The STAR Collaboration reports on the photoproduction of $\pi^+\pi^-$ pairs in gold-gold collisions at a center-of-mass energy of 200 GeV/nucleon-pair. These pion pairs are produced when a nearly-real photon emitted by one ion scatters from the other ion. We fit the $\pi^+\pi^-$ invariant mass spectrum with a combination of $\rho$ and $\omega$ resonances and a direct $\pi^+\pi^-$ continuum. This is the first observation of the $\omega$ in ultra-peripheral collisions, and the first measurement of $\rho-\omega$ interference at energies where photoproduction is dominated by Pomeron exchange. The $\omega$ amplitude is consistent with the measured $\gamma p\rightarrow \omega p$ cross section, a classical Glauber calculation and the $\omega\rightarrow\pi^+\pi^-$ branching ratio. The $\omega$ phase angle is similar to that observed at much lower energies, showing that the $\rho-\omega$ phase difference does not depend significantly on photon energy. The $\rho^0$ differential cross section $d\sigma/dt$ exhibits a clear diffraction pattern, compatible with scattering from a gold nucleus, with 2 minima visible. The positions of the diffractive minima agree better with the predictions of a quantum Glauber calculation that does not include nuclear shadowing than with a calculation that does include shadowing.
The $\pi^+\pi^-$ invariant-mass distribution for all selected $\pi\pi$ candidates with $p_T~<~100~\textrm{MeV}/c$.
The ratio $|B/A|$ of amplitudes of nonresonant $\pi^+\pi^-$ and $\rho^0$ mesons in the present STAR analysis.
The ratio $|B/A|$ of amplitudes of nonresonant $\pi^+\pi^-$ and $\rho^0$ mesons in the previous STAR analysis, Phys. Rev. C 77 034910 (2008).
Results of a high-statistics study of elastic scattering and meson resonances produced by π−p interactions at 8 GeV/c are presented. Large statistics and small systematic errors permit examination of the complete kinematic region. Total differential cross sections are given for ρ0,−, f0, g0,−, Δ±, Δ0, and N* resonances. Spin-density matrix elements and Legendre-polynomial moments are given for ρ, f, and Δ resonances. The results for ρ0 and f0 resonances are compared with the predictions of a Regge-pole-exchange model. Properties of the above resonances are compared and discussed. In particular, we present evidence that the ρ0 and f0 production mechanisms are similar. The similarity of the g0 t distribution to that of the ρ0 and f0 suggests a common production mechanism for all three resonances.
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SLOPE REFERS TO EXPONENTIAL FIT IN U.
We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t' < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.
Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.
Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).
Photon diffractive dissociation, $\gamma p \to Xp$, has been studied at HERA with the ZEUS detector using $ep$ interactions where the virtuality $Q^2$ of the exchanged photon is smaller than 0.02 GeV$^2$. The squared four-momentum $t$ exchanged at the proton vertex was determined in the range $0.073<|t|<0.40$ GeV$^2$ by measuring the scattered proton in the ZEUS Leading Proton Spectrometer. In the photon-proton centre-of-mass energy interval $176<W<225$ GeV and for masses of the dissociated photon system $4<M_X<32$ GeV, the $t$ distribution has an exponential shape, $dN/d|t| \propto \exp{(-b|t|)}$, with a slope parameter $b=6.8 \pm 0.9$~(stat.)~$ ^{+1.2}_{-1.1}$~(syst.)~GeV$^{-2}$.
T is the squared four momentum transfer at the proton vertex.
SLOPE of the DN/DT distribution.
Results are presented onK+p elastic scattering and on the reactionK+p→K+pπ+π− at 70 GeV/c. For the
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INTEGRATION OVER RANGE OF ABS(T) FROM 0 TO 1 GEV.
A spin-parity analysis is performed of the low-mass (≤ 1.75 GeV/c2) pπ− system in diffractive np→(pπ−)p using new data at 13 GeV/c and 20 GeV/c. In the context of a Deck-plus-resonances model a good fit to the pπ− angular moments is found only if the Gribov-Morrison parity-change rule does not hold and spin states up to j=52 are included. In particular the presence of a considerable fraction of spin-parity ½− state is indicated.
DECK MODEL PLUS RESONANCES FIT TO DIFFRACTIVE EVENTS.
Cross-sections for diffractive particle production and pseudorapidity distributions of the decay products of diffractive states are presented. The data were obtained with the UA 5 streamer chamber detector at the CERNpp Collider operated in a new pulsed mode yieldingpp interactions at c.m. energies of 900 and 200 GeV. Data recorded with a special trigger designed to select a sample of events enriched in single-diffractive interactions clearly favour apt-limited fragmentation of diffractive states. The cross-section for single-diffractive particle production ϊ was found to be 7.8±0.5±1.1 mb at 900 GeV and 4.8±0.5±0.8 mb at 200 GeV (first error statistical, second systematic). From the pseudorapidity distribution of diffractive states we deduce the average number of charged particles to be 6.5±1.0 at 900 GeV and 4.1±1.1 at 200 GeV. Furthermore we report on our estimates for the cross-section of double-diffractive particle production at both Collider energies.
Single diffractive cross sections.
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We discuss the structure of the momentum transfer distributions for the diffractive dissociation processes p → n π + , p → Δ ++ π − and K − → K 890 ∗0 π − . In the near-threshold mass region a clear break of slope is found around t ′KK ∼ 0.25 GeV 2 for the two baryonic channels, whereas no comparable structure is seen for the mesonic system. The K → K ∗ π differential cross section exhibits a nearly exponential behaviour up to t ′ pp ∼ 0.6 GeV 2 , falling over three orders of magnitude. The slope variations and breaks are strongly correlated both to the mass region considered and to the decay angle of the fragmentation system.
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Forum