Sea Quarks Research Articles

Sivers function of sea quarks in the light-cone model

We calculate the Sivers function of u¯ and d¯ quarks using the overlap representation within the light-cone formalism. The light-cone wave functions of the proton are obtained in terms of the |q¯qB〉 Fock states motivated by the meson-baryon fluctuation model. We consider the final-state interaction at the level of one gluon exchange. In a simplified scenario, the Sivers function of u¯ and d¯ can be expressed as the convolution of the Sivers function of the pion inside the proton and the unpolarized distribution of q¯ inside the pion. The model parameters are fixed by fitting the unpolarized sea quark distributions to the known parameterizations. We present the numerical results for f1⊥u¯/p(x,kT2) and f1⊥d¯/p(x,kT2). The first transverse moment of the sea quark Sivers functions in our model are find to be negative and the magnitude is about 0.004 at most.

NNNPDF3.0: evidence for a modified partonic structure in heavy nuclei

We present an updated determination of nuclear parton distributions (nPDFs) from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus and proton-nucleus together with collider proton-nucleus experiments. In addition to neutral- and charged-current deep-inelastic and Drell–Yan measurements on nuclear targets, we consider the information provided by the production of electroweak gauge bosons, isolated photons, jet pairs, and charmed mesons in proton-lead collisions at the LHC across centre-of-mass energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a global nPDF analysis, the constraints from these various processes are accounted for both in the nuclear PDFs and in the free-proton PDF baseline. The extensive dataset underlying the nNNPDF3.0 determination, combined with its model-independent parametrisation, reveals strong evidence for nuclear-induced modifications of the partonic structure of heavy nuclei, specifically for the small-x shadowing of gluons and sea quarks, as well as the large-x anti-shadowing of gluons. As a representative phenomenological application, we provide predictions for ultra-high-energy neutrino-nucleon cross-sections, relevant for data interpretation at neutrino observatories. Our results provide key input for ongoing and future experimental programs, from that of heavy-ion collisions in controlled collider environments to the study of high-energy astrophysical processes.

Handedness correlation from quark polarization

Jet handedness as a measure of quark and/or gluon polarizations has been proposed for nearly 30 years. It was demonstrated by measuring the correlation of jet handedness in the electron positron annihilation process. Once parameters are determined, the method could be used to measure quark and/or gluon polarizations in other experiments. The reported data provided evidence for the jet handedness and handedness correlation. However, the jet handedness correlation measured in the electron positron annihilation process from the opposite jets contradicts theoretical prediction by a sign. In order to explain this, we present a chromo-hydrogen-like model in this paper. According to calculations, both jet handedness and handedness correlation depend on not only the polarization of the fragmenting valence quark but also the polarization of the sea quark. It is the appearance of the sea quark polarization that can solve the contradiction. In other words, measurements of jet handedness and handedness correlation can be used to determine the sea quark polarization.

Nonperturbative running of the quark mass for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the quark mass, for ${N}_{f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schr\"odinger functional (SF) boundary conditions for sea quarks and chirally rotated Schr\"odinger functional ($\ensuremath{\chi}\mathrm{SF}$) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor ${z}_{\mathrm{f}}({g}_{0}^{2})$ of the $\ensuremath{\chi}\mathrm{SF}$ valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios ${Z}_{S}/{Z}_{P}$ and ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ of the renormalization parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our ${Z}_{S}/{Z}_{P}$ results are found to agree with previous determinations, based on a mass ratio method [G. M. de Divitiis et al. (ALPHA Collaboration), Eur. Phys. J. C 79, 797 (2019)] and Ward identities [ J. Heitger et al. (ALPHA Collaboration), Eur. Phys. J. C 80, 765 (2020); J. Heitger et al., Eur. Phys. J. C 81, 606 (2021)], with Schr\"odinger functional boundary conditions. The behavior of ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ confirms the theoretical expectations of $\ensuremath{\chi}\mathrm{SF}$ QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step-scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schr\"odinger functional boundary conditions [I. Campos et al., Eur. Phys. J. C 78, 387 (2018)], and provides a strong universality test for the two lattice setups.

Sea quark contributions to the electromagnetic form factors of Σ hyperons

We study the sea quark contributions to the electromagnetic form factors of $\Sigma$ baryons with nonlocal chiral effective theory. Both octet and decuplet intermediate states are included in the one loop calculation. $G_{\Sigma^{-}}^{u}$ and $G_{\Sigma^{+}}^{d}$ could be priority observables for the examination of sea quark contributions to baryon structure because these quantities are much larger than the strange form factors of nucleon. It will be less difficult for lattice simulation to determine the sign of these pure sea quark contributions unambiguously. In $\Sigma^0$, the light sea quark form factors $G_{\Sigma^{0}}^{u}$ and $G_{\Sigma^{0}}^{d}$ are identical. Since the light sea quark form factors in proton are different, it will be more meaningful to compare lattice result of the light sea quark form factors in $\Sigma^0$ with that obtained from effective field theory.

Form factors for the processes Bc+→D0ℓ+νℓ and Bc+→Ds+ℓ+ℓ−(νν¯) from lattice QCD

We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^+ \to D^0 \ell^+ \nu_{\ell}$, $B_c^+ \to D_s^+ \ell^+ \ell^-$ and $B_c^+ \to D_s^+ \nu \overline{\nu}$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu}) /\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12} \mathrm{~s}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find $\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu )/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to D}(18)_{B_c \to J/\psi}$. We calculate the differential decay widths of $B_c^+ \to D_s^+ \ell^+ \ell^-$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u \overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2 = 1 \; \mathrm{GeV}^2 - 6 \; \mathrm{GeV}^2$ for $B_c^+ \to D_s^+ \mu^+ \mu^-$ and $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to J/\psi} \times 10^{-6}$. We also give results for the branching fraction of $B_c^+ \to D_s^+ \nu \overline{\nu}$. Prospects for reducing our errors in the future are discussed.

The Gluon Exchange Model in Proton–Nucleus Collisions

We apply our recently formulated Gluon Exchange Model (GEM) to baryon production in proton-nucleus reactions involving N>1 proton-nucleon collisions. We propose a description scheme for the process of soft color octet (gluon) exchange, based on the assumption that probabilities to form an effective diquark are equal for all allowed pairs of quarks. The latter effective diquark can form either from two valence, one valence and one sea, or from two sea quarks. Consequently we calculate the probabilities for different color configurations involving diquarks of valence-valence, valence-sea and sea-sea type. These probabilities appear to depend on the number of exchanged gluons, which results in increasing baryon stopping as a function of the number of proton-nucleon collisions in the nucleus. As such, the nuclear stopping power appears to be governed by the emergence of new color configurations as a function of N rather than by the energy loss of the original valence diquark. The advantage of our approach lies in its high predictive power which makes it verifiable by the new, precise data on proton and neutron production from the CERN SPS. The latter verification, and a set of predictions for the N-dependence of the baryon stopping process, are included in the letter.

Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional Qcd

Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional Qcd

On the evaluation of the Gottfried sum and d̄−ū asymmetry with the use of the TMM method

In this paper, we obtain the integrated flavor asymmetry of the sea quarks in the proton, [Formula: see text], with the help of the truncated moments approach elaborated in our previous papers. We use the difference between the light sea-quark distributions [Formula: see text] extracted from Drell–Yan (DY) NuSea/E866 measurements of the cross-section ratio [Formula: see text] and from the recent global analysis of deep inelastic scattering (DIS) [Formula: see text] data incorporating the reanalyzed neutron structure function. In our analysis, we also include the most recent DY data from the Fermilab SeaQuest/E906 experiment.

Pion form factor and charge radius from lattice QCD at the physical point

We present our results on the electromagnetic form factor of pion over a wide range of $Q^2$ using lattice QCD simulations with Wilson-clover valence quarks and HISQ sea quarks. We study the form factor at the physical point with a lattice spacing $a=0.076$ fm. To study the lattice spacing and quark mass effects, we also present results for 300 MeV pion at two different lattice spacings $a=0.04$ and 0.06 fm. The lattice calculations at the physical quark mass appear to agree with the experimental results. Through fits to the form factor, we estimate the charge radius of pion for physical pion mass to be $\langle r_{\pi}^2 \rangle=0.42(2)~{\rm fm}^2$.

Chiral condensates for neutron stars in hadron-quark crossover: From a parity doublet nucleon model to a Nambu–Jona-Lasinio quark model

We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 \gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B \sim 2-3n_0$ ($n_0\simeq 0.16\,{\rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B \gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.

The diffractive contribution to deep inelastic lepton-proton scattering: Implications for QCD momentum sum rules and parton distributions

The cross section for deep inelastic lepton-proton scattering (DIS) ℓp→ℓ′X includes a diffractive deep inelastic (DDIS) contribution ℓp→ℓ′p′X, in which the proton remains intact with a large longitudinal momentum fraction xF greater than 0.9 and small transverse momentum. The DDIS events, which can be identified with Pomeron exchange in the t-channel, account for approximately 10% of all of the DIS events. Thus, when one measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS events as a contribution to the DIS cross section, whether or not the final-state proton p′ is detected. In such events, the missing momentum fraction xp′∼0.9 carried by the final-state proton p′ in the DDIS events could be misidentified with the light-front momentum fraction carried by sea quarks or gluons in the protons' Fock structure. As we shall show in this article, the underlying QCD Pomeron-exchange amplitude which produces the DDIS events does not obey the operator product expansion nor satisfy momentum sum rules. Thus we conclude that the quark and gluon distributions measured in DIS experiments will be misidentified, unless the measurements explicitly exclude the DDIS events and that a correct determination of the parton distribution functions (PDFs) derived from the DIS data requires the explicit subtraction of the DDIS contribution from the full DIS cross section.

Global QCD Analysis of Pion Parton Distributions with Threshold Resummation.

We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian MonteCarlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-x asymptotics of the valence quark distribution ∼(1-x)^{β_{v}} can differ significantly, with β_{v} ranging from ≈1 to >2.5 at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts the total momentum carried by gluons to ≈40%, increasing the gluon contribution to the pion mass to ≈40 MeV.

Linking continuum and lattice quark mass functions via an effective charge

The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and Domain-Wall fermion actions for valence and sea quarks, respectively. The results are confronted and seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running-interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing thus a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.

Quarkyonic stars with isospin-flavor asymmetry

We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $\beta$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps differentiating the nucleon and the quark sectors. In addition, we impose the conservation of the isospin-flavor asymmetry in the nucleon and the quark phases. Within this model, several quarkyonic stars are constructed on top of the SLy4 model for the nucleon sector, producing a bump in the sound speed, which implies that quarkyonic stars are systematically bigger and have a larger maximum mass than the associated neutron stars. They also predict lower proton fraction at $\beta$-equilibrium, which potentially quenches fast cooling in massive compact stars.

Another look at the proton sea

Johanna Miller nicely summarizes the current experimental situation with the puzzling asymmetry of the proton's antiquark "sea" in the May 2021 issue of Physics Today (page 14). She describes the SeaQuest experiment, which found that there are about 50% more d‾ antiquarks than u‾ antiquarks. The result is surprising, since the traditional mechanism generating the sea was commonly expected to be mediated by gluons, which are “flavor blind” and cannot tell u‾ from d‾.Miller’s report mentions two theoretical ideas proposed to explain the asymmetry. One is that the presence of two u valence quarks leads to “Pauli blocking” of sea u quarks, the twin brothers of u‾ antiquarks. But quarks have six states available: three colors × two spin orientations. In addition, valence and sea quarks overlap little in momentum space. Pauli blocking is therefore way too small to explain the data. (I’ll turn to the second idea—the contribution of the pion cloud—at the end.)Unfortunately, Miller does not mention a third idea that has been put forth, which is more nontrivial and seems likelier to explain the puzzling asymmetry. It started with an observation by Alexander Dorokhov and Nikolai Kochelev11. A. E. Dorokhov, N. I. Kochelev, Phys. Lett. B 304, 167 (1993). https://doi.org/10.1016/0370-2693(93)91417-L that the so-called ’t Hooft effective four-quark Lagrangian22. G. ’t Hooft, Phys. Rev. D 14, 3432 (1976). https://doi.org/10.1103/PhysRevD.14.3432 is “flavor nondiagonal,” leading to processes u→u(d‾d) and d→d(u‾u) but not to u→u(u‾u) and d→d(d‾d).In a way, the effect is also due to the Pauli exclusion principle, but at a different level. Topological tunneling events, known as instantons, create fields so strong that they fix the color and spin states of participating quarks uniquely. Instead of six possibilities, there remains only one, thus a complete blocking. Since the proton has two valence u quarks and only one valence d quark, that mechanism would suggest d‾/u‾ = 2 rather than 1.Recently I made the first attempt to evaluate that effect quantitatively, by calculating the wavefunction of the five-quark uuduu‾ and uuddd‾ sectors of the proton induced by the ’t Hooft Lagrangian.33. E. Shuryak, Phys. Rev. D 100, 114018 (2019). https://doi.org/10.1103/PhysRevD.100.114018 The results approximately match the data, in magnitude and momentum dependence.How can one test that idea further? If that explanation is true, the sea of Δ++ baryons, which have three up quarks, would have only d‾ antiquarks (at corresponding momentum fraction x). It is hardly possible to check that experimentally, but it can be tested numerically, via lattice gauge theory.A second test is related to the other explanation Miller mentions, the pion cloud. While pions can indeed generate asymmetry in the isospin of the sea, they will not do so for the spin, since pions have spin zero. The ’t Hooft Lagrangian, on the other hand, leads to strict predictions for the quark polarizations. For example, a left-handed up quark uL can produce only a 100% polarized d‾RdL pair. Therefore, a key to the sea’s antiquark asymmetry should come from future theoretical and experimental investigations that relate isospin and the spin asymmetry.ReferencesSection:ChooseTop of pageReferences <<1. A. E. Dorokhov, N. I. Kochelev, Phys. Lett. B 304, 167 (1993). https://doi.org/10.1016/0370-2693(93)91417-L, Google ScholarCrossref2. G. ’t Hooft, Phys. Rev. D 14, 3432 (1976). https://doi.org/10.1103/PhysRevD.14.3432, Google ScholarCrossref3. E. Shuryak, Phys. Rev. D 100, 114018 (2019). https://doi.org/10.1103/PhysRevD.100.114018, Google ScholarCrossref© 2021 American Institute of Physics.

Lattice calculation of pion form factors with overlap fermions

We present a precise calculation of the pion form factor using overlap fermions on seven ensembles of 2+1-flavor domain-wall configurations with pion masses varying from 139 to 340 MeV. Taking advantage of the fast Fourier transform and other techniques to access many combinations of source and sink momenta, we find the pion mean square charge radius to be $\langle {r_\pi^2} \rangle= 0.430(5)(13)\ {\rm{fm^2}}$, which agrees well with the experimental result, and includes the systematic uncertainties from chiral extrapolation, lattice spacing and finite-volume dependence. We also find that $\langle {r_\pi^2} \rangle$ depends on both the valence and sea quark masses strongly and predict the pion form factor up to $Q^2 = 1.0 \ {\rm{GeV^2}}$ which agrees with experiments very well.

Neutrino-nucleon DIS from holographic QCD: PDFs of sea and valence quarks, form factors, and structure functions of the proton

We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic scattering using a chiral doublet of baryonic sources with explicit symmetry breaking, in a slice of ${\mathrm{AdS}}_{5}$ with both a hard and soft wall. We explicitly derive the direct and transition form factors for the vector and axial-vector currents for the holographic dual of a proton and neutron. We use them to derive the $s$-channel structure functions for neutrino and antineutrino scattering on a proton and neutron in bulk. The $t$-channel contributions stemming from the Pomeron and Reggeon exchanges are also evaluated explicitly. The pertinent even and odd structure functions in the limit of large and small parton momentum fraction $x$ are given. The results allow for the extraction of the nonperturbative parton distribution functions carried by the sea and valence quarks both at large-$x$ and small-$x$ regimes. Our holographic parton distribution function (PDF) sets compare well with the Les Houches accord PDF (LHAPDF) and the coordinated theoretical-experiment project on QCD (CTEQ) PDF sets in the large-$x$ and small-$x$ regimes in the intermediate range of ${Q}^{2}&lt;10\text{ }\text{ }{\mathrm{GeV}}^{2}$.

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.

Determining the helicity structure of the nucleon at the Electron Ion Collider in China

Understanding how sea quarks behave inside a nucleon is one of the most important physics goals of the proposed Electron-Ion Collider in China (EicC), which is designed to have a 3.5 GeV polarized electron beam (80% polarization) colliding with a 20 GeV polarized proton beam (70% polarization) at instantaneous luminosity of 2 × 1033cm−2s−1. A specific topic at EicC is to understand the polarization of individual quarks inside a longitudinally polarized nucleon. The potential of various future EicC data, including the inclusive and semi-inclusive deep inelastic scattering data from both doubly polarized electron-proton and electron-3He collisions, to reduce the uncertainties of parton helicity distributions is explored at the next-to-leading order in QCD, using the Error PDF Updating Method Package (ePump) which is based on the Hessian profiling method. We show that the semi-inclusive data are well able to provide good separation between flavour distributions, and to constrain their uncertainties in the x > 0.005 region, especially when electron-3He collisions, acting as effective electron-neutron collisions, are taken into account. To enable this study, we have generated a Hessian representation of the DSSV14 set of PDF replicas, named DSSV14H PDFs.