Confinement Criterion Research Articles

A second Higgs near 0.5 TeV from bottom-up holographic modeling of beyond the Standard Model strong sector

One of the simplest extensions of the Standard Model (SM) consists in adding a scalar singlet. This second Higgs boson is able to solve several fundamental problems of SM. Additional scalar particles arise naturally in composite Higgs scenarios in which some confining “strong sector” beyond the SM drives the electroweak symmetry breaking. The underlying strongly coupled gauge theory may be similar to QCD and could be modeled holographically. We construct a bottom-up holographic model for description of the spectrum of composite Higgs particles. The model is based on the holographic Soft Wall model and the Wilson confinement criterion. The constructed model predicts the existence of a second Higgs boson with a mass of about 515 GeV.

Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum

It is well known that the soft-wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the “linear plus Coulomb” confinement potential, which is similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not exist in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up holographic models. The standard soft-wall model is merely a particular representative of this class. This fact is relatively unknown, so we provide a comprehensive discussion of the point. As an example, we consider a soft-wall-like model with linear dilaton background in the metric. This model leads to a hydrogen-like spectrum. A “linear plus Coulomb” confinement potential within this model is calculated. The calculation of renormalized potential at short distances turns out to be complicated by a new subtlety that was skipped in general discussions of the issue existing in the literature. However, the confinement potential of the model is shown to be not very different from the potential obtained in the standard soft-wall model with a quadratic background.

Development of a point-source model to improve simulations of manure lagoon interactions with the environment

In recent decades animal agriculture in the U.S. has moved from small, distributed operations to larger, concentrated animal feeding operations (CAFOs). CAFOs are defined by federal regulations based on animal numbers and confinement criteria. Because of the size of these operations, the excessive amount of manure generated is typically stored in lagoons, pits, or barns prior to field application or transport to other farms. Water and air quality near CAFOs can be impaired through the overflow of lagoons, stormwater runoff, lagoon seepage or emissions, motivating the following research question: what manure lagoon parameters impact pollutant fate and transport across multiple mechanisms? To address this question, a CAFO lagoon module was developed to assess lagoon overflow risk, groundwater quality, and ammonia emissions of a dairy lagoon. The results from 10,000 Monte Carlo simulations indicated that lagoon overflow is a rare occurrence for simulated environmental conditions in Washington (3.17%). Second, we developed a groundwater module to complete a groundwater quality assessment of a Dairy Lagoon in Washington using analytical and semi-analytical solutions for groundwater solute transport. The long-term effects of this lagoon on water quality were explored as well as the effectiveness of improving the lagoon lining to reduce seepage. Doubling the lagoon liner thickness attenuated peak groundwater ammonia-N concentrations by 2.8. Lastly, we constructed an air quality module and found that ammonia emissions were not sensitive to changes in lagoon liner construction, but small reductions in lagoon pH significantly reduced yearly average ammonia emissions. The combined model can be used to improve understanding of the impacts of CAFO lagoon overflow and seepage and develop sustainable management practices at the field scale for these key components of the agricultural landscape.

Confinement, mass gap and gauge symmetry in the Yang-Mills theory -- restoration of residual local gauge symmetry --

In this talk we want to discuss the color confinement criterion which guarantees confinement of all colored particles including dynamical quarks and gluons. The most well-known criterion is the Kugo-Ojima color confinement criterion derived in the Lorenz gauge. However, it was pointed out that the Kugo-Ojima criterion breaks down for the Maximal Abelian gauge in which quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations. We give the color confinement criterion based on the restoration of the residual local gauge symmetry which can be applied to the Abelian and non-Abelian gauge theories as well irrespective of the compact or non-compact formulation, and enables us to understand confinement in all the cases. Indeed, the restoration of the residual local gauge symmetry which was shown by Hata in the Lorenz gauge to be equivalent to the Kugo-Ojima criterion indeed occurs in the Maximal Abelian gauge for the SU(N) Yang-Mills theory in two-, three- and four-dimensional Euclidean spacetime once the singular topological configurations of gauge fields are taken into account. This result indicates that the color confinement phase is a disordered phase caused by non-trivial topological configurations irrespective of the gauge choice.

Gluon string breaking and meson spectrum in the holographic Soft Wall model

We propose a general method for finding a string-like meson spectrum which is based on a certain condition for the breaking of closed gluon string. A model is constructed that successfully realizes the proposed method. The model is based on the holographic Soft Wall model for QCD and the use of the Wilson confinement criterion. We applied our approach to the vector and scalar cases and obtained numerical predictions for the intercepts of corresponding Regge like radial meson spectra. A good agreement is obtained both with the existing experimental data and with some other known phenomenological approaches. Remarkably, our closed string breaking condition has two branches. We argue that they should correspond to states of opposite parity. The Wilson confinement criterion leads then to a natural mass splitting between parity partners. The constructed model represents thus the first example of bottom-up holographic model in which the effects of chiral symmetry breaking can emerge automatically, i.e., without additional assumptions taken outside of the holographic approach.

Flower Shaped Oscillating Heat Pipe at the thermosyphon condition: Performance at different rotational speeds, filling ratios, and heat supplies

The performance of a very effective and innovative thermal device based on Pulsating Heat Pipes (PHP) in a rotating system is studied and analysed in the paper. The appliance called a Flower Shaped Oscillating Heat Pipe (FSOHP) is developed for use in industrial sectors and is arranged in the specific shape of a flower so as to obtain homogeneous heat reception from technological processes. The capillaries, with an inner diameter of 2.7mm, were filled and tested, with HFE−7000 as a working fluid. This fluid, according to a confinement criterion based on the Bond or Garimella numbers, places the device in the range of thermosyphon operation, the description and experimental verification of which is addressed in this paper. The influence of rotational speed (0–300rpm), heat input (300–450W), and filling ratio (40–90%) on the thermal performance has been studied as an experimental research. Current research shows that a low boiling point liquid such as HFE−7000 can be used as a working fluid in a rotating system, and the thermal resistance of the process is characterised by a value of almost 100% higher compared to water. The maximum value of the heat flux value achieved was equal to 22.1kW/m2 for HFE−7000, while for water it was more than four times higher and equal to 98.4kW/m2. It was also observed that by increasing the Filling Ratio (FR) by up to 80%, the thermal resistance decreases to the lowest value of 0.05K/W in speed conditions such as above 200rpm. Results have shown that with respect to dimensionless numbers, despite going beyond the scope of the confinement criterion, FSOHP achieves a low value of thermal resistance and temperature stabilisation with characteristics very similar to those that describe standard pulsating heat pipe solutions in a stationary system. Furthermore, in a rotating system, an increase in heating power improves the thermal efficiency of the device only for FR >70%, while in a stationary system, an increase in the power supply range studied is always associated with a decrease in thermal resistance, regardless of the FR.

Color confinement and restoration of residual local gauge symmetries

Abstract All colored particles including dynamical quarks and gluons are confined if the color confinement criterion proposed by Kugo and Ojima is satisfied. The criterion was obtained under a gauge fixing of the Lorenz type. However, it was pointed out that the Kugo–Ojima criterion breaks down for the maximal Abelian gauge, which is quite strange in view of the fact that quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations. In order to make a bridge between Kugo–Ojima color confinement and the dual superconductor picture for quark confinement, we investigate a generalization of the color confinement criterion to obtain a unified picture for confinement. We show that the restoration of the residual local gauge symmetry which was shown in the Lorenz gauge by Hata to be equivalent to the Kugo–Ojima criterion indeed occurs in the maximal Abelian gauge for the SU(N) Yang–Mills theory in two-, three-, and four-dimensional Euclidean spacetime once the singular topological configurations of gauge fields are taken into account. This result indicates that the color confinement phase is a disordered phase caused by non-trivial topological configurations irrespective of the gauge choice. As a by-product, we show that the compact U(1) gauge theory can have a disordered confinement phase, while the non-compact U(1) gauge theory has a deconfined Coulomb phase.

Case study of hydraulic fracturing in an offshore carbonate oil reservoir

Maximizing petroleum production while efficiently managing the operational costs is the oil and gas industry's primary goal which requires innovative engineering approaches and production-enhancing treatments such as hydraulic fracturing (HF). During the HF process, the injected fluid mixed with sands or proppants will create permanent fluid channels to drain more of the reservoir volume. The level of complexity and various constraints involved in real field treatments have made HF even more challenging in layered carbonate reservoirs with the water drive mechanism. A prominent concern is the downward fracture growth to the oil/water contact zone that may cause unfavorable water cut levels. This fracture height confinement criterion necessitates optimization of fracture dimension design. Fracture height development is mainly a function of in-situ stress conditions and stress magnitude differences between geologic layers. In cases with a water table at the proximity of the wellbore, fracture height directly affects the operational success. This paper demonstrates a practical step-by-step approach towards the design of hydraulic fracturing treatment in an offshore carbonate oil reservoir. The modeling process involves optimization of the location, number, and conductivity of the proposed fractures. Injection of high viscosity fluid causes a bi-wing vertical planar fracture to propagate perpendicular to the direction of minimum horizontal stress in the strike-slip faulting regime. Dimensions of the induced hydraulic fractures are also impacted by the amount and type of proppants. However, as with this case study, the magnitude of vertical stress is in the same range as the maximum horizontal stress; the fracture height growth is the limiting factor. The LGR method is used to define fractures in the dynamic reservoir model which has been built based on a complete set of data ranging from the analyses of logs, core samples, and seismic details, to perform production forecasts and economic evaluation. Then a hydraulic fracture software is implemented to provide a timetable for fracturing fluid volume and mixing proppant concentration for the desired fracture dimensions. The results show that, despite the operator's previous perception, five hydraulic fractures per well would be economical, which include a 150 ft long fracture and four shorter fractures with an approximate length of 75 ft designed to manage the risk of penetration into the water-bearing formations. Due to the reservoir pressure drop by time and more flexible fracture dimension constraints at earlier stages of production, executing such stimulations earlier than later would improve the commercial outcomes.

Confinement and renormalization group equations in string-inspired nonlocal gauge theories

As an extension of weak perturbation theory obtained in a recent analysis of infinite-derivative nonlocal non-Abelian gauge theories motivated from $p$-adic string field theory, and postulated as a direction of UV completion in four-dimensional quantum field theory, here we investigate the confinement conditions and $\ensuremath{\beta}$ function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin invariance, to the nonlocal theory by using a set of exact solutions of the corresponding local theory. We show that the infinite derivatives which are active in the UV provide finite contributions also in the infrared limit and provide a proof of confinement, granted by the absence of the Landau pole. We also show that in the limit of the energy scale of nonlocality $M\ensuremath{\rightarrow}\ensuremath{\infty}$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.

A criterion to characterize interacting theories in the Wightman framework

We propose that a criterion to characterize interacting theories in a suitable Wightman framework of relativistic quantum field theories which incorporates a “singularity hypothesis”, which has been conjectured for a long time, is supported by renormalization group theory, but has never been formulated mathematically. The (nonperturbative) wave function renormalization Z occurring in these theories is shown not to be necessarily equal to zero, except if the equal time commutation relations (ETCR) are assumed. Since the ETCR are not justified in general (because the interacting fields cannot in general be restricted to sharp times, as is known from model studies), the condition $$Z=0$$ is not of general validity in interacting theories. We conjecture that it characterizes either unstable (composite) particles or the charge-carrying particles, which become infraparticles in the presence of massless particles. In the case of QED, such “dressed” electrons are not expected to be confined, but in QCD, we propose a quark confinement criterion, which follows naturally from lines suggested by the works of Casher, Kogut and Susskind, and Lowenstein and Swieca.

Super-QRT and 4D-mappings reduced from the lattice super-KdV equation

Starting from the complete integrable lattice super-KdV equation, two super-mappings are obtained by performing a travelling-wave reduction. The first one is linear and the second is a four dimensional super-QRT mapping containing both Grassmann commuting and anti-commuting dependent variables. Adapting the classical "staircase" method to the Lax super-matrices of the lattice super-KdV equation, we compute the Lax super-matrices of the mapping and the two invariants; the first one is a pure nilpotent commuting quantity and the second one is given by an elliptic curve containing nilpotent commuting Grassmann coefficients as well. In the case of finitely generated Grassmann algebra with two generators, the super-QRT mapping becomes a four-dimensional ordinary discrete dynamical system that has two invariants but does not satisfy singularity confinement criterion. It is also observed that the dynamical degree of this system grows quadratically.

Detailed engineering geological assessment of a shotcrete lined pressure tunnel in the Himalayan rock mass conditions: a case study from Nepal

The complex topography, geology, and tectonic environment prevailing in the Himalaya are the main challenges while applying the unlined or shotcrete lined pressure tunnel concept for hydropower projects. In addition, rock masses in the Himalayan region are influenced by faulting, folding, schistosity, and jointing to a varying degree representing geological complexity. Similarly, frequent occurrence of large scale earthquakes changes in situ stress dynamics. In spite of these challenges, an unlined/shotcrete lined pressure tunnel is being constructed at the headrace tunnel system of Upper Tamakoshi Hydroelectric Project (UTHP) in the Nepal Himalaya. This article studies the unlined or shotcrete lined pressure tunnel in terms of the topographical conditions, in situ stress state, and overall rock engineering aspects. First, the pressure tunnel alignment is assessed using the Norwegian confinement criteria. Second, the minimum principal stress state is assessed using numerical simulation by validating measured in situ stress conditions. Finally, a comprehensive assessment on the rock engineering aspects of the headrace tunnel is carried out. It has been found that if there exist good quality rock mass with tight joints, it is possible to apply the unlined/shotcrete lined pressure tunnel system in the Himalaya provided that the stress requirement is fulfilled. It was also found that the Norwegian confinement criteria are too optimistic for direct use in the design of high pressure headrace tunnel alignment. The detailed rock engineering assessment and stress state analysis indicated that there are some critical locations along the Upper Tamakoshi headrace tunnel alignment. This is specially the case for an about 700 m downstream stretch of the headrace tunnel from where there is a risk of hydraulic jacking, which may possibly lead to excessive water leakage during power plant operation.

Quantum confinement on non-complete Riemannian manifolds

We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold M equipped with a smooth measure \omega , possibly degenerate or singular near the metric boundary of M , and in presence of a real-valued potential V\in L^2_\mathrm {loc}(M) . The main merit of this paper is the identification of an intrinsic quantity, the effective potential V_\mathrm {eff} , which allows to formulate simple criteria for quantum confinement. Let \delta be the distance from the possibly non-compact metric boundary of M . A simplified version of the main result guarantees quantum completeness if V\ge -c\delta^2 far from the metric boundary and V_\mathrm {eff}+V\ge \frac3{4\delta^2}-\frac{\kappa}{\delta}, \quad \mathrm {close \:to \:the \:metric \:boundary}. These criteria allow us to: (i) obtain quantum confinement results for measures with degeneracies or singularities near the metric boundary of M ; (ii) generalize the Kalf–Walter–Schmincke–Simon Theorem for strongly singular potentials to the Riemannian setting for any dimension of the singularity; (iii) give the first, to our knowledge, curvature-based criteria for self-adjointness of the Laplace–Beltrami operator; (iv) prove, under mild regularity assumptions, that the Laplace–Beltrami operator in almost-Riemannian geometry is essentially self-adjoint, partially settling a conjecture formulated in [9].

Condition for confinement in non-Abelian gauge theories

We show that a criterion for confinement, based on the BRST invariance, holds in four dimensions, by solving a non-Abelian gauge theory with a set of exact solutions. The confinement condition we consider was obtained by Kugo and Ojima some decades ago. The current understanding of gauge theories permits us to apply the techniques straightforwardly for checking the validity of this criterion. In this way, we are able to show that the non-Abelian gauge theory is confining and that confinement is rooted in the BRST invariance and asymptotic freedom.

Analysis of unlined pressure shafts and tunnels of selected Norwegian hydropower projects

Norwegian hydropower industry has more than 100 years of experiences in constructing more than 4000 km-long unlined pressure shafts and tunnels with maximum static head of 1047 m (equivalent to almost 10.5 MPa) reached at unlined pressure tunnel of Nye Tyin project. Experiences gained from construction and operation of these unlined pressure shafts and tunnels were the foundation to develop design criteria and principles applied in Norway and some other countries. In addition to the confinement criteria, Norwegian state-of-the-art design principle for unlined pressure shaft and tunnel is that the minor principal stress at the location of unlined pressure shaft or tunnel should be more than the water pressure in the shaft or tunnel. This condition of the minor principal stress is prerequisite for the hydraulic jacking/splitting not to occur through joints and fractures in rock mass. Another common problem in unlined pressure shafts and tunnels is water leakage through hydraulically splitted joints or pre-existing open joints. This article reviews some of the first attempts of the use of unlined pressure shaft and tunnel concepts in Norway, highlights major failure cases and two successful cases of significance, applies Norwegian criteria to the cases and reviews and evaluates triggering factors for failure. This article further evaluates detailed engineering geology of failure cases and also assesses common geological features that could have aggravated the failure. The minor principal stress is investigated and quantified along unlined shaft and tunnel alignment of six selected project cases by using three-dimensional numerical model. Furthermore, conditions of failure through pre-existing open joints by hydraulic jacking and leakage are assessed by using two-dimensional fluid flow analysis. Finally, both favorable and unfavorable ground conditions required for the applicability of Norwegian confinement criteria in locating the unlined pressure shafts and tunnels for geotectonic environment different from that of Norway are highlighted.

Observation of a Coulomb flux tube

In Coulomb gauge there is a longitudinal color electric field associated with a static quark-antiquark pair. We have measured the spatial distribution of this field, and find that it falls off exponentially with transverse distance from a line joining the two quarks. In other words there is a Coulomb flux tube, with a width that is somewhat smaller than that of the minimal energy flux tube associated with the asymptotic string tension. A confinement criterion for gauge theories with matter fields is also proposed.

Confinement criterion for gauge theories with matter fields

A generalization of the Wilson loop area-law criterion is proposed, which is applicable to gauge theories with matter in the fundamental representation of the gauge group. This new criterion, like the area law, is stronger than the statement that asymptotic particle states are massive color singlets, which holds even for theories described by the Brout-Englert-Higgs mechanism.

Spanwise domain effects on streamwise vortices in the plane turbulent mixing layer

Large Eddy Simulation is used to assess the influence of the spanwise domain extent on the evolution of the spatially stationary streamwise structure that exists in the simulated plane turbulent mixing layer. The mixing layers originate from a physically-correlated inflow condition, which produces accurate mixing layer mean flow statistics. For all three spanwise domains considered a spatially stationary streamwise structure is present. The streamwise structure is artificially confined when its wavelength matches that of the spanwise domain extent, and a criterion for confinement is postulated. The confinement has no significant negative impact on either the computed flow statistics, or the growth of the large-scale spanwise structures. These results demonstrate that the streamwise structure rides passively on the large-scale spanwise vortex structure. A simulation lacking in a spanwise direction produces poor turbulence statistics, and is not a reliable representation of the real mixing layer flow.

Singularity analysis for difference Painlevé equations associated with the affine Weyl group E8

We propose a new expression for the generic additive discrete Painlevé equation associated with the affine Weyl group . This expression makes the singularity analysis of the mapping perfectly straightforward and allows the implementation of the singularity confinement criterion in an extremely simple way. Using this new approach we derive new classes of discrete Painlevé equations related to .

Some Developments in Gribov’s Approach to QCD

We review several developments in the formulation of QCD provided by the GZ action. These include the GZ-action at finite temperature, the relation of the horizon condition and the Kugo-Ojima confinement criterion, the relation of the horizon condition and the dual-Meisssner effect, the alternative derivation of the GZ action provided by the Maggiore-Schaden shift, and the spontaneous breaking of BRST symmetry. We conclude with a proposal for the definition of physical states in the presence of BRST breaking.