We report the first measurement of strange ($\Lambda$) and anti-strange ($\bar{\Lambda}$) baryon production from $\sqrt{s_{_{NN}}}=130$ GeV Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Rapidity density and transverse mass distributions at mid-rapidity are presented as a function of centrality. The yield of $\Lambda$ and $\bar{\Lambda}$ hyperons is found to be approximately proportional to the number of negative hadrons. The production of $\bar{\Lambda}$ hyperons relative to negative hadrons increases very rapidly with transverse momentum. The magnitude of the increase cannot be described by existing hadronic string fragmentation models.
Transverse mass distributions of $\Lambda$ at mid-rapidity ($|y|<0.5$) for selected centrality bins. Only statistical errors are listed. Combined systematic errors estimated to be $10\%$. The dashed lines are Boltzmann fits. Note that multiplicative factors have been applied to data from the two most central data sets for display.
Transverse mass distributions of $\bar\Lambda$ at mid-rapidity ($|y|<0.5$) for selected centrality bins. Only statistical errors are listed. Combined systematic errors estimated to be $10\%$. The dashed lines are Boltzmann fits. Note that multiplicative factors have been applied to data from the two most central data sets for display.
The mid-rapidity $\bar\Lambda$ ($|y|<0.5$) transverse momentum distribution from the top $5\%$ most central collisions. For comparison the distributions for negative hadrons ($d^{2}N/(2 \pi p_{T})dp_{T}d\eta$, $|\eta|<0.1$) and anti-protons ($|y|<0.1$) for the similar centrality bin are included. Only statistical errors are listed. Statistical errors are less than the size of the data points. Combined systematic errors on hyperons estimated to be $10\%$. Correlated systematic errors for negative hadrons estimated to be $6\%$. Systematic errors on antiprotons are $8\%$ point-to-point and $10\%$ in the overall normalization.
We present the first measurement of midrapidity vector meson φ production in Au+Au collisions at RHIC (sNN=130 GeV) from the STAR detector. For the 11% highest multiplicity collisions, the slope parameter from an exponential fit to the transverse mass distribution is T=379±50(stat)±45(syst) MeV, the yield dN/dy=5.73±0.37(stat)±0.69(syst) per event, and the ratio Nφ/Nh− is found to be 0.021±0.001(stat)±0.004(syst). The measured ratio Nφ/Nh− and T for the φ meson at midrapidity do not change for the selected multiplicity bins.
Transverse mass distriution of $\phi$ for 0-11% centrality in Au+Au collisions at 130 GeV.
Transverse mass distriution of $\phi$ for 11-26% centrality in Au+Au collisions at 130 GeV.
Transverse mass distriution of $\phi$ for 26-85% centrality in Au+Au collisions at 130 GeV.
Distributions of event-by-event fluctuations of the mean transverse momentum and mean transverse energy near mid-rapidity have been measured in Au+Au collisions at sqrt(s_NN) = 130 GeV at RHIC. By comparing the distributions to what is expected for statistically independent particle emission, the magnitude of non-statistical fluctuations in mean transverse momentum is determined to be consistent with zero. Also, no significant non-random fluctuations in mean transverse energy are observed. By constructing a fluctuation model with two event classes that preserve the mean and variance of the semi-inclusive p_T or e_T spectra, we exclude a region of fluctuations in sqrt(s_NN) = 130 GeV Au+Au collisions.
The $N_{tracks}$ distribution for the $0-10\%$ centrality class (data points) compared to the $N_{mix}$ distribution from the mixed event sample (curve).
The $M_{p_T}$ distributions for four different centrality classes. The curves are the random baseline mixed event distributions.
The residual distribution between the data and mixed event $M_{p_T}$ in units of standard deviations for all centrality classes. The total ${\chi}^2$ and the number of degrees of freedom for the $0-5\%$, $0-10\%$, $10-20\%$, $20-30\%$ centrality classes are 89.0/39, 155.7/40,163.3/47, and 218.4/61, respectively.
Data from Au + Au interactions at sqrt(s_NN) = 130 GeV, obtained with the PHENIX detector at RHIC, are used to investigate local net charge fluctuations among particles produced near mid-rapidity. According to recent suggestions, such fluctuations may carry information from the Quark Gluon Plasma. This analysis shows that the fluctuations are dominated by a stochastic distribution of particles, but are also sensitive to other effects, like global charge conservation and resonance decays.
The normalized variance $v(Q)$as a function of $n_{ch}$.
The normalized variance $v(R)$ as a function of $n_{ch}$.
The normalized variance $v(Q)$ for different centrality classes.
Strange baryon pair production in two-photon collisions is studied with the L3 detector at LEP. The analysis is based on data collected at e+e- centre-of-mass energies from 91 GeV to 208 GeV, corresponding to an integrated luminosity of 844 pb-1. The processes gamma gamma -> Lambda Anti-lambda and gamma gamma -> Sigma0 Anti-sigma0 are identified. Their cross sections as a function of the gamma gamma centre-of-mass energy are measured and results are compared to predictions of the quark-diquark model.
Cross sections for LAMBDA and SIGMA0 pair production in the mass region 2.23 to 3.5 GeV.
Cross sections for LAMBDA pair production as a function of the 2 photon invariant mass W. The average W of each bin is assumes a W**(-8) distribution.
Cross sections for SIGMA0 pair production as a function of the 2 photon invariant mass W. The average W of each bin is assumes a W**(-8) distribution.
Results are presented from a study of the structure of high energy hadronic events recorded by the L3 detector at sqrt(s)>192 GeV. The distributions of several event shape variables are compared to resummed O(alphaS^2) QCD calculations. We determine the strong coupling constant at three average centre-of-mass energies: 194.4, 200.2 and 206.2 GeV. These measurements, combined with previous L3 measurements at lower energies, demonstrate the running of alphaS as expected in QCD and yield alphaS(mZ) = 0.1227 +- 0.0012 +- 0.0058, where the first uncertainty is experimental and the second is theoretical.
The measured ALPHA_S at three centre-of-mass energies from fits to the individual event shape distributions. The first error is statistcal, the first DSYS error is the experimental systematic uncertainty, and the second DSYS error is the theoryuncertainty.
Updated ALPHA_S measurements from the BT, BW and C-Parameter distributions,from earlier L3 data at lower centre-of-mass energies.. The first error is the total experimental error (stat+sys in quadrature) and the DSYS error is the theory uncertainty.
Combined ALPHA_S values from the five event shape variables. The first error is statistical, the first DSYS error is the experimental systematic uncertainity, the second DSYS error is the uncertainty from the hadronisdation models, andthethird DSYS errpr is the uncertainty due to uncalculated higher orders in the QCDpredictions.
Inclusive D^{*+-} production in two-photon collisions is studied with the L3 detector at LEP, using 683 pb^{-1} of data collected at centre-of-mass energies from 183 to 208 GeV. Differential cross sections are determined as functions of the transverse momentum and pseudorapidity of the D^{*+-} mesons in the kinematic region 1 GeV < P_T < 12 GeV and |eta| < 1.4. The cross sections sigma(e^+e^- -> e^+e^-D^{*+-}X) in this kinematical region is measured and the sigma(e^+e^- -> e^+e^- cc{bar}X) cross section is derived. The measurements are compared with next-to-leading order perturbative QCD calculations.
Visible D*+- production cross section in the given phase space range. Data are given for each D* decay channel, and the average.
Total cross section for open charm production. Data are given for each D* decay channel, and the combined average. The second systematic (DSYS) error is the uncertainty on the extrapolation from the visible to the full phase space region.
The measured D*+- production cross section in the region ABS(ETARAP) < 1.4.The DSIG/DPT points refer to the centre of the bin and the SIG points are the integrated over the bin.
The hadronic structure of the photon F2gamma is measured as a function of Bjorken x and of the photon virtuality Q2 using deep-inelastic scattering data taken by the OPAL detector at LEP at e+e- centre-of-mass energies from 183 to 209 GeV. Previous OPAL measurements of the x dependence of F2gamma are extended to an average Q2 of <Q2>=780GeV2 using data in the kinematic range 0.15 < x < 0.98. The Q2 evolution of F2gamma is studied for 12.1 < <Q2> < 780GeV2 using three ranges of x. As predicted by QCD, the data show positive scaling violations in F2gamma for the central x region 0.10-0.60. Several parameterisations of F2gamma are in qualitative agreement with the measurements whereas the quark-parton model prediction fails to describe the data.
F2 and DSIG/DX for the EE sample in the high Q**2 region as a function of X.
Statistical correlations between the bins in the preceding table.
The measured value of F2 and DSIG/DX for the SW data sample in the Q**2 range 9 to 15 GeV**2.
We present a measurement of the b-quark inclusive fragmentation function in Z0 decays using a novel kinematic B-hadron energy reconstruction technique. The measurement was performed using 350,000 hadronic Z0 events recorded in the SLD experiment at SLAC between 1997 and 1998. We compared the sacled B-hadron energy distribution with models of b-quark fragmentation and with several ad hoc functional forms. A number of models and functions are excluded by the data. The average scaled energy of weakly-decaying B hadrons was measured to be <x_B>= 0.709 +-0.003 (stat) +-0.003 (syst) +-0.002 (model).
DATA FROM THE ERRATUM (PR D66,079905,2002). Measurement of the fragmentation function of weakly decaying B-hadrons in Z0 decays. First systematic (DSYS) error is the systematic error, the second is the estimated error due to the model dependence of the unfolding procedure.
DATA FROM ORIGINAL PAPER, SUPERSEDED BY ERRATUM (SEE ABOVE TABLE). Measurement of the fragmentation function of weakly decaying B-hadrons in Z0 decays. First systematic (DSYS) error is the systematic error, the second is the estimated error due to the model dependence of the unfolding procedure.
Transverse momentum spectra of electrons from Au+Au collisions at sqrt(s_NN) = 130 GeV have been measured by the PHENIX experiment at RHIC. The spectra show an excess above the background from photon conversions and light hadron decays. The electron signal is consistent with that expected from semi-leptonic decays of charm. The yield of the electron signal dN_e/dy for p_T > 0.8 GeV/c is 0.025 +/- 0.004 (stat.) +/- 0.010 (sys.) in central collisions, and the corresponding charm cross section is 380 +/- 60 (stat.) +/- 200 (sys.) micro barns per binary nucleon-nucleon collision.
Transverse momentum spectra of electrons in PHENIX from Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV.
Transverse momentum spectra of electrons in PHENIX from Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV.
Transverse momentum spectra of electrons in PHENIX from Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV. The upper limit for 1.9 GeV/$c$ is 4.10224e-05.
We have measured the cross sections $d^2\sigma/dP_T d\eta$ for production of isolated direct photons in \pbarp collisions at two different center-of-mass energies, 1.8 TeV and 0.63 TeV, using the Collider Detector at Fermilab (CDF). The normalization of both data sets agree with the predictions of Quantum Chromodynamics (QCD) for photon transverse momentum ($P_T$) of 25 GeV/c, but the shapes versus photon $P_T$ do not. These shape differences lead to a significant disagreement in the ratio of cross sections in the scaling variable $x_T (\equiv 2P_T/\sqrt{s}$). This disagreement in the $x_T$ ratio is difficult to explain with conventional theoretical uncertainties such as scale dependence and parton distribution parameterizations.
The 1800 GeV isolated photon cross section. The systematic (DSYS) uncertainties include the normalisation uncertainties which are 100 PCT correlated bin tobin.
The 630 GeV isolated photon cross section. The systematic (DSYS) uncertainties include the normalisation uncertainties which are 100 PCT correlated bin to bin.
The photoproduction of eta-mesons from 2H and 4He has been studied for energies close to the production thresholds. The experiments were carried out with the tagged photon beam of the Mainz MAMI accelerator. The eta-mesons were detected via their two photon decays with the electromagnetic calorimeter TAPS. Total cross sections, angular and momentum distributions of the eta-mesons have been determined for both reactions. The total cross sections in the threshold region show a large enhancement over the predictions of a participant - spectator model, indicating significant final state interaction effects. The results are compared to recent model calculations taking into account nucleon-nucleon and nucleon-eta final state interaction effects on different levels of sophistication.
Total inclusive photoproduction cross sections. Statistical errors only.
Angular distributions of ETA mesons from the Deuterium target in the photon-nucleus cm system. Statistical errors only.
Angular distributions of ETA mesons from the Deuterium target in the photon-nucleus cm system. Statistical errors only.
Dijet cross sections as functions of several jet observables are measured in photoproduction using the H1 detector at HERA. The data sample comprises e^+p data with an integrated luminosity of 34.9 pb^(-1). Jets are selected using the inclusive k_T algorithm with a minimum transverse energy of 25 GeV for the leading jet. The phase space covers longitudinal proton momentum fraction x_p and photon longitudinal momentum fraction x_gamma in the ranges 0.05<x_p<0.6 and 0.1<x_gamma<1. The predictions of next-to-leading order perturbative QCD, including recent photon and proton parton densities, are found to be compatible with the data in a wide kinematical range.
Differential ep cross section for dijet production as a function of the invariant mass of the two jets.
Differential ep cross section for dijet production as a function of the average transverse energy the two jets.
Differential ep cross section for dijet production as a function of the maximum transverse energy the leading jet.
The exclusive photoproduction of J/psi mesons, gamma p->J/psi p, has been studied in ep collisions with the ZEUS detector at HERA, in the kinematic range 20<W<290 GeV, where W is the photon-proton centre-of-mass energy. The J/psi mesons were reconstructed in the muon and the electron decay channels using integrated luminosities of 38 pb^-1 and 55 pb^-1, respectively. The helicity structure of J/psi production shows that the hypothesis of s-channel helicity conservation is satisfied at the two standard-deviation level. The total cross section and the differential cross-section dsigma/dt, where t is the squared four-momentum transfer at the proton vertex, are presented as a function of W, for |t|<1.8 GeV^2. The t distribution exhibits an exponential shape with a slope parameter increasing logarithmically with W with a value b=4.15 \pm 0.05 (stat.)^{+0.30}_{-0.18} (syst.) GeV^-2 at W=90 GeV. The effective parameters of the Pomeron trajectory are alphapom(0) = 1.200 \pm 0.009(stat.)^{+0.004}_{-0.010}(syst.) and alphappom= 0.115 \pm 0.018(stat.)^{+0.008}_{-0.015}(syst.) GeV^-2.
The total exclusive J/PSI photoproduction cross section, the differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence as afunction of W, the photon-proton c.m. energy, for data from J/PSI muon decay.
The total exclusive J/PSI photoproduction cross section as a function of W,the photon-proton c.m. energy, for data from J/PSI electron decays.
The differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence for exclusive J/PSI photoproduction as a function of W, the photon-proton c.m. energy for data from J/PSI electron decays.
Differential cross sections for γp→ηp have been measured with tagged real photons for incident photon energies from 0.75 to 1.95 GeV. Mesons were identified by missing mass reconstruction using kinematical information for protons scattered in the production process. The data provide the first extensive angular distribution measurements for the process above W=1.75 GeV. Comparison with preliminary results from a constituent quark model support the suggestion that a third S11 resonance with mass ∼1.8 GeV couples to the ηN channel.
Cross sections for photon energies 0.775 to 0.925 GeV.
Cross sections for photon energies 0.975 to 1.125 GeV.
Cross sections for photon energies 1.175 to 1.325 GeV.
Two-pion correlations in sqrt(s_NN)=130 GeV Au+Au collisions at RHIC have been measured over a broad range of pair transverse momentum k_T by the PHENIX experiment at RHIC. The k_T dependent transverse radii are similar to results from heavy ion collisions at sqrt(s_NN) = 4.1, 4.9, and 17.3 GeV, whereas the longitudinal radius increases monotonically with beam energy. The ratio of the outwards to sidewards transverse radii (R_out/R_side) is consistent with unity and independent of k_T.
HBT radii for pion pairs as a function of $k_T$ measured at mid-rapidity for various energies for Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV. Values used are from the Longitudinal Co-Moving System (LCMS) frame.
HBT radii for pion pairs as a function of $k_T$ measured at mid-rapidity for various energies for Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV. Values used are from the Pair Center-of-Mass System (PCMS) frame.
The top panel shows the measured $R_{side}$ from identical pions for PHENIX. The bottom panel shows the ratio $R_{out}/R_{side}$ as a function of $k_T$. Longitudinal Co-Moving System (LCMS) frame for $\pi^+$
The photon-proton total cross section has been measured in the process e+ p -> e+ gamma p -> e+ X with the ZEUS detector at HERA. Events were collected with photon virtuality Q^2 < 0.02 GeV^2 and average gamma-p center-of-mass energy W_{gamma p} = 209 GeV in a dedicated run, designed to control systematic effects, with an integrated luminosity of 49 nb^{-1}. The measured total cross section is sigma_{tot}^{gamma p} = 174 +- 1 (stat.) +- 13 (syst.) microbarns. The energy dependence of the cross section is compatible with parameterizations of high-energy p-p and p-pbar data.
Total GAMMA P cross section.
The dijet cross section in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 38.6 pb$^{-1}$. The events were required to have a virtuality of the incoming photon, $Q^2$, of less than 1 GeV$^2$ and a photon-proton centre-of-mass energy in the range $134 < W_{\gamma p} < 277$ GeV. Each event contains at least two jets satisfying transverse-energy requirements of $E_{T}^{\rm jet1}>14$ GeV and $E_{T}^{\rm jet2}>11$ GeV and pseudorapidity requirements of $-1<\eta^{\rm jet1,2}<2.4$. The measurements are compared to next-to-leading-order QCD predictions. The data show particular sensitivity to the density of partons in the photon, allowing the validity of the current parameterisations to be tested.
Measured cross section as a function of COS(THETA*), where THETA* is the dijet angle in the parton-parton c.m. frame. The data are shown in two X(C=GAMMA) regions.
Measured cross section as a function of ET(JET1) for X(C=GAMMA) > 0.75 for:. -1 < ETARAP(JET1) < 0. -1 < ETARAP(JET2) < 0.
Measured cross section as a function of ET(JET1) for X(C=GAMMA) > 0.75 for:. 0 < ETARAP(JET1) < 1. -1 < ETARAP(JET2) < 0.
Identified pi^[+/-] K^[+/-], p and p-bar transverse momentum spectra at mid-rapidity in sqrt(s_NN)=130 GeV Au-Au collisions were measured by the PHENIX experiment at RHIC as a function of collision centrality. Average transverse momenta increase with the number of participating nucleons in a similar way for all particle species. The multiplicity densities scale faster than the number of participating nucleons. Kaon and nucleon yields per participant increase faster than the pion yields. In central collisions at high transverse momenta (p_T greater than 2 GeV/c), anti-proton and proton yields are comparable to the pion yields.
Transverse momentum spectra for PI+ in the midrapidity range for the centrality region 0 to 5 PCT. Errors are combined statistical and systematics.
Transverse momentum spectra for PI- in the midrapidity range for the centrality region 0 to 5 PCT. Errors are combined statistical and systematics.
Transverse momentum spectra for K+ in the midrapidity range for the centrality region 0 to 5 PCT. Errors are combined statistical and systematics.
The inclusive production of the omega(782) vector meson in hadronic Z decays is measured and compared to model predictions. The analysis is based on 4 million hadronic Z decays recorded by the ALEPH detector between 1991 and 1995. The production rate for x_p = p_meson/p_beam > 0.05 is measured in the omega -> pi^+ pi^- pi^0 decay mode and found to be 0.585 +- 0.019_stat +- 0.033_sys per event. Inclusive eta meson production is also measured in the same decay channel for x_p > 0.10, obtaining 0.355 +- 0.011_stat +- 0.024_sys per event. The branching ratio for omega -> mu^+ mu^- is investigated. A total of 18.1 +- 5.9 events are observed, from which the muonic branching ratio is measured for the first time to be BR(omega -> mu^+ mu^-) = (9.0 +- 2.9_stat +- 1.1_sys)*10^-5.
Extrapolation using JETSET 7.4 is used to correct down to X = 0.0. The second DSYS error, where relevant, shows the estimated uncertainty on the extrapolation.
Production rate and differential cross sections for the ETA.
Production rate and differential cross sections for the OMEGA.
We present measurements of the B+ meson total cross section and differential cross section $d\sigma/ dp_T$. The measurements use a $98\pm 4$ pb^{-1} sample of $p \bar p$ collisions at $\sqrt{s}=1.8$ TeV collected by the CDF detector. Charged $B$ meson candidates are reconstructed through the decay $B^{\pm} \to J/\psi K^{\pm}$ with $J/\psi\to \mu^+ \mu^-$. The total cross section, measured in the central rapidity region $|y|<1.0$ for $p_T(B)>6.0$ GeV/$c$, is $3.6 \pm 0.6 ({\rm stat} \oplus {\rm syst)} \mu$b. The measured differential cross section is substantially larger than typical QCD predictions calculated to next-to-leading order.
Measured differential cross section for B+ production. The first (DSYS) error is the PT dependent systematic error and the second is the full correlated systematic error.
The total integrated B+ meson cross section. The first error is the combined statistical and PT dependent systematic error. The DSYS error is the fully correlated systematic error.
We report on measurements of the ϒ(1S), ϒ(2S), and ϒ(3S) differential cross sections (d2σ/dpTdy)|y|<0.4, as well as on the ϒ(1S) polarization in pp¯ collisions at s=1.8TeV using a sample of 77±3pb−1 collected by the collider detector at Fermilab. The three resonances were reconstructed through the decay ϒ→μ+μ−. The measured angular distribution of the muons in the ϒ(1S) rest frame is consistent with unpolarized meson production.
The differential cross section times the branching ratio into mu+ mu- for UPSILON(1S) production.
The differential cross section times the branching ratio into mu+ mu- for UPSILON(2S) production. The first DSYS error is the systematic error due to the polarization of the UPSILON which is shown seperately from the other systematic errors.
The differential cross section times the branching ratio into mu+ mu- for UPSILON(3S) production. The first DSYS error is the systematic error due to the polarization of the UPSILON which is shown seperately from the other systematic errors.
A search was made among ν μ charged current events collected in the NOMAD experiment for the reaction: ν μ +N→μ − +D ★+ + hadrons ↪ D 0 +π + ↪ K − +π + . A high purity D ★+ sample composed of 35 events was extracted. The D ★+ yield in ν μ charged current interactions was measured to be T =(0.79±0.17(stat.)±0.10(syst.))%. The mean fraction of the hadronic jet energy taken by the D ★+ is 0.67±0.02(stat.)±0.02(syst.). The distributions of the fragmentation variables z, P T 2 and x F for D ★+ are also presented.
Distribution in Feynman X.
Distribution in transverse momentum.
Distribution in fractional energy Z.
A study of strange particle production in muon neutrino charged current interactions has been performed using the data from the NOMAD experiment. Yields of neutral strange particles K0s, Lambda, AntiLambda have been measured. Mean multiplicities are reported as a function of the event kinematic variables Enu, W2 and Q2 as well as of the variables describing particle behaviour within a hadronic jet: xF, z and pT2. Decays of resonances and heavy hyperons with identified K0s and Lambda in the final state have been analyzed. Clear signals corresponding to K*+-, Sigma*+-, Xi- and Sigma0 have been observed.
Measured yields of the neutral strange particles measured in this analysis.The second line (marked *) is a recalculation taking into account contributions from both primary and secondary V0. The values for K0 are the K0S rates multipl ied by 2.
Measured yields as a function of E, the neutrino energy.
Measured yields as a function of W**2.
The interaction of virtual photons is investigated using the reaction e+e- -> e+e- hadrons based on data taken by the OPAL experiment at e+e- centre-of-mass energies sqrt(s_ee)=189-209 GeV, for W>5 GeV and at an average Q^2 of 17.9 GeV^2. The measured cross-sections are compared to predictions of the Quark Parton Model (QPM), to the Leading Order QCD Monte Carlo model PHOJET to the NLO prediction for the reaction e+e- -> e+e-qqbar, and to BFKL calculations. PHOJET, NLO e+e- -> e+e-qqbar, and QPM describe the data reasonably well, whereas the cross-section predicted by a Leading Order BFKL calculation is too large.
Total cross section in the given phase space and assuming ALPHA = 1/137.
Differential cross section as a function of X where X is the maximum value of X1 or X2, the upper and lower vertex values.
Differential cross section as a function of Q**2 where Q**2 is the maximum value of Q1**2 or Q2**2, the upper and lower vertex values.
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