Helicity Density Matrix Research Articles

Two and three particles entanglement; helicity and spin with momentum

Construction of the reduced spin and helicity density matrix for systems of two and three particles are described by a wave packet with sharp and Gaussian momentum distribution. The entropy for the spin and helicity part of the systems is calculated from the viewpoint of moving observers.

HELICITY ENTANGLEMENT OF MOVING BODIES

We investigate the Lorentz transformation of the reduced helicity density matrix for a pair of massive spin 1/2 particles. The corresponding Wootters concurrence shows no invariant meaning, which implies that we can generate helicity entanglement simply by the transformation from one reference frame to another. The difference between the helicity and spin case is also discussed.

ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

PHENOMENOLOGICAL TESTS FOR THE FREEZING OF THE QCD RUNNING COUPLING CONSTANT

We discuss phenomenological tests for the frozen infrared behavior of the running coupling constant and gluon propagators found in some solutions of Schwinger–Dyson equations of the gluonic sector of QCD. We verify that several observables can be used in order to select the different expressions of αs found in the literature. We test the effect of the nonperturbative coupling in the τ-lepton decay rate into nonstrange hadrons, in the ρ vector meson helicity density matrix that are produced in the χc2→ρρ decay, in the photon to pion transition form factor, and compute the cross-sections for elastic proton–proton scattering and exclusive ρ production in deep inelastic scattering. These quantities depend on the infrared behavior of the coupling constant at different levels, we discuss the reasons for this dependence and argue that the existent and future data can be used to test the approximations performed to solve the Schwinger–Dyson equations and they already seem to select one specific infrared behavior of the coupling.

SPIN ALIGNMENT OF VECTOR MESON IN HIGH ENERGY REACTIONS

The recent data on the polarization of vector meson at LEP show that the vector mesons favor the helicity zero state. We calculate the helicity density matrix of vector meson which contains a polarized fragmenting quark by adding the spin of the fragmenting quark and that of the antiquark created in the fragmentation. The data at LEP imply a significant polarization for the antiquark in the opposite direction as that of the fragmenting quark. We extend the calculations to other reactions and make predictions for vector mesons in deeply inelastic lepton-nucleon scatterings and polarized pp collisions.

NLO corrections in MC event generator for angular distribution of Drell-Yan lepton pair production

Using a subtraction method, we derive the formulae suitable for use in Monte-Carlo event generators to give the angular distribution for the gluon-quark induced NLO corrections in Drell-Yan lepton pair production. We also give the corresponding helicity density matrix for W and Z boson production.

Off-diagonal helicity density matrix elements for vector mesons produced in polarized $e^+e^-$ processes

Final-state $q \bar q$ interactions give origin to nonzero values of the off-diagonal element $\rho_{1,-1}$ of the helicity density matrix of vector mesons produced in $e^+ e^-$ annihilations, as has been confirmed by recent OPAL data on $\phi$ , $D^*$ , and $K^*$ . New predictions are given for $\rho_{1,-1}$ of several mesons produced at large $x_{_\mathrm{E}}$ and small $p_\mathrm{T}$ – i.e., collinear with the parent jet – in the annihilation of polarized $e^+$ and $e^-$ ; the results depend strongly on the elementary dynamics and allow further nontrivial tests of the standard model.

A study of spin alignment of $\rho(770)^{\pm}$ and $\omega(782)$ mesons in hadronic Z $^0$ decays

The helicity density matrix elements $\rho_{00}$ of $\rho(770)^{\pm}$ and $\omega(782)$ mesons produced in Z $^0$ decays have been measured using the OPAL detector at LEP. Over the measured meson energy range, the values are compatible with 1/3, corresponding to a statistical mix of helicity $-1$ , 0 and +1 states. For the highest accessible scaled energy range 0.3 $<$ $x_E$ $<$ 0.6, the measured $\rho_{00}$ values of the $\rho^{\pm}$ and the $\omega$ are 0.373 $\pm$ 0.052 and 0.142 $\pm$ 0.114, respectively. These results are compared to measurements of other vector mesons.

Spin alignment in heavy and light flavour systems at OPAL

Spin alignment of inclusive vector mesons and longitudinal polarization of A hyperons have been measured in a sample of 4.3 million hadronic Z 0 decays from the OPAL detector at LEP. Leading, light vector mesons have been found to populate preferentially the helicity-zero state, a result which has no firm theoretical explanation. The values of off-diagonal elements of the helicity density matrix are in agreement with a theory based on the Standard Model with coherent fragmentation. The longitudinal polarization of the A is well described by a model in which the constituent strange quark carries all of the hyperon spin.

Off-diagonal helicity density matrix elements for vector mesons produced in polarized

Final state quark-antiquark interactions give origin to non zero values of the off-diagonal element rho_{1,-1} of the helicity density matrix of vector mesons produced in e+e- annihilations, as confirmed by recent OPAL data on Phi, D^* and K^*'s. New predictions are given for rho_{1,-1} of several mesons produced at large x_E and small p_T -- i.e. collinear with the parent jet -- in the annihilation of polarized e+ and e-; the results depend strongly on the elementary dynamics and allow further non trivial tests of the Standard Model.

Off-diagonal helicity density matrix elements for heavy vector mesons inclusively produced in NN, γN and ℓ N interactions

Final state interactions in quark fragmentation may give origin to non zero values of the off-diagonal element ρ 1,−1 of the helicity density matrix of vector mesons V produced in current jets, with a large energy fraction x E ; the value of ρ 1,−1( V) is related to the hard constituent dynamics and tests unusual properties of it. Some recent data on φ, K ∗ and D ∗ produced in e + e − annihilations at LEP show such effects. Predictions are given here for ρ 1,−1 of heavy mesons produced in nucleon-nucleon, γ-nucleon and ℓ-nucleon interactions.

Off-diagonal helicity density matrix elements for vector mesons produced at LEP

Final state $q\bar q$ interactions may give origin to non-zero values of the off-diagonal element $\rho_{1,-1}$ of the helicity density matrix of vector mesons produced in $e^+ e^-$ annihilations, as confirmed by recent OPAL data on $\phi$ and $D^*$ 's. Predictions are given for $\rho_{1,-1}$ of several mesons produced at large $z$ and small $p_T$ , i.e. collinear with the parent jet; the values obtained for $\phi$ and $D^*$ are in agreement with data. The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made.

Interference Fragmentation Functions and the Nucleon's Transversity

We introduce twist-two quark interference fragmentation functions in helicity density matrix formalism and study their physical implications. We show how the nucleon's transversity distribution can be probed through the final state interaction between two mesons ( ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $K\overline{K}$, or $\ensuremath{\pi}K$) produced in the current fragmentation region in deep inelastic scattering on a transversely polarized nucleon.

Spin alignment of leading K∗(892)0 mesons in hadronic Z0 decays

Helicity density matrix elements for inclusive K ∗ (892) 0 mesons from hadronic Z 0 decays have been measured over the full range of K ∗ 0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x p values above 0.3, with the matrix element ϱ 00 rising to 0.66 ± 0.11 for x p > 0.7. The values of the real part of the off-diagonal element ϱ 1 - 1 are negative at large x p , with a weighted average value of −0.09 ± 0.03 for x p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the q q system from the Z 0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x p range. The K ∗ 0 fragmentation function has also been measured and the total rate determined to be 0.74 ± 0.02 ± 0.02 K ∗ (892) 0 mesons per hadronic Z 0 decay.

Off-diagonal helicity density matrix elements for vector mesons produced at LEP

Final state quark-antiquark interactions may give origin to non zero values of the off-diagonal element rho_{1,-1} of the helicity density matrix of vector mesons produced in e+e- annihilations, as confirmed by recent OPAL data on phi and D^*'s. Predictions are given for rho_{1,-1} of several mesons produced at large z and small p_T, i.e. collinear with the parent jet; the values obtained for phi and D^* are in agreement with data.

Study of $\phi(1020)$ , ${\rm D}^{*\pm}$ and B $^*$ spin alignment in hadronic Z $^0$ decays

Measurements of helicity density matrix elements have been made for the φ(1020), D*± and B* vector mesons in multihadronic Z0 decays in the OPAL experiment at LEP. Results for inclusive φ produced with high energy show evidence for production preferentially in the helicity zero state, with ρ00 = 0.54 ± 0.08, compared to the value of 1/3 expected for no spin alignment. The corresponding element for the D*± has a value of 0.40 ± 0.02, also suggesting a deviation from 1/3. The B* result, with ρ00 = 0.36 ± 0.09, is consistent with no spin alignment. Off-diagonal elements have been measured for the f and D* mesons; for the D* the element Re ρ1−1 is non-zero, indicating non-independent fragmentation of the primary quarks.

Polarized inclusive leptoproduction, lN-->hX, and the hadron helicity density matrix rho (h): Possible measurements and predictions.

We discuss the production of hadrons in polarized lepton-nucleon interactions and in the current jet fragmentation region; using the QCD hard scattering formalism we compute the helicity density matrix of the hadron and show how its elements, when measurable, can give information on the spin structure of the nucleon and the spin dependence of the quark fragmentation process. The cases of $\ensuremath{\rho}$ vector mesons and $\ensuremath{\Lambda}$ baryons are considered in more detail and, within simplifying assumptions, some estimates are given.

χc2→ρρ and the ρ polarization in massless perturbative QCD: How to test the distribution amplitudes

We compute the helicity density matrix of \ensuremath{\rho} vector mesons produced in the two-body decays of polarized ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}2}$'s in the framework of massless perturbative QCD. The ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}2}$'s are either exclusively or inclusively produced in pp\ifmmode\bar\else\textasciimacron\fi{} or pp interactions, via quark-antiquark annihilation or gluon fusion. Our results show unambiguous significant differences depending on the choice of the \ensuremath{\rho} distribution amplitudes and allow us to discriminate between different proposed models. \textcopyright{} 1996 The American Physical Society.

Chi c2--> rho rho decay and the rho polarization in inclusive processes: A test of mass effects.

We compute the helicity density matrix of $\rho$ vector mesons produced in the two-body decays of $\chi_{c2}$'s in the framework of perturbative QCD, allowing for mass corrections. The $\chi_{c2}$'s are inclusively produced in hadronic interactions via gluon fusion and are shown to be strongly polarized. Both the case in which the light quarks inside the final mesons are treated as massless current quarks and the case in which they are seen as constituent massive ones are considered. Our results show significant differences between the two cases; the measurement of the $\rho$ helicity density matrix should allow a test of the importance of these mass effects.

Chi c0,c2--> rho rho decays and the rho polarization: Massless versus constituent quarks.

We compute the helicity density matrix of vector mesons produced in the decays [chi][sub [ital c]0,][ital c2][r arrow][ital M][sub 1][ital M2], in the framework of perturbative QCD, allowing for mass corrections. Both the case in which the light quarks inside the final mesons are treated as massless current quarks and the case in which they are seen as constituent massive ones are considered. Explicit results are given for the helicity density matrix of [rho] mesons, [rho]([rho]), showing significant differences between the two cases; the measurement of [rho]([rho]) should then allow a precise evaluation of these mass effects.