Quadrupole Amplitude Research Articles

Comparing the same-side ridge inp−pangular correlations at 7 TeV to data measured at the BNL Relativistic Heavy Ion Collider

The Compact Muon Solenoid Collaboration (CMS) has recently reported the appearance of a same-side ridge structure in two-particle angular correlations from 7-TeV $p$-$p$ collisions. The ridge in $p$-$p$ collisions at 7 TeV has been compared to a ridge structure in more-central Au-Au collisions at 200 GeV, interpreted by some as evidence for a dense, flowing QCD medium. In this study we make a detailed comparison between 200-GeV $p$-$p$ correlations and the CMS results. We find that 7-TeV minimum-bias jet correlations are remarkably similar to those at 200 GeV, even to the details of the same-side peak geometry. Appearance of a same-side ridge reflects a change in the sign of the azimuth curvature determined by the ratio of azimuth quadrupole-to-dipole amplitudes. Extrapolation of quadrupole systematics from 200 GeV suggests that the same-side ridge at 7 TeV is a manifestation of the quadrupole amplitude enhanced relative to the dipole by the energy increase and applied cuts.

Azimuth Quadrupole Systematics in Au-Au Collisions

We have measured pt-dependent two-particle number correlations on azimuth and pseudorapidity for eleven centralities of = 62 and 200 GeV Au-Au collisions at STAR. 2D fits to these angular correlations isolate the azimuth quadrupole amplitude, denoted 2v22{2D}(pt), from localized same-side correlations. Event-plane V2(pt) measurements within the STAR TPC acceptance can be expressed as a sum of the azimuth quadrupole and the quadrupole component of the same-side peak. V2{2D}(pt) can be transformed to reveal quadrupole pt spectra which are approximately described by a fixed transverse boost and universal Levy form nearly independent of centrality. A parametrization of V2{2D}(pt) can be factored into centrality and pt-dependent pieces with a simple pt dependence above 0.75 GeV/c. Results from STAR are compared to published data and model predictions.

Direct Determination of the Magnetic Quadrupole Contribution to the Lyman-α1Transition in a Hydrogenlike Ion

We report the observation of an interference between the electric dipole (E1) and the magnetic quadrupole (M2) amplitudes for the linear polarization of the Ly-α1 (2p3/2→1s1/2) radiation of hydrogenlike uranium. This multipole mixing arises from the coupling of the ion to different multipole components of the radiation field. Our observation indicates a significant depolarization of the Ly-α1 radiation due to the E1-M2 amplitude mixing. It proves that a combined measurement of the linear polarization and of the angular distribution enables a very precise determination of the ratio of the E1 and the M2 transition amplitudes and the corresponding transition rates without any assumptions concerning the population mechanism for the 2p3/2 state.

Higher-order multipole amplitudes in charmonium radiative transitions

Using 24×106 ψ′≡ψ(2S) decays in CLEO-c, we have searched for higher multipole admixtures in electric-dipole-dominated radiative transitions in charmonia. We find good agreement between our data and theoretical predictions for magnetic quadrupole (M2) amplitudes in the transitions ψ′→γχc1,c2 and χc1,c2→γJ/ψ, in striking contrast to some previous measurements. Let b2J and a2J denote the normalized M2 amplitudes in the respective aforementioned decays, where the superscript J refers to the angular momentum of the χcJ. By performing unbinned maximum likelihood fits to full five-parameter angular distributions, we found the following values of M2 admixtures for Jχ=1: a2J=1=(−6.26±0.63±0.24)×10−2 and b2J=1=(2.76±0.73±0.23)×10−2, which agree well with theoretical expectations for a vanishing anomalous magnetic moment of the charm quark. For Jχ=2, if we fix the electric octupole (E3) amplitudes to zero as theory predicts for transitions between charmonium S states and P states, we find a2J=2=(−9.3±1.6±0.3)×10−2 and b2J=2=(1.0±1.3±0.3)×10−2. If we allow for E3 amplitudes we find, with a four-parameter fit, a2J=2=(−7.9±1.9±0.3)×10−2, b2J=2=(0.2±1.4±0.4)×10−2, a3J=2=(1.7±1.4±0.3)×10−2, and b3J=2=(−0.8±1.2±0.2)×10−2. We determine the ratios a2J=1/a2J=2=0.67−0.13+0.19 and a2J=1/b2J=1=−2.27−0.99+0.57, where the theoretical predictions are independent of the charmed quark magnetic moment and are a2J=1/a2J=2=0.676±0.071 and a2J=1/b2J=1=−2.27±0.16.Received 1 October 2009DOI:https://doi.org/10.1103/PhysRevD.80.112003©2009 American Physical Society

Description of nuclear octupole and quadrupole deformation close to axial symmetry: Critical-point behavior ofRa224andTh224

The model, introduced in a previous paper, for the description of the octupole and quadrupole degrees of freedom in conditions close to axial symmetry, is applied to situations of shape phase transitions where the quadrupole amplitude can reach zero. The transitional nuclei $^{224,226}\mathrm{Ra}$ and $^{224}\mathrm{Th}$ are discussed in the frame of this model. Their level schemes can be reasonably accounted for by assuming a square-well potential in two dimensions. Electromagnetic transition amplitudes are also evaluated and compared with existing experimental data.

WMAP 3-yr data with Correlated Component Analysis: anomalous emission and impact of component separation on the CMB power spectrum

Correlated Component Analysis (CCA) allows us to estimate how the different diffuse emissions mix in observations by cosmic microwave background (CMB) experiments, also taking into account complementary information from other surveys. It is especially useful for dealing with possible additional components for which little or no prior information exists. An application of CCA to the Wilkinson Microwave Anisotropy Probe (WMAP) maps assuming that only the canonical Galactic emissions (synchrotron, free–free and thermal dust) are present highlights the widespread presence of a spectrally flat ‘synchrotron’ component, largely uncorrelated with the synchrotron template, suggesting that an additional foreground is indeed required. We have tested various spectral shapes for such a component, namely a power law as is expected if it is flat synchrotron, and two spectral shapes that may fit the spinning dust emission: a parabola in the log S− log ν plane and a grey body. If the spatial distribution of the additional (‘anomalous’) component is not constrained a priori, it is found to be always tightly correlated with thermal dust, but the correlation is not perfect. Quality tests applied to the reconstructed CMB maps clearly disfavour two of the models. The CMB power spectra, estimated from CMB maps reconstructed exploiting the three surviving foreground models, are generally consistent with those obtained by the WMAP team, although at least one of the models gives a significantly higher quadrupole moment than found by WMAP. Taking foreground modelling uncertainties into account, we find that the mean quadrupole amplitude for the three ‘good’ models is less than 1σ below the expectation from the standard Λcold dark matter (ΛCDM) model. Also, the other reported deviations from model predictions are found not to be statistically significant, except for the excess power at l≃ 40. We confirm the evidence for a marked north–south asymmetry in the large-scale (l < 20) CMB anisotropies, which is stable with respect to the foreground parametrization we adopted. We also present a first, albeit preliminary, all-sky template of the ‘anomalous emission’.

Cosmic microwave background quadrupole and ellipsoidal universe

Recent Wilkinson Microwave Anisotropy Probe (WMAP) data confirm the cosmic microwave background (CMB) quadrupole anomaly. We further elaborate our previous proposal that the quadrupole power can be naturally suppressed in axis-symmetric universes. In particular, we discuss in greater detail the CMB quadrupole anisotropy and considerably improve our analysis. As a result, we obtain tighter constraints on the direction of the axis of symmetry as well as on the eccentricity at decoupling. We find that the quadrupole amplitude can be brought in accordance with observations with an eccentricity at decoupling of about 0.64x10{sup -2}. Moreover, our determination of the direction of the symmetry axis is in reasonable agreement with recent statistical analyses of cleaned CMB temperature fluctuation maps obtained by means of improved internal linear combination methods as galactic foreground subtraction technique.

Determination of quadrupole strengths in the [formula omitted] transition at [formula omitted

We report new precise p(e→,e′p)π0 measurements at the peak of the Δ+(1232) resonance at Q2=0.20(GeV/c)2 performed at the Mainz Microtron (MAMI). The new data are sensitive to both the electric (E2) and the Coulomb (C2) quadrupole amplitudes of the γ∗N→Δ transition. They yield precise quadrupole to dipole amplitude ratios: CMR=(−5.09±0.28stat+sys±0.30model)% and EMR=(−1.96±0.68stat+sys±0.41model)% for M1+3/2=(39.57±0.75stat+sys±0.40model)(10−3/mπ+). The new results are in disagreement with Constituent Quark Model predictions and in qualitative agreement with models that account for mesonic contributions, including recent Lattice calculations. They thus give further credence to the conjecture of deformation in hadronic systems favoring the attribution of the origin of deformation to the dominance of mesonic effects.

Ellipsoidal Universe Can Solve the Cosmic Microwave Background Quadrupole Problem

The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit Lambda-cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order 10(-2), the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

Evidence of Vorticity and Shear at Large Angular Scales in the WMAP Data: A Violation of Cosmological Isotropy?

Motivated by the large-scale asymmetry observed in the cosmic microwave background sky, we consider a specific class of anisotropic cosmological models—Bianchi type VIIh—and compare them to the WMAP first-year data on large angular scales. Remarkably, we find evidence of a correlation that is ruled out as a chance alignment at the 3 σ level. The best-fit Bianchi model corresponds to x = 0.55, Ω0 = 0.5, a rotation axis in the direction (l, b) = (222°, -62°), shear 0 = 2.4 × 10-10, and a right-handed vorticity 0 = 4.3 × 10-10. Correcting for this component greatly reduces the significance of the large-scale power asymmetry, resolves several anomalies detected on large angular scales (i.e., the low quadrupole amplitude and quadrupole/octopole planarity and alignment), and can account for a non-Gaussian cold spot on the sky. Despite the apparent inconsistency with the best-fit parameters required in inflationary models to account for the acoustic peaks, we consider the results sufficiently provocative to merit further consideration.

STUDYING γ*N→Δ→πN WITH CROSS SECTIONS AND POLARIZATION OBSERVABLES

Preliminary results are presented of the reaction γ*N→Δ→πN that was studied at the Jefferson Laboratory for transferred four momentum of 1.0 (GeV/c)2. Angular distributions of the cross sections and polarizations were measured over much of the available phase space. Out of the eighteen response functions involved in this reaction, fourteen separate responses and two additional response combinations were extracted. All resonant and background multipole amplitudes were decomposed for s- and p-waves as well as several of the d-wave multipole amplitudes. The responses and multipoles were compared to model calculations. Significant differences were observed between the experimental values and those of the models for several of the responses and multipoles. The ratios of the electric and longitudinal quadrupole amplitudes to the magnetic dipole amplitude were extracted. These values are different from previously reported values.

N-to-ΔElectromagnetic-Transition Form Factors from Lattice QCD

The magnetic dipole (M1), the electric quadrupole (E2), and the Coulomb quadrupole (C2) amplitudes for gammaN-->Delta are calculated in quenched lattice QCD. Using a new method, which combines an optimal choice of interpolating fields for the Delta and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios R(EM)=E2/M1 and R(SM)=C2/M1, up to momentum transfer squared 1.5 GeV2. We show for the first time, using lattice QCD, that both R(EM) and R(SM) are nonzero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the N/Delta system.

Testing the cosmological principle of isotropy: local power-spectrum estimates of theWMAPdata

We apply the Gabor transform methodology proposed by Hansen et al. to the WMAP data in order to test the statistical properties of the cosmic microwave background (CMB) fluctuation field and specifically to evaluate the fundamental assumption of cosmological isotropy. In particular, we apply the transform with several apodization scales, thus allowing the determination of the positional dependence of the angular power spectrum with either high spatial localization or high angular resolution (i.e. narrow bins in multipole space). Practically, this implies that we estimate the angular power spectrum locally in discs of various sizes positioned in different directions: small discs allow the greatest sensitivity to positional dependence, whereas larger discs allow greater sensitivity to variations over different angular scales. In addition, we determine whether the spatial position of a few outliers in the angular power spectrum could suggest the presence of residual foregrounds or systematic effects. For multipoles close to the first peak, the most deviant local estimates from the best-fitting WMAP model are associated with a few particular areas close to the Galactic plane. Such deviations also include the ‘dent’ in the spectrum just shortward of the first peak which was remarked upon by the WMAP team. Estimating the angular power spectrum excluding these areas gives a slightly higher first Doppler peak amplitude. Finally, we probe the isotropy of the largest angular scales by estimating the power spectrum on hemispheres and reconfirm strong indications of a north–south asymmetry previously reported by other authors. Indeed, there is a remarkable lack of power in a region associated with the North ecliptic Pole. With the greater fidelity in ℓ-space allowed by this larger sky coverage, we find tentative evidence for residual foregrounds in the range ℓ= 2–4, which could be associated with the low measured quadrupole amplitudes and other anomalies on these angular scales (e.g. planarity and alignment). However, over the range ℓ= 5–40 the observed asymmetry is much harder to explain in terms of residual foregrounds and known systematic effects. By reorienting the coordinate axes, we partition the sky into different hemispheres and search for the reference frame which maximizes the asymmetric distribution of power. The North Pole for this coordinate frame is found to intersect the sphere at (80°, 57°) in Galactic colatitude and longitude over almost the entire multipole range ℓ= 5–40. Furthermore, the strong negative outlier at ℓ= 21 and the strong positive outlier at ℓ= 39, as determined from the global power spectrum by the WMAP team, are found to be associated with the Northern and Southern hemispheres, respectively (in this frame of maximum asymmetry). Thus, these two outliers follow the general tendency of the multipoles ℓ= 5–40 to be of systematically lower amplitude in the north and higher in the south. Such asymmetric distributions of power on the sky provide a serious test for the cosmological principle of isotropy.

NtoΔelectromagnetic transition form factors from lattice QCD

The magnetic dipole, the electric quadrupole, and the Coulomb quadrupole amplitudes for the transition $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}$ are evaluated both in quenched lattice QCD at $\ensuremath{\beta}=6.0$ and using two dynamical Wilson fermions simulated at $\ensuremath{\beta}=5.6.$ The dipole transition form factor is accurately determined at several values of momentum transfer. On the lattices studied in this work, the electric quadrupole amplitude is found to be nonzero, yielding a negative value for the ratio ${R}_{\mathrm{EM}}$ of electric quadrupole to magnetic dipole amplitudes at three values of momentum transfer.

A maximum likelihood analysis of the low cosmic microwave background multipoles from theWilkinson Microwave Anisotropy Probe

The amplitudes of the quadrupole and octopole measured from the Wilkinson Microwave Anisotropy Probe (WMAP) appear to be lower than expected according to the concordance A cold dark matter (ACDM) cosmology. However, the pseudo-C l estimator used by the WMAP team is non-optimal. In this paper, we discuss the effects of Galactic cuts on pseudo-C l and quadratic maximum likelihood estimators. An application of a quadratic maximum likelihood estimator to Galaxy-subtracted maps produced by the WMAP team and Tegmark, de Oliveira-Costa & Hamilton shows that the amplitudes of the low multipoles are stable to different Galactic cuts. In particular, the quadrupole and octopole amplitudes are found to lie in the ranges ΔT 2 2 = 176-250 (μK) 2 and ΔT 2 3 = 794-1183 (μK) 2 (and more likely to be at the upper ends of these ranges) rather than the values ΔT 2 2 = 123 (μK) 2 and ΔT 2 3 = 611 (μK) 2 found by the WMAP team. These results indicate that the discrepancy with the concordance ACDM model at low multipoles is not particularly significant and is in the region of a few per cent. This conclusion is consistent with an analysis of the low amplitude of the angular correlation function computed from quadratic maximum likelihood power spectrum estimates.

γN → Δ transition form factors in quenched and NF = 2 QCD

Abstract Calculations of the magnetic dipole, electric quadrupole and Coulomb quadrupole amplitudes for the transition γN → Δ are presented both in quenched QCD and with two flavours of degenerate dynamical quarks.

Δ→Nγ*Coulomb quadrupole amplitude in PQCD

We present a leading-order pQCD calculation of the helicity-flip $\Delta\to N\gamma^*$ matrix element $G_0$ (Coulomb quadrupole amplitude $C2$), taking into account the transverse momenta of the quarks and the contribution from the gluons. In the large $Q^2$ limit, its scaling behavior acquires a double-logarithmic correction $\log^2{(Q^2/\Lambda^2)}$ compared with the standard scaling analysis, due to the contribution from the orbital motion of the small-$x$ partons. Based on this and on the latest JLab experimental results of the $C2-M1$ ratio $R_{SM}$ at $Q^2$ = 3 $\sim$ 4 GeV$^2$, we make a phenomenological prediction for the latter at higher values of $Q^2$.

Is the low cosmic microwave background quadrupole a signature of spatial curvature?

The temperature anisotropy power spectrum measured with the Wilkinson Microwave Anisotropy Probe (WMAP) at high multipoles is in spectacular agreement with an inflationary Λ-dominated cold dark matter cosmology. However, the low-order multipoles (especially the quadrupole) have lower amplitudes than expected from this cosmology, indicating a need for new physics. Here we speculate that the low quadrupole amplitude is associated with spatial curvature. We show that positively curved models are consistent with the WMAP data and that the quadrupole amplitude can be reproduced if the primordial spectrum truncates on scales comparable to the curvature scale.

Measurement of the transverse–longitudinal cross sections in the [formula omitted] reaction in the Δ region

Accurate measurements of the p(e→,e′p)π0 reaction were performed at Q2=0.127 (GeV/c)2 in the Δ resonance energy region. The experiments at the MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam with the out-of-plane magnetic spectrometer system (OOPS). In this Letter we report the first simultaneous determination of both the TL and TL′ (“fifth” or polarized) cross sections at low Q2 where the pion cloud contribution is predicted to dominate the quadrupole amplitudes (E2 and C2). These are the real and imaginary parts of the transverse–longitudinal interference amplitudes and provide a sensitive determination of the Coulomb quadrupole amplitude and a test of reaction calculations. Comparisons with model calculations are presented. The empirical MAID calculation gives the best overall agreement with this accurate data. The parameters of this model for the values of the resonant multipoles are |M1+(I=3/2)|=(40.9±0.3)×10−3/mπ, CMR=C2/M1=−6.5±0.3%, EMR=E2/M1=−2.2±0.9%, where the errors are due to the experimental uncertainties.

Measurement of theRLTresponse function forπ0electroproduction atQ2=0.070(GeV/c)2in theN→Δtransition

Quadrupole amplitudes in the $\gamma^{*}N\to\Delta$ transition are associated with the issue of nucleon deformation. A search for these small amplitudes has been the focus of a series of measurements undertaken at Bates/MIT by the OOPS collaboration. We report on results from H$(e,e^\prime p)\pi^0$ data obtained at $Q^2= 0.070$ (GeV/c)$^2$ and invariant mass of W=1155 MeV using the out-of-plane detection technique with the OOPS spectrometers. The $\sigma_{LT}$ and $\sigma_{T}+\epsilon\cdot$ $\sigma_{L}$ response functions were isolated. These results, along with those of previous measurements at $W$=1172 MeV and $Q^2= 0.127$ (GeV/c)$^2$, aim in elucidating the interplay between resonant and non resonant amplitudes.