated in four-dimensional Euclidean and Minkowski space–time. The calculation uses gluon field strength correlators with perturbative gluon exchange and non-perturbative correlations from the stochastic vacuum model. The expectation value of a Wegner–Wilson loop forming a hyperbolic angle in Minkowski space–time is connected by an analytical continuation to the expectation value of the Wegner–Wilson loop in Euclidean four-space. The obtained result shows how confinement enters into the light-cone Hamiltonian for valence quarks independently of the chosen model.

Calorons and the bilocal correlator of the gluon-field strength

The bilocal correlator for finite-temperature gluodynamics is calculated in the instanton gas model. It is shown that the correlation length of vacuum in this model decreases when temperature increases. The results are compared with finite-temperature lattice calculations for the bilocal correlator. The instanton density and possible structures of nonperturbative vacuum are discussed.

Confining QCD strings, Casimir scaling, and a Euclidean approach to high-energy scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.