The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions

Direct observation of the dead-cone effect in quantum chromodynamics

The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron

Direct observation of the dead-cone effect in quantum chromodynamics

At particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD) [1]. The vacuum is not transparent to the partons and induces gluon radiation and quark pair production in a process that can be described as a parton shower [2]. Studying the pattern of the parton shower is one of the key experimental tools in understanding the properties of QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass m and energy E, within a cone of angular size m/E around the emitter [3]. A direct observation of the dead-cone effect in QCD has not been possible until now, due to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible bound hadronic states. Here we show the first direct observation of the QCD dead-cone by using new iterative declustering techniques [4, 5] to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD, which is derived more generally from its origin as a gauge quantum field theory. Furthermore, the measurement of a dead-cone angle constitutes the first direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics.The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron.In particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD). These partons subsequently emit further partons in a process that can be described as a parton shower which culminates in the formation of detectable hadrons. Studying the pattern of the parton shower is one of the key experimental tools for testing QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass $m_{\rm{Q}}$ and energy $E$, within a cone of angular size $m_{\rm{Q}}$/$E$ around the emitter. Previously, a direct observation of the dead-cone effect in QCD had not been possible, owing to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible hadrons. We report the direct observation of the QCD dead cone by using new iterative declustering techniques to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD. Furthermore, the measurement of a dead-cone angle constitutes a direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics

Production of inclusive ϒ(1S) and ϒ(2S) in p–Pb collisions at √sNN = 5.02 TeV

We report on the production of inclusive Υ(1S) and Υ(2S) in p-Pb collisions at sNN−−−√=5.02 TeV at the LHC. The measurement is performed with the ALICE detector at backward (−4.46<ycms<−2.96) and forward (2.03<ycms<3.53) rapidity down to zero transverse momentum. The production cross sections of the Υ(1S) and Υ(2S) are presented, as well as the nuclear modification factor and the ratio of the forward to backward yields of Υ(1S). A suppression of the inclusive Υ(1S) yield in p-Pb collisions with respect to the yield from pp collisions scaled by the number of binary nucleon-nucleon collisions is observed at forward rapidity but not at backward rapidity. The results are compared to theoretical model calculations including nuclear shadowing or partonic energy loss effects

Measurement of pion, kaon and proton production in proton-proton collisions at √s = 7 TeV

The measurement of primary π±, K±, p and p¯¯¯ production at mid-rapidity (|y|< 0.5) in proton-proton collisions at s√=7 TeV performed with ALICE (A Large Ion Collider Experiment) at the Large Hadron Collider (LHC) is reported. Particle identification is performed using the specific ionization energy loss and time-of-flight information, the ring-imaging Cherenkov technique and the kink-topology identification of weak decays of charged kaons. Transverse momentum spectra are measured from 0.1 up to 3 GeV/c for pions, from 0.2 up to 6 GeV/c for kaons and from 0.3 up to 6 GeV/c for protons. The measured spectra and particle ratios are compared with QCD-inspired models, tuned to reproduce also the earlier measurements performed at the LHC. Furthermore, the integrated particle yields and ratios as well as the average transverse momenta are compared with results at lower collision energies

Elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity in Pb–Pb collisions at √sNN = 2.76 TeV

The elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity (|y| < 0.7) is measured in Pb-Pb collisions at sNN−−−√=2.76 TeV with ALICE at the LHC. The particle azimuthal distribution with respect to the reaction plane can be parametrized with a Fourier expansion, where the second coefficient (v2) represents the elliptic flow. The v2 coefficient of inclusive electrons is measured in three centrality classes (0-10%, 10-20% and 20-40%) with the event plane and the scalar product methods in the transverse momentum (pT) intervals 0.5-13 GeV/c and 0.5-8 GeV/c, respectively. After subtracting the background, mainly from photon conversions and Dalitz decays of neutral mesons, a positive v2 of electrons from heavy-flavour hadron decays is observed in all centrality classes, with a maximum significance of 5.9σ in the interval 2< pT < 2.5 GeV/c in semi-central collisions (20-40%). The value of v2 decreases towards more central collisions at low and intermediate pT (0.5 < pT < 3 GeV/c). The v2 of electrons from heavy-flavour hadron decays at mid-rapidity is found to be similar to the one of muons from heavy-flavour hadron decays at forward rapidity (2.5 < y < 4). The results are described within uncertainties by model calculations including substantial elastic interactions of heavy quarks with an expanding strongly-interacting medium

Measurement of dijet kT in p–Pb collisions at √sNN = 5.02 TeV

A measurement of dijet correlations in p-Pb collisions at sNN−−−√=5.02 TeV with the ALICE detector is presented. Jets are reconstructed from charged particles measured in the central tracking detectors and neutral energy deposited in the electromagnetic calorimeter. The transverse momentum of the full jet (clustered from charged and neutral constituents) and charged jet (clustered from charged particles only) is corrected event-by-event for the contribution of the underlying event, while corrections for underlying event fluctuations and finite detector resolution are applied on an inclusive basis. A projection of the dijet transverse momentum, kTy=pch+neT,jetsin(Δφdijet) with Δφdijet the azimuthal angle between a full and charged jet and pch+neT,jet the transverse momentum of the full jet, is used to study nuclear matter effects in p-Pb collisions. This observable is sensitive to the acoplanarity of dijet production and its potential modification in p-Pb collisions with respect to pp collisions. Measurements of the dijet kTy as a function of the transverse momentum of the full and recoil charged jet, and the event multiplicity are presented. No significant modification of kTy due to nuclear matter effects in p-Pb collisions with respect to the event multiplicity or a PYTHIA8 reference is observed

Centrality dependence of the charged-particle multiplicity density at midrapidity in Pb–Pb collisions at √sNN = 5.02 TeV

The pseudorapidity density of charged particles (dNch/dη) at mid-rapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of sNN−−−√ = 5.02 TeV. It increases with centrality and reaches a value of 1943±54 in |η|<0.5 for the 5% most central collisions. A rise in dNch/dη as a function of sNN−−−√ for the most central collisions is observed, steeper than that observed in proton-proton collisions and following the trend established by measurements at lower energy. The centrality dependence of dNch/dη as a function of the average number of participant nucleons, ⟨Npart⟩, calculated in a Glauber model, is compared with the previous measurement at lower energy. A constant factor of about 1.2 describes the increase in 2⟨Npart⟩⟨dNch/dη⟩ from sNN−−−√ = 2.76 TeV to sNN−−−√ = 5.02 TeV for all centrality intervals, within the measured range of 0-80% centrality. The results are also compared to models based on different mechanisms for particle production in nuclear collisions

Two-pion femtoscopy in p–Pb collisions at √sNN = 5.02 TeV

We report the results of the femtoscopic analysis of pairs of identical pions measured in p-Pb collisions at sNN−−−√=5.02 TeV. Femtoscopic radii are determined as a function of event multiplicity and pair momentum in three spatial dimensions. As in the pp collision system, the analysis is complicated by the presence of sizable background correlation structures in addition to the femtoscopic signal. The radii increase with event multiplicity and decrease with pair transverse momentum. When taken at comparable multiplicity, the radii measured in p-Pb collisions, at high multiplicity and low pair transverse momentum, are 10-20% higher than those observed in pp collisions but below those observed in A-A collisions. The results are compared to hydrodynamic predictions at large event multiplicity as well as discussed in the context of calculations based on gluon saturation