Low Momentum Transfer Region Research Articles

Modeling W+W− production with rapidity gaps at the LHC

We present a new calculation of $W^+ W^-$ production in the semi-exclusive channel, that is either with intact outgoing protons or rapidity gaps present in the final state, and with no colour flow between the colliding protons. This study provides the first complete prediction of the $W^+ W^-$ semi-exclusive cross section, as well as the breakdown between elastic and proton dissociative channels. It combines the structure function calculation for a precise modelling of the region of low momentum transfers with a parton-level calculation in the region of high momentum transfers. The survival factor probability of no additional proton-proton interactions is fully accounted for, including its kinematic and process dependence. We analyse in detail the role that the pure photon-initiated ($\gamma\gamma \to W^+ W^-$) subprocess plays, a comparison that is only viable by working in the electroweak axial gauge. In this way, we find that the dominance of this is not complete in the proton dissociative cases, although once $Z$-initiated production is included a significantly better matching to the complete calculation is achieved. A direct consequence of this is that the relative elastic, single and double dissociative fractions are in general different in comparison to the case of lepton pair production. We present a direct comparison to the recent ATLAS data on semi-exclusive $W^+ W^-$ production, finding excellent agreement within uncertainties. Our calculation is provided in the publicly available SuperChic 4.1 Monte Carlo (MC) generator, and can be passed to a general purpose MC for showering and hadronization of the final state.

Nucleon structure from basis light-front quantization

We produce the light-front wave functions (LFWFs) of the nucleon from a basis light-front approach in the leading Fock-sector representation. We solve for the mass eigenstates from a light-front effective Hamiltonian, which includes a confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with fixed coupling. We then employ the LFWFs to obtain the electromagnetic and axial form factors, the parton distribution functions (PDFs), and the generalized parton distribution functions for the nucleon. The electromagnetic and axial form factors of the proton agree with the experimental data, whereas the neutron form factors deviate somewhat from the experiments in the low-momentum transfer region. The unpolarized, the helicity, and the transversity valence quark PDFs, after QCD scale evolution, are fairly consistent with the global fits to the data at the relevant experimental scales. The helicity asymmetry for the down quark also agrees well with the measurements; however, the asymmetry for the up quark shows a deviation from the data, especially in the small $x$ region. We also find that the tensor charge agrees well with the extracted data and the lattice QCD predictions, while the axial charge is somewhat outside the experimental error bar. The electromagnetic radii of the protons, the magnetic radius of the neutron, and the axial radius are in excellent agreement with the measurements, while the neutron charge radius deviates from the experiment.

Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory

A unified treatment of both chiral and radiative corrections to the low-energy elastic lepton-proton scattering processes is presented in Heavy Baryon Chiral Perturbations Theory. The proton hadronic chiral corrections include the next-to-next-to leading order corrections whereas the radiative corrections include the next-to-leading order terms in our novel power counting scheme. We find that the net fractional well-defined chiral corrections with respect to the leading order Born cross section can be as large as $10\%$ ($20\%$) for electron (muon) scattering process for MUon proton Scattering Experiment (MUSE) kinematics. We show {\it via} our model-independent treatment of the low-energy lepton-proton kinematics, that the largest theoretical uncertainty is due to the recent different published values of the proton's rms radius while, e.g., the next higher order hadronic chiral terms are expected to give rather nominal errors. For the radiative corrections we demonstrate a systematic order by order cancellation of all infrared singularities and present our finite ultraviolet regularization results. We find that the radiative corrections for muon-proton scattering is of the order of $2\%$, whereas for electron scattering the radiative corrections could be as large as $25\%$. We attribute such a contrasting result partially to the fact that in muon scattering the leading radiative order correction goes through zero in some intermediate low-momentum transfer region, leaving the sub-leading radiative chiral order effects to play a dominant role in this particular kinematic region. For the low-energy MUSE experiment, the often neglected lepton mass as well as the Pauli form factor contributions of the relativistic leptons are incorporated in all our computations.

Measurement of the proton spin structure at long distances

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 GeV$^2$. 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, e.g. 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.

Study of the Dressed State of Hydrogen Atom in Electron Atom Elastic Collision in Laser Field

We discuss the various important aspects of the theory of electron-atom elastic collision in laser field. We analyze the collision accompanied by the transfer of photons. We study the free electron states i.e. Volkov states and target atomic states i.e. Dressed states. We calculate the first-Born scattering matrix for electron-atom elastic collision. The present work accounts the calculation for hydrogen as target atom in soft photon limits i.e., in weak field. The dressing effect becomes significant in the region of low momentum transfer, reaches maximum of value of 25000 a.u. at momentum transfer of 0.44. This work explains that the differential cross-section does not occur very low and at very high momentum transfer. However, it occurs at moderate momentum transfer.

Constraints in modeling the quasielastic response in inclusive lepton-nucleus scattering

We show that the quasielastic (QE) response calculated with the SuSAv2 (superscaling approach) model, that relies on the scaling phenomenon observed in the analysis of (e,e') data and on the relativistic mean-field theory, is very similar to that from a relativistic distorted wave impulse approximation model when only the real part of the optical potentials is employed. The coincidence between the results from these two completely independent approaches, which satisfactorily agree with the inclusive data, reinforces the reliability of the quasielastic predictions stemming from both models and sets constraints for the QE response. We also study the low energy and momentum transfer region of the inclusive response by confronting the results of the relativistic mean-field model with those of the Hartree-Fock continuum random-phase approximation model, which accounts for nuclear long-range correlations. Finally, we present a comparison of our results with the recent JLab (e,e') data for argon, titanium and carbon, finding good agreement with the three data sets.

Precision Measurement of the Proton Charge Radius in Electron Proton Scattering

This report presents a project of an experiment for precision studies of the elastic electron proton scattering in the low momentum transfer region. The project is based on an innovative experimental method which allows for detection of recoil protons in a hydrogen "active target". The goal of the experiment is to measure the $ep$ elastic scattering differential cross section in the $Q^2$ range from 0.001 GeV$^2$ to 0.04 GeV$^2$ with 0.1% relative and 0.2% absolute precision and to determine the proton charge radius with a sub-percent precision. The important advantages of the proposed experiment are low radiative corrections, inherent to the recoil proton method, and absolute measurements of the differential cross sections. The experiment will be performed in the 720 MeV electron beam of the Mainz electron accelerator MAMI. This accelerator can provide an electron beam with optimal for this experiment parameters. The Proposal was approved by the MAMI Program Advisory Committee, and a special Agreement aimed at realization of this experiment was signed between Petersburg Nuclear Physics Institute and Institute of Nuclear Physics of the Mainz University. Also, scientists from the following institutes will participate in this project: GSI Centre for Heavy Ion Research, Germany; Joint Institute for Nuclear Research, Russia; William and Mary College, USA; Mount Allison University, Canada; University of Regina, Canada; Saint Mary's University, Canada. The first measurements should be started in 2020.

Nucleon-deuteron scattering with the JISP16 potential

The nucleon-nucleon J-matrix Inverse Scattering Potential JISP16 is applied to elastic nucleon-deuteron (Nd) scattering and the deuteron breakup process at the lab. nucleon energies up to 135 MeV. The formalism of the Faddeev equations is used to obtain 3N scattering states. We compare predictions based on the JISP16 force with data and with results based on various NN interactions: the CD Bonn, the AV18, the chiral force with the semi-local regularization at the 5th order of the chiral expansion and with low-momentum interactions obtained from the CD Bonn force as well as with the predictions from the combination of the AV18 NN interaction and the Urbana IX 3N force. JISP16 provides a satisfactory description of some observables at low energies but strong deviations from data as well as from standard and chiral potential predictions with increasing energy. However, there are also polarization observables at low energies for which the JISP16 predictions differ from those based on the other forces by a factor of two. The reason for such a behavior can be traced back to the P-wave components of the JISP16 force. At higher energies the deviations can be enhanced by an interference with higher partial waves and by the properties of the JISP16 deuteron wave function. In addition, we compare the energy and angular dependence of predictions based on the JISP16 force with the results of the low-momentum forces obtained with different values of the momentum cutoff parameter. We found that such low-momentum forces can be employed to interpret the Nd elastic scattering data only below some specific energy which depends on the cutoff parameter. Since JISP16 is defined in a finite oscillator basis, it has properties similar to low momentum interactions and its application to the description of Nd scattering data is limited to a low momentum transfer region.

Maxima in the thermodynamic response and correlation functions of deeply supercooled water.

Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low-momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

Spacelike and timelike form factors for the (π0,η,η′)→γ*γ transitions in the light-front quark model

We investigate the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resorting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at $q^2=0$ with the recent experimental data from the Dalitz decays of $(\pi^0,\eta,\eta')$. For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.

Two-photon exchange corrections to elastic e− -proton scattering: Full dispersive treatment of πN states at low momentum transfers

We evaluate the pion-nucleon intermediate-state contribution to the two-photon exchange (TPE) correction in the elastic electron-nucleon scattering within a dispersive framework. We calculate the contribution from all $\pi N$ partial waves using the MAID parametrization. We provide the corresponding TPE correction to the unpolarized $e p$ scattering cross section in the region of low momentum transfer $ Q^2 \lesssim 0.064~\mathrm{GeV}^2$, where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. We compare our result in the forward angular region with an alternative TPE calculation, in terms of structure functions, and find a good agreement, indicating a small contribution at low $Q^2$ due to discontinuities beyond $ \pi N$. We also compare our results with empirical fits.

Near-threshold incoherentϕphotoproduction on the deuteron: Searching for traces of a resonance

We study the near-threshold incoherent $\phi$ photoproduction on the deuteron based on a model of $\gamma N \to \phi N$, consisting of Pomeron, $(\pi, \eta)$ exchanges, and a $J^P = 3/2^-$ resonance, which describes the low energy $\gamma p \to \phi p$ LEPS data well, including the peak in the forward differential cross section. The calculation is done up to double rescatterings, with the spin dependence of the elementary $\gamma N \to \phi N$ amplitude retained throughout the calculation. The Fermi motion and final-state interactions (FSI) are all properly treated as prescribed by realistic nucleon-nucleon interaction. The couplings of the resonance to $\gamma n$ and $\phi n$ channels are estimated with the help of a constituent quark model. The main features of the LEPS and CLAS data are described reasonably well except for some quantitative discrepancies at very low energies and low momentum transfers regions. It is found that contributions of Fermi motion, $pn$ FSI, and resonance are all indispensable in bridging the differences between the single-scattering results and the data. The off-shell rescattering is found to be important as it cancels out a large portion of the on-shell contribution. The discrepancies at low momentum transfer region might be related to the binning size of the data. No peak is found to be associated with the weak resonance as it gets smeared out by the Fermi motion and FSI with deuterium target. The problem at very low energy region hints at the possible contributions from other mechanisms and should be investigated in depth with the use of recent high statistics $\gamma p \to \phi p$ data from CLAS.

Electroexcitation of the Δ+(1232) at low momentum transfer

We report on new p$(e,e^\prime p)\pi^\circ$ measurements at the $\Delta^{+}(1232)$ resonance at the low momentum transfer region. The mesonic cloud dynamics is predicted to be dominant and rapidly changing in this kinematic region offering a test bed for chiral effective field theory calculations. The new data explore the low $Q^2$ dependence of the resonant quadrupole amplitudes while extending the measurements of the Coulomb quadrupole amplitude to the lowest momentum transfer ever reached. The results disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations that include pion cloud effects, chiral effective field theory and lattice calculations. The reported measurements suggest that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements.

Electroweak properties of octet baryons in a light-cone quark-diquark model

We study the electroweak properties of ground state octet baryons in a relativistic quark-spectator-diquark model, with light-front formalism applied to take relativistic effects into account. Our model provides a consistent picture of the electroweak properties of the ground state octet baryons in the low momentum transfer region. The Melosh-Wigner rotation is applied as the transformation relation between spinors in the instant form and front form. Numerical results are presented for the magnetic moments, weak transition charges and Sachs form factors. Our results are in good agreement with experimental measurements and other theoretical results.

Structure near theK−+ p + pthreshold in the in-flight3He(K−, Λp)nreaction

To search for an S= -1 di-baryonic state which decays to $\Lambda p$, the $ {\rm{}^3He}(K^-,\Lambda p)n_{missing}$ reaction was studied at 1.0 GeV/$c$. Unobserved neutrons were kinematically identified from the missing mass $M_X$ of the $ {\rm{}^3He}(K^-,\Lambda p)X$ reaction in order to have a large acceptance for the $\Lambda pn$ final state. The observed $\Lambda p n$ events, distributed widely over the kinematically allowed region of the Dalitz plot, establish that the major component comes from a three nucleon absorption process. A concentration of events at a specific neutron kinetic energy was observed in a region of low momentum transfer to the $\Lambda p$. To account for the observed peak structure, the simplest S-wave pole was assumed to exist in the reaction channel, having Breit-Wigner form in energy and with a Gaussian form-factor. A minimum $\chi^2$ method was applied to deduce its mass $M_X\ =$ 2355 $ ^{+ 6}_{ - 8}$ (stat.) $ \pm 12$ (syst.) MeV/c$^2$, and decay-width $\Gamma_X\ = $ 110 $ ^{+ 19}_{ - 17}$ (stat.) $ \pm 27$ (syst.) MeV/c$^2$, respectively. The form factor parameter $Q_X \sim$ 400 MeV/$c$ implies that the range of interaction is about 0.5

Moments of nucleon structure functions at next-to-leading order in baryon chiral perturbation theory

We obtain leading- and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$ GeV$^2$). Especially surprising is the situation for the spin polarizability $\delta_{LT}$, which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the "$\delta_{LT}$ puzzle," is not seen in the present calculation.

Coherent and Incoherent Scattering Cross Sections of Some Lead and Sodium Compounds at Angles below 10° for 241Am Gamma Rays

We report the total (coherent + incoherent) scattering cross sections of some lead and sodium compounds measured at angles less than 10° for 241Am (59.54 keV) gamma rays. The experimental cross sections so obtained are compared with the data interpolated from theoretical compilations based on nonrelativistic Hartree-Fock (NRHF) model for the samples of interest. In the low momentum transfer region studied, it is observed that the nonrelativistic theoretical total scattering cross sections computed using HF form factor and scattering function tabulated by NRHF are quite adequate in explaining the measured total scattering cross sections.

Measurements of the γ*p → Δ reaction at low Q2

We report new p$(\vec{e},e^\prime p)\pi^\circ$ measurements in the $\Delta^{+}(1232)$ resonance at the low momentum transfer region utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The mesonic cloud dynamics are predicted to be dominant and appreciably changing in this region while the momentum transfer is sufficiently low to be able to test chiral effective calculations. The results disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations with pion cloud effects, chiral effective field theory and lattice calculations. The reported measurements suggest that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements.

Gamow–Teller strength extraction from (3He, t) reactions

Abstract Details of Gamow–Teller (GT) and Fermi (F) strength extraction from charge-exchange reactions at intermediate energies, as well as the concept of using the phenomenological effective interaction for the description of the reactions are reviewed. The focus lies on high-resolution ( 3 He, t ) data, yet new data on ( d , 2 He) charge-exchange reactions are presented as well to indicate the connection and the similarity of both probes to the elementary ( p , n ) , resp. ( n , p ) reactions. We show that for the extraction of B ( GT ) and B ( F ) strength a proper extrapolation of the charge-exchange cross section to the zero momentum transfer point, q = 0 , gets to be increasingly important for medium to high-mass target nuclei and at moderate excitation energies of a few MeV. Numerous ( 3 He, t ) and ( p , n ) spectra are being compared, and, once adjusted for the different momentum transfers, they reveal a remarkable similarity up to the highest measured excitation energies of ≈ 25 MeV . Further, we remark that the precision, with which GT and F transition strengths can be extracted, is limited by the relatively poor knowledge of the absorption processes, and a more thorough theoretical understanding of the nuclear structure leading to absorption in charge-exchange reactions, especially in the restricted kinematic region of low-momentum transfers, is warranted. Finally, B ( GT ) values for the 136 Xe( 3 He, t ) are being re-evaluated in the light of the present discussion.

Weak response of neutron matter at low momentum transfer

The Landau parameters obtained from the matrix elements of an effective interaction recently derived within the formalism of correlated basis functions are used to carry out a study of the weak response of neutron matter in the region of low momentum transfer. The proposed approach allows for a consistent description of different interaction effects and can be extended to describe matter at nonvanishing temperature. The results show that interactions lead to a sizable enhancement of the neutrino mean free path in cold neutron matter. The dependence of the mean free path on temperature and neutrino energy is also analyzed.