Atomic nuclei are self-organized, many-body quantum systems bound by strong nuclear forces within femtometer-scale space. These complex systems manifest a variety of shapes, traditionally explored using non-invasive spectroscopic techniques at low energies. However, at these energies, their instantaneous shapes are obscured by long-timescale quantum fluctuations, making direct observation challenging. Here we introduce the ``collective flow assisted nuclear shape imaging'' method, which images the nuclear global shape by colliding them at ultrarelativistic speeds and analyzing the collective response of outgoing debris. This technique captures a collision-specific snapshot of the spatial matter distribution within the nuclei, which, through the hydrodynamic expansion, imprints patterns on the particle momentum distribution observed in detectors. We benchmark this method in collisions of ground state Uranium-238 nuclei, known for their elongated, axial-symmetric shape. Our findings show a large deformation with a slight deviation from axial symmetry in the nuclear ground state, aligning broadly with previous low-energy experiments. This approach offers a new method for imaging nuclear shapes, enhances our understanding of the initial conditions in high-energy collisions and addresses the important issue of nuclear structure evolution across energy scales.
Data from Figure 2, panel a, Au+Au, 0-0.5% Centrality, 0.2<p_{T}<3 GeV/c, systematics include non-flow difference in the two systems, but correlated non-flow systematics with the value of $\delta \left\langle v_{2}^{2}\right\rangle$ =+-3.2e-5 included
Data from Figure 2, panel a, U+U, 0-0.5% Centrality, 0.2<p_{T}<3 GeV/c, systematics include non-flow difference in the two systems, but correlated non-flow systematics with the value of $\delta \left\langle v_{2}^{2}\right\rangle$ =+-3.2e-5 included
Data from Figure 2, panel b, Au+Au, 0-0.5% Centrality, 0.2<p_{T}<3 GeV/c
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>
New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in ($x$, $Q^2$) bins.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^{\rm p}$ for the 2007 COMPASS data at 160 GeV in ($x$, $Q^2$) bins.
Multiplicities of charged hadrons produced in deep inelastic muon scattering off a $^6$LiD target have been measured as a function of the DIS variables $x_{Bj}$, $Q^2$, $W^2$ and the final state hadron variables $p_T$ and $z$. The $p_T^2$ distributions are fitted with a single exponential function at low values of $p_T^2$ to determine the dependence of $\langle p_T^2 \rangle$ on $x_{Bj}$, $Q^2$, $W^2$ and $z$. The $z$-dependence of $\langle p_T^2 \rangle$ is shown to be a potential tool to extract the average intrinsic transverse momentum squared of partons, $\langle k_{\perp}^2 \rangle$, as a function of $x_{Bj}$ and $Q^2$ in a leading order QCD parton model.
PT dependences of the differential multiplicities for 0.0045 < x_Bjorken < 0.0060 and 1.00 < Q^2 < 1.25 GeV^2 for Positive hadrons.
PT dependences of the differential multiplicities for 0.0060 < x_Bjorken < 0.0080 and 1.00 < Q^2 < 1.30 GeV^2 for Positive hadrons.
PT dependences of the differential multiplicities for 0.0060 < x_Bjorken < 0.0080 and 1.30 < Q^2 < 1.70 GeV^2 for Positive hadrons.
The muon-proton and muon-deuteron inclusive deep inelastic scattering cross sections were measured in the kinematic range 0.002 < x < 0.60 and 0.5 < Q2 < 75 GeV2 at incident muon energies of 90, 120, 200 and 280 GeV. These results are based on the full data set collected by the New Muon Collaboration, including the data taken with a small angle trigger. The extracted values of the structure functions F2p and F2d are in good agreement with those from other experiments. The data cover a sufficient range of y to allow the determination of the ratio of the longitudinally to transversely polarised virtual photon absorption cross sections, R= sigma(L)/sigma(T), for 0.002 < x < 0.12 . The values of R are compatible with a perturbative QCD prediction; they agree with earlier measurements and extend to smaller x.
Corrected F2P measurements averaged over all energies. Data are the statistically weighted averages given at the centre of each bin.
Corrected F2P measurements averaged over all energies. Data are the statistically weighted averages given at the centre of each bin.
Corrected F2P measurements averaged over all energies. Data are the statistically weighted averages given at the centre of each bin.
The proton and deuteron structure functions F2p and F2d were measured in the kinematic range 0.006
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We present a re-evaluation of the structure function ratios F2(He)/F2(D), F2(C)/F2(D) and F2(Ca)/F2(D) measured in deep inelastic muon-nucleus scattering at an incident muon momentum of 200 GeV. We also present the ratios F2(C)/F2(Li), F2(Ca)/F2(Li) and F2(Ca)/F2(C) measured at 90 GeV. The results are based on data already published by NMC; the main difference in the analysis is a correction for the masses of the deuterium targets and an improvement in the radiative corrections. The kinematic range covered is 0.0035 < x < 0.65, 0.5 < Q^2 <90 GeV^2 for the He/D, C/D and Ca/D data and 0.0085 < x < 0.6, 0.84 < Q^2 < 17 GeV^2 for the Li/C/Ca ones.
Additional normalization uncertainty of 0.4 pct not included.
Additional normalization uncertainty of 0.4 pct not included.
Additional normalization uncertainty of 0.4 pct not included.
: We have measured the spin-dependent structure function $g_1~p$ of the proton in deep inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003
Results on the virtual photon proton asymmetry.
Results on the spin structure function of the proton.
Data for g1 at fixed Q**2 = 10 GeV (assuming no Q**2 dependence of A1).
We compare the particle flow in the event plane of three-jet qq¯g (quark-antiquark-gluon) events with the particle flow in radiative annihilation events qq¯γ (quark-antiquark-photon) for similar kinematic configurations. In the angular region between quark and antiquark jet, we find a significant decrease in particle density for qq¯g as compared to qq¯γ. This effect is predicted in QCD as a result of destructive interference between soft-gluon radiation from quark, antiquark, and hard gluon.
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