Center-of-mass Frame Research Articles

Displaced Higgs production in Type-III seesaw at the LHC/FCC, MATHUSLA and muon collider

In this article, we explore the possibility of displaced Higgs production from the decays of the heavy fermions in the Type-III seesaw extension of the Standard Model at the LHC/FCC and the muon collider. The displaced heavy fermions and the Higgs boson can be traced back by measuring the displaced charged tracks of the charged leptons along with the b-jets. A very small Yukawa coupling can lead to two successive displaced decays which makes the phenomenology even more interesting. The prospects of the transverse and longitudinal displaced decay lengths are extensively studied in the context of the boost at the LHC/FCC. Due to the parton distribution function, the longitudinal boosts leads to larger displacement compared to the transverse one, which can reach MATHUSLA and beyond. The longitudinal measurements are indeed possible by the visible part of the finalstate, which captures the complete information about the longitudinal momenta. The comparative studies are made at the LHC/FCC with the centre of mass energies of 14, 27 and 100 TeV, respectively. A futuristic study of the muon collider where the collision happen in the centre of mass frame is analysed for centre of mass energies of 3.5, 14 and 30 TeV. Contrary to LHC/FCC, here the transverse momentum diverges, however, the maximum reach in both the direction are identical due to the constant total momentum in each collision. The reach of the Yukawa couplings and fermion masses are appraised for both the colliders. FCC at 100 TeV can probe a mass of 4.25 TeV and a lowest Yukawa coupling of {mathcal {O}}(5 times 10^{-11}).

Collision Analysis of Solid Spheres in Laboratory Coordinate System and Center of mass Coordinate System

Collision Analysis of Solid Spheres in Laboratory Coordinate System and Center of mass Coordinate System

Noether symmetry in Newtonian dynamics and cosmology

A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the gravitational potential \(\phi \) which can be used to cancel the gravitational field induced by going to the accelerated from, the combination of these two operations produces then a symmetry. This symmetry leads then to a Noether current which is conserved. The conserved charges are analyzed in special cases. The charges may not be conserved if the Noether current produces flux at infinity, but such flux can be eliminated by going to the CM (center of mass) system in the case of an isolated system. In the CM frame the Noether charge vanishes, Then we study connection between the Cosmological Principle and the Newtonian Dynamics which was formulated via a symmetry (Benisty and Guendelman in Mod Phys Lett A 35:2050131, 2020) of this type, but without an action formulation. Homogeneous behavior for the coordinate system relevant to cosmology leads to a zero Noether current and the requirement of the Newtonian potential to be invariant under the symmetry in this case yields the Friedmann equations, which appear as a consistency condition for the symmetry.

Formula omitted]-boson production via the weak process [formula omitted] in the presence of a circularly polarized laser field

In the centre of mass frame, we have studied theoretically the Z-boson resonant production in the presence of an intense laser field via the weak process e+e−→μ+μ−. Dressing the incident particles by a Circularly Polarized laser field (CP-laser field), at the first step, shows that for a given laser field’s parameters, the Z-boson cross section decreases by several orders of magnitude. We have compared the Total Cross Section (TCS) obtained by using the scattering matrix method with that given by the Breit-Wigner approach in the presence of a CP-laser field and the results are found to be very consistent. This result indicates that Breit-Wigner formula is valid not only for the laser-free process but also in the presence of a CP-laser field. The dependence of the laser-assisted differential cross section on the Centre of Mass Energy (CME) for different scattering angles proves that it reaches its maximum for small and high scattering angles. At the next step and by dressing both incident and scattered particles, we have shown that the CP-laser field largely affects the TCS, especially when its strength reaches 109Vcm−1. This result is interpreted by the fact that heavy interacting particles require high laser field intensities to affect the collision’s cross section.

Technics for experimental determination of CubeSat mass-centering and inertial characteristics

Due to inability to set a high accuracy of initial data in theoretical calculations of mass-centering and inertial characteristics of nanosatellites, a problem arises concerning the experimental determination of their actual values. For a number of reasons, the devices designed for large spacecraft are not appropriate for small ones. This paper describes a device for measuring the center of mass coordinates and moments of inertia developed at Samara University specifically for CubeSat nanosatellites, as well as a technology for experimental determination of the design parameters of nanoclass spacecraft. The accuracy of determining the design parameters using the proposed device is confirmed by a series of experiments with standards. Key words: nanosatellite, center of mass coordinates, moment of inertia, inertia tensor, measuring platform.

Laser-assisted neutral Higgs-boson pair production in Inert Higgs Doublet Model (IHDM)

In the framework of the Inert Higgs Doublet model (IHDM), we have investigated, in the centre of mass frame, the neutral Higgs-boson pair production in the presence of an intense and circularly polarized laser field via e+e− annihilation (e+e−→H0A0) at the lowest order. By using the scattering matrix method, we have derived the analytical expression of the differential cross section. The latter is numerically integrated over the solid angle to obtain the total cross section. Then, we have shown how this total cross section depends on the outgoing particles mass for different number of exchanged photons. Next, we have illustrated its variation as a function of the centre of mass energy for different neutral Higgs-boson masses. Finally, we have indicated how it changes as a function of the laser field amplitudes for both different number of exchanged photons and different neutral Higgs-bosons masses.

Higgs-strahlung boson production in the presence of a circularly polarized laser field

In the framework of the electroweak standard model, we investigated, in the center of mass frame, the Higgs boson production in the presence of an intense laser field via annihilation . By comparing our results with those obtained by Djouadi (2008 Phys. Rept. 457 1) for laser-free process, we show that the circularly polarized laser field affects significantly the s-channel Higgs boson production. We find that for a given number of exchanged photons, laser field strength and frequency, the total cross section decreases by several orders of magnitude. These effects of laser field on cross section are found to be consistent with what was found for muon pair production via QED process in the presence of a circularly polarized laser field (Müller et al 2006 Phys. Rev. D 74 074017).

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

Polarization effects in the search for a dark vector boson at e+e− colliders

We argue that the search for dark vector boson through $e^+e^-\to Z_d\gamma$ can determine the Lorentz structure of $Z_dl^+l^-$ couplings with the detection of leptonic decays $Z_d\to l^+l^-$. We assume a general framework that the dark vector boson interacts with ordinary fermions through vector and axial-vector couplings. As a consequence of Ward-Takahashi identity, $Z_d$ is transversely polarized in the limit $m_{Z_d}\ll \sqrt{s}$. On the other hand, the fraction of longitudinal $Z_d$ is non-negligible for $m_{Z_d}$ comparable to $\sqrt{s}$. Such polarization effects can be analyzed through angular distributions of final-state particles in $Z_d$ decays. Taking $l^{\pm}\equiv \mu^{\pm}$, we study the correlation between $Z_d$ angle relative to $e^-$ beam direction in $e^+e^-$ CM frame and $\mu^-$ angle relative to the boost direction of $Z_d$ in $Z_d$ rest frame. This correlation is shown to be useful for probing the Lorentz structure of $Z_dl^+l^-$ couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.

Dynamics of two particles on a vertically driven plate

We experimentally investigate the dynamics of two particles driven vertically and free to collide in a nearly one-dimensional channel. Both spherical particles are Delrin with a diameter of d = 5.0 mm. We obtained data for driving frequencies, f, ranging from 26.06 to 29.52 HZ and acceleration magnitudes, Γ, from 1.79 to 2.42 g. High speed digital imaging is used to extract the positions of the two particles from experiment, with digital imaging analysis used to extract velocities and accelerations from sequential images. The total energy and the velocity of the particles before and after collisions are studied in both the lab frame and centre of mass frame. Most of the experimental results suggest a linear dependence for the relative velocity after collision on the relative velocity before collision with the coefficient of restitution approximately constant at 0.8. However, some data in the low impact velocity regime indicates the possibility of an occasional energy transfer between the rotational and translational degrees of freedom.

Model Predictive Control With Environment Adaptation for Legged Locomotion

Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improves adaptation to the terrain features. Our NMPC is based on the real-time iteration scheme that allows us to re-plan online at $25\,\mathrm{Hz}$ with a prediction horizon of $2$ seconds. We use the single rigid body dynamic model defined in the center of mass frame in order to increase the computational efficiency. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, to walk into a V-shaped chimney,and to locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT's $87\, \mathrm{kg}$ quadruped robot HyQ to achieve an omni-directional walk on flat terrain, to traverse a static pallet, and to adapt to a repositioned pallet during a walk.

Root Mean Square Radius of 6Li Nucleus using Cluster Model Wavefunction

The calculation of root mean square nuclear charge radius is one of the most important nuclear parameters regarding the size and structure of the nucleus. In this paper calculations for root mean square (r.m.s.) radius of the ground state of 6Li nucleus using high energy electron scattering is presented. The initial work involves writing first the cluster model wavefunction employing the resonating group method, generator coordinate method and complex generator coordinate technique. The wavefunction is written with definite parity, spin, total angular momentum and relative motion between the alpha cluster and deuteron cluster and the center-of-mass of the two clusters. The application of complex generator coordinate technique transforms the cluster model wavefunction into antisymmetrized products of single particle wavefunction written in terms of single particle co-ordinates, the centerof-mass coordinates, parameter coordinates and generator coordinates. The width parameters of alpha and deuteron clusters are adjusted to obtain predictions close to experimental values.

Nonoverlap proportion and the representation of point-biserial variation.

We consider the problem of constructing a complete set of parameters that account for all of the degrees of freedom for point-biserial variation. We devise an algorithm where sort as an intrinsic property of both numbers and labels, is used to generate the parameters. Algebraically, point-biserial variation is represented by a Cartesian product of statistical parameters for two sets of [Formula: see text] data, and the difference between mean values (δ) corresponds to the representation of variation in the center of mass coordinates, (δ, μ). The existence of alternative effect size measures is explained by the fact that mathematical considerations alone do not specify a preferred coordinate system for the representation of point-biserial variation. We develop a novel algorithm for estimating the nonoverlap proportion (ρpb) of two sets of [Formula: see text] data. ρpb is obtained by sorting the labeled [Formula: see text] data and analyzing the induced order in the categorical data using a diagonally symmetric 2 × 2 contingency table. We examine the correspondence between ρpb and point-biserial correlation (rpb) for uniform and normal distributions. We identify the [Formula: see text], [Formula: see text], and [Formula: see text] representations for Pearson product-moment correlation, Cohen's d, and rpb. We compare the performance of rpb versus ρpb and the sample size proportion corrected correlation (rpbd), confirm that invariance with respect to the sample size proportion is important in the formulation of the effect size, and give an example where three parameters (rpbd, μ, ρpb) are needed to distinguish different forms of point-biserial variation in CART regression tree analysis. We discuss the importance of providing an assessment of cost-benefit trade-offs between relevant system parameters because 'substantive significance' is specified by mapping functional or engineering requirements into the effect size coordinates. Distributions and confidence intervals for the statistical parameters are obtained using Monte Carlo methods.

Analysis of analytical and numerical dynamic lunar ephemerides

This work considers the analysis of libration dynamics of the planets’ moons. To study such processes, it is necessary to use methods for investigating complex systems, as an influence from neighboring celestial bodies on spin-orbital motion of a moon should be taken into account. This fully applies to the Moon’s rotation about its axis. The construction of modern theories of the physical libration of the Moon (PhLM) is based on gravimetric, seismic, satellite observations, and lunar laser ranging, which in its turn has allowed to increase the accuracy by several orders of magnitude compared to the PhLM theories of the end of the 20th century. To satisfy the modern requirements for accuracy of the physical libration theory, it is necessary to apply a precise ephemeris of the Moon’s motion. In this paper, the DE421 modern numerical ephemeris is analyzed. The features of its construction and practical application are studied. The accurate values of ephemeris parameters are produced and an algorithm for determining the Moon’s center of mass coordinates and establishing the angles of physical libration on the basis of DE421 is developed. As a result, a comparative analysis of the physical libration angles with the values produced by the analytic theory of physical libration is conducted. The calculations are made over a time period of 800 years. The comparative analysis shows that significant differences in the ephemerides of 15 and 80 arc seconds in longitude and latitude respectively are caused by the planets’ gravity field, and those impacts should be considered when working with the analytic ephemeris.

Special case of the Bañados-Silk-West effect

If two particles collide near the rotating extremal black hole and one of them is fine-tuned, the energy in the center of mass frame $E_{c.m.}$ can grow unbounded. This is the so-called Ba\~{n}ados-Silk-West (BSW) effect. Recently, another type of high energy collisions was considered in which all processes happen in the Schwarzschild background with free falling particles. If the Killing energy $E$ of one of particle is sufficiently small, $E_{c.m.}$ grows unbounded. We show that, however, such a particle cannot be created in any precedent collision with finite energies, angular momenta and masses. Therefore, in contrast to the standard BSW effect, this one cannot be realized if initial particles fall from infinity. If the black hole is electrically charged, such a type of collisions is indeed possible, when a particle with very small $E$ collides with one more particle coming from infinity. Thus the BSW effect is achieved due to collisions of neutral particles in the background of a charged black hole. This requires, however, at least two-step process.

Extremal Kerr white holes as a source of ultrahigh energy particles

We consider a process where two identical massive particles fall inwards, starting from rest at infinity towards the extremal Kerr black hole, collide outside the event horizon in its vicinity and produce two massless particles. The center of mass energy of collision between the two particles diverges if one of the particle admits a specific critical value of the angular momentum and if the collision takes place at a location arbitrarily close to the event horizon. Assuming the isotropic emission of particles in the center of mass frame we show that one of the massless particles produced has divergent conserved energy comparable to the center of mass energy with probability slightly less than half. This particle enters the black hole event horizon which coincides with the Cauchy horizon, turns back, and emerges through the white hole event horizon into another asymptotic region in the maximal extension of Kerr spacetime. Since conserved energy is preserved in this process, it is perceived as a particle with divergent energy by the observer when it reaches infinity. Thus the extremal white hole appears to be a source of ultra high energy particles. Similar processes wherein collision takes place slightly inside the black hole event horizon or just outside or inside of white hole event horizon also produce high energy particles.

The production of the doubly charmed baryon in deeply inelastic ep scattering at the Large Hadron Electron Collider

In this paper, we carry out a detailed study on the production of the doubly charmed baryon in deeply inelastic ep scattering (DIS) for Q2 ∈ [2, 100] GeV2, at the Large Hadron Electron Collider (LHeC) with Ee = 60(140) GeV and Ep = 7000 GeV. To exclude the contributions from the diffractive productions and the b hadron decays, we impose the kinematic cuts 0.3 < z < 0.9, and {p}_{t,mathrm{baryon}}^{star 2} > 1 GeV2 in the center-of-mass (CM) frame of γ∗p. Based on the designed LHeC luminosity, by detecting the decay channel {Xi}_{cc}^{+}left({Xi}_{cc}^{++}right)to {Lambda}_c^{+} with the subsequent decay {Lambda}_c^{+}to {pK}^{-}{pi}^{+} , we predict that about 1880 (2700) {Xi}_{cc}^{+} events and 3750 (5400) {Xi}_{cc}^{++} events can be accumulated per year, which signifies the prospect of observing them via the DIS at the forthcoming LHeC. In addition, we also predict the distributions of a rich variety of physical observables in the laboratory frame and the γ∗p CM frame, including Q2, {p}_t^2 , Y (rapidity), {p}_t^{star 2},{Y}^{star } , W, and z distributions, respectively, which can provide helpful references for studying the doubly charmed baryon. In conclusion, we think that in addition to the LHC, the LHeC is also a helpful platform for studying the properties of the doubly charmed baryon.

High-energy asymptotic behavior of the S matrix in the saturation region with the smallest dipole running coupling prescription

We present results from analytic solutions to the running coupling, full next-to-leading order, and collinearly improved next-to-leading order Balitsky-Kovchegov equations in the saturation region with the smallest dipole size QCD running coupling prescription. The analytic results of the $S$-matrix of the latter two equations show that the $\exp(-\mathcal{O}(Y^{3/2}))$ rapidity dependence of the solutions are replaced by $\exp(-\mathcal{O}(Y))$ dependence once the running coupling prescription is switched from parent dipole to the smallest dipole prescription, which indicate that the $S$-matrix has a strong dependence on the choice of running coupling prescription. We compute the numerical solutions of these Balitsky-Kovchegov equations with the smallest and parent dipole running coupling prescriptions, the numerical results confirm the analytic outcomes. The rare fluctuations of the $S$-matrix on top of next-to-leading order corrections are also studied under the smallest dipole running coupling prescription in the center of mass frame. It shows that the rare fluctuations are strongly suppressed and less important in the smallest dipole running coupling prescription case as compared to the parent dipole running coupling prescription case.

Ergodicity, mixing, and recurrence in the three rotor problem.

In the classical three rotor problem, three equal point masses move on a circle subject to attractive cosine potentials of strength g. In the center of mass frame, energy E is the only known conserved quantity. In earlier works [Krishnaswami and Senapati, Indian Acad. Sci. Conf. Ser. 2(1), 139 (2019), and Chaos 29(12), 123121 (2019)], an order-chaos-order transition was discovered in this system along with a band of global chaos for 5.33g≤E≤5.6g. Here, we provide numerical evidence for ergodicity and mixing in this band. The distributions of relative angles and angular momenta along generic trajectories are shown to approach the corresponding distributions over constant energy hypersurfaces (weighted by the Liouville measure) as a power-law in time. Moreover, trajectories emanating from a small volume are shown to become uniformly distributed over constant energy hypersurfaces, indicating that the dynamics is mixing. Outside this band, ergodicity and mixing fail, though the distributions of angular momenta over constant energy hypersurfaces show interesting phase transitions from Wignerian to bimodal with increasing energy. Finally, in the band of global chaos, the distribution of recurrence times to finite size cells is found to follow an exponential law with the mean recurrence time satisfying a scaling law involving an exponent consistent with global chaos and ergodicity.

Super-Penrose process

If two particles collide near a rotating black hole, their energy in the centre of mass frame can become unbounded under certain conditions. In doing so, the Killing energy [Formula: see text] of debris at infinity is, in general, remain restricted. If [Formula: see text] is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. We also discuss the case of a pure electric super-Penrose process that is valid even in the flat space-time. The key role in consideration is played by the Wald inequalities.