Triangle Loops Research Articles

Pionic transitions of the spin-2 partner of X(3872) to χcJ

We investigated the pionic transitions between the X2 [spin-2 partner of the X(3872)] and χc1,2 using a nonrelativistic effective field theory. The X2 is assumed to be a bound state of the D* and D¯* mesons and to decay through several kinds of loops, including the bubble, triangle, and box loops. Within the present model, the widths for the single-pion decays X2→π0χcJ are predicted to be about 3–30 keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of 10−3–10−2. The ratio Rc0=Γ(X2→π+π−χcJ)/Γ(X2→π0π0χcJ)≃1.6, which is a bit smaller than the expected value of 2, and R21=Γ(X2→ππχc2)/Γ(X2→ππχc1)≃0.85. These ratios are nearly independent of the X2 mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the π0χcJ final state for the dipion processes are presented, showing a cusp structure at the DD¯* threshold enhanced and narrowed by the nearby triangle singularity. Published by the American Physical Society 2024

Subtleties in triangle loops for Ds+→ρ+η→π+π0η in a0(980) production

We address a general problem in the evaluation of triangle loops stemming from the consideration of the range of the interaction involved in some of the vertices, as well as the energy dependence of the width of some unstable particles in the loop. We find sizeable corrections from both effects. We apply that to a loop relevant to the Ds+→π+π0η decay, and find reductions of about a factor of 4 in the mass distribution of invariant mass of the πη in the region of the a0(980). The method used is based on the explicit analytical evaluation of the q0 integration in the d4q loop integration, using Cauchy’s residues method, which at the same time offers an insight on the convergence of the integrals and the effect of form factors and cutoffs. Published by the American Physical Society 2024

Geometric and Statistical Assessments on Horizontal Positioning Accuracy in Relation with GNSS CORS Triangulations of NRTK Positioning Services in Thailand

Thailand has implemented GNSS Continuously Operating Reference Stations (CORS) and Network Real-Time Kinematic (NRTK) Positioning services collaborated by several government agencies and universities for various applications. This research includes 114 GNSS CORSs; providing 143 triangle loops and covering 63 provinces nationwide, to determine and analyse the obtained horizontal positioning accuracy and their ground station geometries. Triangulation networks are categorised in terms of shapes and baseline distances. Well- and ill-conditioned triangles are defined in accordance with different baseline lengths. The horizontal positioning accuracy is computed using static and NRTK positioning determinations whilst static positioning results are defined as the ground truth. Student's T tests are used to ensure the significance of calculated results according to each test case. The results show obtained horizontal positioning accuracies are within the specified accuracy of less than 4 centimetres and do not show any significant differences based on the defined significant level of 0.05. This GNSS CORS triangulation network geometry scheme does not influence the computed horizontal positioning accuracy obtained from NRTK-Virtual Reference Station (VRS) GNSS positioning services; however, the positioning accuracy is still directly due to distances between nearest GNSS CORS or its triangulation network, therefore, further suggestions are provided.

Investigations on the light hadron decays of Zb(10610) and Zb(10650)

The light hadron decay processes of $Z_b(10610)/Z_b(10650)$ provide us a way to study their nature and decay mechanism. In this work, we evaluate the branching ratios of $Z_b(10610)/Z_b(10650) \to VP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) using an effective Lagrangian approach, in which the contributions of intermediate bottomed meson triangle loops are considered. In our calculations, the $Z_b(10610)$ and $Z_b(10650)$ are regarded as $B\bar{B}^*+c.c.$ and $B^*\bar{B}^*$ molecular states, respectively. The predicted branching ratios of $Z_b(10610)\rightarrow VP$ are about in the order of $10^{-2}$, while the branching ratios of $Z_b(10650)\rightarrow VP$ are in the order of $10^{-3}$. Furthermore, the dependence of these ratios between different decay modes of $Z_b(10610)/Z_b(10650)$ on the mixing $\eta-\eta^\prime$ angle $\theta_P$ is investigated, which may be a good quantity for the experiments. It is hoped that the calculations here could be tested by future experiments.

Radiative decays of the neutral Zc(3900) and Zc(4020)

We study the radiative decays $Z_c(3900)/Z_c(4020) \to \gamma \chi_{cJ}(\gamma\chi_{cJ}^\prime)$ ($J=0, 1, 2$), with the assumption that the $Z_c(3900)$ and $Z_c(4020)$ couple strongly to $D\bar D^* +c.c$ and $D^*{\bar D}^*$ channel, respectively. By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900) \to \gamma \chi_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020) \to \gamma \chi_{cJ}$ are about tens of keVs. The predicted partial widths of $Z_c(3900)\to\gamma\chi_{c0,1}^\prime$ are less than 1 keV, which mainly due to the very small phase space. For $Z_c(4020)\to\gamma\chi_{c0,2}^\prime$, the calculated partial widths are usually smaller than 1 keV. For the $Z_c(4020)\to\gamma\chi_{c1}^\prime$ process, the obtained partial widths can reach up to the order of 10 keV. Furthermore, the dependence of these ratios between different decay modes on the masses of $Z_c(3900)$ or $Z_c(4020)$ are also investigated, which may be a good quantity for the experiments. It is hoped that these calculations here could be tested by future experiments.

Possible precise measurements of the X(3872) mass with the e+e−→π0γX(3872) and pp¯→γX(3872) reactions

It was recently proposed that the $X(3872)$ binding energy, the difference between the $D^0\bar D^{*0}$ threshold and the $X(3872)$ mass, can be precisely determined by measuring the $\gamma X(3872)$ line shape from a short-distance $D^{*0}\bar D^{*0}$ source produced at high-energy experiments. Here, we investigate the feasibility of such a proposal by estimating the cross sections for the $e^+e^-\to\pi^0\gamma X(3872)$ and $p\bar p\to\gamma X(3872)$ processes considering the $D^{*0}\bar D^{*0}D^0/\bar D^{*0}D^{*0}\bar D^0$ triangle loops. These loops can produce a triangle singularity slightly above the $D^{*0}\bar D^{*0}$ threshold. It is found that the peak structures originating from the $D^{*0}\bar D^{*0}$ threshold cusp and the triangle singularity are not altered much by the energy dependence introduced by the $e^+e^-\to\pi^0D^{*0}\bar D^{*0}$ and $p\bar p\to\bar D^{*0}D^{*0}$ production parts or by considering a finite width for the $X(3872)$. We find that $\sigma(e^+e^-\to\pi^0\gamma X(3872)) \times {\rm Br}(X(3872)\to\pi^+\pi^-J/\psi)$ is $\mathcal{O}(0.1~{\rm fb})$ with the $\gamma X(3872)$ invariant mass integrated from 4.01 to 4.02 GeV and the c.m. energy of the $e^+e^-$ pair fixed at 4.23 GeV. The cross section $\sigma(p\bar p\to\gamma X(3872))\times {\rm Br}(X(3872)\to\pi^+\pi^-J/\psi)$ is estimated to be of $\mathcal{O}(10~{\rm pb})$. Our results suggest that a precise measurement of the $X(3872)$ binding energy can be done at PANDA.

Microvascular Scaffolds: A Biomimetic 3D‐Self‐Forming Approach for Microvascular Scaffolds (Adv. Sci. 9/2020)

Inspired by drying‐driven curling of apple peels, hydrogel‐based micro‐scaled hollow tubules are proposed in article number 1903553 by Yuguang Zhang, Xiaoming Sun, Helder A. Santos, Wenguo Cui, and co‐workers for biomimicking microvessels with diameters of 50–500 μm, which promote microcirculation and improve the survival of random skin flaps. The 3D‐shape‐morphing technique is of great flexibility and potential to lay the foundation for the construction of complex vascular networks, such as Y‐branches, anastomosis rings, and triangle loops.

Role of the triangle mechanism in the Λb→Λcπ−f0(980) reaction

We investigate the $\Lambda_b\to\Lambda_c\pi^-f_0(980)$ production with a $f_0(980)$ decay into $\pi^+\pi^-$ via the $K^{*0}K^-K^+$ and $K^{*-}K^0\bar{K}^0$ triangle loops. These loops produce a peak around 1.42 GeV in the $\pi^-f_0(980)$ invariant mass distribution, which is the same mechanism as the one considered to explain the $a_1(1420)$ peak. In the $\pi^+\pi^-$ distribution obtained by fixing the $\pi^-f_0(980)$ invariant mass to some values, a clear peak of $f_0(980)$ is seen, and the $\pi^-f_0(980)$ distribution has a peak around $M_{\pi^-f_0}=1.42$ GeV, which is caused by the triangle mechanism of the $K^*\bar KK$ loop. The branching ratio of $\Lambda_b\rightarrow\Lambda_c\pi^-f_0(980)$ with $f_0(980)\rightarrow\pi^+\pi^-$ by the triangle mechanism, obtained by integrating the $\pi^-f_0(980)$ distribution from 1 to 1.6 GeV, is estimated to be the order $10^{-4}$. Future measurements of the $\Lambda_b\to\Lambda_c\pi^-f_0(980)$ branching ratio and the $\pi^-f_0(980)$ invariant mass distribution predicted in this work would give further clues to clarify the nature of the $a_1(1420)$ peak.

A Biomimetic 3D-Self-Forming Approach for Microvascular Scaffolds.

The development of science and technology often drew lessons from natural phenomena. Herein, inspired by drying‐driven curling of apple peels, hydrogel‐based micro‐scaled hollow tubules (MHTs) are proposed for biomimicking microvessels, which promote microcirculation and improve the survival of random skin flaps. MHTs with various pipeline structures are fabricated using hydrogel in corresponding shapes, such as Y‐branches, anastomosis rings, and triangle loops. Adjustable diameters can be achieved by altering the concentration and cross‐linking time of the hydrogel. Based on this rationale, biomimetic microvessels with diameters of 50–500 µm are cultivated in vitro by coculture of MHTs and human umbilical vein endothelial cells. In vivo studies show their excellent performance to promote microcirculation and improve the survival of random skin flaps. In conclusion, the present work proposes and validifies a biomimetic 3D self‐forming method for the fabrication of biomimetic vessels and microvascular scaffolds with high biocompatibility and stability based on hydrogel materials, such as gelatin and hyaluronic acid.

Charm rescattering contribution in rare [formula omitted] decay

Following the experimental results from LHCb on the rare decay Bc+→K−K+π+, we investigate the possibility where this process is dominated by a double charm rescattering. The Bc decay to double charm channels have a weak topology that is favored in comparison with the direct production of K−K+π+ in the final state, suppressed by quark annihilation. The decay amplitude for Bc+→K−K+π+ with Bc decaying first to double charm channels is described by charm hadronic triangle loops, which reach the final state of interest after DD¯→KK¯ or D+Ds−→π+K− transitions. We show that these processes give rise to non-resonant amplitudes with a clear signature in the Dalitz plot. In a near future, the new data from LHCb run II will be able to confirme if the main hypotheses of this work is correct and the dominant mechanism to produce K+K+π− from the decay of Bc+ is through charm rescattering.

Symmetric spin–orbit interaction in triple quantum dot and minimisation of spin–orbit leakage in CNOT gate

We analyse spin–orbit interaction in triple quantum dots and show that a symmetric spin–orbit Hamiltonian does not follow the standard form used in double quantum dots, as a consequence of the presence of the third dot in the setup. Furthermore, CNOT implementation schemes based on the exchange interaction were studied. It was shown that an antisymmetric Dzyaloshinsky–Moriya term is the dominant source of spin–orbit leakage from the computational space. We present a simple scheme for the minimisation of leakage that can be implemented in cases where interacting spins enclose parallelogram or equilateral triangle loops.

Top-quark loops and the muon anomalous magnetic moment

The current status of electroweak radiative corrections to the muon anomalous magnetic moment is discussed. Asymptotic expansions for some important electroweak two-loop top quark triangle diagrams are illustrated and extended to higher order. Results are compared with the more general integral representation solution for generic fermion triangle loops coupled to pseudoscalar and scalar bosons of arbitrary mass. Excellent agreement is found for a broader than expected range of mass parameters.

Radiative decays of a singlet scalar boson through vectorlike quarks

If the standard model Higgs boson were much heavier, it would appear as a broad resonance since its decay into a pair of longitudinally polarized gauge bosons is highly enhanced. We study whether the same enhancement happens at loop level in a simple extension of the standard model with a singlet scalar boson $S$. In order to focus on the loop effects, we assume that $S$ does not interact with the standard model particles at tree level. The singlet scalar $S$ is linked to the standard model world by vector-like quarks running in the loop. We introduce three vector-like quark multiplets, an $SU(2)_L$ doublet, an up-type singlet, and a down-type singlet. There are two kinds of loop effects in the $S$ phenomenology, the mixing with the Higgs boson and the radiative decays into $hh$, $WW$, $ZZ$, $gg$, and $\gamma\gamma$ through the triangle loops. We show that the crucial condition for enhancing loop effects including the longitudinal polarization enhancement is the large mass differences among vector-like quarks. The current LHC constraints on $S$ from the heavy scalar searches and the Higgs precision data are shown to be very significant: the mixing angle with the Higgs boson should be smaller than about 0.1 for $m_S= 750$ GeV.

Gauged Two Higgs Doublet Model confronts the LHC 750 GeV diphoton anomaly

In light of the recent 750 GeV diphoton anomaly observed at the LHC, we study the possibility of accommodating the deviation from the standard model prediction based on the recently proposed Gauged Two Higgs Doublet Model. The model embeds two Higgs doublets into a doublet of a non-abelian gauge group SU(2)H, while the standard model SU(2)L right-handed fermion singlets are paired up with new heavy fermions to form SU(2)H doublets, and SU(2)L left-handed fermion doublets are singlets under SU(2)H. An SU(2)H scalar doublet, which provides masses to the new heavy fermions as well as the SU(2)H gauge bosons, can be produced via gluon fusion and subsequently decays into two photons with the new fermions circulating the triangle loops to account for the deviation from the standard model prediction.

Bulk mixed ion electron conduction in amorphous gallium oxide causes memristive behaviour

In thin films of mixed ionic electronic conductors sandwiched by two ion-blocking electrodes, the homogeneous migration of ions and their polarization will modify the electronic carrier distribution across the conductor, thereby enabling homogeneous resistive switching. Here we report non-filamentary memristive switching based on the bulk oxide ion conductivity of amorphous GaOx (x~1.1) thin films. We directly observe reversible enrichment and depletion of oxygen ions at the blocking electrodes responding to the bias polarity by using photoemission and transmission electron microscopies, thus proving that oxygen ion mobility at room temperature causes memristive behaviour. The shape of the hysteresis I-V curves is tunable by the bias history, ranging from narrow counter figure-eight loops to wide hysteresis, triangle loops as found in the mathematically derived memristor model. This dynamical behaviour can be attributed to the coupled ion drift and diffusion motion and the oxygen concentration profile acting as a state function of the memristor.

P 211. Efficient method for computing the TMS-induced electric field in spherically symmetric head models, the triangle Construction

In transcranial magnetic stimulation (TMS), we are interested in calculating the TMS-induced electric field (E-field), which defines the given stimulus. This is known as the forward problem, and there exist no general analytic solution for it. This is because the electric field is dictated by Maxwell’s equations, which are partial differential equations. Thus, for non-trivial boundary conditions, numerical methods are needed. General methods for solving these equations are the finite element method (FEM), where we split the volume into small polyhedrons, and the boundary element method (BEM), where we divide the system into uniform-conductance regions and split the formed boundaries into small polygons. Both of these methods can be applied for nearly arbitrary geometries but are hard to parallelize. However, often one can simplify the analysis by using a spherically symmetric head model. For example, if one is to assess the general properties of a stimulator coil, using a more complicated head model will just increase the computational cost and complicate the analysis of the results. Also when the head can be approximated being locally spherical, the spherical symmetric head model allows a significant simplification in the computations. This is because the spherical symmetry of the conducting medium allows us to compute an analytic solution for the forward problem. We will present an efficient method for computing the induced E-field. The model works for spherically symmetric head models and is based on the triangle construction, (Ilmoniemi RJ, Hamalainen MS, Knuutila J. The forward and inverse problems in the spherical model. In: Biomagnetism: Applications & Theory, H. Weinberg, G. Stroink, T. Katila (eds.), Pergamon Press, Amsterdam 1985, pp. 278–282); see Fig. 1 . Devices based on the triangle construction have been used to calibrate magnetoencephalography (MEG) and TMS systems. Now, to obtain the two tangential components (the radial component is always zero) of the induced E-field in a point, one simply has to calculate the mutual inductance between the TMS coil and two perpendicular triangular loops with one corner at the sphere center and the opposite edge tangential to the spherical surface. For the mutual-inductance calculations, the TMS coil can be modeled as a set of current-carrying filaments. Then, the mutual inductance between the coil and the triangle loops can be calculated using analytic formulas. Using the triangle construction, we developed an O (n) time and memory algorithm for the TMS forward problem, where n is the number of points where the induced E-field is computed. This is a considerable improvement over O (M2) for the BEM or O (N) for the FEM, where M is the number of surface elements, and N is the number of volume elements. (For FEM, we need much more 3D volume elements than points in our construction because we have to sample also the volume surrounding the system. For BEM, we need to sample all the 2D surfaces, also the uninteresting ones. Thus, for a small region of interest, N ≫ M ≫ n.) The developed algorithm is very simple compared to those for BEM or FEM as it does not require any tessellation. Also, because in our model the computation for the field in a point does not depend on the field in the other points, the algorithm is embarrassingly parallel, i.e., trivial to parallelize with minimal overhead.

Feedback reciprocity mechanism promotes the cooperation of highly clustered scale-free networks

We study how the clustering coefficient influences the evolution of cooperation in scale-free public goods games. In games played by groups of individuals, triangle loops provide stronger support for mutual cooperation to resist invasion of selfish behavior than that in the absence of such loops, so that diffusion of cooperative behavior is relatively promoted. The feedback reciprocity mechanism of triangle plays a key role in facilitating cooperation in high clustered networks.

Scalar and pseudoscalar meson pole terms in the hadronic light-by-light contributions to aμhad

Third QED order hadronic light-by-light (LBL) contributions a μ LBL( M) to the anomalous magnetic moment of the muon a μ had from the pole terms of scalar σ, a 0(980) and pseudoscalar π 0, η, η′ mesons ( M) in the framework of the linearized extended Nambu–Jona–Lasinio model are evaluated. The off-shell structure of the photon–photon–meson vertices is taken into account by means of constituent quark triangle loops. The mass of the quark is taken to be m u = m d = m q =(280±20) MeV. The unknown strong coupling constants of π 0, η, η′ and a 0 mesons with quarks are evaluated in a comparison of the corresponding theoretical two-photon widths calculated in the framework of our approach with experimental ones. The σ-meson coupling constant is taken to be equal to π 0-meson coupling constant as it follows from the linearized Nambu–Jona–Lasinio model Lagrangian. Then one obtains a μ LBL( π 0)=(81.83±16.50)×10 −11, a μ LBL( η)=(5.62±1.25)×10 −11, a μ LBL( η′)=(8.00±1.74)×10 −11, a μ LBL( σ)=(11.67±2.38)×10 −11 and a μ LBL( a 0)=(0.62±0.24)×10 −11. The total contribution of meson poles in LBL is a μ LBL( M)=(107.74±16.81)×10 −11.

Pseudo Goldstone boson effects intt¯productions at high energy hadron colliders and testing technicolor models

We study the top quark pair production process $pp(\overline{p})\ensuremath{\rightarrow}t\overline{t}$ in various kinds of technicolor (TC) models at the Fermilab Tevatron run II and the CERN LHC. The s-channel neutral pseudo Goldstone bosons (PGBs) contribute dominantly to the production amplitudes from their coupling to the gluons through the triangle loops of techniquarks and the top quark. Cross sections in different TC models with s-channel PGB contributions are calculated. It is shown that the PGB effects can be experimentally tested and different TC models under consideration can be distinguished at the LHC. Therefore, the $p\stackrel{\ensuremath{\rightarrow}}{p}t\overline{t}$ process at the LHC provides feasible tests of technicolor models.

COMPLEXITY OF HADRONIC AMPLITUDES VIA QUARK LOOPS

The structure of hadronic transition amplitudes h→h′+h″ via quark triangle loops is investigated in terms of hadron quark vertex functions [Formula: see text], using for illustration the case of the ρ→ππ transition. A Bethe-Salpeter model based on the Covariant-Instantaneity-Ansatz (CIA) for its kernel which provides an exact interconnection between the 3D and 4D forms the BS wave function, determines the structure [Formula: see text]. The nonlocality feature inherent in the vertex function causes the imaginary part of gρππ calculated from the loop integral to be generally different from its dispersion relation value which would be obtained from analyticity of gρππ in the ρ-mass. Pending a proper understanding of this nonlocality (associated with confining interactions) only the real part of gρππ is found unambiguous while the imaginary part is model-dependent.