Dimensions Of Operators Research Articles

Higgs to bb¯ from vector boson fusion for high-scale physics

Vector boson fusion is arguably the most direct collider probe of electroweak symmetry breaking. Typically, the signature includes two forward/backward jets with low transverse momenta with a scale that is set by the mass of the vector boson. For this reason, an upper cut is used when searching for vector boson fusion processes in the Standard Model. Alternatively, the upper cut on the forward jets can be removed and the high-momentum exchange region of vector boson fusion can be studied. This phase space region has sensitivity to new physics via higher dimensional operators and form factors. In this work, we study the high-momentum region of the vector boson fusion channel where the Higgs decays to bb¯. We show that, depending on the form of new physics, the limits on the new physics scale range from 0.5 to 1.8 TeV. Published by the American Physical Society 2024

State diagrams to determine tree tensor network operators

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.

Interpolating bremsstrahlung function in ABJM model

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in L. Castiglioni [L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, .]. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper, we revisit the study of these operators, but instead of circular contours, we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines. Published by the American Physical Society 2024

A collinear perspective on the Regge limit

The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order.

The unitary Fermi gas at large charge and large N

We study the unitary Fermi gas in a harmonic trapping potential starting from a microscopic theory in the limit of large charge and large number of fermion flavors N. In this regime, we present an algorithmic procedure for extracting data from perturbation theory, order-by-order, without the need for other assumptions. We perform a gradient expansion in the interior of the particle cloud, sufficiently far from the cloud edge where the particle density drops rapidly to zero. In this latter region we present the first microscopic computation characterizing the contribution of the edge terms. The microscopic theory reproduces the predictions of the superfluid eft, including the action, the form of the gap equation, and the energy of the system in a harmonic trap (which maps, via the non-relativistic state-operator correspondence, to the scaling dimension of the lowest operator of charge Q). We additionally give the Wilsonian coefficients at leading order in N up to nnlo in the large-charge expansion.

Complete UV resonances of the dimension-8 SMEFT operators

The effective field theory approach parameterizes the low energy behaviors of all possible ultraviolet (UV) theories in a systematic way. One of the most important tasks is thus to find the connection between the effective operators and their UV origins. The redundancy relations among operators make the connection very subtle, hence we proposed the J-basis prescription to illuminate the correspondence between operators and their UV resonances in the bottom-up way. In this work, we work out the dimension-8 J-basis operators in the standard model effective field theory (SMEFT), and find all the 146 (82) tree-level UV resonances along with their couplings up to mass dimension 5 (4). Furthermore, we point out a few subtleties on operator generation via field redefinition and on the UV Lagrangian for generic spin resonances. We also provide a data base storing our results and a Mathematica notebook for extracting those results for the reader’s conveinence.

Searching for gluon quartic gauge couplings at muon colliders using the autoencoder

One of the difficulties one has to face in the future phenomenological studies of new physics (NP), is the need to deal with increasing amounts of data. It is therefore increasingly important to improve the efficiency in the phenomenological study of NP. Whether it is the use of the Standard Model effective field theory (SMEFT), the use of machine learning (ML) algorithms, or the use of quantum computing, all are means of improving the efficiency. In this paper, we use a ML algorithm, the autoencoder (AE), to study the dimension-8 operators in the SMEFT which contribute to the gluon quartic gauge couplings (gQGCs) at muon colliders. The AE is one of the ML algorithms that has the potential to be accelerated by the quantum computing. It is found that the AE-based anomaly detection algorithm can be used as event selection strategy to study the gQGCs at the muon colliders, and is effective compared with traditional event selection strategies. Published by the American Physical Society 2024

Performance Evaluation of Railway Infrastructure Managers: A Novel Hybrid Fuzzy MCDM Model

Modern challenges such as the liberalization of the railway sector and growing demands for sustainability, high-quality services, and user satisfaction set new standards in railway operations. In this context, railway infrastructure managers (RIMs) play a crucial role in ensuring innovative approaches that will strengthen the position of railways in the market by enhancing efficiency and competitiveness. Evaluating their performance is essential for assessing the achieved objectives, and it is conducted through a wide range of key performance indicators (KPIs), which encompass various dimensions of operations. Monitoring and analyzing KPIs are crucial for improving service quality, achieving sustainability, and establishing a foundation for research and development of new strategies in the railway sector. This paper provides a detailed overview and evaluation of KPIs for RIMs. This paper creates a framework for RIM evaluation using various scientific methods, from identifying KPIs to applying complex analysis methods. A novel hybrid model, which integrates the fuzzy Delphi method for aggregating expert opinions on the KPIs’ importance, the extended fuzzy analytic hierarchy process (AHP) method for determining the relative weights of these KPIs, and the ADAM method for ranking RIMs, has been developed in this paper. This approach enables a detailed analysis and comparison of RIMs and their performances, providing the basis for informed decision-making and the development of new strategies within the railway sector. The analysis results provide insight into the current state of railway infrastructure and encourage further efforts to improve the railway sector by identifying key areas for enhancement. The main contributions of the research include a detailed overview of KPIs for RIMs and the development of a hybrid multi-criteria decision making (MCDM) model. The hybrid model represents a significant step in RIM performance analysis, providing a basis for future research in this area. The model is universal and, as such, represents a valuable contribution to MCDM theory.

Probing positivity at the LHC with exclusive photon-fusion processes

By tagging one or two intact protons in the forward direction, it is possible to select and measure exclusive photon-fusion processes at the LHC. The same processes can also be measured in heavy ion collisions, and are often denoted as ultraperipheral collisions (UPC) processes. Such measurements open up the possibility of probing certain dimension-8 operators and their positivity bounds at the LHC. As a demonstration, we perform a phenomenological study on the γγ → ℓ+ℓ− processes, and find out that the measurements of this process at the HL-LHC provide reaches on a set of dimension-8 operator coefficients that are comparable to the ones at future lepton colliders. We also point out that the γq → γq process could potentially have better reaches on similar types of operators due to its larger cross section, but a more detailed experimental study is need to estimate the signal and background rates of this process. The validity of effective field theory (EFT) and the robustness of the positivity interpretation are also discussed.

ALPs, the on-shell way

We study how the coupling between axion-like particles (ALPs) and matter can be obtained at the level of on-shell scattering amplitudes. We identify three conditions that allow us to compute amplitudes that correspond to shift-symmetric Lagrangians, at the level of operators with dimension 5 or higher, and we discuss how they relate and extend the Adler’s zero condition. These conditions are necessary to reduce the number of coefficients consistent with the little-group scaling to the one expected from the Lagrangian approach. We also show how our formalism easily explains that the dimension-5 interaction involving one ALP and two massless spin-1 bosons receive corrections from higher order operators only when the ALP has a non-vanishing mass. As a direct application of our results, we perform a phenomenological study of the inelastic scattering ℓ+ℓ− → ϕh (with ℓ± two charged leptons, ϕ the ALP and h the Higgs boson) for which, as a result of the structure of the 3-point and 4-point amplitudes, dimension-7 operators can dominate over the dimension-5 ones well before the energy reaches the cutoff of the theory.

Probing the interactions of axion-like particles with electroweak bosons and the Higgs boson in the high energy regime at LHC

We study the interactions of axion-like particles (ALPs) with the Standard Model particles, aiming to probe their phenomenology via non-resonant searches at the LHC. These interactions are mediated by higher dimensional effective operators within two possible frameworks of linearly and non-linearly realised electroweak symmetry breaking. We consider the ALPs to be light enough to be produced on-shell and exploit their derivative couplings with the SM Higgs boson and the gauge bosons. We will use the high momentum transfer processes, namely hZ, Zγ, WW and WWγ production from pp collisions. We derive upper limits on the gauge-invariant interactions of ALPs with the electroweak bosons and/or Higgs boson that contribute to these processes, from the re-interpretation of the latest Run 2 available LHC data. The constraints we obtain are strong for ALP masses below 100 GeV. These allowed effective interactions in the ALP parameter space yield better significance at HL-LHC and thus, offer promising avenues for subsequent studies. Furthermore, we augment our cut-based analysis with gradient-boosted decision trees, which improve the statistical significance distinctly across these interaction channels. We briefly compare the results with the complementary probe of these couplings via direct production of ALPs in association with the Higgs boson or a vector boson.

Local existence and uniqueness of spatially quasi-periodic solutions to the generalized KdV equation

In this paper, we study the existence and uniqueness of spatially quasi-periodic solutions to the p-generalized KdV equation on the real line with quasi-periodic initial data whose Fourier coefficients are exponentially decaying. In order to solve for the Fourier coefficients of the solution, we first reduce the nonlinear dispersive partial differential equation to a nonlinear infinite system of coupled ordinary differential equations, and then construct the Picard sequence to approximate them. However, we meet, and have to deal with, the difficulty of studying the higher dimensional discrete convolution operation for several functions:c×⋯×c︸p(total distance):=∑♣1,⋯,♣p∈Zν♣1+⋯+♣p=total distance∏j=1pc(♣j). In order to overcome it, we apply a combinatorial method to reformulate the Picard sequence as a tree. Based on this form, we prove that the Picard sequence is exponentially decaying and fundamental (i.e., a Cauchy sequence). The result has been known for p=2[11], and the combinatorics become harder for larger values of p. For the sake of clarity, we first give a detailed discussion of the proof of the existence and uniqueness result in the simplest case not covered by previous results, p=3. Next, we prove existence and uniqueness in the general case p≥2, which then covers the remaining cases p≥4. As a byproduct, we recover the local result from [11]. In the process of proof, we give a combinatorial structure of tensor (multi-linear operator), exhibit the most important combinatorial index σ (it's related to the degree or multiplicity of the power-law nonlinearity), and obtain a relationship with other indices, which is essential to our proofs in the case of general p.

Subhomogeneous Operator Systems and Classification of Operator Systems Generated by Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}-Commuting Unitaries

A unital C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebra is called N-subhomogeneous if its irreducible representations are finite dimensional with dimension at most N. We extend this notion to operator systems, replacing irreducible representations by boundary representations. This is done by considering UCP(S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {UCP }(\\mathcal {S})$$\\end{document} which is the matrix state space associated with an operator system S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}$$\\end{document} and identifying the boundary representations as absolute matrix extreme points. We show that two N-subhomogeneous operator systems are completely order equivalent if and only if they are N-order equivalent. Moreover, we show that a unital N-positive map into a finite dimensional N-subhomogeneous operator system is completely positive. We apply these tools to classify pairs of q-commuting unitaries up to ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}-isomorphism. Similar results are obtained for operator systems related to higher dimensional non-commutative tori.

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

Modular flavor symmetric models

We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor symmetry gives interesting phenomena at the fixed point of modulus. As a representative, we show the successful texture structure at the fixed point [Formula: see text]. We also study CP violation, which occurs through the modulus stabilization. Finally, we study SMEFT with modular flavor symmetry by including higher dimensional operators.

On the two-loop penguin contributions to the Anomalous Dimensions of four-quark operators

We revisit the Next-to-Leading Order (two-loop) contributions to the Anomalous Dimensions of ∆F = 1 four-quark operators in QCD. We devise a test for anomalous dimensions, that we regard as of general interest, and by means of which we detect a problem in the results available in the literature. Deconstructing the steps leading to the available result, we identify the source of the problem, which is related to the operator known as Q11. We show how to fix the problem and provide the corrected anomalous dimensions. With the insight of our findings, we propose an alternative approach to the one used in the literature which does not suffer from the identified disease, and which confirms our corrected results. We assess the numerical impact of our corrections, which happens to be in the ballpark of 5% in certain entries of the evolution matrix. Our results are important for the correct resummation of Next-to-Leading Logarithms in analyses of physics beyond the Standard Model in ∆F = 1 processes, such as the decays of Kaons and B-mesons.

Leading directions in the SMEFT: Renormalization effects

The stability of the electroweak scale, challenged by the absence of deviations in flavor physics, prompts the consideration of SMEFT scenarios governed by approximate SM flavor symmetries. This study examines microscopic theories that match onto a set of U(3)5-symmetric dimension-6 operators. Renormalization group (RG) mixing from the ultraviolet to the electroweak scale yields significant phenomenological constraints, particularly pronounced for UV-motivated directions. To demonstrate this, we explore a complete suite of tree-level models featuring new spin-0, spin-1/2, and spin-1 fields, categorized by their irreducible representations under the flavor group. We find that for the leading directions, corresponding to a single-mediator dominance, RG mixing effects occasionally serve as the primary indirect probe. Published by the American Physical Society 2024

Anomalous and linear holographic hard wall models for glueballs and the pomeron

In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin S of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference S−1/S. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to S, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form Δ=aS+b, where a and b are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins (J∼100) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models. Published by the American Physical Society 2024

On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling

We consider the one-loop effective vertex for the interaction of a gluon with a Reggeized gluon and a Higgs boson in the infinite-top-mass limit, which is described by a dimension-5 non-renormalizable operator. This vertex enters the calculation of differential cross sections for the forward inclusive production of a Higgs boson in high-energy proton-proton collisions, possibly in association with a backward jet or identified hadron, in a framework where next-to-leading logarithms of the energy are resummed to all orders. The effective vertex is extracted from the high-energy behavior of two-to-two amplitudes for the Higgs production in parton-parton collisions and relies on the validity of the Regge form for these amplitudes. We find that the usual eikonal approximation (Gribov prescription) for the Regge limit and the known region-expansion technique in this limit lead to an incomplete result for the amplitude. The discrepancy is traced back to the non-renormalizable nature of the involved operator. However, the Regge limit of the exact QCD amplitude agrees with the Regge-pole exchange form at one loop, nontrivially supporting the Reggeization hypothesis.

Casimir Forces in CFT with Defects and Boundaries

We investigate the quantum forces occurring between the defects and/or boundaries of a conformal field theory (CFT). We propose to model imperfect defects and boundaries as localized relevant double-trace operators that deform the CFT. Our focus is on pointlike and codimension-one planar defects. In the case of two parallel membranes, we point out that the CFT 2-point function tends to get confined and develops a tower of resonances with a constant decay rate when the operator dimension approaches the free field dimension. Using a functional formalism, we compute the quantum forces induced by the CFT between a variety of configurations of pointlike defects, infinite plates and membranes. Consistency arguments imply that these quantum forces are attractive at any distance. Forces of the Casimir–Polder type appear in the UV (ultraviolet), while forces of the Casimir type appear in the IR (infrared), in which case the CFT gets repelled from the defects. Most of the forces behave as a non-integer power of the separation, controlled by the dimension of the double-trace deformation. In the Casimir regime of the membrane–membrane configuration, the quantum pressure behaves universally as 1/ℓd; however, information about the double-trace nature of the defects still remains encoded in the strength of the pressure.