Function Of Momentum Research Articles

Measurement of prompt [formula omitted]-meson production and azimuthal anisotropy in Pb–Pb collisions at [formula omitted

The production yield and angular anisotropy of prompt Ds+ mesons were measured as a function of transverse momentum (pT) in Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV collected with the ALICE detector at the LHC. Ds+ mesons and their charge conjugates were reconstructed at midrapidity (|y|<0.5) from their hadronic decay channel Ds+→ϕπ+, with ϕ→K−K+, in the pT intervals 2<pT<50GeV/c and 2<pT<36GeV/c for the 0–10% and 30–50% centrality intervals. For pT>10GeV/c, the measured Ds+-meson nuclear modification factor RAA is consistent with the one of non-strange D mesons within uncertainties, while at lower pT a hint for a Ds+-meson RAA larger than that of non-strange D mesons is seen. The enhanced production of Ds+ relative to non-strange D mesons is also studied by comparing the pT-dependent Ds+/D0 production yield ratios in Pb–Pb and in pp collisions. The ratio measured in Pb–Pb collisions is found to be on average higher than that in pp collisions in the interval 2<pT<8GeV/c with a significance of 2.3σ and 2.4σ for the 0–10% and 30–50% centrality intervals. The azimuthal anisotropy coefficient v2 of prompt Ds+ mesons was measured in Pb–Pb collisions in the 30–50% centrality interval and is found to be compatible with that of non-strange D mesons. The main features of the measured RAA, Ds+/D0 ratio, and v2 as a function of pT are described by theoretical calculations of charm-quark transport in a hydrodynamically expanding quark–gluon plasma including hadronisation via charm-quark recombination with light quarks from the medium. The pT-integrated production yield of Ds+ mesons is compatible with the prediction of the statistical hadronisation model.

Measurement of inclusive electrons from open heavy-flavor hadron decays in p+p collisions at s=200 GeV with the STAR detector

We report a new measurement of the production cross section for inclusive electrons from open heavy-flavor hadron decays as a function of transverse momentum ($p_{\rm T}$) at mid-rapidity ($|y|<$ 0.7) in $p$+$p$ collisions at $\sqrt{s} = 200$ GeV. The result is presented for 2.5 $<p_{\rm T}<$ 10 GeV/$c$ with an improved precision above 6 GeV/$c$ with respect to the previous measurements, providing more constraints on perturbative QCD calculations. Moreover, this measurement also provides a high-precision reference for measurements of nuclear modification factors for inclusive electrons from open-charm and -bottom hadron decays in heavy-ion collisions.

Measurement of the Inclusive and Differential Higgs Boson Production Cross Sections in the Decay Mode to a Pair of τ Leptons in pp Collisions at sqrt[s]=13 TeV.

Measurements of the inclusive and differential fiducial cross sections of the Higgs boson are presented, using the τ lepton decay channel. The differential cross sections are measured as functions of the Higgs boson transverse momentum, jet multiplicity, and transverse momentum of the leading jet in the event, if any. The analysis is performed using proton-proton collision data collected with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb^{-1}. These are the first differential measurements of the Higgs boson cross section in the final state of two τ leptons. In final states with a large jet multiplicity or with a Lorentz-boosted Higgs boson, these measurements constitute a significant improvement over measurements performed in other final states.

Event-by-Event Investigation of the Two-Particle Source Function in Heavy-Ion Collisions with EPOS.

Exploring the shape of the pair-source function for particles such as pions or kaons has been an important goal of heavy-ion physics, and substantial effort has been made in order to understand the underlying physics behind the experimental observations of non-Gaussian behavior. In experiments, since no direct measurement of the source function is possible, quantum-statistical momentum correlations are utilized to gain information about the space-time geometry of the particle emitting source. Event generators, such as EPOS, however, provide direct access to the freeze-out coordinates of final state particles, and thus the source function can be constructed and investigated. The EPOS model is a sophisticated hybrid model where the initial stage evolution of the system is governed by Parton-Based Gribov–Regge theory, and subsequently a hydrodynamic evolution is utilized, followed by hadronization and hadron dynamics. EPOS has already proven to be successful in describing several different experimental observations for systems characterized by baryon chemical potential close to zero, but so far the source shape has not been explored in detail. In this paper we discuss an event-by-event analysis of the two-particle source function in = 200 GeV Au+Au collisions generated by the EPOS model. We find that when utilizing all stages of the model, Lévy-shaped distributions (unlike Gaussian distributions) provide a good description of the source shape in the individual events. Hence it is clear that it is not the event averaging that creates the non-Gaussian features in the pair distributions. Based on this observation, we determine Lévy-parameters of the source as a function of event centrality and particle momentum.

Poynting vector controversy in axion modified electrodynamics

The most sensitive haloscopes that search for axion dark matter through the two photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one similar to the Abraham Poynting vector and the other to the Minkowski Poynting vector in electrodynamics. The latter picks up the extra non-conservative terms while the former does not. To understand the source of energy conversion and power flow in the detection systems, we apply the two Poynting theorems to axion modified electrodynamics, for both the resonant cavity and broadband low-mass axion detectors. We show that both Poynting theorems give the same sensitivity for a resonant cavity axion haloscope, but predict markedly different sensitivity for a low-mass broadband capacitive haloscope. Hence we ask the question, can understanding which one is the correct one for axion dark matter detection, be considered under the framework of the Abraham-Minkowski controversy? In reality, this should be confirmed by experiment when the axion is detected. However, many electrodynamic experiments have ruled in favour of the Minkowski Poynting vector when considering the canonical momentum in dielectric media. In light of this, we show that the axion modified Minkowski Poynting vector should indeed be taken seriously for sensitivity calculation for low-mass axion haloscope detectors in the quasi static limit, and predict orders of magnitude better sensitivity than the Abraham Poynting vector equivalent.

Checking nonflow assumptions and results via PHENIX published correlations in p+p , p+Au , d+Au , and He3+Au at sNN=200 GeV

Recently the PHENIX Collaboration has made available two-particle correlation Fourier coefficients for multiple detector combinations in minimum bias p+p and 0-5% central p+Au, d+Au, 3He+Au collisions at 200 GeV [1]. Using these coefficients for three sets of two-particle correlations, azimuthal anisotropy coefficients $v_2$ and $v_3$ are extracted for midrapidity charged hadrons as a function of transverse momentum. In this paper, we use the available coefficients to explore various non-flow hypotheses as well as compare the results with theoretical model calculations. The non-flow methods fail basic closure tests with AMPT and PYTHIA/ANGANTYR, particularly when including correlations with particles in the low multiplicity light-projectile going direction. In data, the non-flow adjusted $v_2$ results are modestly lower in p+Au and the adjusted $v_3$ results are more significantly higher in p+Au and d+Au. However, the resulting higher values for the ratio $v_3/v_2$ in p+Au at RHIC compared to p+Pb at the LHC is additional evidence for a significant over-correction. Incorporating these additional checks, the conclusion that these flow coefficients are dominated by initial geometry coupled with final-state interactions (e.g.~hydrodynamic expansion of quark-gluon plasma) remains true, and explanations based on initial-state glasma are ruled out. The detailed balance between intrinsic and fluctuation-driven geometry and the exact role of weakly versus strongly-coupled pre-hydrodynamic evolution remains an open question for triangular flow, requiring further theoretical and experimental investigation.

Two Approaches to Hamiltonian Bigravity

Bigravity is one of the most natural modifications of General Relativity (GR), as it is based on the equivalence principle. However, its canonical structure appears rather complicated because of the unusual form of the interaction between two metrics. As a consequence, there are different approaches that are difficult to compare in detail. This work is a first attempt to obtain a synthetic picture of the Hamiltonian formalism for bigravity. Here, we are trying to combine two rather different approaches to gain a binocular view of the theory. The first publications on the subject were based on metric formalism. It was proved that both massive gravity and bigravity with de Rham–Gabadadze–Tolley (dRGT) potential were free of Boulware–Deser (BD) ghosts. This proof was based on the transformation of variables involving a 3×3-matrix which could be treated as the root of a quadratic equation involving two spatial metrics and a new 3-vector introduced instead of the standard shift variable. Therefore, this matrix occurred as an implicit function of the abovementioned variables. After a substantial amount of time, it became possible to calculate the algebra of constraints in full using this method. However, in another approach also based on metric variables and implicit functions, similar calculations were completed earlier. It is not a new matrix, but the potential itself has been taken as an implicit function of two spatial metrics and four functions constructed of two pairs of lapses and shifts. Finally, a straightforward route to canonical bigravity is to apply tetrad (or vierbein) variables. The matrix square root involved in the dRGT potential can be explicitly extracted if tetrads fulfill the symmetry condition. A full treatment has been developed in first-order formalism by treating tetrads and connections as independent variables. In that case, the theory contains many more variables and constraints than in metric formalism. An essential simplification occurs in second-order vierbein formalism. The potential is given explicitly as a polynomial of bilinear combinations of the two tetrads. The 3×3-matrix introduced in the pioneer papers can be expressed explicitly through canonical coordinates, and the celebrated transformation of variables arises in the Dirac constraint analysis.

Transverse single spin asymmetries of forward neutrons in p+p , p+Al , and p+Au collisions at sNN=200 GeV as a function of transverse and longitudinal momenta

In 2015 the PHENIX collaboration at the Relativistic Heavy Ion Collider recorded $p$$+$$p$, $p$$+$Al, and $p$$+$Au collision data at center of mass energies of $\sqrt{s_{_{NN}}}=200$ GeV with the proton beam(s) transversely polarized. At very forward rapidities $\eta>6.8$ relative to the polarized proton beam, neutrons were detected either inclusively or in (anti)correlation with detector activity related to hard collisions. The resulting single spin asymmetries, that were previously reported, have now been extracted as a function of the transverse momentum of the neutron as well as its longitudinal momentum fraction $x_F$. The explicit kinematic dependence, combined with the correlation information allows for a closer look at the interplay of different mechanisms suggested to describe these asymmetries, such as hadronic interactions or electromagnetic interactions in ultra-peripheral collisions, UPC. Events that are correlated with a hard collision indeed display a mostly negative asymmetry that increases in magnitude as a function of transverse momentum with only little dependence on $x_F$. In contrast, events that are not likely to have emerged from a hard collision display positive asymmetries for the nuclear collisions with a kinematic dependence that resembles that of a UPC based model. Because the UPC interaction depends strongly on the charge of the nucleus, those effects are very small for $p$$+$$p$ collisions, moderate for $p$$+$Al collisions, and large for $p$$+$Au collisions.

Lagrangian regularity of the electron magnetohydrodynamics flow on a bounded domain

In this paper we investigate the regularity in time of the Lagrangian flow associated with the electron magnetohydrodynamics (e-MHD) equations on a bounded domain with a smooth (ultradifferentiable) boundary. This model is widely used in controlled magnetic fusion, in space and astrophysics plasmas and also in physics of solids. We show that initial data with limited smoothness in Sobolev spaces induce a Lagrangian flow-map X and a Lagrangian magnetic vector potential A (viz. the magnetic vector potential evaluated at the Lagrangian spatial point X), which are ultradifferentiable in time, with the two particular cases of real analytic and Gevrey time regularity. It turns out that the Lagrangian canonical momentum P, the Lagrangian magnetic field B, and the Lagrangian electric field E inherit this Lagrangian regularity property. Among others, the proof makes crucial use of a novel Lagrangian formulation of the e-MHD in terms of the Lagrangian fields (X,A,P,B,E). A by-product of this Lagrangian and constructive proof is the design of arbitrary high-order semi-Lagrangian schemes to solve the e-MHD equations on a bounded domain.

Identification of charm jets at LHCb

The identification of charm jets is achieved at LHCb for data collected in 2015–2018 using a method based on the properties of displaced vertices reconstructed and matched with jets. The performance of this method is determined using a dijet calibration dataset recorded by the LHCb detector and selected such that the jets are unbiased in quantities used in the tagging algorithm. The charm-tagging efficiency is reported as a function of the transverse momentum of the jet. The measured efficiencies are compared to those obtained from simulation and found to be in good agreement.

On the validity of the guiding-center approximation in a magnetic dipole field

The problem of the charged-particle motion in an axisymmetric magnetic-dipole geometry is used to assess the validity of Hamiltonian guiding-center theory, which includes higher-order corrections associated with guiding-center polarization induced by magnetic-field nonuniformity. When a magnetically confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when guiding-center polarization effects are taken into account.

A super-resolution technique to analyze single-crystal inelastic neutron scattering measurements using direct-geometry chopper spectrometers.

Direct-geometry time-of-flight chopper neutron spectroscopy is instrumental in studying dynamics in liquid, powder, and single crystal systems. We report here that real-space techniques in optical imagery can be adapted to obtain reciprocal-space super resolution dispersion for phonon or magnetic excitations from single-crystal neutron spectroscopy measurements. The procedure to reconstruct super-resolution energy dispersion of excitations relies on an accurate determination of the momentum and energy-dependent point spread function and a dispersion correction technique inspired by an image disparity calculation technique commonly used in stereo imaging. Applying these methods to spinwave dispersion data from a virtual neutron experiment demonstrates ∼5-fold improvement over nominal energy resolution.

Absence of temperature-dependent phonon anomalies in Sr2IrO4 and Sr3Ir2O7

Following previous works reporting an anomalous behavior of several zone-center optical phonons across the magnetic transition of square lattice iridates ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ and ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, we have investigated the lattice dynamics as a function of momentum in these materials by means of high-resolution inelastic x-ray scattering. The observed phonon energies and scattering intensities across the Brillouin zone are in excellent agreement with ab initio lattice dynamical calculations based on nonmagnetic density-functional-perturbation theory. Our results do not evidence any renormalization of the phonons at finite momentum across the magnetic transition of ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. The only anomalous behavior was detected for the in-plane polarized longitudinal-acoustic phonon branch in ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, which anomalously softens towards low temperatures and might be related to anisotropic negative thermal expansion in this compound. No anomalies related to potential charge ordering were observed.

Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices

We present several inequalities related to the Robertson-Schr\"odinger uncertainty relation. In all these inequalities, we consider a decomposition of the density matrix into a mixture of states, and use the fact that the Robertson-Schr\"odinger uncertainty relation is valid for all these components. By considering a convex roof of the bound, we obtain an alternative derivation of the relation in Fr\"owis et al. [Phys. Rev. A 92, 012102 (2015)], and we can also list a number of conditions that are needed to saturate the relation. We present a formulation of the Cram\'er-Rao bound involving the convex roof of the variance. By considering a concave roof of the bound in the Robertson-Schr\"odinger uncertainty relation over decompositions to mixed states, we obtain an improvement of the Robertson-Schr\"odinger uncertainty relation. We consider similar techniques for uncertainty relations with three variances. Finally, we present further uncertainty relations that provide lower bounds on the metrological usefulness of bipartite quantum states based on the variances of the canonical position and momentum operators for two-mode continuous variable systems. We show that the violation of well-known entanglement conditions in these systems discussed in Duan et al., [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] implies that the state is more useful metrologically than certain relevant subsets of separable states. We present similar results concerning entanglement conditions with angular momentum operators for spin systems.

The role of geometric and dynamical phases in the Dirac–Bohm picture

In this paper we explore a different but unitarily equivalent picture to the standard Schrödinger and Heisenberg pictures, namely the Dirac–Bohm picture introduced by Hiley and Dennis. This is not merely another interpretation as it allows us to examine the unfolding quantum process in terms of the algebraic structure of the dynamical variables, which in turn allows us to explore the geometric implications of quantum phenomena. Furthermore this enables us to exploit the double valued nature of the orthogonal and symplectic symmetry groups and show how they profoundly affect the nature of the conjugate momentum by enabling the introduction of classes of vector potentials into Hamiltonian systems. This throws more light on the significance of gauge invariance both in classical and quantum mechanics.The connection with geometric aspects of quantum phenomena allows us to introduce Clifford algebras in a natural way so that it is possible to extend the Dirac–Bohm approach to include spin and relativity, offering new geometric insights into quantum phenomena. In particular the bi-vector aspects allow us to introduce the Gromov non-squeezing theorem in a new way, ultimately offering the possibility of relating our work to the non-commutative geometry of M-theory.

On the motion of billiards in ellipses

For billiards in an ellipse e with an ellipse as caustic, there exist canonical coordinates on e such that the billiard transformation from vertex to vertex is equivalent to a shift of coordinates. A kinematic analysis of billiard motions offers a new approach to canonical parametrizations of billiards and associated Poncelet grids. This parametrization uses Jacobian elliptic functions with the modulus equal to the numerical eccentricity of the caustic and is the basis for proving a few invariants of periodic billiards.

Field theory spin and momentum in water waves.

Spin is a fundamental yet nontrivial intrinsic angular momentum property of quantum particles or fields, which appears within relativistic field theory. The spin density in wave fields is described by the theoretical Belinfante-Rosenfeld construction based on the difference between the canonical and kinetic momentum densities. These quantities are usually considered as abstract and non-observable per se. Here, we demonstrate, both theoretically and experimentally, that the Belinfante-Rosenfeld construction naturally arises in gravity (water surface) waves. There, the canonical momentum is associated with the generalized Stokes drift phenomenon, while the spin is generated by subwavelength circular motion of water particles. Thus, we directly observe these fundamental field theory properties as microscopic mechanical properties of a classical wave system. Our findings shed light onto the nature of spin and momentum in wave fields, demonstrate the universality of relativistic field theory concepts, and offer a new platform for their studies.

Explicit solving of the system of natural PDEs of minimal Lorentz surfaces in [formula omitted

A minimal Lorentz surface in R24 is said to be of general type if its corresponding null curves are non-degenerate. These surfaces admit canonical isothermal and canonical isotropic coordinates. It is known that the Gauss curvature K and the normal curvature ϰ of such a surface considered as functions of the canonical coordinates satisfy a system of two natural PDEs. Using the Weierstrass type representations of the corresponding null curves, we solve explicitly the system of natural PDEs, expressing any solution by means of four real functions of one variable. We obtain the transformation formulas for the functions in the Weierstrass representation of a null curve under a proper motion in R24. Using this, we find the relation between two quadruples of real functions generating one and the same solution to the system of natural PDEs.

Stokes Manifolds and Cluster Algebras

Stokes' manifolds, also known as wild character varieties, carry a natural symplectic structure. Our goal is to provide explicit log-canonical coordinates for these natural Poisson structures on the Stokes' manifolds of polynomial connections of rank $2$, thus including the second Painlev\'e\ hierarchy. This construction provides the explicit linearization of the Poisson structure first discovered by Flaschka and Newell and then rediscovered and generalized by Boalch. We show that, for a connection of degree $K$, the Stokes' manifold is a cluster manifold of type $A_{2K}$. The main idea is then applied to express explicitly also the log--canonical coordinates for the Poisson bracket introduced by Ugaglia in the context of Frobenius manifolds and then also applied by Bondal in the study of the symplectic groupoid of quadratic forms.

Horizon thermalization of Kerr black hole through local instability

The validity of our already proposed conjecture – horizon creates a local instability which acts as the source of the quantum temperature of black hole – is being tested here for Kerr black hole. Earlier this has been explicitly shown for spherically symmetric static black hole (SSS BH). The more realistic situation like Kerr spacetime, being stationary and axisymmetric, is a non-trivial example to analyze. We show that for a chargeless massless particle, the near horizon radial motion in Kerr spacetime, like SSS BH, can be locally unstable. The radial contribution in the corresponding Hamiltonian is ∼xp kind, where p is the canonical momentum and x is its conjugate position of particle. Finally we show that the horizon thermalization can be explained through this Hamiltonian when one dose a semi-classical analysis. It again confirms that near horizon instability is liable for its own temperature and moreover generalizes the validity of our conjectured mechanism for the black hole horizon thermalization.