Gluon Operators Research Articles

The gluonic operator matrix elements at [formula omitted] for DIS heavy flavor production

We calculate the O(αs2) gluonic operator matrix elements for the twist-2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q2≫m2, up to the linear terms in the dimensional parameter ε (D=4+ε). These quantities are required for the description of parton distribution functions in the variable flavor number scheme (VFNS). The O(αs2ε) terms contribute at the level of the O(αs3) corrections through renormalization. We also comment on additional terms, which have to be considered in the fixed (FFNV) and variable flavor number scheme, adopting the MS¯ scheme for the running coupling constant.

Precision holography for non-conformal branes

We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p \leq 4, including the case of fundamental string solutions, is conformal to AdS_{p+2} x S^{8-p} with a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropriate Dirichlet boundary conditions, find the corresponding counterterms and compute the holographic 1-point functions, all in complete generality and at the full non-linear level. The result for the stress energy tensor properly defines the notion of mass for backgrounds with such asymptotics. The analysis is done both in the original formulation of the method and also using a radial Hamiltonian analysis. The latter formulation exhibits most clearly the existence of an underlying generalized conformal structure. In the cases of Dp-branes, the corresponding dual boundary theory, the maximally supersymmetric Yang-Mills theory SYM_{p+1}, indeed exhibits the generalized conformal structure found at strong coupling. We compute the holographic 2-point functions of the stress energy tensor and gluon operator and show they satisfy the expected Ward identities and the constraints of generalized conformal structure. The holographic results are also manifestly compatible with the M-theory uplift, with the asymptotic solutions, counterterms, one and two point functions etc of the IIA F1 and D4 appropriately descending from those of M2 and M5 branes, respectively. We present a few applications including the computation of condensates in Witten's model of holographic YM_4 theory.

Reciprocity of gauge operators in 𝒩 = 4 SYM

A recently discovered generalized Gribov-Lipatov reciprocity holds for the anomalous dimensions of various twist operators in Script N = 4 SYM. Here, we consider a class of scaling operators that reduce at one-loop to twist-3 maximal helicity gluonic operators. We extract from the asymptotic long-range Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections.

Probing electroweak physics for allB→XMdecays in the endpoint region

Using soft-collinear effective theory we describe at leading order in $1/{m}_{b}$ all the semi-inclusive hadronic $B\ensuremath{\rightarrow}XM$ decays near the endpoint, where an energetic light meson $M$ recoils against an inclusive jet $X$. Here we extend to the decays in which spectator quarks go into the jet $X$, and also include the decays involving $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons that receive additional contributions from gluonic operators. The predicted branching ratios and $CP$ asymmetries depend on fewer hadronic parameters than the corresponding two-body $B$ decays. This makes semi-inclusive hadronic $B\ensuremath{\rightarrow}XM$ decays a powerful probe of the potential nonperturbative nature of charming penguins as well as a useful probe of new physics effects in electroweak flavor changing transitions. A comparison with $B\ensuremath{\rightarrow}KX$ data from BABAR points to an enhanced charming penguin, albeit with large experimental errors.

Anomalous dimensions of finite size field strength operators in 𝒩 = 4 SYM

In the Script N = 4 super Yang-Mills theory, we consider the higher order anomalous dimensions γL(g) of purely gluonic operators Tr Script FL where Script F is a component of the self-dual field strength. We propose compact closed expressions depending parametrically on L that reproduce the prediction of Bethe Ansatz equations up to five loop order, including transcendental dressing corrections. The size dependence follows a simple pattern as the perturbative order is increased and suggests hidden relations for these special operators.

Renormalizability of the dimension two gluon operator A2 in a class of nonlinear covariant gauges

In this work we discuss a class of nonlinear covariant gauges for Yang–Mills theories which enjoy the property of being multiplicatively renormalizable to all orders. This property follows from the validity of a linearly broken identity, known as the ghost Ward identity. Furthermore, thanks to this identity, it turns out that the local composite dimension two gluon operator AaμAaμ can be introduced in a multiplicatively renormalizable way.

Study of the maximal Abelian gauge inSU(2)Euclidean Yang-Mills theory in the presence of the Gribov horizon

We pursue the study of $SU(2)$ Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual $U(1)$ Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, ${Z}_{g}{Z}_{A}^{1/2}=1$, relating the renormalization factors of the gauge coupling constant ${Z}_{g}$ and of the diagonal gluon field ${Z}_{A}$, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.

ααs2corrections to the first moment of the polarized virtual photon structure functiong1γ(x,Q2,P2)

We present the next-to-next-to-leading order ({alpha}{alpha}{sub s}{sup 2}) corrections to the first moment of the polarized virtual photon structure function g{sub 1}{sup {gamma}}(x,Q{sup 2},P{sup 2}) in the kinematical region {lambda}{sup 2}<<P{sup 2}<<Q{sup 2}, where -Q{sup 2}(-P{sup 2}) is the mass squared of the probe (target) photon and {lambda} is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The {alpha}{alpha}{sub s}{sup 2} corrections are found to be about 3% of the sum of the leading order ({alpha}) and the next-to-leading order ({alpha}{alpha}{sub s}) contributions, when Q{sup 2}=30{approx}100 GeV{sup 2} and P{sup 2}=3 GeV{sup 2}, and the number of active quark flavors n{sub f} is three to five.

Glueball spectrum and matrix elements on anisotropic lattices

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/\psi$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.

One-loop QCD spin chain and its spectrum

We study the renormalization of gauge invariant operators in large N c QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with selfdual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX 1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation.

Interaction of slowJ/ψandψ′with nucleons

The interaction of the charmonium resonances J/psi and psi' with nucleons at low energies is considered using the multipole expansion and low-energy theorems in QCD. A lower bound is established for the relevant gluonic operator average over the nucleon. As a result we find the discussed interaction to be significantly stronger than previously estimated in the literature. In particular we conclude that the cross section of the J/psi - nucleon elastic scattering at the threshold is very likely to exceed 17 millibarn and that existence of bound states of the J/psi in light nuclei is possible. For the psi' resonance we estimate even larger elastic scattering cross section and also a very large cross section of the process psi'+N -> psi+N giving rise to the decay width of tens of MeV for the psi' resonance in heavy nuclei.

Quantum integrability in (super) Yang–Mills theory on the light-cone

We employ the light-cone formalism to construct in the (super) Yang–Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N=4 Yang–Mills theory it exhausts all Wilson operators of the maximal Lorentz spin while in nonsupersymmetric Yang–Mills theory it is restricted to the sector of maximal helicity gluonic operators. We show that the dilatation operator in all N-extended super-Yang–Mills theories is given by the same integral operator which acts on the (N+1)-dimensional superspace and is invariant under the SL(2|N) superconformal transformations. We construct the R-matrix on this space and identify the dilatation operator as the Hamiltonian of the Heisenberg SL(2|N) spin chain.

Solution of twist-3 evolution equation in double logarithmic approximation in QCD

The solution of the DGLAP evolution equation for the twist-3 gluon operators is obtained in the double logarithmic approximation of QCD perturbation theory. The method used for the solution is similar to the reggeon field theory. The asymptotics of the twist-3 parton correlation function for small Bjorken variables x B is found.

Glueball matrix elements on anisotropic lattices

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing in the range 0.1fm -- 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/\psi$ radiative decays which will help to identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check, and the finite volume effects are also studied. The lattice spacing dependence of our results is very small and the continuum limits are reliably extrapolated.

CP-violating asymmetry in Λ → pπ in the Skyrme model

We study the CP-violating asymmetry in nonleptonic decay Λ → pπ. By employing the Skyrme model to calculate this decay amplitude contributed by the gluonic diploe operator, we find that a possible large CP-violating asymmetry could be expected, which is consistent with the previous study.

Gluonic penguin contribution to $B \rightarrow \pi \pi$ decays

We use the light-cone sum rule technique to calculate the contribution of the gluonic penguin operator O 8g to the decay of the B-meson to two pions. Leading-order perturbative and non-perturbative corrections are included, corresponding to hard and soft exchanged gluons, respectively. While the overall contribution of this operator to the decay is small as expected before, we find that the so-called soft-gluon part of this contribution is of the order of the hard-gluon one. This implies that the inclusion of soft gluons in the calculation of $B \rightarrow \pi \pi$ matrix elements may be important.

Analysis of the axial anomaly on the lattice with O( a)-improved Wilson action

Flavor singlet and non-singlet axial Ward identities are investigated using the Wilson formulation of lattice QCD with Clover O( a)-improvement, which breaks explicitly chiral symmetry. The matching at one-loop order of all the relevant renormalization constants with the continuum MS scheme is presented. Our calculations include: (1) the contributions arising from the Clover term of the action; (2) the complete mixing of the gluon operator G G with the divergence of the singlet axial current; (3) the use of both local and extended definitions of the fermionic bilinear operators. A definition of the gluon operator G G on the lattice outside the chiral limit is proposed. Our definition takes into account the possible power-divergent mixing with the pseudoscalar density, generated by the breaking of chiral symmetry. A non-perturbative procedure for the evaluation of such mixing constant is worked out. Finally, the renormalization properties of the composite insertion of the topological charge operator ∫d 4x G G(x) relevant for the lattice calculation of the neutron electric dipole moment, induced by the strong CP-violating term of the QCD Lagrangian, are discussed.

Gluonic penguin contributions inB→ππfrom QCD light-cone sum rules

The $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}\ensuremath{\pi}$ hadronic matrix element of the chromomagnetic dipole operator ${O}_{8g}$ (gluonic penguin operator) is calculated using the QCD light-cone sum rule approach. The resulting sum rule for $〈\ensuremath{\pi}\ensuremath{\pi}|{O}_{8g}|B〉$ contains, in addition to the $O({\ensuremath{\alpha}}_{s})$ part induced by hard-gluon exchanges, a contribution due to soft gluons. We find that in the limit ${m}_{b}\ensuremath{\rightarrow}\ensuremath{\infty}$ the soft-gluon contribution is suppressed as a second power of ${1/m}_{b}$ with respect to the leading-order factorizable $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}\ensuremath{\pi}$ amplitude, whereas the hard-gluon contribution has only an ${\ensuremath{\alpha}}_{s}$ suppression. Nevertheless, at finite ${m}_{b},$ the soft and hard effects of the gluonic penguin operator in $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}\ensuremath{\pi}$ are of the same order. Our result indicates that soft contributions are indispensable for an accurate counting of nonfactorizable effects in charmless B decays. On the phenomenological side we predict that the impact of gluonic penguin operators on ${B}_{d}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is very small, but is noticeable for ${B}_{d}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}.$

On absence of spontaneous parity breaking in QCD

We argue that the Vafa–Witten proof on absence of spontaneous parity breaking in QCD has the following two loopholes: first, when perturbed by an external field coupled to a parity-odd quark operator, the QCD vacuum energy could be a decreasing function of the field, contrary to the observation used in the proof. The difference comes from that the effective gluonic operator has in general a parity-even part which does not contribute to the path integral as a pure phase. Second, when perturbed by an external field coupled to a parity-odd gluonic operator, the vacuum energy is always a rising function of the field, independent of the existence of spontaneous parity breaking. This is because the parity-odd gluonic perturbations contribute to the path integral as a pure phase, and could not serve to select a physical vacuum should parity be spontaneously broken.