Dimensions Of Operators Research Articles

Dark Matter Production during Warm Inflation via Freeze-In

We present a novel perspective on the role of inflation in the production of dark matter (DM). Specifically, we explore the DM production during warm inflation via ultraviolet freeze-in (WIFI). We demonstrate that in a warm inflation (WI) setting the persistent thermal bath, sustained by the dissipative interactions with the inflaton field, can source a sizable DM abundance via the nonrenormalizable interactions that connect the DM with the bath. Compared to the (conventional) radiation-dominated (RD) UV freeze-in scenario for the same reheat temperature (after inflation), the resulting DM yield in WIFI is always enhanced showing a strongly positive dependence on the mass dimension of the nonrenormalizable operator. Of particular interest, for a sufficiently large mass dimension of the operator, the entirety of the DM abundance of the Universe can be created during the inflationary phase. For the specific models we study, we find that the enhancement in DM yield, relative to RD UV freeze-in, is at least an order of magnitude for an operator of mass dimension 5, and as large as 18 orders of magnitude for an operator of mass dimension 10. Our findings also suggest a broader applicability for producing other cosmological relics, which may have a substantial impact on the evolution of the early Universe. Published by the American Physical Society 2024

Constraints for twist-two alien operators in QCD

Abstract Parton evolution equations in QCD are controlled by the anomalous dimensions of gauge-invariant twist-two spin-N quark and gluon operators. Under renormalization, these mix with gauge-variant operators of the same quantum numbers, referred to as alien operators. Our work addresses the systematic study of these alien operators at arbitrary spin N, using generalized BRST symmetry relations to derive their couplings and Feynman rules at all values of N. We observe how the all-N structure of the generalized (anti-)BRST constraints relates the couplings of alien operators with n + 1 gluons to those with n gluons. Realizing a bootstrap, we present all one-loop results necessary for performing the operator renormalization up to four loops in QCD.

ENHANCING BUSINESS SUSTAINABILITY THROUGH CSR: A CASE STUDY OF "BETTER LIVING IN MALAHING” IN THE PERSPECTIVE OF CARROLL'S PYRAMID

This study examines PT PKT's CSR initiative, "Better Living in Malahing," in relation to business sustainability and its alignment with the Sustainable Development Goals (SDGs). The research underscores the critical role of economic responsibility and profitability in sustaining both social and environmental goals. Using a qualitative case study approach, the study delves into the implementation of the CSR program based on Carroll's Pyramid of responsibilities, encompassing economic, legal, ethical, and philanthropic dimensions. Data collection methods include in-depth interviews, observations, and document analysis. Findings reveal that the program significantly improved the quality of life for coastal communities in Bontang while simultaneously bolstering the company's reputation. Moreover, a strong correlation between corporate social responsibility and sustainable financial performance is identified. The conclusion emphasizes that integrating CSR into core business strategies is crucial for long-term sustainability. This research contributes by illustrating the necessity of well-structured, enduring CSR initiatives in supporting economic, social, and environmental dimensions of corporate operations.

Large landscape of 4d superconformal field theories from small gauge theories

We systematically explore the space of renormalization group flows of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges (a, c), a correlation between the number of relevant operators and the ratio a/c, and trends in the lightest operator dimension versus a/c. The ratio a/c of this set is distributed between 0.7228 and 1.2100, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges ac=63320006832000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left(a,c\\right)=\\left(\\frac{633}{2000},\\frac{683}{2000}\\right) $$\\end{document} than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 deformed Argyres-Douglas theories. We provide a website https://qft.kaist.ac.kr/landscape to navigate through our set of fixed points.

Majorana phases beyond neutrinoless double beta decay

The νM SM is defined as the SM extended to include dimension-5 operators. In this model neutrino masses violate lepton number, and two parameters of the lepton mixing matrix, the Majorana phases, are yet to be constrained. One combination of these phases and the neutrino masses, often denoted by mee, is probed by neutrinoless double beta decays (0νββ). We explore what information may be obtained beyond 0νββ, and how it depends on the lightest neutrino mass. We point out that with current central values of the mixing parameters, ∆Le = 2 and ∆Le = ∆Lμ = 1 (or ∆Le = 2 and ∆Lμ = 2) processes cannot simultaneously vanish, providing a no-lose theorem, in principle, for excluding the νM SM, even in the case of normal mass ordering.

Disentangling new physics in K→πνν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ K\ o \\pi \ u \\overline{\ u} $$\\end{document} and B→KK∗νν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B\ o K\\left({K}^{\\ast}\\right)\ u \\overline{\ u} $$\\end{document} observables

We investigate the possibility of disentangling different new physics contributions to the rare meson decays and through kinematic distributions in the missing energy . We employ dimension-6 operators within the Low-Energy Effective Field Theory (LEFT), identifying the invisible part of the final state as either active or sterile neutrinos. Special emphasis is given to lepton-number violating (LNV) operators with scalar and tensor currents. We show analytically that contributions from vector, scalar, and tensor quark currents can be uniquely determined from experimental data of kinematic distributions. In addition, we present new correlations of branching ratios for K and B-decays involving scalar and tensor currents. As there could a priori also be new invisible particles in the final states, we include dark-sector operators giving rise to two dark scalars, fermions, or vectors in the final state. In this context, we present new calculations of the inclusive decay rate for dark operators. We show that careful measurements of kinematic distributions make it theoretically possible to disentangle the contribution from LEFT operators from most of the dark-sector operators, even when multiple operators are contributing. We revisit sum rules for vector currents in LEFT and show that the latter are also satisfied in some new dark-physics scenarios that could mimic LEFT. Finally, we point out that an excess in rare meson decays consistent with a LNV hypothesis would point towards highly flavor non-democratic physics in the UV, and could put high-scale leptogenesis under tension.

Release note: VBFNLO 3.0

Vbfnlo is a flexible parton level Monte Carlo program for the simulation of vector boson fusion (VBF), QCD-induced single and double vector boson production plus two jets, and double and triple vector boson production (plus jet) in hadronic collisions at next-to-leading order (NLO) in the strong coupling constant, as well as Higgs boson plus two and three jet production via gluon fusion at the one-loop level. For the new version – Version 3.0 – several major enhancements have been included. An interface according to the Binoth Les Houches Accord (BLHA) has been added for all VBF and di/tri-boson processes including fully leptonic decays. For all dimension-8 operators affecting vector boson scattering (VBS) processes, a modified T-matrix unitarization procedure has been implemented. Several new production processes have been added, namely the VBS Zγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z\\gamma jj$$\\end{document} and γγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\gamma jj$$\\end{document} processes at NLO, γγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\gamma jj $$\\end{document}, WWj and ZZj production at NLO including the loop-induced gluon-fusion contributions and the gluon-fusion one-loop induced Φjjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi jjj$$\\end{document} (Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document} is a CP-even or CP-odd scalar boson) process at LO, retaining the full top-mass dependence. Finally, the code has been parallelized using Openmpi.

On the class 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} origin of spindle solutions

We analyse the backreacted geometry corresponding to a stack of M5-branes wrapped on a spindle, with a view towards precision tests of the dual N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal field theory. We carefully study the singular loci of the uplifted geometry and show that these correspond to C3/Zn conical singularities. Therefore, these solutions present one of the first explicit realisations of honest locally N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 preserving punctures in class 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}. Additionally we study the symmetries and anomalies of the dual field theory through anomaly inflow and compute a variety of holographic observables including dimensions of BPS operators. This work paves the way for advancements in the study and identification of the precise dual field theories.

Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

Conformal BK equation at QCD Wilson-Fisher point

High-energy scattering in pQCD in the Regge limit is described by the evolution of Wilson lines governed by the BK equation [1, 2]. In the leading order, the BK equation is conformally invariant and the eigenfunctions of the linearized BFKL equation are powers. It is a common belief that at d ≠ 4 the BFKL equation is useless since unlike d = 4 case it cannot be solved by usual methods. However, we demonstrate that at critical Wilson-Fisher point of QCD the relevant part of NLO BK restores the conformal invariance so the solutions are again powers. As a check of our approach to high-energy amplitudes at the Wilson-Fisher point, we calculate the anomalous dimensions of twist-2 light-ray operators in the Regge limit j → 1.

Exploring constraints on Simplified Dark Matter model through flavour and electroweak observables

This study focuses on a combined analysis of various available inputs to constrain the parameter spaces of a simplified dark matter (SDM) model featuring a spin-0 mediator and fermionic dark matter (DM). The spin-0 mediator interacts with standard model (SM) fermions, SM gauge bosons, and DM. We constrain the parameter spaces of different relevant couplings, DM mass, and the mediator mass, using the data from flavour-changing charged and neutral current processes, CKM matrices, W and Z-pole observables, DM relic density, direct and indirect detection bounds. We have calculated bounds on the couplings from both separate and simultaneous analyses of the mentioned processes. We identify correlated parameter spaces for all the relevant parameters which include the couplings and the masses. For the DM and mediator masses, we have scanned the region between 100 GeV and 1000 GeV. Using our results, we have obtained bounds on the couplings of possible higher dimensional operators from which we can formulate our SDM.

High current density operation of proton exchange membrane fuel cells at a constant relative humidity

To further reduce the size and cost of proton exchange membrane fuel cells, it is desired to operate at high current densities exceeding 2 A/cm2, and consequently achieve power densities above 1 W/cm2. In a prior one-dimensional modeling study that employed the Engineering Equation Solver (EES), it was suggested that proton exchange membrane fuel cells might operate at current densities as high as 10 A/cm2 and even more when appropriate operating and channel dimensions are chosen, and perforated metal plates are used as porous transport layers instead of carbon fiber papers. The current study verifies the general findings of the previous 1-D model by a 3-D multiphase computational fluid dynamics model in Ansys CFX to obtain additional insights. Operating a proton exchange membrane fuel cell at a constant humidity (100%, 80%, 60%) from the inlet to the outlet at the cathode side appears feasible, and results for a current density above 6 A/cm2 were obtained. This mode of operation is promising also for automotive applications.

High current density operation of proton exchange membrane fuel cells at a constant relative humidity

To further reduce the size and cost of proton exchange membrane fuel cells, it is desired to operate at high current densities exceeding 2 A/cm2, and consequently achieve power densities above 1 W/cm2. In a prior one-dimensional modeling study that employed the Engineering Equation Solver (EES), it was suggested that proton exchange membrane fuel cells might operate at current densities as high as 10 A/cm2 and even more when appropriate operating and channel dimensions are chosen, and perforated metal plates are used as porous transport layers instead of carbon fiber papers. The current study verifies the general findings of the previous 1-D model by a 3-D multiphase computational fluid dynamics model in Ansys CFX to obtain additional insights. Operating a proton exchange membrane fuel cell at a constant humidity (100%, 80%, 60%) from the inlet to the outlet at the cathode side appears feasible, and results for a current density above 6 A/cm2 were obtained. This mode of operation is promising also for automotive applications.

Automatic generation of helicity amplitudes in the Feynman-diagram gauge

We develop a method to calculate helicity amplitudes of an arbitrary tree-level process in the Feynman-diagram (FD) gauge for an arbitrary gauge model with adraph5_a@. We start from the ’t Hooft–Feynman gauge Lagrangian in eynules and generate scattering amplitudes by identifying the Goldstone boson as the 5th component of each weak boson. All the vertices of the 5-component weak bosons are then created automatically by assembling the relevant weak boson and Goldstone boson vertices in the Feynman gauge. The 5-component weak boson vertices are then connected by the 5×5 matrix propagator in the FD gauge. As a demonstration of the method we calculate the cross section for the process μ−μ+→νμν¯μtt¯H with complex top Yukawa coupling, which can be obtained by adding a gauge invariant dimension-6 operator to the Standard Model (SM) Lagrangian. The FD gauge and the unitary (U) gauge amplitudes give exactly the same cross section, and subtle gauge theory cancellation among diagrams in the U gauge at high energies is absent in the FD gauge, as has been observed for various SM processes. In addition, we find that the total cross sections at high energies are dominated by a single, or a set of nonvanishing Feynman amplitudes with the higher dimensional vertices in the FD gauge. Published by the American Physical Society 2024

Basis for non-factorizable superamplitudes in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetry

In this paper we develop a semi-standard Young tableau (SSYT) approach to construct a basis of non-factorizable superamplitudes in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 massless supersymmetry. This amplitude basis can be directly translated to a basis for higher dimensional supersymmetric operators, yielding both the number of independent operators and their form. We deal with distinguishable (massless) chiral/vector superfields at first, then generalize the result to the indistinguishable case. Finally, we discuss the advantages and disadvantages of this method compared to the previously studied Hilbert series approach.

Sterile neutrino dark matter within the νSMEFT

Sterile neutrinos with masses at the keV scale and mixing to the active neutrinos offer an elegant explanation of the observed dark matter (DM) density. However, the very same mixing inevitably leads to radiative photon emission and the non-observation of such peaked X-ray lines rules out this minimal sterile neutrino DM hypothesis. We show that in the context of the Standard Model effective field theory with sterile neutrinos (νSMEFT), higher dimensional operators can produce sterile neutrino DM in a broad range of parameter space. In particular, νSMEFT interactions can open the large mixing parameter space due to their destructive interference, through operator mixing or matching, in the X-ray emission. We also find that, even in the zero mixing limit, the DM density can always be explained by νSMEFT operators. The testability of the studied νSMEFT operators in searches for electric dipole moments, neutrinoless double beta decay, and pion decay measurements is discussed.

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two ‘hydrodynamic’ Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form ℤ2 symmetry of the bosonic theory and its gauging, which originates the fermion number (−1)F, the spin sectors and the time reversal symmetry obeying T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}2 = (−1)F. These results are detailed for the effective action and the partition function on the geometry S2 × S1.

On embedding the Koopmanization into controlled nonlinear systems, its comparison with the Carleman linearisation and concerning results: beyond the feedback linearisation

The feedback linearisation has found its striking applications in many practical situations for control problems that exploit the ideas from the linear system theory. Towards linearisation techniques for controlled nonlinear systems, operator-theoretic frameworks from functional analysis have received attentions as well. The Koopman operator is a linear, but an infinite dimensional operator. Most notably, the novelties of the paper are the following. (i) Sketching a rigorous and comprehensive proof of the Koopmanization of the controlled nonlinear system using the notion of the operator-invariant subspace and unifying the minimiser inequality formula with the Koopmanized system. The proof unfolds that the Koopmanization meets the bilinearisation in control context with the augmented state space. (ii) A formal construction of an observer encompassing the generalised Riccati equation in the Koopman setting of the original controlled nonlinear system. The Carleman version of the generalised Riccati equation is rephrased as well. (iii) Unfolding the usefulness of the Koopman observer. To achieve extensive illustrations of the theory of the paper, we construct two Koopman observers for two practical control problems, i.e. a controlled Duffing system with a cubic nonlinearity and a controlled system with a square nonlinearity. Then, we compare the Koopman observers with the Carleman observers.

Probing new physics at the LHC and future colliders: SMEFT and beyond

In this talk, I review our progresses on probing new physics at the LHC and future colliders by using the Standard Model Effective Field Theory (SMEFT) and beyond. This includes to probe new physics effects in the Higgs boson couplings via leading dimension-6 operators and in the neutral triple gauge couplings (nTGCs) via leading dimension-8 operators. I also discuss the probe of Higgs self-couplings involving the SM Higgs-boson-pair plus a new heavy Higgs boson of the extended Higgs sector via the resonant diHiggs production channels.

Baryon-number-violating nucleon decays in ALP effective field theories

The search for baryon-number-violating (BNV) nucleon decay is an intriguing probe of new physics beyond the SM in future neutrino experiments with enhanced sensitivity. The dark sector states such as an axion or axion-like particle (ALP) can induce nucleon decays with distinct signature and kinematics from the conventional nucleon decays. In this work, we study the ALP effective field theories (EFTs) with baryon number violation and the impact of light ALP on BNV nucleon decays. We revisit the dimension-8 BNV operators in the extended EFTs with an ALP field a respecting shift symmetry. The low-energy EFT operators with |∆(B – L)| = 2 and |∆(B – L)| = 0 are matched to the baryon chiral perturbation theory. We obtain the effective chiral Lagrangian and the BNV interactions between ALP and baryons/mesons. The ALP interactions lead to two-body baryon decays B → ℓ (or ν) a and three-body nucleon decays N → M ℓ (or ν) a. We obtain the constraints on the UV scale from the invisible Λ0 decay search at BESIII, the invisible neutron decay search at KamLAND and proton decay search at Super-K. We also show the projections of some other baryon/nucleon decays and present the distinct distributions of kinematic observable.