Momentum Spectra Research Articles

Analysis of charged hadrons’ transverse momentum distributions in p + Pb and Xe + Xe collisions at LHC energies

This paper is focused on comparative analysis of transverse momentum ( pT ) distributions across two different sets of experimental data from ALICE at the LHC, juxtaposing with the Monte-Carlo models EPOS-LHC and EPOS 1.99 simulations. The chosen collision sets have approximately same per nucleon energy. We analyze the transverse momentum spectra of hadrons ( π++π−, K++K− and p+p¯ ) in p+Pb collisions at sNN= 5.02 TeV, and Xe + Xe collisions at sNN= 5.44 TeV spanning a rapidity range of 0 < yCM < 0.5, centrality of 0 to 5% (the most central or head-on collisions). Analysis of the Hadrons yield is crucial for understanding the mechanism of underlying hadronization in the hot and dense quark matter produced in relativistic heavy ion collisions. The experimental results are compared with the predictions of hydrodynamic models EPOS-LHC and EPOS-1.99. It is notably found that the maximum yields of various particles occur at low pT. Furthermore, the comparison showed a slightly better agreement between experimental results and the predictions of the EPOS-LHC as opposed to that of EPOS-1.99. The EPOS-LHC model significantly shows an enhanced agreement with experimental results in the case of Xe+Xe collisions as compared to p+Pb collisions.

Characterization of relativistic electron bunch duration and traveling wave structure phase velocity based on momentum spectra measurements

Characterization of relativistic electron bunch duration and traveling wave structure phase velocity based on momentum spectra measurements

Exploring anisotropic flow via the Boltzmann transport equation employing the Tsallis blast wave description at LHC energies

Anisotropic flows i.e. azimuthal anisotropies in the particle production are one of the important probes in characterizing the properties of the strongly interacting matter created in the relativistic heavy-ion collisions. These observables are sensitive to both the transport properties as well as the equation of state of the quantum chromodynamics matter. We have adopted the Boltzmann transport equation (BTE) in the relaxation time approximation to describe the experimental data for harmonic flows such as elliptic flow (v 2), triangular flow (v 3), quadrangular flow (v 4) obtained in heavy-ion collisions at large hadron collider (LHC) energies. In this analysis, we have used Tsallis statistics as an initial distribution and the Tsallis blast wave description is used as the equilibrium distribution function while describing the evolution of the particle production in BTE. We have fitted the transverse momentum spectra, v 2, v 3, and v 4 of identified hadrons such as pion, kaon, and proton for Pb–Pb and Xe–Xe collisions at the LHC energies of sNN = 5.02 TeV and sNN = 5.44 TeV, respectively for various centralities. Our study offers the comparative analysis between the two distinct collision systems operating at comparable collision energies. The present formulation successfully fits the experimental data for p T - spectra upto p T = 8 GeV and effectively explains the anisotropic flows data upto p T = 10 GeV with a very favourable χ 2/ndf. We observe that the average transverse flow velocity (〈β〉) and the kinetic freeze-out temperature (T) extracted in our analysis decrease as we go towards the peripheral collisions. Non-extensive parameters (q AA and q pp ) exhibit an ascending trend from central to peripheral collisions, signifying an almost thermalized system in the most central collisions and a non-equilibrium state in peripheral ones. The azimuthal modulation amplitudes (ρ a ) for v 2, v 3, and v 4 exhibit an increasing pattern as one moves from the most central to peripheral collisions in both the Pb–Pb and Xe–Xe nuclei interactions.

Design of quantum backflow in the complex plane

Abstract A way is presented to design quantum wave functions that exhibit backflow, namely negative probability current despite having a strictly positive spectrum of momentum. These wave functions are derived from rational complex functions which are analytic in the upper half-plane and have zeros in the lower half-plane through which the backflowing behavior is controlled. In analogy, backflowing periodic wave functions are derived from rational complex functions which are analytic in the interior and have appropriately placed zeros or poles in the exterior of the unit circle. The concept is combined with a Padé-type procedure to design wave functions of this type that approximate a desired profile along the interval of backflow. It is finally shown that the time evolution of these wave packets is elegantly expressed in terms of the well-known Fresnel integrals.

Controlling the photoelectron holography with shaped intense ultrashort laser pulses

We perform a theoretical investigation on the control of photoelectron holography with shaped intense ultrashort laser pulses. By adjusting the π phase-flip position in the frequency domain, the shape of the time-dependent envelope of the input laser electric field changes from Gaussian to trapezoidal and finally to double-peak pulse. The photoelectron momentum spectra for different pulse shapes are calculated by both three-dimensional time-dependent Schrödinger equation (TDSE) method and Quantum-trajectory Monte Carlo (QTMC) model, and good agreement is achieved between results calculated by the two methods. Interference pattern in photoelectron holography exhibits a strong dependence on the shape of the electric field. Analysis shows that adjacent and nonadjacent intercycle interference as well as intracycle interference are all effectively regulated by the shaped pulse.

Momentum spectrum of Schwinger pair production in four-dimensional e-dipole fields

We calculate the momentum spectrum of electron-positron pairs created via the Schwinger mechanism by a class of four-dimensional electromagnetic fields called e-dipole fields. To the best of our knowledge, this is the first time the momentum spectrum has been calculated for 4D, exact solutions to Maxwell’s equations. Moreover, these solutions give fields that are optimally focused, and are hence particularly relevant for future experiments. To achieve this we have developed a worldline instanton formalism where we separate the process into a formation and an acceleration region. Published by the American Physical Society 2024

Breaking the symmetric spiral spectrum distribution of a Laguerre-Gaussian beam propagating in moderate-to-strong isotropic atmospheric turbulence.

We demonstrate that the spiral spectrum (also known as orbital angular momentum spectrum) of a Laguerre-Gaussian (LG) beam with topological charge (TC) l is asymmetrically broadened propagating through moderate-to-strong atmospheric turbulence, even the statistics of turbulence is isotropic. This phenomenon is quite different from that predicted in weak turbulence where the spiral spectrum of a disturbed LG beam is symmetric with respect to its TC number l. An explicit analytical expression of the spiral spectrum of the LG beam with l = 1 is derived based on the extend Huygens-Fresnel integral and quadratic approximation, which is used to illustrate the transition scenarios of the spiral spectrum from symmetry to asymmetry in weak-to-strong turbulence. The physical mechanism for the asymmetric spiral spectrum in moderate-to-strong turbulence is thoroughly discussed. Our results are confirmed by the multi-phase screen numerical simulations and are consistent with the experimental results reported in Phys. Rev. A105, 053513 (2022)10.1103/PhysRevA.105.053513 and Opt. Lett.38, 4062 (2013)10.1364/OL.38.004062.

Numerical modeling of time dependent Diffusive Shock Acceleration

Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use the stochastic differential equation solver (DiffusionSDE) of the cosmic ray propagation framework CRPropa3.2 with two modifications: An importance sampling module is introduced to improve statistics at high energies in order to keep the simulation time short. An adaptive time step is implemented in the DiffusionSDE module. This ensures to efficiently meet constraints on the time and diffusion step, which is crucial to obtain the correct shock spectra. The time evolution of the spectrum at a one-dimensional planar shock is verified against the solution obtained by the grid-based solver VLUGR3 for both energy-independent and energy-dependent diffusion. We show that the injection of pre-accelerated particles can lead to a broken power law spectrum in momentum if the incoming spectrum of CRs is harder than the re-accelerated spectrum. If the injected spectrum is steeper, the shock spectrum dominates at all energies. We finally apply the developed model to the GWTS by considering a spherically symmetric shock, a spiral Galactic magnetic field, and anisotropic diffusion. The time-dependent spectrum at the shock is modeled as a basis for further studies.

Effects of adiabatic focusing and free-escape boundaries in coronal shock acceleration

Solar energetic particles (SEPs) are considered a serious radiation threat to space technologies and humans in space. SEPs are accelerated to high energies by solar explosive phenomena such as solar flares and in particular by shocks driven by coronal mass ejections (CMEs). We aim to better understand the effects of magnetic field gradient-induced adiabatic focusing on the coronal acceleration of SEPs and to test whether free-escape boundaries produce the same effects as focusing. We present results from a one-dimensional oblique shock model with a mean free path similar to Bell’s (1978) theory using Monte Carlo simulations. We show that the momentum spectrum at a shock and far upstream will attain a steady state in a model with adiabatic focusing, whereas it does not in a non-focusing model. However, the effects of focusing can be mimicked in a non-focused simulation by introducing a free-escape boundary ahead of the shock close to the position where the particles will escape from the shock by focusing in a focused transport simulation. This provides a promising avenue for constructing computationally efficient codes that can model the particle emission from shocks.

Subcycle Conservation Law in Strong-Field Ionization

Exploiting the infinite-order continuous dynamical rotational symmetry of circularly or elliptically polarized classical light pulses, we establish the conservation law between the angular momentum and energy in strong-field ionization that is applicable at the subcycle level. We illustrate the conservation law through the correlated spectrum of angular momentum and energy of photoelectrons, both at the tunnel exit and in the asymptotic region. Moreover, we propose a protocol based on electron vortices to directly visualize the existence of the subcycle conservation law. Our work paves the pathway toward a deeper understanding of fundamental light–matter interactions on the subcycle scale.

Theoretical study of double oscillating fields induced electron-positron pairs creation process

&lt;sec&gt;We investigate an important aspect of electron-positron pair creation from vacuum in the presence of a strong background field, where the combined field plays a key role in the pair creation process. By utilizing computational quantum field theory, we explore electron-positron pair creation induced by double-located oscillating electric fields by numerically solving the Dirac equation in full spacetime dimensions. We demonstrate theoretically that computational quantum field theory is equivalent to the first-order time-dependent perturbation theory for single-photon transition pair creation in a spatially inhomogeneous and time-dependent electric field, and verify their equivalence through numerical simulations of pair creation in double-located oscillating fields. We show some interesting results about the periodic oscillation of the momentum spectrum structure of the created particle and the asymmetric multi-photon pair creation process due to the interference between two fields. By using first-order time-dependent perturbation theory, we find that the periodic oscillation in the momentum distribution of the created particle is affected by the field width, the field frequency and the distance between two fields. The period of the oscillation of momentum spectrum structure is changed by the distance between two fields, while the field width has an influence on both the difference between the peak and valley of the momentum spectra and the width of the momentum space available to the created particle. Increasing the frequency of the electric field results in larger momentum for the created particle pairs, while correspondingly reducing the coupling matrix element &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \langle p|V|n \rangle $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and diminishing the probability of electron-positron pair creation.&lt;/sec&gt;&lt;sec&gt;The interference between two fields significantly enhances the yield of pair numbers for small distances between two fields. When the distance is too large, the number of pairs created by double oscillating fields is twice that created by a single field, and the enhancement is vanished. When the distance between two fields increases, the period of oscillation decreases. In turn, the creation of electron-positron pairs can become more monochromatic in momentum (energy), while the number of pairs created remains almost constant. As the electric field broadens, the yield of the created pairs decreases for constant potential height. Increasing the field width will reduce the number of particles for each momentum and narrow the momentum space of the created particle. Increasing the field frequency leads to the reduction of the coupling matrix element &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ \langle p|V|n \rangle $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and subsequently reduces the total number of electron-positron pairs created. The field profile parameters such as frequency, width, and distance between two fields can be utilized to select a specific momentum (energy) of particles in future electron-positron pair creation experiments.&lt;/sec&gt;

Insight into the light-flavour particle production mechanism from studies of the transverse spherocity dependence in pp collisions at √s =13 TeV with ALICE at the LHC

The Large Hadron Collider (LHC) Run 1 and Run 2 data revealed heavy-ion-like features such as enhanced strangeness production and long-range azimuthal correlation in high-multiplicity pp collisions paving the way to rethink particle production in small collision systems. Event shape observables like transverse spherocity are sensitive to isotropic and jet-like topologies, which are useful tools to distinguish the pp collisions dominated by soft or hard physics. The interplay between multiplicity and transverse spherocity on light-flavour particle production can be understood by comparing the results obtained by selecting multiplicity and/or transverse spherocity. This contribution presents recent results on light-flavour particle production (π, K, p, ф, K*0, K0s, Λ, ξ) at midrapidity obtained by the ALICE experiment in pp collisions at √s = 13 TeV as a function of event multiplicities and transverse spherocity. The results are even obtained by going to the most extreme selections such as the highest 0–1% in multiplicity and the highest 0–10% in transverse sphe rocity. The results include the transverse momentum spectra, yields, 〈pT〉 and their ratios. These measurements will be compared with the Monte Carlo (MC) predictions obtained from models such as PYTHIA8, EPOS and Herwig7.

The Coulomb effect in nonsequential double ionization by counter-rotating two-color elliptical polarization fields.

Using a three-dimensional classical ensemble model, nonsequential double ionization (NSDI) of Ar atoms by counter-rotating two-color elliptical polarization (TCEP) fields is investigated. The major axes of the two elliptical fields are aligned in different directions. The relative alignment of the two elliptical fields strongly affects the waveform of the combined electric field and the ultrafast dynamics of NSDI in TCEP fields. Numerical results show that the correlated electron momentum distributions in the x direction evolve from a V-shaped structure near the axis to a distribution concentrated on the diagonal with the angle between the two elliptical major axes increasing. The asymmetry of the energy sharing between the two electrons during recollision results in the V-shaped structure in the correlated momentum spectrum. Back analysis indicates that the recollision times of a part of the trajectories move from the peak to the valley of the combined electric field with the angle between the two elliptical major axes increasing. Therefore, for the case of a larger angle between the two elliptical major axes, the electrons experience a longer time to escape away from the vicinity of the parent ion and thus the stronger Coulomb effect from the parent ion makes the momentum difference between two electrons small, which results in a distribution concentrated on the diagonal. This provides an effective avenue to control the electron ultrafast dynamics in NSDI.

Time-resolved subcycle and intercycle interference influenced momentum shift in nonadiabatic tunnelling ionization

Momentum shift is an important sign of nonadiabatic tunnelling ionization process. To investigate the mechanism of momentum shift, we use the strong-field approximation theory to track the formation of ionization momentum spectra of hydrogen atom under the action of different laser pulses in the time domain. By observing the ionization momentum spectra of different structures over time, we find that the momentum shift is formed by the continuous interference and evolution of ionization signals. Meanwhile, we further analyze how subcycle and intercycle interference influence the formation of momentum shift. Before the duration is long enough for intercycle interference to emerge, momentum shift grows smoothly. Our findings reveal different intrinsic mechanisms for the formation of momentum shift in many-cycle and few-cycle laser pulses, showing that subcycle interference plays a dominant role in the former while intercycle interference is critical in the latter. This work lays the foundation for a deeper understanding of the nonadiabatic tunnelling process and makes the regulation of momentum shift possible.

Measurement of the radius dependence of charged-particle jet suppression in Pb–Pb collisions at [formula omitted

The ALICE Collaboration reports a differential measurement of inclusive jet suppression using pp and Pb–Pb collision data at a center-of-mass energy per nucleon–nucleon collision sNN=5.02 TeV. Charged-particle jets are reconstructed using the anti-kT algorithm with resolution parameters R=0.2, 0.3, 0.4, 0.5, and 0.6 in pp collisions and R=0.2, 0.4, 0.6 in central (0–10%), semi-central (30–50%), and peripheral (60–80%) Pb–Pb collisions. A novel approach based on machine learning is employed to mitigate the influence of jet background. This enables measurements of inclusive jet suppression in new regions of phase space, including down to the lowest jet pT≥40 GeV/c at R=0.6 in central Pb–Pb collisions. This is an important step for discriminating different models of jet quenching in the quark–gluon plasma. The transverse momentum spectra, nuclear modification factors, derived cross section, and nuclear modification factor ratios for different jet resolution parameters of charged-particle jets are presented and compared to model predictions. A mild dependence of the nuclear modification factor ratios on collision centrality and resolution parameter is observed. The results are compared to a variety of jet-quenching models with varying levels of agreement.

Transverse momentum spectra of f0(980) from coalescence model

We use a coalescence model to generate f0(980) particles for four configurations: ss¯ meson, uu¯ss¯ tetraquark, KK¯ molecule, and uu¯ p-wave state. The phase-space information of the coalescing constituents is taken from a multi-phase transport (AMPT) simulation of proton-proton (pp) and proton-lead (pPb) collisions at the LHC. It is shown that the transverse momentum spectra and production yields of f0(980) differ significantly among the configurations. It is suggested that the pT spectra of the f0(980) compared to those of other hadrons (such as pion) and the ratio of the f0(980)pT spectra in pPb over pp collisions can be exploited to tell the configuration of the f0(980).

The Spectrum of Low-pTJ/ψ in Heavy-Ion Collisions in a Statistical Two-Body Fractal Model.

We establish a statistical two-body fractal (STF) model to study the spectrum of J/ψ. J/ψ serves as a reliable probe in heavy-ion collisions. The distribution of J/ψ in hadron gas is influenced by flow, quantum and strong interaction effects. Previous models have predominantly focused on one or two of these effects while neglecting the others, resulting in the inclusion of unconsidered effects in the fitted parameters. Here, we study the issue from a new point of view by analyzing the fact that all three effects induce a self-similarity structure, involving a J/ψ-π two-meson state and a J/ψ, π two-quark state, respectively. We introduce modification factor qTBS and q2 into the probability and entropy of charmonium. qTBS denotes the modification of self-similarity on J/ψ, q2 denotes that of self-similarity and strong interaction between c and c¯ on quarks. By solving the probability and entropy equations, we derive the values of qTBS and q2 at various collision energies and centralities. Substituting the value of qTBS into distribution function, we successfully obtain the transverse momentum spectrum of low-pT J/ψ, which demonstrates good agreement with experimental data. The STF model can be employed to investigate other mesons and resonance states.

Study of octupole deformations in Pb-Pb collisions at 5.02 TeV

In this letter, we present the study of the role of octupole deformation in non-spherical nuclei in most-central Pb-Pb collisions at LHC energy regime. The sensitivity of octupole deformation β3 to the QGP observables is presented by employing Monte-Carlo HYDJET++ model. Motivated by the discrepancies in the v2-to-v3 puzzle found in Pb-Pb collisions and the low-energy nuclear structure calculations of nuclear deformation, we studied the first basic observables necessary for any study in heavy-ion collisions. Using HYDJET++ framework, we calculate the pseudorapidity distribution, transverse momentum (pT) spectra and average anisotropic flow (v2 and v3) of primary charged hadrons with different parameters in two geometrical configurations: body-body and tip-tip type of Pb-Pb collisions. The kinematic ranges 0<pT<20 GeV/c and |η|<0.8 are considered. We observe that the charged hadron multiplicity and transverse momentum spectra are dependent on the strength of octupole deformation parameter. 〈v2〉 and 〈v3〉 in body-body collisions show weak positive correlation with β3 while average anisotropic flow in tip-tip collisions are weakly correlated to β3 in most-central collision region.

Squeezed spectra and elliptic flow of bosons and anti-bosons with in-medium mass splitting

We study the impact of the in-medium mass splitting between bosons and anti-bosons on their spectra and elliptic flow. The in-medium mass splitting may cause a separation in the transverse momentum spectra, as well as a division in the elliptic flow between bosons and anti-bosons. The magnitude of this effect becomes greater as the in-medium mass splitting increases. With the increasing rapidity, the splitting effect of the spectra increases and the splitting effect of the elliptic flow decreases. These phenomena may provide a way to differentiate whether the influences on boson and anti-boson in the medium are consistent.

Excitation function of thermal freeze-out parameters and their correlations from strange hadrons spectra in Au–Au collision at 54.4 GeV

We present a systematic study of Gold–Gold (Au–Au) collision system at 54.4 GeV conducted by the STAR Collaboration at RHIC. The transverse momentum spectra of the strange hadrons, namely KS0, Λ, Λ̄, Ξ̄+ and Ξ− are studied at mid-rapidity |y|<0.5 for seven centrality classes. We applied the blast wave model with Tsallis statistics (TBW) with two flow profiles (n0 = 1 and n0 = 2) in order to compare the results and to check the sensitivity of n0 to the freeze-out parameters. It is found that the TBW model with both the flow profiles can describe the particle spectra. In addition, the bulk properties in terms of kinetic freeze-out temperature (T0), transverse flow velocity (βT), the non-extensive parameter (q), the kinetic freeze-out volume (V), the mean transverse momentum (〈pT〉), and the multiplicity parameter (N0) are also extracted. All the parameters decrease with decreasing the event centrality, however, the non-extensive parameter q has the opposite behavior. There is an abrupt decrease seen in 0–5% to 30–40% centrality, while a slight decrease appears in 40–60% and 60–80% centrality in T0, βT, V, and 〈pT〉. On the other hand, the parameter q follows the same scenario with an opposite trend with centrality. T0 and 〈pT〉 are larger for massive particles while βT, q, V and N0 are larger for lighter particles. The larger T0 and 〈pT〉, and smaller βT, V, and q for the massive particles affirm that the heavy particles freeze-out early. Moreover, the multiple kinetic freeze-out and volume differential freeze-out scenarios are reported, as the former increase while the latter decrease with particle mass. In addition, T0, q, V, and N0 obtained from TBW model with n0 = 1 are compatible to that of n0 = 2. On the other hand, βT is slightly larger in n0 = 2, while 〈pT〉 is slightly larger in n0 = 1. Furthermore, we also reported some important correlations among the extracted parameters. Among these correlations, the positive correlation exist between T0 and βT, T0 and V, T0 and 〈pT〉, T0 and N0, βT and 〈pT〉, βT and V, βT and N0, V and N0, and 〈pT〉 and N0, while the negative correlation of T0 and q, and 〈pT〉 and q.