Proton Wave Function Research Articles

Asymmetric intrinsic charm in the nucleon and its implications for the D0 production in the LHCb p+Ne20 fixed-target experiment

Recent results indicate that charm quarks are intrinsic components of the proton wave function, and that the charm and anticharm distributions for a given value of the Bjorken-x variable can be different. In this paper, we will investigate the impact of this asymmetric intrinsic charm on the production of D0 and D¯0 mesons for fixed target p+Ne20 collisions at the LHCb. In our calculations, we include the contribution of the gluon-gluon fusion, gluon-charm and recombination processes and assume distinct models for the treatment of the intrinsic charm component. We demonstrate that the presence of an intrinsic charm improves the description of the current data for the rapidity and transverse momentum distributions of D mesons. However, such models are not able to describe the LHCb data for the D0−D¯0 asymmetry at large transverse momentum, which point out that the description of the intrinsic charm needs to be improved and/or new effects should be taken into account in the production of heavy mesons at forward rapidities in fixed-target collisions. Published by the American Physical Society 2024

B-meson production at forward rapidities in pp collisions at the LHC: estimating the intrinsic bottom contribution

The production of B mesons at forward rapidities is strongly sensitive to the behavior of the gluon and bottom distribution functions for small and large values of the Bjorken-x variable. In this exploratory study, we estimate the cross-section for the B±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^{\\pm }$$\\end{document} meson production in the kinematic range probed by the LHCb detector and that will be analyzed by the future Forward Physics Facility (FPF) considering the hybrid formalism, the solution of the running coupling Balitsky–Kovchegov equation and distinct descriptions for the bottom distribution function. We assume an ansatz for the intrinsic bottom component in the proton wave function, and estimate its impact on the transverse momentum, rapidity and Feynman-x distributions. Our results indicate that the presence of an intrinsic bottom strongly modifies the magnitude of the cross-section at ultra-forward rapidities (y≥6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y \\ge 6$$\\end{document}), which implies an enhancement of the B±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^{\\pm }$$\\end{document} production at the FPF. Possible implications on the prompt neutrino flux at ultra-high energies are also briefly discussed.

Nuclear-Electronic Orbital Time-Dependent Configuration Interaction Method.

Combining real-time electronic structure with the nuclear-electronic orbital (NEO) method has enabled the simulation of complex nonadiabatic chemical processes. However, accurate descriptions of hydrogen tunneling and double excitations require multiconfigurational treatments. Herein, we develop and implement the real-time NEO time-dependent configuration interaction (NEO-TDCI) approach. Comparison to NEO-full CI calculations of absorption spectra for a molecular system shows that the NEO-TDCI approach can accurately capture the tunneling splitting associated with the electronic ground state as well as vibronic progressions corresponding to double electron-proton excitations associated with excited electronic states. Both of these features are absent from spectra obtained with single reference real-time NEO methods. Our simulations of hydrogen tunneling dynamics illustrate the oscillation of the proton density from one side to the other via a delocalized, bilobal proton wave function. These results indicate that the NEO-TDCI approach is highly suitable for studying hydrogen tunneling and other inherently multiconfigurational systems.

Strong H-bonding from Zeolite Bro̷nsted Acid Site to Water: Origin of the Broad IR Doublet.

Hydrogen bonding between water molecules and zeolite Bro̷nsted acid sites (BAS) has received much attention due to the significant influence of water on the adsorption and catalytic properties of these widely used porous materials. When a single water molecule is adsorbed at the BAS, the zeolite O-H stretch vibration decreases in frequency and splits into two extraordinarily broad bands peaked near 2500 and 2900 cm-1 in the infrared (IR) spectrum. This broad doublet feature is the predominant IR signature used to identify and interpret water-BAS H-bonding at low hydration levels, but the origin of the band splitting is not well understood. In this study, we used broadband two-dimensional infrared (2D IR) spectroscopy to investigate zeolite HZSM-5 prepared with a single water molecule per BAS. We find that the 2D IR spectrum is not explained by the most common interpretation of Fermi resonance coupling between the stretch and the bend of the BAS OH group, which predicts intense excited-state transitions that are absent from the experimental results. We present an alternative model of a double-well proton stretch potential, where the band splitting is caused by excited-state tunneling through the proton-transfer barrier. This one-dimensional model reproduces the basic experimental pattern of transition frequencies and amplitudes, suggesting that the doublet bands may originate from a highly anharmonic potential in which the excited state proton wave functions are delocalized over the H-bond between zeolite BAS and adsorbed H2O. Additional details about molecular orientation and coordination of the adsorbed water molecule are also resolved in the 2D IR spectroscopy.

Entangelement entropy in high energy collisions of electrons and protons

We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering of electrons and proton in the region of low Bjorken x. Using their proposed relation between parton number and entanglement entropy, we determine the latter using both conventional parton distribution functions and parton distribution functions obtained from an unintegrated gluon distribution subject to next-to-leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution as well as from a dipole cross-section, subject to running coupling Balitsky-Kovchegov (rcBK) evolution. We compare our results to hadronic entropy obtained from final state hadron multiplicity.

The 46Ar(3He, d)47K direct reaction as a probe of the 46Ar proton wavefunction

The discrepancy between shell-model calculations and intermediate-energy Coulomb excitation measurements in 46Ar still stands as an unsolved puzzle in understanding the N = 28 shell evolution. This phenomenon has significant relevance considering the remarkable achievements of the shell model and the SDPF-U interaction in the region which is able to predict the fading of the N = 28 shell gap in neutron-rich 44S. Recent measurements narrowed down this discrepancy to an overestimation of the proton amplitude to the quadrupole transition matrix element. The current work aims to propose a different perspective on the puzzle, by studying a direct proton-transfer reaction on 46Ar as a means to directly probe the proton wavefunction of the ground state this isotope. By measuring the amount of l = 0 transfer to the ground state (1/2+) of 47K with respect to the l = 2 to the first excited state (3/2+), we aim to gain insight into the ground state proton wavefunction of 46Ar. We will present a brief description of the experiment performed at the SPIRAL1 facility in GANIL (France). The experimental apparatus allowed a full reconstruction of the two-body reaction thanks to the combination of AGATA, VAMOS, MUGAST, CATS2, and HECTOR.

Nonperturbative gluon exchange in pp elastic scattering at TeV energies

We investigate the two-gluon-exchange model of the Pomeron using nonperturbative gluon propagators characterized by a dynamical mass scale. We present the results for an analysis of the available $pp$ differential cross section data at TeV energies which accounts for dynamical gluon masses obtained from a non-linear version of the Schwinger-Dyson equations. We show that our two-gluon exchange model gives a very good description of the LHC data, provided we demand the Reggeization of the scattering amplitude and make a suitable choice for the convolution of proton wave functions.

Gamow shell model description of the radiative capture reaction B8(p,γ)C9

Background: In low metallicity supermassive stars, the hot $pp$ chain can serve as an alternative to produce the CNO nuclei. In the astrophysical environment of high temperature, the proton capture of $^{8}\mathrm{B}$ can be faster than its $\ensuremath{\beta}$ decay, so that the $^{8}\mathrm{B}(p,\ensuremath{\gamma})^{9}\mathrm{C}$ reaction plays an important role in the hot $pp$ chain. Due to the unstable nature of $^{8}\mathrm{B}$ and the unavailability of $^{8}\mathrm{B}$ beams, the study of the $^{8}\mathrm{B}(p,\ensuremath{\gamma})^{9}\mathrm{C}$ reaction can only be achieved by indirect methods, so that large uncertainties exist.Purpose: The Gamow shell model in the coupled-channel representation (GSM-CC) is applied to study the proton radiative capture reaction $^{8}\mathrm{B}(p,\ensuremath{\gamma})^{9}\mathrm{C}$.Method: The GSM-CC is a unified microscopic theory for the description of nuclear structure and nuclear reaction properties. A translationally invariant Hamiltonian is considered for that matter, making use of a finite-range two-body interaction, whose parameters are adjusted to reproduce the low-energy spectra of $^{8}\mathrm{B}$ and $^{9}\mathrm{C}$. The reaction channels are then built through the coupling of the wave functions of the ground state ${2}_{1}^{+}$, the first excited state ${1}_{1}^{+}$, and the second excited state ${3}_{1}^{+}$ in $^{8}\mathrm{B}$ to a projectile proton wave function in different partial waves. For the calculation of the $^{8}\mathrm{B}(p,\ensuremath{\gamma})^{9}\mathrm{C}$ astrophysical factor, all $E1, M1$, and $E2$ transitions from the initial continuum states to the final bound states ${3/2}_{1}^{\ensuremath{-}}\mathrm{of}\phantom{\rule{4pt}{0ex}}^{9}\mathrm{C}$ are considered. The resonant capture to the first resonant state ${1/2}_{1}^{\ensuremath{-}}$ of $^{9}\mathrm{C}$ is also calculated.Results: The experimental low-energy levels and the proton emission threshold in $^{9}\mathrm{C}$ are reproduced by the GSM-CC. The calculated astrophysical factor agrees with experimental data obtained from indirect measurements. The reaction rates from the direct capture and resonant capture are calculated for the temperature range of astrophysical interest.Conclusion: The calculated total astrophysical $S$ factor is dominated by the $E1$ transition to the ground state of $^{9}\mathrm{C}$. The GSM-CC calculations suggest that $S$ first increases with the energy of the center of mass ${E}_{\mathrm{c}.\mathrm{m}.}$, and then decrease with the energy. This agrees with existing data, which has smaller values around zero energy and larger values in the energy range of 0.2 MeV $\ensuremath{\le}{E}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\le}$ 0.6 MeV.

Multiplicity fluctuations and correlations in 5.02 TeV p+Pb collisions at zero impact parameter

We present a Bayesian method to reconstruct event-by-event multiplicity fluctuations and rapidity correlations in $p+\mathrm{Pb}$ collisions at zero impact parameter from minimum-bias data, without assuming any model of the collision dynamics. We test it on Monte Carlo simulations with the Angantyr model, then apply it to ATLAS data on the distribution of charged multiplicity and transverse energy in $p+\mathrm{Pb}$ collisions at $\sqrt{{s}_{NN}}=5.02$ TeV. Fluctuations in $b=0$ collisions are quantum fluctuations which originate mostly from the proton wave function, and therefore have the potential to constrain the subnucleonic structure of the proton. The Angantyr model is found to overestimate fluctuations. In addition, we find that as the rapidity increases (towards the Pb-going side), not only the multiplicity density increases, but also its relative event-by-event fluctuation. This counterintuitive phenomenon is also observed in simulations with Angantyr, and with the quantum chromodynamics dipole model, where its origin can be traced back to the branching process through which gluons are produced.

Evidence for intrinsic charm quarks in the proton

The theory of the strong force, quantum chromodynamics, describes the proton in terms of quarks and gluons. The proton is a state of two up quarks and one down quark bound by gluons, but quantum theory predicts that in addition there is an infinite number of quark–antiquark pairs. Both light and heavy quarks, whose mass is respectively smaller or bigger than the mass of the proton, are revealed inside the proton in high-energy collisions. However, it is unclear whether heavy quarks also exist as a part of the proton wavefunction, which is determined by non-perturbative dynamics and accordingly unknown: so-called intrinsic heavy quarks1. It has been argued for a long time that the proton could have a sizable intrinsic component of the lightest heavy quark, the charm quark. Innumerable efforts to establish intrinsic charm in the proton2 have remained inconclusive. Here we provide evidence for intrinsic charm by exploiting a high-precision determination of the quark–gluon content of the nucleon3 based on machine learning and a large experimental dataset. We disentangle the intrinsic charm component from charm–anticharm pairs arising from high-energy radiation4. We establish the existence of intrinsic charm at the 3-standard-deviation level, with a momentum distribution in remarkable agreement with model predictions1,5.We confirm these findings by comparing them to very recent data on Z-boson production with charm jets from the Large Hadron Collider beauty (LHCb) experiment6.

Intrinsic charm in the nucleon and forward production of charm: a new constrain from IceCube Neutrino Observatory

The predictions for the atmospheric neutrino flux at high energies strongly depend on the contribution of prompt neutrinos, which are determined by the production of charmed meson in the atmosphere at very forward rapidities. Here we estimate the related cross sections taking into account the presence of an intrinsic charm (IC) component in the proton wave function. The impact on the predictions for the prompt neutrino flux is investigated assuming different values for the probability to find the IC in the nucleon.

Proton wave function in a water molecule: Breakdown of degeneration caused by interactions with the magnetic field of a Magnetic Resonance Imaging device

The concept of a Magnetic Resonance Imaging (MRI) device is based on the emission of radio waves produced by the protons of the hydrogen atoms in water molecules when placed in a constant magnetic field after they interact with a pulsed radio frequency (RF) current. When the RF field is turned on, the protons are brought to a spin excited state. When the RF field is turned off, the MRI sensors are able to detect the energy released as the protons realign their spins with the magnetic field. In this work we provide a simple model to describe the basic physical mechanism responsible for the operation of MRI devices. We model the water molecule in terms of a central force problem, where the protons move around the (unstructured) doubly negatively charged oxygen atom. First, we employ an analytical treatment to obtain the system's wave function as well as its energy levels, which we show are degenerate. Next, the energy levels from the water molecule are studied in the presence of a uniform external magnetic field. As a result, they get shifted and the degeneration is lifted. We provide numerical results for a magnetic field strength commonly used in MRI devices.

Impact of intrinsic charm amount in the nucleon and saturation effects on the prompt atmospheric nu _{mu } flux for IceCube

The predictions for the atmospheric neutrino flux at high energies strongly depend on the contribution of prompt neutrinos, which are determined by the production of charmed mesons in the atmosphere at very forward rapidities. In this paper we estimate the related cross sections taking into account the presence of an intrinsic charm (IC) component in the proton wave function and the QCD dynamics modified by the onset of saturation effects. The impact on the predictions for the prompt neutrino flux is investigated assuming different values for the probability to find the IC in the nucleon (P_{ic}). We demonstrate that for P_{ic} sim 1%, the IC component dominates the high-energy prompt neutrino flux. A first comparison with the IceCube data is performed and upper limits on the amount of IC are obtained for the linear and nonlinear descriptions of the QCD dynamics.

Study of Z Bosons Produced in Association with Charm in the Forward Region

Events containing a Z boson and a charm jet are studied for the first time in the forward region of proton-proton collisions. The data sample used corresponds to an integrated luminosity of 6 fb^{-1} collected at a center-of-mass energy of 13 TeV with the LHCb detector. In events with a Z boson and a jet, the fraction of charm jets is determined in intervals of Z-boson rapidity in the range 2.0<y(Z)<4.5. A sizable enhancement is observed in the forwardmost y(Z) interval, which could be indicative of a valencelike intrinsic-charm component in the proton wave function.

Evidence for the maximally entangled low x proton in Deep Inelastic Scattering from H1 data

We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low x and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low x, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky–Fadin–Kuraev–Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small x resummation, where the latter provides an acceptable description of data.

Deep inelastic scattering as a probe of entanglement: Confronting experimental data

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 hadronic state in DIS, and studied its relation to the gluon structure function; poor agreement with the predicted relation was found. In this letter we argue that a more accurate account of the number of color-singlet dipoles in the kinematics of H1 experiment (where hadrons are detected in the current fragmentation region) is given not by $xG(x,Q^2)$ but by the sea quark structure function $x\Sigma(x,Q^2)$. Sea quarks originate from the splitting of gluons, so at small $x$ $x\Sigma(x,Q^2)\,\sim\, xG(x,Q^2)$, but in the current fragmentation region this proportionality is distorted by the contribution of the quark-antiquark pair produced by the virtual photon splitting. In addition, the multiplicity of color-singlet dipoles in the current fragmentation region is quite small, and one needs to include $\sim 1/N$ corrections to $S= \ln N$ asymptotic formula. Taking both of these modifications into account, we find that the data from the H1 Collaboration in fact agree well with the prediction based on entanglement.

Axial charges of the proton within an extended chiral constituent quark model

We have performed a study of the isovector, octet and singlet axial charges of the proton in an extended chiral constituent quark model, where all the possible $uudq\bar{q}$~($q=u,d,s$) five-quark Fock components in the proton wave function are taken into account. The $^3P_0$ quark-antiquark creation mechanism is assumed to account for the transition coupling between three- and five-quark components in proton, and the corresponding transition coupling strength is fixed by fitting the intrinsic sea flavor asymmetry $\bar{d}-\bar{u}$ data for proton. Accordingly, with all the parameters fixed by empirical values, the probabilities of the intrinsic five-quark Fock components in proton wave function should be $\sim30 - 50\%$, which lead to the numerical results for quark spin $\Delta u$, $\Delta d$ and $\Delta s$, as well the axial charges of proton consistent with the experimental data and predictions by other theoretical approaches.

&amp;beta;-decay and isospin symmetry breaking

<p indent=0mm>The elegant concept of isospin symmetry is of fundamental importance in nuclear and elementary particle physics. As a β-decay process changes an up quark to a down quark or <italic>vice versa</italic>, studies of nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, can be a powerful means to probe isospin symmetry breaking. A series of β-decay experiments of sd-shell nuclei near the proton drip line produced by projectile fragmentation were performed at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1) using a silicon array with a high detection efficiency and a low detection threshold. The secondary ions were identified by the combination of Δ<italic>E</italic>-TOF and magnetic rigidity (<italic>Bρ</italic>) in which the time of flight (TOF) was measured by two plastic scintillators at the second and fourth focal planes of the RIBLL1 and the energy loss (Δ<italic>E</italic>) was measured by two silicon detectors in the front of the silicon array. Double-sided silicon strip detectors (DSSDs) in the center of the array served to measure the residual energies of secondary ions on an event-by-event basis and study their decay properties with an implantation-decay correlation. Several quadrant silicon detectors (QSDs) placed behind DSSDs were used for anticoincidences of the penetrating fragments and light particles coming along with the beam, and measurements of β particles and high-energy protons. The β-delayed proton peaks with known energies and their corresponding absolute intensities were used for the energy and detection efficiency calibrations of the DSSDs. The system allows us to measure protons with energies down to about <sc>200 keV</sc> without obvious β background in the proton spectrum and was successful to measure the energies, time, and positions of implanted ions and decay protons efficiently, supporting researchers to study the decay properties of nuclei towards the proton drip line. The β-decay data, together with the large-scale shell-model calculations, allows detailed investigations on the mirror-nuclei systems resulting in the systematic study of isospin symmetry breaking in the sd-shell nuclear region. It was found that the mirror asymmetry parameters become larger due to the smaller separation energies while approaching the proton drip line for the extremely proton-rich sulfur nuclei ^27,28,29S and the Coulomb forces and other isospin-symmetry nonconserving forces acting between protons would lead to extended proton wave functions and cause mirror asymmetries. The properties of ²²Si β-decay for the transitions to the low-lying states of ²²Al were measured, and the reduced transition probabilities were determined. Comparing with the data on the β-decay of the mirror nucleus ²²O, we found a mirror asymmetry of <italic>δ</italic>=209(96)% in the transition to the first 1⁺ excited state of the respective daughters. This is by far the largest value of <italic>δ</italic> observed in the low-lying states. Shell-model calculations with isospin-nonconserving forces, including the <italic>T</italic>=1,<italic> J</italic>=2, 3 interactions related to the s_1/2 orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s_1/2 orbit, can reproduce the observed data well and demonstrate that this dramatically large mirror asymmetry is attributed to the significant proton occupation and loosely bound nature of the wave functions of the s_1/2 orbit, which suggests that ²²Al is a proton-halo nucleus.

Universal proton emission systematics

We investigate proton systematics in terms of the barrier penetration and formation probability. To this purpose we approximate the realistic proton-core interaction by a parabolic dependence describing the nuclear part matched to a pure Coulomb potential. In this way we can use analytic semiclassical solutions to describe the proton dynamics inside the barrier. We then carefully investigate effects induced by the centrifugal barrier and quadrupole deformation. It turns out that the nuclear centrifugal and deformation effects are much smaller than their Coulomb counterparts. On the other hand, the Coulomb action defining the semiclassical penetrability is larger by one order of magnitude than its nuclear counterpart. We evidence a dependence of the Coulomb action upon the Coulomb parameter in terms of two parallel lines separated by $A=145$. Such a dependence was previously discovered for the logarithm of the experimental decay width corrected by the Coulomb centrifugal barrier. We also evidence an additional but smaller residual linear decrease of the proton formation probability versus ${A}^{1/3}$ along two parallel lines separated by $A=145$, induced by the internal proton wave function. Therefore, the dependence between the experimental decay width corrected by the centrifugal barrier and the Coulomb penetrability multiplied by the proton formation probability in the doubly logarithmic scale can be fitted within a factor of two by a universal straight line.

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels.

Artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.