Gauge Invariant Operators Research Articles

Final charged-lepton angular distribution and possible anomalous top-quark couplings in [formula omitted

Possible anomalous (or nonstandard) top-quark interactions with the gluon and those with the W boson induced by SU(3)×SU(2)×U(1) gauge-invariant dimension-6 effective operators are studied in pp→tt¯X→ℓ+X′ (ℓ=e or μ) at the Large Hadron Collider (LHC). The final charged-lepton (ℓ+) angular distribution is first computed for nonvanishing nonstandard top-gluon and top-W couplings with a cut on its transverse momentum. The optimal-observable procedure is then applied to this distribution in order to estimate the expected statistical uncertainties in measurements of those couplings that contribute to this process in the leading order.

Thermal power terms in the Einstein-dilaton system

We employ the gauge/string duality to study the thermal power terms of various thermodynamic quantities in gauge theories and the renormalized Polyakov loop above the deconfinement phase transition. We restrict ourselves to the five-dimensional Einstein gravity coupled to a single scalar, the dilaton. The asymptotic solutions of the system for a general dilaton potential are employed to study the power contributions of various quantities. If the dilaton is dual to the dimension-4 operator ${\rm Tr} F_{\mu\nu}^2$, no power corrections would be generated. Then the thermal quantities approach their asymptotic values much more quickly than those observed in lattice simulation. When the dimension of the dual operator is different from 4, various power terms are generated. The lowest power contributions to the thermal quantities are always quadratic in the dilaton, while that of the Polyakov loop is linear. As a result, the quadratic terms in inverse temperature for both the trace anomaly and the Polyakov loop, observed in lattice simulation, cannot be implemented consistently in the system. This is in accordance with the field theory expectation, where no gauge-invariant operator can accommodate such contributions. Two simple models, where the dilaton is dual to operators with different dimensions, are studied in detail to clarify the conclusion.

Calculation of the transverse parton distribution functions at next-to-next-to-leading order

We describe the perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate the cancellation of light-cone divergences and show that universal process-independent transverse parton distribution functions can be obtained through a refactorization. Our results serve as the first explicit higher-order calculation of these functions starting from first principles, and can be used to perform next-to-next-to-next-to-leading logarithmic $q_T$ resummation for a large class of processes at hadron colliders.

Lattice study of the jet quenching parameter.

We present a first-principle computation of the jet quenching parameter, which describes the momentum broadening of a high-energy parton moving through the deconfined state of QCD matter at high temperature. Following an idea originally proposed by Caron-Huot, we explain how one can evaluate the soft contribution to the collision kernel characterizing this real-time phenomenon, analyzing certain gauge-invariant operators in a dimensionally reduced effective theory (electrostatic QCD), which can be studied nonperturbatively via simulations on a Euclidean lattice. Our high-precision numerical computations at two different temperatures indicate that soft contributions to the jet quenching parameter are large. After discussing the systematic uncertainties involved, we present a quantitative estimate for the jet quenching parameter in the temperature range accessible at heavy-ion colliders, and compare it to results from phenomenological models as well as to strong-coupling computations based on the holographic correspondence.

Higgs bosons from top quark decays

In light of the discovery of a standard model (SM)-like Higgs boson ($h$) at the LHC, we investigate the top quark to Higgs boson transition $t\ensuremath{\rightarrow}{W}^{*}bh$, which is the leading $t\ensuremath{\rightarrow}h$ decay mode in the SM. We find the decay branching fraction to be $1.80\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}9}$. In comparison, the two-body, loop-induced $t\ensuremath{\rightarrow}ch$ transition occurs at $\ensuremath{\sim}1{0}^{\ensuremath{-}14}$ in the SM. We consider the consequences of gauge-invariant dimension-six operators affecting the $t\overline{t}h$ interaction and find that the decay branching fraction may be increased by a factor of 2 within current constraints on the coupling parameters from collider experiments. We also extend the calculation to the $CP$-conserving Type I and Type II two-Higgs-doublet models, including both $CP$-even and $CP$-odd Higgs bosons. For neutral scalar masses at about 100 GeV, the decay rates can be several times larger than the SM result in the allowed range of model parameters. Observation prospects at present and future colliders are briefly addressed.

Remarks on entanglement entropy for gauge fields

In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center --- a set of operators which commute with all others --- in the gauge invariant operator algebra corresponding to finite region. A unique entropy can be assigned to algebras with center, giving place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.

Padé approximation and glueball mass estimates in 3d and 4d with [formula omitted] colors

A Padé approximation approach, rooted in an infrared moment technique, is employed to provide mass estimates for various glueball states in pure gauge theories. The main input in this analysis are theoretically well-motivated fits to lattice gluon propagator data, which are by now available for both SU(2) and SU(3) in 3 and 4 space–time dimensions. We construct appropriate gauge invariant and Lorentz covariant operators in the (pseudo)scalar and (pseudo)tensor sector. Our estimates compare reasonably well with a variety of lattice sources directly aimed at extracting glueball masses.

Supercurrent multiplet correlators at weak and strong coupling

Correlators of gauge invariant operators provide useful information on the dynamics, phases and spectra of a quantum field theory. In this paper, we consider N=1 supersymmetric theories and focus our attention on the supercurrent multiplet. We give a complete characterization of two-point functions of operators belonging to such multiplet, like the energy-momentum tensor and the supercurrent, and study the relations between them. We discuss instances of weakly coupled and strongly coupled theories, in which different symmetries, like conformal invariance and supersymmetry, may be conserved and/or spontaneously or explicitly broken. For theories at strong coupling, we exploit AdS/CFT techniques. We provide a holographic description of different properties of a strongly coupled theory, including a realization of the Goldstino mode in a simple illustrative model.

Gauge invariant electromagnetic properties of fermions induced by CPT-violation in the Standard Model Extension

Low-energy Lorentz-invariant quantities could receive contributions from a fundamental theory producing small Lorentz-violating effects. Within the Lorentz-violating extension of quantum electrodynamics, we investigate, perturbatively, the contributions to the one-loop ffγ vertex from the CPT-violating axial coupling of a vector background field to fermions. We find that the resulting vertex function has a larger set of Lorentz structures than the one characterizing the usual, Lorentz-invariant, parametrization of the ffγ vertex. We prove gauge invariance of the resulting one-loop expression through a set of gauge invariant nonrenormalizable operators introducing new-physics effects at the first- and second-orders in Lorentz-violation, and which generate tree-level contributions to the ffγ vertex. Whereas loop contributions involving parameters that violate Lorentz-invariance at the first-order are CPT-odd, those arising at the second-order are CPT-even, so that contributions to low-energy physics are restricted to emerge for the first time at the second-order. In this context, we derive a contribution to anomalous magnetic moment (AMM) of fermions, which we use to set a bound on Lorentz-violation.

Higher dimensional operators and the LHC Higgs data: The role of modified kinematics

The inclusion of higher-dimensional gauge invariant operators induces new Lorentz structures in Higgs couplings with electroweak gauge boson pairs. This in principle affects the kinematics of Higgs production and decay, thereby modifying the efficiencies of the experimental cuts compared to what simulations based on the standard model interactions yield. Taking some sample cases, we perform a rigorous analysis of how the efficiencies differ for various strengths of the additional operator vis-a-vis the standard model interactions, scanning over the values of both of them. While the response to cuts can be markedly different in some regions, we find that the sensitivity to new operator structures is relatively limited, so long as we remain confined to the 2-sigma regions around the best fit signal strengths measured at the Large Hadron Collider. We also show modifications to certain kinematical distributions including the new operators in the diphoton final state.

Effects of Lorentz violation through the γe → Wνe process in the Standard Model extension

Physics beyond the Fermi scale could show up through deviations of the gauge couplings predicted by the electroweak Yang–Mills sector. This possibility is explored in the context of the International Linear Collider through the helicity amplitudes for the γe → Wνe reaction to which the trilinear WWγ coupling contributes. The new physics effects on this vertex are parametrized in a model-independent fashion through an effective electroweak Yang–Mills sector, which is constructed by considering two essentially different sources of new physics. In one scenario, Lorentz violation will be considered exclusively as the source of new physics effects. This type of new physics is considered in an extension of the Standard Model (SM) that is known as the SM extension (SME), which is an effective field theory that contemplates CPT and Lorentz violation in a model-independent fashion. Any source of new physics that respects the Lorentz symmetry will be considered within the general context of the well-known conventional effective SM (CESM) extension. Both the SME and CESM descriptions include gauge invariant operators of dimension higher than 4, which, in general, transform as Lorentz tensors of rank higher than zero. In the former theory, observer Lorentz invariants are constructed by contracting these operators with constant Lorentz tensors, whereas in the latter the corresponding Lorentz invariant interactions are obtained contracting such operators with products of the metric tensor. In this work, we focus on a dimension 6 Lorentz 2-tensor, , which arises from an effective SU(2)L Yang–Mills sector. Contributions to the WWγ coupling arising from dimension 4 operators are ignored since they are strongly constrained. When these operators are contracted with a constant antisymmetric background tensor, bαβ, the corresponding observer invariant belongs to the SME, whereas if they are contracted with the metric tensor, gαβ, an effective interaction in the context of the CESM is obtained. We focus our study on the possibility of experimentally distinguishing both types of new physics effects on the WWγ vertex. It is found that for a new physics scale of the same order of magnitude and under determined circumstances, both types of new physics effects will be clearly distinguished.

Fuzzy bags, Polyakov loop and gauge/string duality

Confinement in SU($N$) gauge theory is due to the linear potential between colored objects. At short distances, the linear contribution could be considered as the quadratic correction to the leading Coulomb term. Recent lattice data show that such quadratic corrections also appear in the deconfined phase, in both the thermal quantities and the Polyakov loop. These contributions are studied systematically employing the gauge/string duality. "Confinement" in ${\mathcal N}=4$ SU($N$) Super Yang-Mills (SYM) theory could be achieved kinematically when the theory is defined on a compact space manifold. In the large-$N$ limit, deconfinement of ${\mathcal N}=4$ SYM on $\mathbb{S}^3$ at strong coupling is dual to the Hawking-Page phase transition in the global Anti-de Sitter spacetime. Meantime, all the thermal quantities and the Polyakov loop achieve significant quadratic contributions. Similar results can also be obtained at weak coupling. However, when confinement is induced dynamically through the local dilaton field in the gravity-dilaton system, these contributions can not be generated consistently. This is in accordance with the fact that there is no dimension-2 gauge-invariant operator in the boundary gauge theory. Based on these results, we suspect that quadratic corrections, and also confinement, should be due to global or non-local effects in the bulk spacetime.

Hilbert series for moduli spaces of instantons on ℂ2/ℤ n

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p + 4) system with the D(p + 4) branes (with or without O(p + 4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A n−1 ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.

An asymptotic solution of large-N QCD

We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the $LSZ$ reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$, and in particular on any string solution.

Relativistic features and time delay of laser-induced tunnel ionization

The electron dynamics in the classically forbidden region during relativistic tunnel-ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge invariant total energy operator. Introducing position dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel-ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strong field approximation calculation where the binding potential is assumed to be zero-ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deep-tunneling and in the near-threshold-tunneling regimes. It is shown that while in the deep-tunneling regime signatures of the tunneling time delay are not measurable at remote distance, it is detectable, however, in the latter regime.

Gauge invariant composite operators of QED in the exact renormalization group formalism

Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ‘gauge fixing parameter independence,’ we show that any gauge independent composite operators can be made ‘gauge fixing parameter independent’ by appropriate normalization. As an application, we give a concise but careful proof of the Adler–Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A Zee.

ProbingttγandttZcouplings at the LHeC

We study the deep inelastic scattering and photo-production modes of $t\overline{t}$ pairs at the proposed LHeC and its potential to probe the electromagnetic and weak dipole moments (MDM and EDM for $tt\ensuremath{\gamma}$) of the top quark. A framework of eight independent gauge-invariant dimension-six operators involving the top quark and the electroweak gauge bosons is used. Four of these operators modify the charged $tbW$ coupling which can be probed through the single (anti)top production mode, as reported in the literature. One generates $tt\ensuremath{\gamma}(Z)$ as well as $tbW$ couplings, while the other two do not generate $tbW$ but only $tt\ensuremath{\gamma}(Z)$. Our focus is on the MDM and EDM of the top quark for which the photo-production mode of $t\overline{t}$ can be an excellent probe. At the proposed electron energies of ${E}_{e}=60$ and 140 GeV the LHeC could set constraints stronger than the indirect limits from $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ and the potential limits of the LHC through $t\overline{t}\ensuremath{\gamma}$ production.

Testable two-loop radiative neutrino mass model based on an LLQd c Qd c effective operator

A new two-loop radiative Majorana neutrino mass model is constructed from the gauge-invariant effective operator L i L j Q k d c Q l d c ϵ ik ϵ jl that violates lepton number conservation by two units. The ultraviolet completion features two scalar leptoquark flavors and a color-octet Majorana fermion. We show that there exists a region of parameter space where the neutrino oscillation data can be fitted while simultaneously meeting flavor-violation and collider bounds. The model is testable through lepton flavor-violating processes such as μ → eγ, μ → eee, and μN → eN conversion, as well as collider searches for the scalar leptoquarks and color-octet fermion. We computed and compiled a list of necessary Passarino-Veltman integrals up to boxes in the approximation of vanishing external momenta and made them available as a Mathematica package, denoted as ANT.

Structure constants of β deformed super Yang-Mills

We study the structure constants of the ${\cal N}=1$ beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the $AdS_5\times S^5$ geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

Effective gauge-Higgs operators analysis of new physics associated with the Higgs boson

We study the new physics(NP) related to the recent discovered 125 GeV Higgs by employing an important subset of the standard model(SM) gauge invariant dimension-six operators constructed by the the SM Higgs and gauge fields. Explicitly, we perform a model-independent study on the production and decays of the Higgs, the electric dipole moments(EDM) of the neutron and the electron, and we take into account the anomalous magnetic dipole moments of muon and electron as well. We find that, even all Higgs decay channels agree with the SM predictions, the SM theoretical uncertainties provide a lot of room to host NP associated with the 125 GeV boson. A linear relation is revealed in our numerical study that $\mu_{ZZ}\simeq \mu_{WW}$ and $ 0.6 \lesssim \mu_{ZZ,WW} \lesssim 1.4$ at 95% CL with or without the EDM's constraints. The neutron and electron EDM's severely constrain the relevant Wilson coefficients. Therefore the CP violating components in the $h\rightarrow WW, ZZ$ channels are too small, $\sim{\cal O}(10^{-5})$, to be detected at LHC. However, we point out that even the parity of the 125GeV boson has been largely determined to be even in the $h\to ZZ$ channel, one should pay special attention to the potentially large CP violation in the $h\to \gamma\gamma$ and $h\to \gamma Z$ channels. This should be seriously checked in the future spin correlation experiments.