Using non-linear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken $x$ and momentum transfer $q^2 = - Q^2$. We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small $x$ the relation between the entanglement entropy $S(x)$ and the parton distribution $xG(x)$ becomes very simple: $S(x) = \ln[ xG(x) ]$. In this small $x$, large rapidity $Y$ regime, all partonic micro-states have equal probabilities -- the proton is composed by an exponentially large number $\exp(ΔY)$ of micro-states that occur with equal and exponentially small probabilities $\exp(-ΔY)$, where $Δ$ is defined by $xG(x) \sim 1/x^Δ$. For this equipartitioned state, the entanglement entropy is maximal -- so at small $x$, deep inelastic scattering probes a {\it maximally entangled state}. We propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. This will require event-by-event measurements of hadronic final states, and would allow to study the transformation of entanglement entropy into the Boltzmann one. We estimate that the proton is represented by the maximally entangled state at $x \leq 10^{-3}$; this kinematic region will be amenable to studies at the Electron Ion Collider.
Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. Lipatov constructed a spin chain which describes the amplitude of DIS in leading logarithmic approximation. Kharzeev and Levin proposed the entanglement entropy as an observable in DIS [Phys. Rev. D 95, 114008 (2017)], and suggested a relation between the entanglement entropy and parton distributions. Here we represent the DIS process as a local quench in the Lipatov's spin chain, and study the time evolution of the produced entanglement entropy. We show that the resulting entangl…
We calculate the rate of producing deep inelastic events containing an energetic isolated forward photon at HERA. We quantify the enhancement arising from the leading $\log 1/x$ gluon emissions with a view to using such events to identify the underlying dynamics.
The measurement of the polarized gluon distribution function Delta_G/G using current-target correlations in the Breit frame of deep inelastic scattering is proposed. The approach is illustrated using a Monte Carlo simulation of polarized $ep$-collisions for HERA energies.
Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton. For very small $x$, the proton becomes a maximally entangled state. This approach leads to a simple relation $S = \ln N $ between the average number $N$ of color-singlet dipoles in the proton wave function and the entropy of the produced hadronic state $S$. At small $x$, the multiplicity of dipoles is given by the gluon structure function, $N = x G(x,Q^2)$. Recently, the H1 Collaboration analyzed the entropy of the produced…
Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade
Universidad de las Americas Puebla（美洲大学普埃布拉分校）；Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Jagiellonian University（雅盖隆大学）；Jan Kochanowski University（扬·科哈诺夫斯基大学）
该研究利用 QCD 偶极子公式，通过构建密度矩阵、求解低 x 演化方程，考虑横向尺寸和方位角依赖性，研究深度非弹性散射中的纠缠熵，计算偶极子多重性并与香农熵比较，发现 DLLA 解熵更大。
We argue that the production of forward jets in polarised deep inelastic scattering can be a useful tool for probing the double $ln^2(1/x)$ resummation effects which control the polarised deep inelastic scattering for small values of the Bjorken parameter $x$. We solve the corresponding integral equations generating the double $ln^2(1/x)$ resummation and calculate the differential structure function describing the forward jet production in the small $x$ regime which can possibly be probed by the polarised HERA measurements. We show that these structure functions should exhibit the characterist…
The partons model reveals the dynamical structure of nucleons (protons and neutrons). Studies related to thermodynamic quantities of nucleons are interesting and topical questions. In this work, for the first time we apply Page's theory of the studies of black hole to investigate the entropy of proton system. Inspired by the quantum entanglement entropy in black hole information theories, we establish the proton entanglement with the similar way. Based our calculations, the proton entanglement entropy has the approximate form $S = \ln m -1/2$, where $m$ represents the partons density of proton…
Two-particle azimuthal correlations have been measured in neutral current deep $\mbox{inelastic}$ $\textit{ep}$ scattering with virtuality $Q^2 > 5$ GeV$^2$ at a centre-of-mass energy $\sqrt{s}=318$ GeV recorded with the ZEUS detector at HERA. The correlations of charged particles have been measured in the range of laboratory pseudorapidity $-1.5 < η< 2.0$ and transverse momentum $0.1 < p_{\textrm{T}}~< 5.0$ GeV and event multiplicities $N_{\textrm{ch}}$ up to six times larger than the average $\left< N_{\textrm{ch}} \right>\approx5$. The two-particle correlations have been measured in terms o…
We predict the rate of deep inelastic scattering (DIS) events containing an identified forward $π^0$ that is expected in the experiments at the HERA electron-proton collider, in order to see if this process can be used as an indicator of the underlying small $x$ dynamics. We determine the background due to deep inelastic events containing forward photons which are fragments of the forward jet. We compare the DIS + $π^0$ cross section with that of the DIS + parent jet process.
We study the transverse momentum ($p_T$) spectrum of charged particles produced in deep inelastic scattering (DIS) at small Bjorken $x$ in the central region between the current jet and the proton remnants. We calculate the spectrum at large $p_T$ with the BFKL $\ln (1/x)$ resummation included and then repeat the calculation with it omitted. We find that data favour the former. We normalize our BFKL predictions by comparing with HERA data for DIS containing a forward jet. The shape of the $x$ distribution of DIS + jet data are also well described by BFKL dynamics.
Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $\sqrt{s}=319$ GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of $136$ pb${}^{-1}$. Charged particle multiplicities are measured as a function of photon virtuality $Q^2$, inelasticity $y$ and pseudorapidity $η$ in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined …
We study the sensitivity of the Fermilab Short-Baseline Neutrino (SBN) experiments, MicroBooNE, ICARUS, and SBND, to MeV- to GeV-scale inelastic dark matter interacting through a dark photon mediator. These models provide interesting scenarios of light thermal dark matter, which, while challenging to probe with direct and indirect detection experiments, are amenable to accelerator-based searches. We consider production of the dark sector states with both the Fermilab Booster 8 GeV and NuMI 120 GeV proton beams and study the signatures of scattering and decay of the heavy excited dark state in …
We consider an inelastic dark matter model, where a fermion is charged under a broken U(1) gauge symmetry, and introduce a tiny Majorana mass term to split the fermion into two states with the light one being a dark matter candidate. If the gauge boson is light, it can mediate both elastic and inelastic dark matter self-interactions in dark halos, leading to observational consequences. Using a numerical technique based on partial wave analysis, we accurately calculate the elastic and inelastic self-scattering cross sections. We assume a thermal freeze-out scenario and fix the gauge coupling co…
Relying on previous results that link entanglement entropy and parton distribution functions in deep inelastic scattering and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy between observed and unobserved degrees of freedom per nucleon within a nucleus with respect to the free nucleon case. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.
We estimate the cross-section and asymmetry relevant for the production of forward jets in polarised deep inelastic scattering in the region of small values of $x$ which can be probed at possible polarised HERA measurements. The kinematical cuts implemented in our analysis are the same as those which were used in the unpolarised deep inelastic scattering at HERA. The calculations are based on the double ln^2(1/x) resummation which controls the polarised deep inelastic scattering for small values of the Bjorken parameter x. We show that this resummation substantially enhances the corresponding …
We study holographic aspects of mixed state entanglement measures in various large $N$ top-down as well as bottom-up confining models. For the top-down models, we consider wrapped $D3$ and $D4$ branes gravity solutions whereas, for the bottom-up confining model, the Einstein-Maxwell-dilaton gravity solution is considered. We study entanglement entropy, mutual information, entanglement wedge cross-section and entanglement negativity for the strip subsystems and find model independent features of these entanglement measures in all confining theories. The entanglement negativity and entropy exhib…
Extensions of the Standard Model that contain leptophobic Z' gauge bosons are theoretically interesting but difficult to probe directly in high-energy hadron colliders. However, precision measurements of Standard Model neutral current processes can provide powerful indirect tests. We demonstrate that parity-violating deep inelastic scattering of polarized electrons off of deuterium offer a unique probe leptophobic Z' bosons with axial quark couplings and masses above 100 GeV. In addition to covering a wide range of previously uncharted parameter space, planned measurements of the deep inelasti…
We study various entanglement measures in a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons field theories by means of their dual supergravity descriptions. A generic field theory in this family possesses a mass gap but does not have a linear quark-antiquark potential. For the two limiting values of the parameter, the theories flow either to a fixed point or to a confining vacuum in the infrared. We show that entanglement measures are unable to discriminate confining theories from non-confining ones with a mass gap. This lends support on the idea that the ph…
We study the proposal by Kharzeev-Levin to determine entanglement entropy in Deep Inelastic Scattering (DIS) from parton distribution functions (PDFs) and to relate the former to the entropy of final state hadrons. We find several uncertainties in the current comparison to data, in particular the overall normalization, the relation between charged versus total hadron multiplicity in the comparison to experimental results as well as different methods to determine the number of partons in Deep Inelastic Scattering. We further provide a comparison to data based on leading order HERA PDF as well a…
The nucleon structure functions probed in deep-inelastic scattering at large virtualities form an important tool to test Quantum Chromdynamics (QCD) through precision measurements of the strong coupling constant $α_s(M_Z^2)$ and the different parton distribution functions. The exact knowledge of these quantities is also of importance for all precision measurements at hadron colliders. During the last two decades very significant progress has been made in performing precision calculations. We review the theoretical status reached for both unpolarized and polarized lepton-hadron scattering based…
The photon emissivity of quark-gluon plasma probes the interactions in the medium and differs qualitatively between a weakly coupled and a strongly coupled plasma in the soft-photon regime. The photon emissivity is given by the product of kinematic factors and a spectral function associated with the two-point correlator of the electromagnetic current at lightlike kinematics. A certain Euclidean correlator at imaginary spatial momentum can be calculated in lattice QCD and is given by an integral over the relevant spectral function at lightlike kinematics. I present a first exploratory lattice c…
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical studies of saturation and unitarity effects at small $x$ in quarkonium scattering; Renormalons and higher twist contributions; Next-to-leading-order calculations of jet cross sections; Forward jet production as a probe of small-$x$ dynamics.
The problem of electron-proton scattering is handed over both the elastic and inelastic scattering. Two models are presented in this sense. The first, depends on the multi photon exchange ladder diagram, where the transition matrix is expanded in multi steps form. The second model uses the multi peripheral mechanism developed for the electromagnetic field. It allows the particle production in the inelastic scattering processes. An iterative procedure is found and inserted in a Monte Carlo program to reproduce the differential cross section of the reaction. The comparison with the experimental …
Quantum entanglement provides a novel way to test short distance physics in the non-relativistic regime. We will provide a protocol to {\it potentially} test new physics by bringing two charged massive particle interferometers adjacent to each other. Being charged, the two superpositions will be entangled via electromagnetic interactions mediated by the photons, including the Coulomb and the Casimir-Polder potential. We will bring a method of {\it entanglement based tomography} to seek time evolution of very small entanglement phases to probe new physical effects mediated by {\it hitherto unkn…
We show that quantum entanglement between causally separated regions of a nucleon in antineutrino-nucleon scattering manifests itself as a thermal component in the resulting pion momentum distribution. For antineutrino scattering coherently from the (carbon) nucleus as a whole, this thermal component is absent, as expected by our quantum entanglement thermalization proposition. These phenomena, which have been observed in proton-proton collisions at the Large Hadron Collider, and in electromagnetic deep inelastic scattering, are now for the first time shown to exist in electroweak interactions…
The azimuthal dependence of hadrons produced in lepton scattering off a polarized hadron probes the quark transverse-spin distributions. In the calculation of the asymmetries, transverse momenta of quarks in the distribution and fragmentation functions must be incorporated. In addition to the $\sin (ϕ+ ϕ_S)$ asymmetry for transversely polarized hadrons, known as the Collins effect, we find $\sin 2ϕ$ asymmetries for both transversely and longitudinally polarized hadrons.
Photon radiation at large transverse momenta at colliders is a detailed probe of hard interaction dynamics. The isolated photon production cross section in deep inelastic scattering was measured recently by the ZEUS experiment, and found to be considerably larger than theoretical predictions obtained with widely used event generators. To investigate this discrepancy, we perform a dedicated parton-level calculation of this observable, including contributions from fragmentation and large-angle radiation. Our results are in good agreement with all aspects of the experimental measurement.
We consider the inclusive cross section for jet production with large transverse momentum in deep-inelastic scattering. This process has been proposed as a probe of small-x physics, particularly the measurement of `hot spots' inside the proton. We present a numerical calculation of this process, taking into account a larger phase space. The theoretical reliability as well as phenomenological uncertainties of the calculation are discussed.
In this paper we analyze deep inelastic one-particle inclusive processes for the case of spin-one targets or for the case of spin-one produced hadrons, such as rho mesons. This allows the measurement of new distribution and fragmentation functions not available in the spin-half case, and provides new ways to probe functions otherwise difficult to measure. We will analyze only contributions leading order in 1/Q, but we will include effects of the transverse momentum of partons. We also include time-reversal odd functions.
The production of jets in charged-current deep-inelastic scattering (CC DIS) probes simultaneously the strong and the electroweak sectors of the Standard Model; its measurement provides important information on the quark flavour structure of the proton. We compute third-order (N3LO) perturbative QCD corrections to this process, fully differential in the jet and lepton kinematics. We observe a substantial reduction in the theory uncertainty, to sub-percent level throughout the relevant kinematical range, thus enabling precision phenomenology with jet observables.
A new scaling variable is introduced in terms of which nuclear shadowing in deep-inelastic scattering is universal, i.e. independent of $A$, $Q^2$ and $x$. This variable can be interpreted as a measure of the number of gluons probed by the hadronic fluctuations of a virtual photon during their lifetime. The shadowing correction grows at small $x$ substantially less steeply than is suggested by the eikonal approximation. This results from the fact that shadowing is dominated by soft rather than hard interactions.
