Search

The electroweak monopole, when coupled to gravity, turns to the Reissner-Nordstrom type primordial magnetic blackhole whose mass is bounded below, with the lower bound $M_P \sqrt \alpha$. This changes the overall picture of the monopole production mechanism in the early universe drastically and has deep implications in cosmolpgy. In particular, this enhances the possibility that the electroweak monopoles turned to the primordial magnetic blackholes could become the seed of stellar objects and galaxies, and account for the dark matter of the universe. Moreover, this tells that we have a new type of primordial blackhole different from the popular primordial blackhole in cosmology, the electroweak primordial magnetic blackhole based on a totally different production mechanism. We discuss the physical implications of the electroweak primordial magnetic blackhole.

The influence of space weathering on the observed spectra of C-complex asteroids remains uncertain. This has long hindered our understanding of their composition through telescope observations. Multi-band imaging of Ryugu by ONC-T on Hayabusa2 and that of Bennu by MapCam on OSIRIS-REx found opposite spectral trends of space weathering; Ryugu darkened/reddened while Bennu brightened/blued. How the spectra of Ryugu and Bennu evolved relative to each other would place a constraint for understanding their origins and evolutions. In this study, we compared the space weathering trends on Ryugu and Bennu by applying the results of cross calibration between ONC-T and MapCam. We show that the average Bennu surface is brighter by 18.0 $\pm$ 1.5% at 550 nm and bluer by 0.18 $\pm$ 0.03 $\mu$m$^{-1}$ (480-850 nm slope) than Ryugu. The spectral slopes of surface materials are more uniform on Bennu than on Ryugu at spatial scales $\gtrsim$1 m, but Bennu is more heterogeneous at $\lesssim$1 m. This suggests that lateral mixing due to resurfacing may have been more efficient on Bennu. The reflectance-spectral slope distributions of craters on Ryugu and Bennu appeared to follow two trend lines with an offset before cross calibration, but they converged to a single straight trend without a bend after cross calibration. We show that the spectra of the freshest craters on Ryugu and Bennu are indistinguishable within the uncertainty of cross calibration. These results suggest that Ryugu and Bennu initially had similar spectra before space weathering and that they evolved in completely opposite directions along the same trend line, subsequently evolving into asteroids with different disk-averaged spectra. These findings further suggest that space weathering likely expanded the spectral slope variation of C-complex asteroids, implying that they may have formed from materials with more uniform spectral slopes.

Preserving and encouraging mobility in the elderly and adults with chronic conditions is of paramount importance. However, existing walking aids are either inadequate to provide sufficient support to users' stability or too bulky and poorly maneuverable to be used outside hospital environments. In addition, they all lack adaptability to individual requirements. To address these challenges, this paper introduces WANDER, a novel Walking Assistive omNi-Directional Exo-Robot. It consists of an omnidirectional platform and a robust aluminum structure mounted on top of it, which provides partial body weight support. A comfortable and minimally restrictive coupling interface embedded with a force/torque sensor allows to detect users' intentions, which are translated into command velocities by means of a variable admittance controller. An optimization technique based on users' preferences, i.e., Preference-Based Optimization (PBO) guides the choice of the admittance parameters (i.e., virtual mass and damping) to better fit subject-specific needs and characteristics. Experiments with twelve healthy subjects exhibited a significant decrease in energy consumption and jerk when using WANDER with PBO parameters as well as improved user performance and comfort. The great interpersonal variability in the optimized parameters highlights the importance of personalized control settings when walking with an assistive device, aiming to enhance users' comfort and mobility while ensuring reliable physical support., Comment: 6 pages, 4 figures, IEEE International Conference on Robotics and Automation (2024)

The availability of mobile health (mHealth) technology has enabled increased collection of intensive longitudinal data (ILD). ILD have potential to capture rapid fluctuations in outcomes that may be associated with changes in the risk of an event. However, existing methods for jointly modeling longitudinal and event-time outcomes are not well-equipped to handle ILD due to the high computational cost. We propose a joint longitudinal and time-to-event model suitable for analyzing ILD. In this model, we summarize a multivariate longitudinal outcome as a smaller number of time-varying latent factors. These latent factors, which are modeled using an Ornstein-Uhlenbeck stochastic process, capture the risk of a time-to-event outcome in a parametric hazard model. We take a Bayesian approach to fit our joint model and conduct simulations to assess its performance. We use it to analyze data from an mHealth study of smoking cessation. We summarize the longitudinal self-reported intensity of nine emotions as the psychological states of positive and negative affect. These time-varying latent states capture the risk of the first smoking lapse after attempted quit. Understanding factors associated with smoking lapse is of keen interest to smoking cessation researchers., Comment: Main text is 32 pages with 6 figures. Supplementary material is 21 pages

One of the urgent issues in high energy physics is the experimental confirmation of the electroweak monopole predicted by the standard model, and currently MoEDAL at LHC is actively searching for the monopole. However, the present LHC cannot produce the monopole if the mass is bigger than 7 TeV, while the monopole mass is expected to be around $M_W/\alpha \simeq 11~\text{TeV}$. In this paper we discuss how LHC could circumbent this energy constraint and produce the monopole even when the mass is bigger than 7 TeV, based on the following ideas. First, in the topological production of the monopole the baby monopole mass at creation could be considerably smaller than the adolescent mass. Second, the binding energy of the monopole-antimonopole pair could effectively reduce the mass of the bound state. We discuss how these ideas can actually be realized at LHC to produce the monopole pairs. In particular, we argue that LHC could produce the baby electroweak monopoles whose mass could be around 5.3 TeV, smaller than the adolescent monopole mass around 11.0 TeV. Moreover, we show that LHC could produce the monopolium bound state with mass around 2.5 TeV, even when the total mass of the monopole-antimonopole pair is around 10.6 TeV. Our analysis could play an important role for MoEDAL experiment.

We report on a search for magnetic monopoles (MMs) produced in ultraperipheral Pb--Pb collisions during Run-1 of the LHC. The beam pipe surrounding the interaction region of the CMS experiment was exposed to 184.07 \textmu b$^{-1}$ of Pb--Pb collisions at 2.76 TeV center-of-mass energy per collision in December 2011, before being removed in 2013. It was scanned by the MoEDAL experiment using a SQUID magnetometer to search for trapped MMs. No MM signal was observed. The two distinctive features of this search are the use of a trapping volume very close to the collision point and ultra-high magnetic fields generated during the heavy-ion run that could produce MMs via the Schwinger effect. These two advantages allowed setting the first reliable, world-leading mass limits on MMs with high magnetic charge. In particular, the established limits are the strongest available in the range between 2 and 45 Dirac units, excluding MMs with masses of up to 80 GeV at 95\% confidence level., Comment: As accepted by PRL. 7 pages, 4 figures

The Abelian decomposition of QCD tells that there are two types of gluons in QCD, the color neutral neurons and colored chromons, which behave differently. This strongly implies that QCD has two types of gluon jets, the neuron jet and chromon jet. One quarter of the gluon jets is made of the neuron jets which have sharper jet radius and smaller particle multiplicity, while three quarters of them are made of chromon jets which have the broader jet radius and larger particle multiplicity. Moreover, the neuron jet has a distinct color flow which forms an ideal color dipole pattern, while the chromon jets have distorted dipole pattern. In this paper we provide five circumferential evidences of the existence of two types of gluon jets from the existing ALEPH and DELPHI data on $e \bar e \rightarrow Z \rightarrow b \bar b g$ decay and the CMS data on Pb-Pb heavy ion collision.

We propose the ultra high energy cosmic ray recently detected by Telescope Array to be the electroweak monopole, and present theoretical arguments which support this. This strongly motivates the necessity for the ``cosmic" MoEDAL experiment which could back up our proposal. To confirm this we propose Telescope Array to measure the magnetic charge of the ultra high energy cosmic ray particles with SQUID.

Multi-nucleon transfer reaction between 136Xe beam and 198Pt target was performed using the VAMOS++ spectrometer at GANIL to study the structure of n-rich nuclei around N=126. Unambiguous charge state identification was obtained by combining two supervised machine learning methods, deep neural network (DNN) and positional correction using a gradient-boosting decision tree (GBDT). The new method reduced the complexity of the kinetic energy calibration and outperformed the conventional method, improving the charge state resolution by 8%

Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on multiple outcomes measured frequently over time that have the potential to capture short-term and long-term dynamics. Motivated by an mHealth study of smoking cessation in which participants self-report the intensity of many emotions multiple times per day, we describe a dynamic factor model that summarizes the ILD as a low-dimensional, interpretable latent process. This model consists of two submodels: (i) a measurement submodel--a factor model--that summarizes the multivariate longitudinal outcome as lower-dimensional latent variables and (ii) a structural submodel--an Ornstein-Uhlenbeck (OU) stochastic process--that captures the temporal dynamics of the multivariate latent process in continuous time. We derive a closed-form likelihood for the marginal distribution of the outcome and the computationally-simpler sparse precision matrix for the OU process. We propose a block coordinate descent algorithm for estimation. Finally, we apply our method to the mHealth data to summarize the dynamics of 18 different emotions as two latent processes. These latent processes are interpreted by behavioral scientists as the psychological constructs of positive and negative affect and are key in understanding vulnerability to lapsing back to tobacco use among smokers attempting to quit., Comment: Main text is 20 pages with 5 figures and 1 table. Supplementary material is 26 pages

A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of cut links or by cluster merging with suppression of the creation of large clusters. While the microscopic mechanism of the former is understood in detail, a similar framework is missing for the latter. By studying two distinct cluster merging models, we uncover the universal mechanism of the features of HPT-s at a microscopic level. We find that these features occur in three steps: (i) medium-sized clusters accumulate due to the suppression rule hindering the growth of large clusters, (ii) those medium size clusters eventually merge and a giant cluster increases rapidly, and (iii) the suppression effect becomes obsolete and the kinetics is governed by the Erd\H{o}s-R\'enyi type of dynamics. We show that during the second and third period, the growth of the largest component must proceed in the form of a Devil's staircase. We characterize the critical behavior by two sets of exponents associated with the order parameter and cluster size distribution, which are related to each other by a scaling relation. Extensive numerical simulations are carried out to support the theory where a specific method is applied for finite-size scaling analysis to enable handling the large fluctuations of the transition point. Our results provide a unified theoretical framework for the HPT., Comment: 15 pages, 14 figures, 4 tables

Asteroids (162173) Ryugu and (101955) Bennu observed by Hayabusa2 and OSIRIS-REx share many properties, but spectral observations by the telescopic Optical Navigation Camera (ONC-T) and MapCam detected subtle but significant differences, which may reflect differences in their origin and evolution. Comparing these differences on the same absolute scale is necessary for understanding their causes. However, ONC-T and MapCam have a large imager-to-imager systematic error of up to 15% caused by the difference in radiometric calibration targets. To resolve this problem, we cross calibrated albedo and color data between the two instruments using the Moon as the common calibration standard. The images of the Moon taken by ONC-T and MapCam were compared with those simulated using photometry models developed from lunar orbiter data. Our results show that the cross-calibrated reflectance of Ryugu and Bennu can be obtained by upscaling the pre-cross-calibrated reflectance of Bennu by 13.3 +/- 1.6% at b band, 13.2 +/- 1.5% at v band, 13.6 +/- 1.7% at w band, and 14.8 +/- 1.8% at x band, while those for Ryugu are kept the same. These factors compensate for the imager-to-imager bias caused by differences in targets used for radiometric calibration and solar irradiance models used for data reduction. Need for such large upscaling underscore the importance of using the cross-calibrated data for accurately comparing the Ryugu and Bennu data. The uncertainty in these factors show that the reflectance of Ryugu and Bennu can be compared with <2% accuracy after applying our results. By applying our cross calibration, the geometric albedo of Bennu became consistent with those observed by ground-based telescopes and OVIRS. Our result can be simply applied by multiplying a constant to the publicly available data and enables accurate comparison of the optical spectra of Ryugu and Bennu in future studies.

The Abelian decomposition of QCD tells that there are two types of gluons, the color neutral neurons and colored chromons. We propose to confirm the Abelian decomposition testing the existence of two types of gluon jets experimentally. We predict that one quarter of the gluon jet is made of the neurons which has the color factor 3/4 and the sharpest jet radius and smallest charged particle multiplicity, while the three quarters of the gluon jet are made of the chromons with the color factor 9/4 which have the broadest jet radious (broader than the quark jet). Moreover, we argue that the neuron jet has a distinct color flow which forms an ideal color dipole, while the quark and chromon jets have distorted dipole pattern. To test the plausibility of this proposal we suggest to analyse the gluon distribution against the jet shape (the sphericity) and/or particle multiplicity from the existing gluon jet events and look for two distinct peaks in the distribution., Comment: arXiv admin note: substantial text overlap with arXiv:1812.11300

The overabundance of gas molecules in the coldest regions of space point to a non-thermal desorption process. Laboratory simulations show an efficient desorption of CO ice exposed to ultraviolet radiation, known as photodesorption, which decreases for increasing ice deposition temperature. However, the understanding of this abnormal phenomenon has remained elusive. In this work we show the same phenomenon, and in particular, a dramatic drop in the photodesorption yield is observed when the deposition temperature is 19 K and higher. Also the minimum ice thickness that accounts for a constant photodesorption yield of CO ice is deposition temperature dependent, an observation reported here for the first time. We propose that the key parameters that dominate the absorbed photon energy transfer in CO ice, and contribute to the measured photodesorption yields are the energy transfer length, single ice layer contributed desorption yield, and relative effective surface area. This set of parameters should be incorporated in astrophysical models that simulate photodesorption of the top CO-rich ice layer on icy dust populations with the size distribution which is ice thickness related., Comment: 8 pages, 4 figures

We propose an effective theory of non-Abelian superconductivity, an SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory, which could be viewed as an effective theory of ferromagnetic superconductivity made of spin-up and spin-down doublet Cooper pair. Just like the Abelian Landau-Ginzburg theory it has the U(1) electromagnetic interaction, but the new ingredient is the non-Abelian SU(2) gauge interaction between the spin doublet Cooper pair. A remarkable feature of the theory is the mixing between the photon and the diagonal part of the SU(2) gauge boson. After the mixing it has massless gauge boson (the massless non-Abelian spinon) and massive gauge boson (the massive photon), in addition to the massive off-diagonal gauge bosons (the massive non-Abelian spinons) which induces the spin-flip interaction between the spin up and down components of the Cooper pair. So, unlike the ordinary Landau-Ginzburg theory it has a long range interaction mediated by the massless non-Abelian spinon, which could be responsible for the long range magnetic order and spin waves observed in ferromagnetic superconductors. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different penetration lengths, the one fixed by the mass of the photon (which generates the well known Meissner effect) and the other fixed by the mass of the off-diagonal spinons (which determines the scale of the spin flip interaction). The non-Abelian structure of the theory naturally accommodates new topological objects, the non-Abrikosov quantized spin vortex (as well as the well known Abrikosov vortex) and non-Abelian spin monopole. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory., Comment: 12 pages, 2 figures

A search for highly electrically charged objects (HECOs) and magnetic monopoles is presented using 2.2 fb-1 of p - p collision data taken at a centre of mass energy (ECM) of 8 TeV by the MoEDAL detector during LHC's Run-1. The data were collected using MoEDAL's prototype Nuclear Track Detector array and the Trapping Detector array. The results are interpreted in terms of Drell-Yan pair production of stable HECO and monopole pairs with three spin hypotheses (0, 1/2 and 1). The search provides constraints on the direct production of magnetic monopoles carrying one to four Dirac magnetic charges (4gD) and with mass limits ranging from 590 GeV/c^2 to 1 TeV/c^2. Additionally, mass limits are placed on HECOs with charge in the range 10e to 180e, where e is the charge of an electron, for masses between 30 GeV/c^2 and 1 TeV/c^2.

Martian atmospheric neon (Ne) has been detected by Viking and also found as trapped gas in Martian meteorites, though its abundance and isotopic composition have not been well determined. Because the timescale of Ne loss via atmospheric escape estimated from recent measurements with MAVEN is short (0.6--1 $\times$ 10$^8$ years), the abundance and isotope composition of Martian atmospheric Ne reflect recent atmospheric gas supply mostly from volcanic degassing. Thus, it can serve as a probe for the volatile content of the interior. Here we show that the tentatively-informed atmospheric Ne abundance suggests recent active volcanism and the mantle being richer in Ne than Earth's mantle today by more than a factor of 5--80. The estimated mantle Ne abundance requires efficient solar nebular gas capture or accretion of Ne-rich materials such as solar-wind-implanted dust in the planet formation stage, both of which provide important constraints on the abundance of other volatile elements in the interior and the accretion history of Mars. More precise determination of atmospheric Ne abundance and isotopic composition by in situ analysis or Mars sample return is crucial for distinguishing the possible origins of Ne., Comment: 57 pages, 4 figures, accepted for publication in Icarus

Schwinger showed that electrically-charged particles can be produced in a strong electric field by quantum tunnelling through the Coulomb barrier. By electromagnetic duality, if magnetic monopoles (MMs) exist, they would be produced by the same mechanism in a sufficiently strong magnetic field. Unique advantages of the Schwinger mechanism are that its rate can be calculated using semiclassical techniques without relying on perturbation theory, and the finite MM size and strong MM-photon coupling are expected to enhance their production. Pb-Pb heavy-ion collisions at the LHC produce the strongest known magnetic fields in the current Universe, and this article presents the first search for MM production by the Schwinger mechanism. It was conducted by the MoEDAL experiment during the 5.02 TeV/nucleon heavy-ion run at the LHC in November 2018, during which the MoEDAL trapping detectors (MMTs) were exposed to 0.235 nb$^{-1}$ of Pb-Pb collisions. The MMTs were scanned for the presence of magnetic charge using a SQUID magnetometer. MMs with Dirac charges 1$g_D$ $\leq$ $g$ $\leq$ 3$g_D$ and masses up to 75 GeV/c$^2$ were excluded by the analysis. This provides the first lower mass limit for finite-size MMs from a collider search and significantly extends previous mass bounds., Comment: Minor fixes to the authorship list found during production

Using high magnetic fields up to 60 T, we report magneto-transport and photoluminescence (PL) studies of a two-dimensional electron gas (2DEG) in a GaN/AlGaN heterojunction grown by molecular-beam epitaxy. Transport measurements demonstrate that the quantum limit can be exceeded (Landau level filling factor $\nu < 1$), and show evidence for the $\nu =2/3$ fractional quantum Hall state. Simultaneous optical and transport measurements reveal synchronous quantum oscillations of both the PL intensity and longitudinal resistivity in the integer quantum Hall regime. PL spectra directly reveal the dispersion of occupied Landau levels in the 2DEG and therefore the electron mass. These results demonstrate the utility of high (pulsed) magnetic fields for detailed measurements of quantum phenomena in high-density 2DEGs., Comment: 5 pages, 4 figures

We discuss the Abelian and non-Abelian monopoles which could exist in condensed matters. We show how the Dirac monopole can be regularized by the charge screening, and argue that the Dirac monopole of mass of hundred meVs could exist in dielectric condensed matters. Moreover, we generalize this result to non-Abelian condensed matters to show the existence of the non-Abelian monopole configuration in two-gap condensed matters, and present explicit monopole solutions.

The MoEDAL trapping detector, consists of approximately 800 kg of aluminium volumes. It was exposed during Run-2 of the LHC program to 6.46 fb^-1 of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminium volumes comprising the detector through a SQUID magnetometer. The presence of a trapped dyon would be signalled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to 5 Dirac charges, and an electric charge up to 200 times the fundamental electric charge for mass limits in the range 790 - 3130 GeV., Comment: arXiv admin note: text overlap with arXiv:1903.08491

We show that the electroweak monopole can be regularized with a non-vacuum electromagnetic permittivity. This allows us to set a new BPS bound for the monopole mass, which implies that the mass may not be smaller than 2.98 TeV, more probably 3.75 TeV. We demonstrate that the same method can also regularize the Dirac monopole, which enhances the possibility to construct the Dirac monopole of mass of a few hundred meV in condensed matters. We discuss the physical implications of our result.

Photon strength functions describing the average response of the nucleus to an electromagnetic probe are key input information in the theoretical modelling of nuclear reactions. Consequently they are important for a wide range of fields such as nuclear structure, nuclear astrophysics, medical isotope production, fission and fusion reactor technologies. They are also sources of information for widely used reaction libraries such as the IAEA Reference Input Parameter Library and evaluated data files such as EGAF. In the past two decades, the amount of reaction gamma-ray data measured to determine photon strength functions has grown rapidly. Different experimental techniques have led to discrepant results and users are faced with the dilemma which (if any) of the divergent data to adopt. We report on a coordinated effort to compile and assess the existing experimental data on photon strength functions from the giant dipole resonance region to energies below the neutron separation energy. The assessment of the discrepant data at energies around or below the neutron separation energy has been possible only in a few cases where adequate information on the model-dependent analysis and estimation of uncertainties was available. In the giant dipole resonance region, we adopt the recommendations of the new IAEA photonuclear data library. We also present global empirical and semi-microscopic models that describe the photon strength functions in the entire energy region and reproduce reasonably well most of the experimental data. The compiled experimental photon strengths and recommended model calculations are available from the PSF database hosted at the IAEA (URL:www-nds.iaea.org/PSFdatabase)., Comment: IAEA Coordinated Research Project on Generating Reference Database for Photon Strength Functions (F41032)

Photo-induced reaction cross section data are of importance for a variety of current or emerging applications, such as radiation shielding design and radiation transport analyses, calculations of absorbed dose in the human body during radiotherapy, physics and technology of fission reactors (influence of photo-reactions on neutron balance) and fusion reactors (plasma diagnostics and shielding), activation analyses, safeguards and inspection technologies, nuclear waste transmutation, medical isotope production and astrophysical applications. Since the release of the IAEA Photonuclear Data Library in 1999 however, new experimental data as well as new methods to assess the reliability of experimental cross sections have become available. Theoretical models and input parameters used to evaluate photo-induced reactions have improved significantly over the years. In addition, new measurements of partial photoneutron cross sections using mono-energetic photon beams and advanced neutron detection systems have been performed allowing for the validation of the evaluations and assessments of the experimental data. Furthermore, technological advances have led to the construction of new and more powerful gamma-beam facilities, therefore new data needs are emerging. We report our coordinated efforts to address these data needs and present the results of the new evaluations of more than 200 nuclides included in the new updated IAEA Photonuclear Data Library, where the photon energy goes up to 200 MeV. We discuss the new assessment method and make recommendations to the user community in cases where the experimental data are discrepant and the assessments disagree. In addition, in the absence of experimental data, we present model predictions for photo-induced reaction cross section on nuclides of potential interest to medical radioisotope production.

MoEDAL is designed to identify new physics in the form of stable or pseudostable highly ionizing particles produced in high-energy Large Hadron Collider (LHC) collisions. Here we update our previous search for magnetic monopoles in Run 2 using the full trapping detector with almost four times more material and almost twice more integrated luminosity. For the first time at the LHC, the data were interpreted in terms of photon-fusion monopole direct production in addition to the Drell-Yan-like mechanism. The MoEDAL trapping detector, consisting of 794 kg of aluminum samples installed in the forward and lateral regions, was exposed to 4.0 fb$^{-1}$ of 13 TeV proton-proton collisions at the LHCb interaction point and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges equal to or above the Dirac charge are excluded in all samples. Monopole spins 0, 1/2 and 1 are considered and both velocity-independent and -dependent couplings are assumed. This search provides the best current laboratory constraints for monopoles with magnetic charges ranging from two to five times the Dirac charge., Comment: 7 pages REVTeX 4, 11 figures, 1 table, matches published version in Physical Review Letters

We propose a simple way to test the Abelian decomposition of QCD, the existence of two types of gluons, experimentally at LHC. The Abelian decomposition decomposes the gluons to the color neutral neurons and colored chromons gauge independently. This refines the Feynman diagram in a way that the color conservation is explicit, and generalizes the quark model to the quark and chromon model. We predict that the neuron jet has the color factor 3/4 and has a sharpest jet radius and smallest particle multiplicity, while the chromon jet with the color factor 9/4 remains the broadest jet. Moreover, the neuron jet has a distinct color flow which forms an ideal color dipole, while the quark and chromon jets have distorted dipole pattern.

In this paper, we introduce a new class of Bregman generalized $\alpha$-nonexpansive mappings in terms of Bregman distances, and investigate the Ishikawa and Noor iterations for these mappings. We establish weak and strong convergence theorems of Ishikawa and Noor iterative schemes for Bregman generalized $\alpha$-nonexpansive mappings in Banach spaces. Furthermore, we propose an example of our generated mapping and some numerical examples which support our main theorem. Our results are new and improve the recent ones in the literature.

We show how to calculate the effective potential of SU(3) QCD which tells that the true minimum is given by the monopole condensation. To do this we make the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. In the perturbative regime this decomposes the Feynman diagram in such a way that the conservation of color is explicit. Moreover, this shows the existence of two gluon jets, the neuron jet and chromon jet, which can be verified by experiment. In the non-perturbative regime, the decomposition puts QCD to the background field formalism and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry, and provides us an ideal platform to calculate the one-loop effective action of QCD. Integrating out the chromons from the Weyl symmetric Abelian decomposition of QCD gauge invariantly imposing the color reflection invariance, we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result, in particular the possible existence of the vacuum fluctuation mode of the monopole condensation in QCD., Comment: arXiv admin note: text overlap with arXiv:1606.02374