Center-of-mass Frame Research Articles

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.

System of metrological assurance of traceability of measurements of mass geometry characteristics

A system of metrological support is proposed that allows testing for type approval, verification and calibration of stands for measuring mass, coordinates of mass center and moments of inertia. The mathematical model of a special standard has been developed. It is based on the analytical principles for the determination of the mass center coordinates and inertia moments of homogeneous bodies with a regular geometric shape. The standard consists of a set of modules and fasteners of a special shape. Each module is a reference measure of both mass, center of mass coordinates, and moments of inertia, and can be used either separately or in a set with other modules. A scheme for transferring units of values from state primary standards of mass and length to stands using special standards has been developed. A method for calibration of special standards has been developed. It includes indirect measurements of the coordinates of the center of mass and moments of inertia based on the results of direct measurements of the mass and geometric dimensions of the standard modules’ elements, as well as measurements of the form deviations and deviations of position of the standard modules’ surfaces and static balancing of the standard. Technical requirements for special standards have been developed to minimize methodological measurement uncertainties when reproducing units of values by the standard. A line of special standards was created, their certification and approval in Rosstandart was carried out. Stand verification methods using special standards have been developed and approved. The type approval of two stands was carried out using special standards. The decision to grant a patent for the invention “Method for determining the error of the stand for measuring the characteristics of the mass geometry of products and a device for its implementation” was received.

A Quantum Electromagnetic Theory of the Pions, Muons and Their Emitting Particles (I)

In direct accordance to the overall relevant experimental demonstrations, we represent the charged pion π- as a heavy electron h- in precessional-orbital (P-O) motion at essentially the light speed c about -orbit of a normal at quantised angle π − θ1/2 = − arccos to the z axis. h- is the level N = 1 oscillation of charge −e and its electromagnetic radiation originally generated in the weak potential field of another particle. The P-O kinetic energy current and two additional opposite ones created upon π- decay represent confined neutrinos . The muon µ- is a xy-projected h- in two superposing P-O motions along - orbits of normals at angles π − θ1/2, θ1/2 to z. The µ- (rest) mass is a geometric projection of the reduced π- mass, . The µ- mass is fundamentally predetermined by the mixed two states ml = −1, +1 of level n = 2 of a double heavy positronium in the CM frame produced in a relativistic e-, e+ collision, and is ab initio predicted to be , where . The un-projected n = 2 level gives the bound π- mass containing a friction term . Their antiparticles π+, µ+ and the tauons τ∓ can be similarly represented. The remaining unstable elementary particles can be constructed as composites of two or more single charged ones in certain spatial quantised P-O motions.

Investigation of light ion fusion reactions with plasma discharges

The scaling of reaction yields in light ion fusion to low reaction energies is important for our understanding of stellar fuel chains and the development of future energy technologies. Experiments become progressively more challenging at lower reaction energies due to the exponential drop of fusion cross sections below the Coulomb barrier. We report on experiments where deuterium-deuterium (D-D) fusion reactions are studied in a pulsed plasma in the glow discharge regime using a benchtop apparatus. We model plasma conditions using particle-in-cell codes. Advantages of this approach are relatively high peak ion currents and current densities (0.1 to several A/cm2) that can be applied to metal wire cathodes for several days. We detect neutrons from D-D reactions with scintillator-based detectors. For palladium targets, we find neutron yields as a function of cathode voltage that are over 100 times higher than yields expected for bare nuclei fusion at ion energies below 2 keV (center of mass frame). A possible explanation is a correction to the ion energy due to an electron screening potential of 1000 ± 250 eV, which increases the probability for tunneling through the repulsive Coulomb barrier. Our compact, robust setup enables parametric studies of this effect at relatively low reaction energies.

Electron-proton interaction in radio sources

AbstractA method of treating electron-proton interaction is presented. The energies involved in the interaction are estimated. Only elastic collisions are considered. The cross sections of the processes are not taken into account. Calculations are carried out in the centre of mass frame. Relevant quantities are transformed into the laboratory frame. Results indicate that the energy per collision gained by an electron ranges from 0.5 MeV to 0.6 MeV, under suitable conditions.

Center of mass energy of colliding electrically neutral particles and super-Penrose process

We consider collisions of electrically neutral particles in the background of axially symmetric rotating space-times. For reactions of the kind 1+2$% \rightarrow $3+4 we give full classification of possible scenarios based on exact expressions for dynamic characteristics of particles 3 and 4 depending on particles 1 and 2. There are five nonequivalent scenarios valid for different types of space-time (black hole, naked singularity, etc.). We are mainly interested in the situations when particle collisions can give unbounded outcome for (i) the energy $E_{c.m.}$ in the center of mass frame and (ii) Killing energy $E$ at infinity. If (i) is fulfilled, this may or may not lead to (ii). If (ii) holds, this is called the super-Penrose process (SPP). For equatorial particle motion, we establish close relation between the type of behavior of $E_{c.m.}$ depending on the lapse function $% N $ in the point of collision and the possibility of the SPP. This unites separate previous observations in literature in a unified picture as a whole. In doing so, no explicit transformations to the center of mass frame and back are needed, so all consideration is carried out in the original frame. As a result,we suggest classification of sub-classes of scenarios that are able (or unable) to give rise to the SPP particle collision, super-Penrose process, center of mass frame.

Observed geocenter motion from precise orbit determination of GRACE satellites using GPS tracking and accelerometer data

We present a method to estimate geocenter motion through single low-earth orbiter (LEO) precise orbit determination (POD) using global positioning system (GPS) tracking data and accelerometer data from the GRACE satellites. We fix the values of the GPS ephemerides and time-varying clock offsets to precise estimates from the definitive constellation product produced by the Jet Propulsion Laboratory. As part of the POD process of the LEOs, we estimate a translation of the reference coordinate system realized by the GPS orbit and clock product. Doing so accounts for the inconsistency between the Earth’s center of mass coordinate system used for the orbit integration of the LEOs, and the terrestrial reference frame produced by the GPS orbit and clock product. The resulting translation parameters estimated separately from the GRACE-A and GRACE-B satellites show very similar variations from day to day. They represent the geocenter motion, as realized from the difference between the origin of the terrestrial reference frame represented by the GPS orbit and clock product and the Earth’s instantaneous center of mass defined by the GRACE satellite dynamical orbital motion. Comparisons with geocenter motion observations from other techniques show that our daily estimates of geocenter motion agree well, when smoothed, in both the amplitude and phase of the annual signal. This validates both the high sensitivity of the GRACE GPS measurement type to geocenter motion and the high precision of the GRACE force model enabled by accelerometer measurements, the two essential components for estimation of geocenter motion with this technique.

Spin-orbit effects in the 8Li+58Ni elastic scattering

In this work we present an elastic scattering angular distribution for the 8Li+58Ni system measured at Elab = 26.1 MeV. The 8Li beam was produced in the Radioactive Ion Beams in Brasil (RIBRAS) facility using the 7Li primary beam delivered by the 8-UD Pelletron accelerator. The angular distribution covers the angular range from 20 to 85 degrees in the center of mass frame. The data have been analysed by optical model and coupled channels calculations, including couplings to low-lying states in 8Li and the spin-orbit interaction. Our results indicate that the inclusion of the spin-orbit interaction in the calculations is important to describe the data at backward angles.

What do the highest-energy cosmic-ray data suggest about possible new physics around 50 TeV?

The latest observations of extensive air showers (EAS) induced by ultra-high-energy cosmic rays (UHECR) appear to indicate, prima facie, a transition to heavy primaries at the highest energies. However, this interpretation, which is based on extrapolations of the Standard Model (SM) to ultra-LHC energies, is strained from both astrophysical and particle phenomenology perspectives. We consider the alternative that after some energy threshold, the first collision of the primary in the atmosphere results in a state, the decay of which leads to a considerably increased shower particle multiplicity, so that light-primary EAS appear heavy-like. We show that a minimal implementation of such a model yields predictions for the average EAS depth and shower-to-shower fluctuations that are consistent with each other, and an excellent fit to Auger data. If such an effect indeed takes place, we predict that: (a) the center-of-momentum (CM) energy threshold for the effect is of order 50 TeV; (b) the probability with which the effect occurs is high, and it will be detected easily by next-generation accelerators; (c) the increase in multiplicity compared to the SM prediction grows with CM energy roughly as $\sim E_{\rm CM}$; (d) the cosmic-ray composition at the highest energies is light. Remarkably, if the latter is confirmed electromagnetically this would necessitate the existence of new physics by these energies.

Exact solution of an exciton energy for a monolayer medium

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2 + 1 space-time dimensions. The 2 × 2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2 × 2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.

Production cross-section of heavy flavored hadrons in pp collision at s = 7 TeV

The transverse momentum distribution of the differential production cross-sections of heavy flavored charm hadrons [Formula: see text], [Formula: see text] in pp collisions at 7 TeV are simulated. Predictions of DPMJETIII.17-1, HIJING1.383 and Sibyll2.3c are compared to the differential cross-section measurements of the LHCb experimental data presented in the region of [Formula: see text] and [Formula: see text], where the pp center of mass frame is used to measure the transverse momentum and rapidity. The models reproduce only some regions of [Formula: see text] and/or bins of [Formula: see text] but none of them predict completely all the [Formula: see text] bins over the entire [Formula: see text] range.

Rare fluctuations of the S matrix at NLO in QCD

We calculate the rare fluctuations of the $S$-matrix on top of the full next-to-leading order corrections in the center of mass frame. The relevant result in the saturation regime shows that the exponential factor of the $S$-matrix is $\sqrt{2}$ as large as the result which emerges when the rare fluctuation effects are taken into account. We find that the factor of $\sqrt{2}$ change of the exponential factor is induced by the gluon loop corrections which compensate part of rapidity decrease of the $S$-matrix made by quark loops and lead to the rare fluctuations becoming important again. To ensure the relevant results of the $S$-matrix are independent of the frame choice, the rare fluctuations of the $S$-matrix are also derived in a general frame. It is found that all the results are consistent with each other in both frames.

Distinguishing positions and movements in bed from load cell signals

Objective: To characterize and classify six positions and movements for individuals in a bed using the output signals of four load cell sensors. Approach: A bed equipped with four load cell sensors and synchronized video was used to assess the load cell response of 54 healthy individuals in prescribed positions and as they moved between positions. Stationary positions were characterized by the signals from the four load cells and the coordinates of the center of mass (CoM). Movements were characterized by the changes in load cell signals, four parameters associated with the trajectory of the CoM between the initial and final position (Euclidean distance, length of the trajectory, and the x- and y- variances), and the initial position’s CoM coordinates. Classification and decision tree models were used to assess the ability of these parameters to identify specific positions or movements. Main results: Six positions were classified with an accuracy of 74.9% and six movements were classified with an accuracy of 79.7%. Significance: This study demonstrates the feasibility of distinguishing certain positions and movements with load cell sensors. The identification of positions and movements for individuals in bed can be used as a tool in a variety of clinical settings.

Gravitational effects of disformal couplings

We consider how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of gravitationally interacting bodies. We focus on the case of two interacting objects and we obtain the effective metric driving the dynamics of the two body system when reduced to one body in the centre of mass frame. We then concentrate on the case of a light particle in the scalar and gravitational fields generated by a heavy object and find the effects of the conformal and disformal couplings on the body's trajectory such as the advance of perihelion and the Shapiro time delay. The disformal coupling leads to a negligible contribution to the Shapiro effect and therefore no constraint from the Cassini experiment. On the other hand, it contributes to the perihelion advance leading to a weak bound on the strength of the disformal coupling itself. Finally, we remark that the disformal coupling gives rise to a contribution to the perihelion advance which varies quadratically with the mass of the heavy body, leading to possible strong effects for stars in the vicinity of astrophysical black holes. For neutron stars in a binary system, the disformal effects vary as the quartic power of the size of the orbit which might lead to interesting consequences in the inspiralling phase prior to a merger.

Inclusive electron-nucleus cross section within the self-consistent Green's function approach

We compute inclusive electron-nucleus cross sections using ab initio spectral functions of $^4$He and $^{16}$O obtained within the Self Consistent Green's Function approach. The formalism adopted is based on the factorization of the spectral function and the nuclear transition matrix elements. This allows to provide an accurate description of nuclear dynamics and to account for relativistic effects in the interaction vertex. Our calculations use a saturating chiral Hamiltonian in order reproduce the correct nuclear sizes. When final state interactions for the struck particle are accounted for, we find nice agreement between the data and the theory for the inclusive electron-$^{16}$O cross section. The results lay the foundations for future applications of the Self Consistent Green's Function method, in both closed and open shell nuclei, to neutrino data analysis. This work also presents results for the point-proton, charge and single-nucleon momentum distribution of the same two nuclei. The center of mass can affect these quantities for light nuclei and cannot be separated cleanly in most ab initio post-Hartree-Fock methods. In order to address this, we developed a Metropolis Monte Carlo calculation in which the center of mass coordinate can be subtracted exactly from the trial wave function and the expectation values. We gauged this effect for $^4$He by removing the center of mass effect from the Optimal Reference State wave function that is generated during the Self Consistent Green's Function calculations. Our findings clearly indicate that the residual center of mass contribution strongly modifies calculated matter distributions with respect to those obtained in the intrinsic frame. Hence, its subtraction is crucial for a correct description of light nuclei.

I=0 ππ s -wave scattering length from lattice QCD

We deliver lattice results for the $I=0$ $\pi\pi$ elastic $s$-wave scattering length calculated with the MILC $N_f=3$ flavors of the Asqtad-improved staggered fermions. The scattering phase shifts are determined by L\"uscher's formula from the energy-eigenvalues of $\pi\pi$ systems at one center of mass frame and four moving frames using the moving wall source technique. Our measurements are good enough to resolve the scattering length $a$ and effective range $r$, moreover, it allows us to roughly estimate the shape parameter $P$. Using our lattice results, the scattering length $a$ and effective range $r$ at the physical point are extrapolated by chiral perturbation theory. Our results are reasonably consistent with the Roy equation determinations and the newer experimental data. Numerical computations are carried out with two MILC fine ($a\approx0.09$~fm, $L^3 \times T = 40^3\times 96$) and one MILC superfine ($a\approx0.06$~fm, $L^3 \times T = 48^3\times 144$) lattice ensembles at three pion masses of $m_\pi\sim247~{\rm MeV}$, $249~{\rm MeV}$, and $314~{\rm MeV}$, respectively.

Soft gluon evolution and non-global logarithms

We consider soft-gluon evolution at the amplitude level. Our evolution algorithm applies to generic hard-scattering processes involving any number of coloured partons and we present a reformulation of the algorithm in such a way as to make the cancellation of infrared divergences explicit. We also emphasise the special role played by a Lorentz-invariant evolution variable, which coincides with the transverse momentum of the latest emission in a suitably defined dipole zero-momentum frame. Handling large colour matrices presents the most significant challenge to numerical implementations and we present a means to expand systematically about the leading colour approximation. Specifically, we present a systematic procedure to calculate the resulting colour traces, which is based on the colour flow basis. Identifying the leading contribution leads us to re-derive the Banfi-Marchesini-Smye equation. However, our formalism is more general and can systematically perform resummation of contributions enhanced by the t’Hooft coupling αsN ∼ 1, along with successive perturbations that are parametrically suppressed by powers of 1/N . We also discuss how our approach relates to earlier work.

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes

The relations between the baryon-baryon elastic scattering phase shifts and the two-particle energy spectrum in the elongated box are established. We studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. Moreover, we discussed the sensitivity functions σ(q) that represent the sensitivity of higher scattering phases. Our analytical results will be helpful to extract the baryon-baryon elastic scattering phase shifts in the continuum from lattice QCD data by using elongated boxes.

Collisional Penrose process with spinning particles

In this article, we have investigated collisional Penrose process (CPP) using spinning particles in a Kerr spacetime. Recent studies have shown that the collision between two spinning particles can produce a significantly high energy in the center of mass frame. Here, we explicitly compute the energy extraction and efficiency as measured by an observer at infinity. We consider the colliding particles as well as the escaping particles may contain spins. It has been shown that the energy extraction is larger than the non-spinning case and also their possibility to escape to infinity is wider than the geodesics.

On White Holes as Particle Accelerator

We analyze scenarios of particle collisions in the metric of a nonextremal black hole that can potentially lead to ultrahigh energy $E_{c.m.}$ in their centre of mass frame. Particle 1 comes from infinity to the black hole horizon while particle 2 emerges from a white hole region. It is shown that unbounded $E_{c.m.}$ $\ $require that particle 2 pass close to the bifurcation point. The analogy with collisions inside the horizon is discussed.