Showing papers on "Proton spin crisis published in 2021"

What we know and what we don't know about the proton spin after 30 years

Abstract: There are two established approaches to look at the composition of the proton spin: the frame-independent spin structure (or the Ji sum rule) and the infinite-momentum-frame or parton spin structure (or the Jaffe–Manohar sum rule).In the frame-independent approach, the quark orbital and gluon angular momentum contributions can be extracted from the moments of the generalized parton distributions. Results from the Jefferson Lab 6 GeV and HERMES experiments suggest that there is a substantial quark orbital contribution.In terms of partons, the quark and gluon helicity contributions have a simple physical interpretation, and the result from Relativistic Heavy Ion Collider spin experiments has provided a first important constraint on the total gluon helicity.The development of a large-momentum effective theory along with lattice quantum chromodynamics simulations provide first-principles calculations of the spin structure. The results on the quark and gluon helicity contributions, and the quark orbital and gluon angular momentum contributions have provided the first complete theoretical picture.The Jefferson Lab 12 GeV programme will provide better information on the quark orbital angular momentum and gluon angular momentum. The future Electron-Ion Collider will provide high-precision measurements on the gluon helicity and gluon angular momentum.There are two established approaches to look at the composition of the proton spin: the frame-independent spin structure (or the Ji sum rule) and the infinite-momentum-frame or parton spin structure (or the Jaffe–Manohar sum rule).In the frame-independent approach, the quark orbital and gluon angular momentum contributions can be extracted from the moments of the generalized parton distributions. Results from the Jefferson Lab 6 GeV and HERMES experiments suggest that there is a substantial quark orbital contribution.In terms of partons, the quark and gluon helicity contributions have a simple physical interpretation, and the result from Relativistic Heavy Ion Collider spin experiments has provided a first important constraint on the total gluon helicity.The development of a large-momentum effective theory along with lattice quantum chromodynamics simulations provide first-principles calculations of the spin structure. The results on the quark and gluon helicity contributions, and the quark orbital and gluon angular momentum contributions have provided the first complete theoretical picture.The Jefferson Lab 12 GeV programme will provide better information on the quark orbital angular momentum and gluon angular momentum. The future Electron-Ion Collider will provide high-precision measurements on the gluon helicity and gluon angular momentum.

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

Abstract: The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.

Measurement of the proton spin structure at long distances

Abstract: Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. Here we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0 GeV2. This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections. Measurements of the proton’s spin structure in experiments scattering a polarized electron beam off polarized protons in regions of low momentum transfer squared test predictions from chiral effective field theory of the strong interaction.

Residual dipolar line width in magic-angle spinning proton solid-state NMR

Abstract: . Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1 / ω r dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ω r - 2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

Constant-adiabaticity ultralow magnetic field manipulations of parahydrogen-induced polarization: application to an AA'X spin system.

Abstract: The field of magnetic resonance imaging with hyperpolarized contrast agents is rapidly expanding, and parahydrogen-induced polarization (PHIP) is emerging as an inexpensive and easy-to-implement method for generating the required hyperpolarized biomolecules. Hydrogenative PHIP delivers hyperpolarized proton spin order to a substrate via chemical addition of H2 in the spin-singlet state, but it is typically necessary to transfer the proton polarization to a heteronucleus (usually 13C) which has a longer spin lifetime. Adiabatic ultralow magnetic field manipulations can be used to induce the polarization transfer, but this is necessarily a slow process, which is undesirable since the spins continually relax back to thermal equilibrium. Here we demonstrate two constant-adiabaticity field sweep methods, one in which the field passes through zero, and one in which the field is swept from zero, for optimal polarization transfer on a model AA′X spin system, [1-13C]fumarate. We introduce a method for calculating the constant-adiabaticity magnetic field sweeps, and demonstrate that they enable approximately one order of magnitude faster spin-order conversion compared to linear sweeps. The present method can thus be utilized to manipulate nonthermal order in heteronuclear spin systems.

Measurement of the proton spin structure at long distances

Abstract: Measuring the spin structure of nucleons (protons and neutrons) extensively tests our understanding of how nucleons arise from quarks and gluons, the fundamental building blocks of nuclear matter The nucleon spin structure is typically probed in scattering experiments using polarized beams and polarized nucleon targets, and the results are compared with predictions from Quantum Chromodynamics directly or with effective theories that describe the strong nuclear force Here we report on new proton spin structure measurements with significantly better precision and improved coverage than previous data at low momentum transfer squared between $0012$ and $10$ GeV$^2$ This kinematic range provides unique tests of effective field theory predictions Our results show that a complete description of the nucleon spin remains elusive They call for further theoretical works that include the more fundamental lattice gauge method Finally, our data agree with the Gerasimov-Drell-Hearn sum rule, a fundamental prediction of quantum field theory

Inter-pulse delay optimization for dynamical decoupling pulse sequences with up to six refocusing pulses

Abstract: We present a computational optimization of the inter-pulse delays of multiple $$\pi $$ -pulse dynamical decoupling pulse sequences, aiming to preserve the coherence of electron spin embedded in strongly coupled proton spin environments more efficiently. We consider all centrosymmetric multiple $$\pi $$ -pulse spin echo pulse sequences in the range of three to six $$\pi $$ -pulses and parametrize them using up to two free parameters. The parameter space is then surveyed using the nuclear spin bath model and cluster correlation expansion methods. We find one maximum of coherence preservation within the constrained parameter space for each total number of $$\pi $$ -pulses applied and obtain optimized parameters accordingly. We observe that the optimized regimes are essentially identical for both polycrystalline and glassy matrix structures of the proton spin environment. Our methodology also produces good agreements with experimental results reported in the literature.

Development of Triplet Dynamic Nuclear Polarization for Polarization Analysis in Small-Angle Neutron Scattering

Abstract: We present the status of the development of a novel neutron spin filter based on the dynamic nuclear polarization (DNP) of protons in a naphthalene single crystal that uses highly polarized optically excited triplet states of pentacene as the polarizing agent (PA). The filter is applied as spin analyzer in small-angle neutron scattering (SANS) experiments to study magnetism. In order to improve the spin filter performance, a better understanding of the electron polarization creation was essential. For this purpose, careful light absorption measurements have been performed an a theory developed to describe the light propagation and absorption in the biaxial anisotropic absorptive pentacene:naphthalene single crystal and the subsequent triplet production of pentacene molecules. The DNP build-up in a crystal of given size can now be simulated and optimized by the proper choice of the experimental parameters, e.g. the type of excitation light source or the pentacene dopant concentration. As a result 80% proton polarization can now be routinely achieved, close to the theoretical maximum, with extremely long relaxation times. This significantly improved the figure of merit of the spin filter and furthermore allowed to implement a new scheme of filter operation that greatly facilitates its operation in the environment of a large-scale neutron scattering facility. We have made the device transportable, i.e. the filter is conveniently polarized under optimum conditions in the laboratory and then transferred to the neutron beam line where it can be operated during several days with practically frozen polarization while requiring only a minimum of equipment. This saves cost on instrumentation, beam time and work. These improvement allowed to apply the spin filter as neutron polarization analyzer in a series of polarized SANS experiments to study magnetism on the nano-scale. These studies focused on an exotic and elusive physical phenomena – the defect-induced Dzyaloshinskii- Moriya interaction (DMI) in a nanocrystalline two-phase alloy Fe73Si16B7Nb3Cu1. An asymmetric signal is observed in the difference between the two spin-flip cross sections, which is a key signature directly related to the DMI. The result supports the generic relevance of the DMI for the magnetic structure of defect-rich ferromagnets. Two additional studies are presented that do not directly relate to the spin filter subject but further exploit the unique properties of highly polarized proton spin systems with extremely long relaxation times that now can be prepared as a result of all the optimized processes. The first addresses a fundamental issue of DNP that storage and transport of hyperpolarized samples is severely restricted. A procedure and equipment is presented to transport polarized samples over long distance and provide hyperpolarized nuclear spins to users that are not in the possession of DNP equipment. The second studies the long-range nuclear magnetic ordering (ferromagnetic or antiferromagnetic) that is created by adiabatic demagnetization in the rotating frame. We focus on the antiferromagnetic nuclear spin configuration of hydrogen nuclei in a naphthalene single crystal, similar to the antiferromagnetic structure of electron spins ordered by the Heisenberg exchange interaction.

On the Potential of Fourier-Encoded Saturation Transfers for Sensitizing Solid-State Magic-Angle Spinning NMR Experiments

Abstract: Chemical exchange saturation transfer (CEST) is widely used for enhancing the solution NMR signatures of magnetically-dilute spin pools; in particular species at low concentrations undergoing chemical exchanges with an abundant spin pool. CEST's main feature involves encoding and then detecting the weak NMR signals of the magnetically dilute spin pools on a magnetically abundant spin pool of much easier detection - for instance the protons of H2O. Inspired by this method, we propose and exemplify a methodology to enhance the sensitivity of magic-angle spinning (MAS) solid-state NMR spectra. Our proposal uses the abundant 1H reservoir arising in organic solids as the magnetically abundant spin pool, and relies on proton spin diffusion in lieu of chemical exchange to mediate polarization transfer between a magnetically dilute spin pool and this magnetically abundant spin reporter. As an initial test of this idea we target the spectroscopy of naturally-abundant 13C, and rely on a Fourier-encoded version of the CEST experiment for achieving broadbandness in coordination with both MAS and heteronuclear decoupling - features normally absent in CEST. Arbitrary evolutions of multiple 13C sites can thus be imprinted on the entire 1H reservoir, which is subsequently detected. Theoretical predictions suggest that orders-of-magnitude signal enhancements should be achievable in this manner - on the order of the ratio between the 13C and the 1H reservoirs' abundances. Experiments carried out under magic-angle spinning conditions evidenced ca. 5-10x enhancements. Further opportunities and challenges arising in this Fourier-Encoded Saturation Transfer (FEST) MAS NMR approach are briefly discussed.

JAM small-$x$ helicity phenomenology

Abstract: We present the first-ever description the world data on the $g_1^{p,n}$ structure function at small Bjorken $x$ using evolution equations in $x$ derived from first principles QCD. This is a Monte-Carlo analysis within the JAM global framework that allows us to fit all existing polarized DIS data below $x<0.1$ as well as predict future measurements of small $x$ $g_1^{p,n}$ at the EIC. This is a necessary step in determining the quark helicity PDFs and, ultimately, the quark contribution to the proton spin.

Boosting the resolution of multidimensional NMR spectra by complete removal of proton spin multiplicities.

Abstract: Over decades multidimensional NMR spectroscopy has become an indispensable tool for structure elucidation of natural products, peptides and medium sized to large proteins. Heteronuclear single quantum coherence (HSQC) spectroscopy is one of the work horses in that field often used to map structural connectivity between protons and carbons or other hetero nuclei. In overcrowded HSQC spectra, proton multiplet structures of cross peaks set a limit to the power of resolution and make a straightforward assignment difficult. In this work, we provide a solution to improve these penalties by completely removing the proton spin multiplet structure of HSQC cross peaks. Previously reported sideband artefacts are diminished leading to HSQC spectra with singlet responses for all types of proton multiplicities. For sideband suppression, the idea of restricted random delay (RRD) in chunk interrupted data acquisition is introduced and exemplified. The problem of irreducible residual doublet splitting of diastereotopic CH2 groups is simply solved by using a phase sensitive JRES approach in conjunction with echo processing and real time broadband homodecoupling (BBHD) HSQC, applied as a 3D experiment. Advantages and limitations of the method is presented and discussed.

Prediction of $^1$H singlet relaxation via intermolecular dipolar couplings using the molecular dynamics method.

Abstract: Dissolution dynamical nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tag to probe slow dynamic processes, and detection of ligand--protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular and intermolecular dipolar, chemical shift anisotropy, and spin--rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

$^1$H singlet relaxation time prediction via intermolecular dipolar coupling using the molecular dynamics method

Abstract: Dissolution dynamical nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tag to probe slow dynamic processes, and detection of ligand--protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular and intermolecular dipolar, chemical shift anisotropy, and spin--rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

On the Transfer of Polarization from the Initial to the Final Proton in the Elastic Process $ e \vec {p} \to e \vec {p}$

Abstract: The $Q^2$ dependence of the ratio of the cross sections with and without proton spin flip, as well as the polarization asymmetry in the process $e \vec{p} \to e \vec{p}$ has been numerically analyzed using the results of JLab polarization experiments on the measurements of the ratio of the Sachs form factors in the $\vec{e} p \to e \vec{p}$ process. The calculations have been made for the case where the initial (at rest) and final protons are fully polarized and have a common spin quantization axis, which coincides with the direction of motion of the final proton. The longitudinal polarization transfer to the proton has been calculated in the case of the partially polarized initial proton for a kinematics used in the experiment reported in [A. Liyanage et al. (SANE Collaboration), Phys. Rev. C 101, 035206 (2020)], where the double spin asymmetry was measured in the $\vec{e} \vec{p} \to e p$ process. A noticeable sensitivity of the polarization transfer to the proton to the form of the $Q^2$ dependence of the ratio $\mu_p G_E/G_M$ has been found. This sensitivity may be used to conduct a new independent experiment to measure this dependence in the $ e \vec{p} \to e \vec{p}$ process. A criterion to assess the reliability of measurements of the ratio of Sachs form factors using the Rosenbluth technique has been proposed and used to analyze the results of two experiments.

Longitudinal double helicity asymmetry $A_{LL}$ from direct photon, jet and charged pion production in polarized $\vec{p}+\vec{p}$ collisions

Abstract: Understanding the proton spin composition from the quarks and gluons spin polarization and their motion is important to test various kinds of sum rules and nonperturbative properties of hadrons. At the Relativistic Heavy Ion Collider (RHIC), we collide longitudinally polarized proton beams and measure the double helicity asymmetry $A_{LL}$, which is an important physical quantity for extracting the polarized parton distribution functions (PDFs) of the proton. Direct photon, jet and charged pion production are good channels to probe the gluon spin polarization inside the proton, with the ability to probe also the sign of the gluon spin. Direct photon production is the theoretically ``cleanest'' channel, with little fragmentation contribution, but limited by statistics. On the other hand, jet and charged pion production have more statistics, but include more hard processes and hadronization effects. I will present the recent measurements of direct photon, jet and charged pion $A_{LL}$s at PHENIX and show their complementary roles in extracting the gluon spin.