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).
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).
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DD IVENTS SELECTED BY THE RAPIDITY GAP METHOD.
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Deep inelastic scattering and its diffractive component, $ep \to e^{\prime}\gamma^* p \to e^{\prime}XN$, have been studied at HERA with the ZEUS detector using an integrated luminosity of 52.4 pb$^{-1}$. The $M_X$ method has been used to extract the diffractive contribution. A wide range in the centre-of-mass energy $W$ (37 -- 245 GeV), photon virtuality $Q^2$ (20 -- 450 GeV$^2$) and mass $M_X$ (0.28 -- 35 GeV) is covered. The diffractive cross section for $2 < M_X < 15$ GeV rises strongly with $W$, the rise becoming steeper as $Q^2$ increases. The data are also presented in terms of the diffractive structure function, $F^{\rm D(3)}_2$, of the proton. For fixed $Q^2$ and fixed $M_X$, $\xpom F^{\rm D(3)}_2$ shows a strong rise as $\xpom \to 0$, where $\xpom$ is the fraction of the proton momentum carried by the Pomeron. For Bjorken-$x < 1 \cdot 10^{-3}$, $\xpom F^{\rm D(3)}_2$ shows positive $\log Q^2$ scaling violations, while for $x \ge 5 \cdot 10^{-3}$ negative scaling violations are observed. The diffractive structure function is compatible with being leading twist. The data show that Regge factorisation is broken.
Proton structure function F2 at Q**2 = 25 GeV**2.
Proton structure function F2 at Q**2 = 35 GeV**2.
Proton structure function F2 at Q**2 = 45 GeV**2.
Diffractive photoproduction of D*+/-(2010) mesons was measured with the ZEUS detector at the ep collider HERA, using an integrated luminosity of 78.6 pb^{-1}. The D* mesons were reconstructed in the kinematic range: transverse momentum p_T(D*) > 1.9 GeV and pseudorapidity |eta(D*)| < 1.6, using the decay D*+ -> D0 pi+_s followed by D0 -> K- pi+ (+c.c.). Diffractive events were identified by a large gap in pseudorapidity between the produced hadronic state and the outgoing proton. Cross sections are reported for photon-proton centre-of-mass energies in the range 130 < W < 300 GeV and for photon virtualities Q^2 < 1 GeV^2, in two ranges of the Pomeron fractional momentum x_pom < 0.035 and x_pom < 0.01. The relative contribution of diffractive events to the inclusive D*+/-(2010) photoproduction cross section is about 6%. The data are in agreement with perturbative QCD calculations based on various parameterisations of diffractive parton distribution functions. The results are consistent with diffractive QCD factorisation.
Total cross section integrated over the given kinematic range.
Ratio of diffractive to inclusive D* cross section.
Differential cross sections for diffractive photoproduction of D*+- mesons as a function of X(NAME=POMERON).
Deep inelastic scattering and its diffractive component, ep -> e'gamma*p ->e'XN, have been studied at HERA with the ZEUS detector using an integrated luminosity of 4.2 pb-1. The measurement covers a wide range in the gamma*p c.m. energy W (37 - 245 GeV), photon virtuality Q2 (2.2 - 80 GeV2) and mass Mx. The diffractive cross section for Mx > 2 GeV rises strongly with W: the rise is steeper with increasing Q2. The latter observation excludes the description of diffractive deep inelastic scattering in terms of the exchange of a single Pomeron. The ratio of diffractive to total cross section is constant as a function of W, in contradiction to the expectation of Regge phenomenology combined with a naive extension of the optical theorem to gamma*p scattering. Above Mx of 8 GeV, the ratio is flat with Q2, indicating a leading-twist behaviour of the diffractive cross section. The data are also presented in terms of the diffractive structure function, F2D(3)(beta,xpom,Q2), of the proton. For fixed beta, the Q2 dependence of xpom F2D(3) changes with xpom in violation of Regge factorisation. For fixed xpom, xpom F2D(3) rises as beta -> 0, the rise accelerating with increasing Q2. These positive scaling violations suggest substantial contributions of perturbative effects in the diffractive DIS cross section.
Measurement of the proton structure function F2 at Q**2 = 2.7 GeV**2.
Measurement of the proton structure function F2 at Q**2 = 4.0 GeV**2.
Measurement of the proton structure function F2 at Q**2 = 6.0 GeV**2.
Diffractive dissociation of virtual photons, gamma* p-->Xp, has been studied in ep interactions with the ZEUS detector at HERA using an integrated luminosity of approx. 10 pb^-1. The data cover photon virtualities 0.17 < Q^2< 0.70 GeV^2 and 3 < Q^2< 80 GeV^2 with 3<M_X<38 GeV, where M_X is the mass of the hadronic final state.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 0.17 to 0.70 GeV**2.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 3 to 9 GeV**2.
The double differential cross section d2sig/dmx/dt measured with the LPS method for the Q**2 range 9 to 80 GeV**2.
The DIS diffractive cross section, $d\sigma^{diff}_{\gamma^* p \to XN}/dM_X$, has been measured in the mass range $M_X < 15$ GeV for $\gamma^*p$ c.m. energies $60 < W < 200$ GeV and photon virtualities $Q^2 = 7$ to 140 GeV$^2$. For fixed $Q^2$ and $M_X$, the diffractive cross section rises rapidly with $W$, $d\sigma^{diff}_{\gamma^*p \to XN}(M_X,W,Q^2)/dM_X \propto W^{a^{diff}}$ with $a^{diff} = 0.507 \pm 0.034 (stat)^{+0.155}_{-0.046}(syst)$ corresponding to a $t$-averaged pomeron trajectory of $\bar{\alphapom} = 1.127 \pm 0.009 (stat)^{+0.039}_{-0.012} (syst)$ which is larger than $\bar{\alphapom}$ observed in hadron-hadron scattering. The $W$ dependence of the diffractive cross section is found to be the same as that of the total cross section for scattering of virtual photons on protons. The data are consistent with the assumption that the diffractive structure function $F^{D(3)}_2$ factorizes according to $\xpom F^{D(3)}_2 (\xpom,\beta,Q^2) = (x_0/ \xpom)^n F^{D(2)}_2(\beta,Q^2)$. They are also consistent with QCD based models which incorporate factorization breaking. The rise of $\xpom F^{D(3)}_2$ with decreasing $\xpom$ and the weak dependence of $F^{D(2)}_2$ on $Q^2$ suggest a substantial contribution from partonic interactions.
Cross section for diffractive scattering.
Cross section for diffractive scattering.
Cross section for diffracitve scattering.
This paper presents the first analysis of diffractive photon dissociation events in deep inelastic positron-proton scattering at HERA in which the proton in the final state is detected and its momentum measured. The events are selected by requiring a scattered proton in the ZEUS leading proton spectrometer (LPS) with $\xl>0.97$, where $\xl$ is the fraction of the incoming proton beam momentum carried by the scattered proton. The use of the LPS significantly reduces the contamination from events with diffractive dissociation of the proton into low mass states and allows a direct measurement of $t$, the square of the four-momentum exchanged at the proton vertex. The dependence of the cross section on $t$ is measured in the interval $0.073<|t|<0.4$~$\gevtwo$ and is found to be described by an exponential shape with the slope parameter $b=\tslopeerr$. The diffractive structure function $\ftwodfour$ is presented as a function of $\xpom \simeq 1-\xl$ and $\beta$, the momentum fraction of the struck quark with respect to $\xpom$, and averaged over the $t$ interval $0.073<|t|<\ftwodfourtmax$~$\gevtwo$ and the photon virtuality range $5<Q^2<20~\gevtwo$. In the kinematic range $4 \times 10^{-4} < \xpom < 0.03$ and $0.015<\beta<0.5$, the $\xpom$ dependence of $\ftwodfour$ is fitted with a form $\xpoma$, yielding $a= \ftwodfouraerr$. Upon integration over $t$, the structure function $\ftwod$ is determined in a kinematic range extending to higher $\xpom$ and lower $\beta$ compared to our previous analysis; the results are discussed within the framework of Regge theory.
The measured distribution of T, the squared momentum transfer to the virtual pluton.
Slope of the T distribution.
The structure function F2(NAME=D4).
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