Gluon Loop Research Articles

Total cross section of the process e++e−→Σ0+Σ¯0 in the vicinity of charmonium ψ(3770) including the D -meson loop and three-gluon contributions

For the study of the structure of baryons it is necessary to investigate the production of a baryon pair in e+e− annihilation. The baryon-antibaryon pair production at the electron-positron linear collider makes it possible to investigate in detail the basic structure of the Standard Model. The creation of baryon-antibaryon pairs in electron-positron annihilation provides an increasingly powerful tool at higher c.m. energies. We present phenomenological results for Σ0Σ¯0 production in e+e− interaction at the BESIII and Colliders. In the present work, we investigate a hyperon pair produced in the reaction e+e−→Σ0Σ¯0. We calculate the total cross section of the process e+e−→Σ0Σ¯0 taking into account the contributions of the D-meson loop and three gluon loops as well as the interference of all diagrams to the Born approximation. For these contributions large relative phases are generated with respect to the pure electromagnetic mechanism. For the large momentum transferred region we obtain as a byproduct a fit of the electromagnetic form factor of the Σ hyperon. Published by the American Physical Society 2024

The complex heavy quarkonium potential with the Gribov–Zwanziger action

Gribov–Zwanziger prescription in Yang–Mills theory improves the infrared dynamics. In this work, we study the static potential of a heavy quark-antiquark pair with the HTL resummed perturbation method within the Gribov–Zwanziger approach at finite temperature. The real and imaginary parts of the heavy quarkonium complex potential are obtained from the one-loop effective static gluon propagator. The one-loop effective gluon propagator is obtained by calculating the one-loop gluon self-energies containing the quark, gluon, and ghost loop. The gluon and ghost loops are modified in the presence of the Gribov parameter. We also calculate the decay width from the imaginary part of the potential. We also discuss the medium effect of heavy quarkonium potential with the localized action via auxiliary fields.

Energy loss of a fast moving parton in Gribov-Zwanziger plasma

The Gribov-Zwanziger prescription applied within Yang-Mills theory is demonstrated to be an efficient method for refining the theory’s infrared dynamics. We study the collisional energy loss experienced by a high-energetic test parton as it traverses through the Grivov plasma at finite temperature. To achieve this, we employ a semiclassical approach that considers the parton’s energy loss while accounting for the backreaction induced by the polarization effects due to its motion in the medium. The polarization tensor of the medium is estimated within a nonperturbative resummation considering the Gribov-Zwanziger approach. The modification of the gluon and ghost loops due to the presence of the Gribov parameter plays a vital role in our estimation. We observe that the nonperturbative interactions have a sizable effect on the parton energy loss. Further, we discuss the implications of our findings in the context of relativistic heavy-ion collisions. Published by the American Physical Society 2024

Spinning loop amplitudes in anti–de Sitter space

In this work we present a systematic study of ${\mathrm{AdS}}_{d+1}$ loop amplitudes for gluons and gravitons using momentum space techniques. Inspired by the recent progress in tree-level computation, we construct a differential operator that can act on a scalar factor in order to generate gluon and graviton loop integrands: this systematizes the computation for any given loop level Witten diagram. We then give a general prescription in this formalism, and discuss it for bubble, triangle, and box diagrams.

Rare fluctuations of the S matrix at NLO in QCD

We calculate the rare fluctuations of the $S$-matrix on top of the full next-to-leading order corrections in the center of mass frame. The relevant result in the saturation regime shows that the exponential factor of the $S$-matrix is $\sqrt{2}$ as large as the result which emerges when the rare fluctuation effects are taken into account. We find that the factor of $\sqrt{2}$ change of the exponential factor is induced by the gluon loop corrections which compensate part of rapidity decrease of the $S$-matrix made by quark loops and lead to the rare fluctuations becoming important again. To ensure the relevant results of the $S$-matrix are independent of the frame choice, the rare fluctuations of the $S$-matrix are also derived in a general frame. It is found that all the results are consistent with each other in both frames.

Form factor decompositions of the QCD four - gluon vertex

The Bern-Kosower formalism, originally developed around 1990 as a novel way of obtaining on-shell amplitudes in field theory as limits of string amplitudes, has recently been shown to be extremely effcient as a tool for obtaining form factor decompositions of the N - gluon vertices. Its main advantages are that gauge invariant structures can be generated by certain systematic integration-by-parts procedures, making unnecessary the usual tedious analysis of the non-abelian off-shell Ward identities, and that the scalar, spinor and gluon loop cases can be treated in a unified way. After discussing the method in general for the N - gluon case, I will show in detail how to rederive the Ball- Chiu decomposition of the three - gluon vertex, and finally present two slightly different decompositions of the four - gluon vertex, one generalizing the Ball Chiu one, the other one closely linked to the QCD effective action.

Approximate solution to the NLL BK equation in the saturation region

We analytically solve the full next-to-leading logarithmic Balitsky-Kovchegov equation in the saturation regime, which includes corrections from quark and gluon loops, and large double transverse logarithms. The analytic result for the $S$-matrix in the saturation regime shows that the linear rapidity decrease with rapidity of the exponent in running coupling case is replaced by rapidity raised to power of 3/2 decreasing. The collinearly-improved Balitsky-Kovchegov equation are also analytically solved in the saturation regime. It shows that the double collinear logarithms do not contribute to the $S$-matrix and the solution is the same as the one obtained from the leading order Balitsky-Kovchegov equation. The numerical solutions to the leading order and full next-to-leading logarithmic Balitsky-Kovchegov equations are performed in order to test the analytic results derived in the saturation regime.

Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model

We consider a vector-like gauge theory of fermions that confines at the multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone boson. The weak interactions are embedded in the unbroken subgroup $Sp(4)$ of a spontaneously broken $SU(4)$ flavour group. The meson resonances appear as poles in the two-point correlators of fermion bilinears, and include the Goldstone bosons plus a massive pseudoscalar $\eta'$, as well as scalars, vectors and axial vectors. We compute the mass spectrum of these mesons, as well as their decay constants, in the chiral limit, in the approximation where the hypercolour $Sp(2N)$ dynamics is described by four-fermion operators, \`a la Nambu-Jona Lasinio. By resumming the leading diagrams in the $1/N$ expansion, we find that the spin-one states lie beyond the LHC reach, while spin-zero electroweak-singlet states may be as light as the Goldstone-boson decay constant, $f\sim 1$ TeV. We also confront our results with a set of available spectral sum rules. In order to supply composite top-quark partners, the theory contains additional fermions carrying both hypercolour and ordinary colour, with an associated flavour symmetry-breaking pattern $SU(6)/SO(6)$. We identify and analyse several non-trivial features of the complete two-sector gauge theory: the 't~Hooft anomaly matching conditions; the higher-dimension operator which incorporates the effects of the hypercolour axial-singlet anomaly; the coupled mass-gap equations; the mixing between the singlet mesons of the two sectors, resulting in an extra Goldstone boson $\eta_0$, and novel spectral sum rules. Assuming that the strength of the four-fermion interaction is the same in the two sectors, we find that the coloured vector and scalar mesons have masses $\gtrsim 4 f$, while the masses of coloured pseudo-Goldstone bosons, induced by gluon loops, are $\gtrsim 1.5f$.

Gluon and Wilson loop TMDs for hadrons of spin ≤ 1

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small $x$, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small-$x$ `dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small-$x$ limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-$1/2$ and spin-$1$ hadrons), and tensor polarized (relevant for spin-$1$ hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.

Twist-3 T-odd fragmentation functions G ⊥ andG˜⊥in a spectator model

We present a calculation of the twist-3 T-odd chiral-even fragmentation functions G⊥ and G˜⊥ using a spectator model. We consider the effect gluon exchange to calculate all necessary one-loop diagrams for the quark–quark and quark–gluon–quark correlation functions. We find that the gluon loops corrections generate non-zero contribution to these two fragmentation function. We numerically calculate their half-kT moments by integrating over the transverse momentum and also verify the equation of motion relation among G⊥, G˜⊥ and the Collins function.

The two-, three- and four-gluon sector of QCD in the Landau gauge

Due to the nonperturbative masslessness of the ghost field, ghost loops that contribute to gluon Green's functions in the Landau gauge display infrared divergences, akin to those one would encounter in a conventional perturbative treatment. This is in sharp contrast with gluon loops, in which the perturbative divergences are tamed by the dynamical generation of a gluon mass acting as an effective infrared cutoff. In this paper, after reviewing the full nonperturbative origin of this divergence in the two-gluon sector, we discuss its implications for the three- and four-gluon sector, showing in particular that some of the form factors characterizing the corresponding Green's functions are bound to diverge in the infrared.

Multidimensional Dirac strings and the Witten index of SYMCS theories with groups of higher rank

We discuss generalized Dirac strings associated with a given Lie group. They live on C r (r being the rank of the group). Such strings show up in the effective Born-Oppenheimer Hamiltonian for 3d supersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops. We calculate accurately the number of the vacuum states in the effective Hamiltonian associated with these strings. We also show that these states are irrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS theories depends thus only on the strings generated by fermion loops and carrying fractional generalized fluxes.

A covariant representation of the Ball–Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger–Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern–Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball–Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S of this decomposition is not a one-loop accident, but persists at higher-loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4 SYM theory, in the present approach relates to worldline supersymmetry.

String-inspired representations of photon/gluon amplitudes

The string-based Bern-Kosower rules provide an efficient way for obtaining parameter integral representations of the one-loop N -photon/gluon amplitudes involving a scalar, spinor or gluon loop, starting from a master formula and using a certain integration-by-parts (“IBP”) procedure. Strassler observed that this algorithm also relates to gauge invariance, since it leads to the absorption of polarization vectors into field strength tensors. Here we present a systematic IBP algorithm that works for arbitrary N and leads to an integrand that is not only suitable for the application of the Bern-Kosower rules but also optimized with respect to gauge invariance. In the photon case this means manifest transversality at the integrand level, in the gluon case that a form factor decomposition of the amplitude into transversal and longitudinal parts is generated naturally by the IBP, without the necessity to consider the nonabelian Ward identities. Our algorithm is valid off-shell, and provides an extremely efficient way of calculating the one-loop one-particle-irreducible off-shell Green’s functions (“vertices”) in QCD. It can also be applied essentially unchanged to the one-loop gauge boson amplitudes in open string theory. In the abelian case, we study the systematics of the IBP also for the practically important case of the one-loop N -photon amplitudes in a constant field.

Dyson-Schwinger equations for IR Yang-Mills theory in different dimensions

A numerical solution of the coupled Dyson-Schwinger equations for the ghost and gluon propagators in Yang-Mills theory is presented in Landau gauge. Aimed at investigating the infrared behavior of the propagators, the equations are simplified by neglecting the gluon loops, according to the ghost dominance hypothesis motivated by the Gribov-Zwanziger scenario. The equations are solved with an iterative method, eliminating the ultraviolet divergence through a continuous regulator function depending on the cut off scale. The solutions, derived for different values of the Euclidean space-time dimension, present scaling (the infrared exponents are obtained) or decoupling behavior, depending on whether the horizon condition is or not implemented. Moreover, it is shown that the running coupling constant approaches a constant value in the IR, corresponding to an attractive fixed point.

Witten index in supersymmetric 3d theories revisited

We have performed a direct calculation of Witten index in N = 1,2,3 supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the results of Witten, but there is a difference in the way the loop effects are implemented. In Witten's approach, one has only take into account the fermion loops, which bring about a negative shift of the (chosen positive at the tree level) Chern-Simons coupling k. As a result, Witten index vanishes and supersymmetry is broken at small k. In the effective BO Hamiltonian framework, fermion, gluon and ghost loops contribute on an equal footing. Fermion loop contribution to the effective Hamiltonian can be evaluated exactly, and their effect amounts to the negative shift k -> k - h/2 for N =1 and k -> k - h for N = 2,3 in the tree-level formulae for the index. In our approach, with rather natural assumptions on the structure of bosonic corrections, the shift k -> k + h brought about by the gluon loops also affects the index. Since the total shift of k is positive or zero, Witten index appears to be nonzero at nonzero k, and supersymmetry is not broken. We discuss possible reasons for such disagreement.

Next-to-leading order evolution of color dipoles

The small-$x$ deep inelastic scattering in the saturation region is governed by the nonlinear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the Balitsky-Kovchegov equation for the evolution of color dipoles. In the next-to-leading order the Balitsky-Kovchegov equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities. We calculate the gluon contribution to the small-$x$ evolution of Wilson lines (the quark part was obtained earlier).

Quark contribution to the small-xevolution of color dipole

The small-$x$ deep inelastic scattering in the saturation region is governed by the nonlinear evolution of Wilson-lines operators. In the leading logarithmic approximation it is given by the Balitsky-Kovchegov (BK) equation for the evolution of color dipoles. In the next-to-leading order (NLO) the nonlinear equation gets contributions from quark and gluon loops. In this paper I calculate the quark-loop contribution to small-$x$ evolution of Wilson lines in the NLO. It turns out that there are no new operators at the one-loop level---just as at the tree level, the high-energy scattering can be described in terms of Wilson lines. In addition, from the analysis of quark loops I find that the argument of coupling constant in the BK equation is determined by the size of the parent dipole rather than by the size of produced dipoles. These results are to be supported by future calculation of gluon loops.

Radiative Decays of Charmonium into Light Mesons

We apply perturbative QCD to the radiative decays of charmoniaJ/ψ and χcJ into light mesons. We perform a completenumerical calculation for the quark–gluon loop diagrams involvedin these processes. The calculated J/ψ decay branching ratiosinto p-wave mesons f2(1270) and f1(1285) fit the data well,while that of f0(980) (if treated as an ss̄ meson) ispredicted to be 1.6×10−4, which implies thatf0(1710) can not be the ss̄ or (uū+dd̄)/21/2 meson. Decays of p-wave charmonia χcJ→ρ(ω,ϕ)γ (J = 0,1,2) are also studied, and thebranching ratio of χc1→ργ is predicted to be1.4×10−5, which may be tested by CLEO-c collaboration andBESIII collaboration with future experiments.

Soft-gluon production due to a gluon loop in a constant chromoelectric background field

We obtain an exact result for the soft gluon production and its p_T distribution due to a gluon loop in a constant chromo-electric background field E^a with arbitrary color. Unlike Schwinger's result for e^+e^- pair production in QED which depends only on one gauge invariant quantity, the Electric field E, we find that the p_T distribution of the gluons depend on two gauge invariant quantities, E^aE^a and [d_{abc}E^aE^bE^c]^2.