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).
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.
Diffractive scattering of $\gamma~* p \to X + N$, where $N$ is either a proton or a nucleonic system with $M_N<4$GeV has been measured in deep inelastic scattering (DIS) at HERA. The cross section was determined by a novel method as a function of the $\gamma~* p$ c.m. energy $W$ between 60 and 245GeV and of the mass $M_X$ of the system $X$ up to 15GeV at average $Q~2$ values of 14 and 31GeV$~2$. The diffractive cross section $d\sigma~{diff} /dM_X$ is, within errors, found to rise linearly with $W$. Parameterizing the $W$ dependence by the form $d\sigma~{diff}/dM_X \propto (W~2)~{(2\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} -2)}$ the DIS data yield for the pomeron trajectory $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} = 1.23 \pm 0.02(stat) \pm 0.04 (syst)$ averaged over $t$ in the measured kinematic range assuming the longitudinal photon contribution to be zero. This value for the pomeron trajectory is substantially larger than $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ extracted from soft interactions. The value of $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ measured in this analysis suggests that a substantial part of the diffractive DIS cross section originates from processes which can be described by perturbative QCD. From the measured diffractive cross sections the diffractive structure function of the proton $F~{D(3)}_2(\beta,Q~2, \mbox{$x_{_{I\hspace{-0.2em}P}}$})$ has been determined, where $\beta$ is the momentum fraction of the struck quark in the pomeron. The form $F~{D(3)}_2 = constant \cdot (1/ \mbox{$x_{_{I\hspace{-0.2em}P}}$})~a$ gives a good fit to the data in all $\beta$ and $Q~2$ intervals with $a = 1.46 \pm 0.04 (stat) \pm
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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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Data on the reactions (K+/π+)p→(K+/π+)pπ+π- and (K+/π+)p→(K+/π+)p2π+2π-, obtained with the European Hybrid Spectrometer, are presented and compared with data at lower energies. The contribution of beam and target diffractive dissociation and double Pomeron exchange, and porperties of these reactions are discussed.
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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.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 2.7 GeV**2.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 4.0 GeV**2.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 6.0 GeV**2.
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Axis error includes +- 0.0/0.0 contribution (?////).
Axis error includes +- 0.0/0.0 contribution (?////).
Axis error includes +- 0.0/0.0 contribution (?////).
We study the spin-exotic $J^{PC} = 1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\pi^-\pi^-\pi^+$ using a hydrogen target and confirm the $\pi_1(1600) \to \rho(770) \pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile their experimental findings. We study the nonresonant contributions to the $\pi^-\pi^-\pi^+$ final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC} = 1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the $\pi^-\pi^+$ subsystem with $J^{PC} = 1^{--}$ in the $3\pi$ amplitude with $J^{PC} = 1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\pi^-\pi^+$ amplitude to be dominated by the $\rho(770)$ for both the $\pi_1(1600)$ and the nonresonant contribution. We determine the $\rho(770)$ resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC} = 1^{-+}$ amplitude.
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the first $t^\prime$ bin from $0.100$ to $0.141\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 8(a). In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_0.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_0</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the second $t^\prime$ bin from $0.141$ to $0.194\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(a) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_1.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_1</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the third $t^\prime$ bin from $0.194$ to $0.326\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(b) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_2.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_2</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
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