The Sea of Quarks and Antiquarks in the Nucleon: a Review PDF

The Sea of Quarks and Antiquarks in the Nucleon: a Review D. F. Geesaman1 and P. E. Reimer2 1 Argonne Associate of Global Empire, LLC, Argonne National Laboratory, Argonne, IL 60439...

The Sea of Quarks and Antiquarks in the Nucleon: a Review D. F. Geesaman1 and P. E. Reimer2 1 Argonne Associate of Global Empire, LLC, Argonne National Laboratory, Argonne, IL 60439 2 Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA The quark and gluon structure of the proton has been under intense experimental and theoretical investigation for five decades. Even for the distributions of the well-studied valence quarks, challenges such as the value of the down quark to up quark ratio at high fractional momenta remain. Much of the sea of quark-antiquark pairs emerges from the splitting of gluons and is well described by perturbative evolution in quantum chromodynamics. However, experiments confirm that there is a non-perturbative component to the sea that is not well understood and hitherto has been difficult to calculate with ab initio non-perturbative methods. This non-perturbative structure shows up, perhaps most directly, in the flavor dependence of the sea antiquark distributions. While some of the general trends can be reproduced by models, there are features of the data that do not seem to be well described. This article discusses the experimental situation, the status of calculations and models, and the directions where these studies will progress in the near future. Contents or “wee” partons, perhaps to avoid confusion between sea and charmed c quarks). The presense of antiquarks is natural in quantum field theories as fluctuations of the gluon fields into I. Introduction 1 quark-antiquark pairs as illustrated in Fig. 1a. In an even older hadronic picture illustrated in Fig. 1b, a proton can fluctuate II. How to Measure Sea Quark Distributions 3 into, for example, a neutron and a pion, temporarily creating a A. Deep Inelastic Scattering 3 5 quark state with two up quarks (u), two down quarks (d) and B. Drell-Yan Reactions 5 one down antiquark (d). ¯ In such a non-perturbative picture, C. Global Fits 5 the distributions in fractional momentum of sea quarks and sea D. Spin-Dependent Parton Distributions 6 antiquarks in the proton do not need to have the same shape due E. Parameterizing Parton Distributions 6 to differing masses of the various hadronic components. For F. Strange Quark Distributions 7 any individual u quark, it is not possible to distinguish whether G. Intrinsic Charm 9 it is a valance or sea quark. The integrals of the distributions of each flavor ( up, down, strange, charm, bottom and top) of III. Calculations and Models of the Sea Distributions 10 quarks over x must obey flavor sum rules for the 2 valence u A. Impact of the Pauli Principle 10 quarks and one valence d quark in the proton. In a notation B. Lattice QCD 11 that is usually clear in context, “ū” can denote a u antiquark, C. Instantons 12 ū, or the distribution of ū quarks in fractional momentum, x, D. Hadron Models 12 ū(x), where the x dependence has been suppressed. E. Chiral Effective Theory 13 For the up quarks F. Quarks and Mesons 13 G. Chiral Soliton Models 13 ∫ 1 H. Five-Quark Fock States 13 (u(x) − ū(x))dx = 2 (1) 0 IV. Prospects for Future Work 14 For the down quarks V. Summary 14 ∫ 1 ¯ (d(x) − d(x))dx =1 (2) References 15 0 I. Introduction For the strange or heavier quarks ∫ 1 The line in James Joyce’s Finnegans Wake, “Three quarks for Muster Mark”, is said to have inspired the choice of name for (s(x) − s̄(x))dx = 0 (3) 0 the three objects proposed to make up a proton and determine its quantum numbers. But experimental data reveal a rich On the other hand the antiquarks and the strange quarks must structure of quarks, antiquarks and gluons that are far more belong to the sea. Examining their distributions is one of the abundant than the three so-called valence quarks, especially foci of this review. If the glue were polarized, the mechanism of when the fraction, denoted as x, of the momentum of the proton Fig. 1a transfers that polarization to the sea. On the other hand, carried by the quark in a fast moving (infinite momentum) in the specific nucleon-pion model of Fig. 1b, the antiquark reference frame is small (x < 0.1). These quarks and anti- is contained in a spin-zero object and cannot have an overall quarks are usually referred to as sea quarks (in the early days of polarization. So a second focus will be on the polarization of the parton model some used the terminology “ocean” quarks the antiquarks.  2 In the parton model, it was assumed for many years that the mechanism of Fig. 1a and iterations of this mechanism dominate the creation of the sea. This assumption is a good approximation at low x and high energy scales. Since the gluons do not carry flavor, the quark-antiquark pair is flavor neutral. One of the successes of quantum chromodynamics (QCD), the theory that describes the interaction of colored quarks and gluons, is that the change in parton distributions with respect to the scale, µ2 , of the interaction, the QCD evolution (a more precise definition of the meaning of the scale and the evolution equations will be given below), can be quantitatively described. There was speculation that in a proton the Pauli exclusion principle would limit the phase space for the majority quark flavor and lead to more down antiquarks (d)¯ than up antiquarks (ū), d(x) ¯ > ū(x). Ross and Sachrajda showed that the perturbative QCD evolution ¯ − ū(x) was numerically very contribution to the integral of d(x) small and argued that the Pauli blocking was not important (but see Gluck and Reya and the discussion below). Global fits of the distribuions of partons to all the available data built the ¯ = ū(x) into their analyses up to 1989. Gluck assumption d(x) and Reya and others, for example , took this a step further and assumed all the sea quarks and glue were generated by ! " (u$)̅ QCD evolution, i.e. that at some low scale, µ2i , all the sea quark distributions (ū(x, µ2i ), d(x, ¯ µ2 ), s(x, µ2 ), s̄(x, µ2 ) for the up and i i i down antiquarks and the strange and anti-strange quarks) and p (uud) the gluon distribution G(x, µ2i ) were 0. Unless explicitly noted, the contributions for the heavier charm, bottom and top quarks will be ignored. These approaches had considerable success describing the measured parton distributions until the early 1990’s. The situation changed in 1990 when the New Muon Col- n (udd) laboration (NMC) at CERN first reported a deep inelastic scattering measurement of the Gottfried sum of the differ- ence in the structure functions F2 for the proton and the neutron. With the assumption that the strange quarks contributions are the same in the proton and neutron then ∫ 1  1 2 1 ∫ dx  p Figure 1. 1a) Sea quarks created in a gluon splitting fluctuation, 1b) F2 (x) − F2n (x) = + ¯.   dx ū(x) − d(x) 0 x 3 3 0 Sea quarks created in a pion-nucleon fluctuation (4) over a more extended kinematic range (0.015 < x < 0.35). NMC measured the integral on the left-hand side to be 0.240 ± ¯ Their final results for d(x)/ū(x) are shown in Fig. 2 along 0.016 showing that d¯ > ū. The precise relation between the with the NA51 result. The analysis was based on a next-to- structure functions F2 and the experimental cross sections leading order analysis assuming the other parton distributions for deep inelastic scattering will be given in the next section. were well described by contemporaneous global fits( ) Later NMC measurements led to an updated value of and that nuclear corrections for deuterium are small. Figure 3 0.235 ± 0.026. It was quickly pointed out in Ref. that the ¯ − ū(x). The resulting integral shows the inferred values of d(x) Drell-Yan process of hadron-induced di-lepton production ∫ 0.35  ¯ − ū(x) = 0.080 ± 0.011 at an average scale  would be much more sensitive to the antiquark distributions. is.015 dx d(x) 2 of 54 GeV. Extrapolating to the integral from 0 to 1, NUSEA The CERN NA51 collaboration measured proton-induced Drell- Yan reactions on targets of hydrogen and deuterium and obtained 0.118 ± 0.012. This value is 10% of the integrated found in a leading order analysis flavor difference of the valence quarks. The x dependence of the difference was confirmed by semi-inclusive deep inelastic ū scattering measurements of the HERMES collaboration (hxi = 0.18) = 0.51 ± 0.04 ± 0.05. (5) which are also shown in Fig. 3. As will be discussed below, the d¯ apparent reduction of the ratio above x of 0.2, admittedly with The NUSEA collaboration at FNAL was able to perform proton- relatively large uncertainties, is difficult to explain in current induced Drell-Yan measurements on hydrogen and deuterium models. The behavior of the ratio at larger x will be our third  3 focus. Since this integral is a flavor non-singlet quantity where the contributions from gluon splitting cancel out in the difference, the result is essentially scale independent. Therefore, there is no scale at which the sea quarks disappear by perturbative evolution, and this flavor difference of the antiquark distribu- tions must be a manifestation of non-perturbative aspects of quantum chromodynamics (QCD). Despite what one may hear, the proton is never just three valence quarks and glue. II. How to Measure Sea Quark Distributions A. Deep Inelastic Scattering The relationships between the distributions of the quarks of various flavors and experimental data are covered by essentially all textbooks in high energy and nuclear physics. Here it will be quickly reviewed to define the notation and to point out the salient features of each technique. Figure 4 illustrates the kinematics for deep inelastic lepton scattering (DIS) with an incident lepton of four momentum p and outgoing momentum p0 and a target of four momentum P. The momentum transfer through the virtual photon is q = p − p0 and Q2 = −q2 > 0. If the scattering takes place from a very light constituent of Figure 2. The ratios of d/ ¯ ū measured by the NUSEA collabora- mass m carrying a fraction x of the momentum of the target, tion at a scale of 54 GeV2 and NA-51 at scales of 25-30 the squared invariant mass of the quark after the collision is GeV2. The NUSEA analysis was based on a next-to-leading order analysis assuming the other parton distributions were well described by (xP + q)2 = x 2 P2 − Q2 + 2 x P · q ≈ m2 ≈ 0 and the momentum contemporaneous global fits( ) and that nuclear corrections for fraction x = Q2 /(2 P · q). Intuitively (at least to some) if deuterium are small. The curves are next-to-leading order global fits one considers the target in a fast moving reference frame, the of CTEQ6, CTEQ10 and CTEQ14 in MS renormalization lifetime of each virtual state of the target is Lorentz dilated scheme, all at scales of 54 GeV2 , to show how the parameterizations and the longitudinal extent of the target is Lorentz contracted have changed over time, especially in the unmeasured region. so that a hard (large energy and momentum transfer) probe sees a collection of quarks that is frozen in time with the scale defines the separation of short-distance and long-distance probability distribution f(x) for each flavor and interacts with effects. By convention, one often sets the renormalization the appropriate electro-weak cross section. and factorization scales in deep inelastic scattering to Q2 , but It can be proven for deep inelastic scattering that the cross that is not necessary. For hadron-hadron reactions, one must section factorizes. (For details, see the discussion for example integrate over the parton distributions of both the beam and in Ref.. ) target, but the separation of the hard scattering functions from the parton distributions remains. In such reactions, the choice 2 µ2 ! Õ ∫ 1 dξ i x Q of renormalization and factorization scales to be used is less f   σ = h C , 2 , 2 , αs (µ ) φi/h ξ, µ f , µ2 2 0 ξ ξ µ µ obvious. In all cases, since the hard scattering functions depend i= f , f ,G ¯ on the order of perturbation theory, the scheme and scales, (6) the parton distributions are not directly physical observables. where the sum is over all quark flavors and glue. The C i are It is not consistent to use parton distributions obtained from, hard scattering functions that are ultraviolet and infrared safe for example, fits using next to leading order hard scattering and calculable in perturbation theory. They are a function functions in calculations done at a different order or to directly of quark flavor, the physical process (for example the nature compare various parton distribution functions when they are of the vector boson being exchanged in DIS and the order of not defined consistently. perturbation theory of the calculation), the renormalization Another important feature of QCD is that if the factorization scale µ2 , the factorization scale µ2f and the strong coupling and renormalization scales are taken as µ2 = µ2f = Q2 , then constant αs , but not the distribution of partons. The renormal- QCD allows one to calculate the parton distributions at higher ization scheme eliminates the ultraviolet divergences of the Q2. This is the DGLAP QCD evolution of Dokshitzer , hard scattering amplitude. The parton distributions for each Gribov, Lipatov , Altarelli and Parisi. flavor i, φi/h , contain all the infrared sensitivity, are specific to d φi/h x, µ f , µ2
the particular hadron, h, and depend on the factorization scale µ = µ f and the factorization scheme, but do not depend on the hard dµ scattering process. If defined consistently, they are universal. Õ ∫ 1 dξ  x    Therefore, one can combine data from different kinds of exper- Pi j , αs (µ2 ) φi/h ξ, µ f , µ2. (7) x ξ ξ iments to determine the parton distributions. The factorization j= f , f ,G ¯  4 Figure 4. Deep inelastic scattering Feynman diagram and kinematic variables. where i labels either neutral current (NC) or charged current (CC) and the exchanged vector boson, γ, Z or W ±. y = Pp ·q ·q = ¯ − ū(x) (red circles) at a scale of 54 GeV2 Figure 3. Results for d(x) v is the fraction of the lepton’s energy loss in the target rest E obtained from the NUSEA ratio measurements shown in Fig. 2 frame, and α is the fine structure constant. The sign of the last and CTEQ5M or MRST parameterizations of d¯ + ū. The term, which is parity violating, is − for antineutrinos and + blue triangles are the semi-inclusive deep inelastic scattering results for neutrinos. ηi is the relative coupling strength for the weak from the HERMES collaboration in leading order at a scale of 2.5 GeV2. Given the size of the error bars, for this qualitative comparison interaction compared to the electromagnetic interaction. the warning below not to mix results at different scales, renomalization schemes, and order of perturbative expansion in αs has been ignored. ηγNC = 1, (9) The CTEQ14 next-to-leading order global fit results are also !2 !2 G F MZ2 Q2 shown at scales of 54 GeV2 and 2.5 GeV2 to illustrate the size of the η ZNC = √ , (10) scale effect. 2 2 πα Q2 + MZ2 !2 2 The explicit forms of the splitting functions, Pi j , which describe G F MW Q2 ηW CC =4 , (11) gluon emission and absorption from the quarks, gluon splitting 4πα Q2 + MW2 to two quarks and recombination, and gluon-gluon interactions can be found in many textbooks and references (for example where G F is the Fermi constant, MZ and MW the masses of Ref. ). While this is an important test of QCD, it also the neutral and charged weak intermediate vector bosons. allows data taken at different Q2 to be usefully combined At lowest order in terms of the partons for deep inelastic to determine parton distributions. Moreover, the excellent scattering, the C i are just determined by the electroweak inter- quantitative agreement with the data indicate that Pauli blocking action, and with the approximation of the Callan-Gross relation effects are not important at large Q2 since Pauli blocking is not that F2 = 2x F1 then included in the DGLAP equations. γ Õ At extremely small x, the DGLAP evolution loses its validity, F2 = x eq2 [q(x) + q̄(x)] , (12) and it needs to be combined with the BFKL resummation of q small-x logarithms to all orders of perturbation theory. Recent references show the need for this extension in the low where ei are the appropriate electric charges of each quark x HERA data and explore the impact for the LHC. flavor. For incident ν̄ on a proton The cross sections for neutral-current electron and muon deep − F2W = 2 x u(x) + d(x)¯ + s̄(x) + c(x) ,   (13) inelastic scattering (where the small Z exchange contribution W− F3 = 2 u(x) − d(x) ¯ − s̄(x) + c(x).   is ignored) and neutral- and charged-current neutrino deep (14) inelastic scattering from an unpolarized target are In these expressions, weak quark flavor mixing (Cabbibo- Kobayashi-Maskawa mixing) and quark mass threshold effects ( d 2 σi 4 π α2 i x2 y2 M 2  = η 1 − y − F2i (x) have been ignored. To obtain the structure functions for an dx dy x y Q2 Q2 incident ν, interchange d with u and s with c and similarly )  y2  interchange the antiquark flavors. Based on charge symmetry, + x y F1 (x) ∓ y − 2 i x F3 (x) , (8) i that the masses of the u and d quarks are much lighter than 2 any other scale in the proton, interchanging u ↔ d and ū ↔ d¯  5 ¯ The scale ∼ 8, more sensitive to ū quarks in the target than d. is usually chosen as the mass squared of the virtual photon, M 2 = xb xt s − QT2 where QT2 is the square of the transverse momentum of the virtual photon and is usually small compared to M 2. Again, using charge symmetry (ū p = d¯n , d¯p = ūn and assuming the nuclear corrections in the deuteron are small, the ratio of the cross section on deuterium to that on hydrogen ¯ directly measures d(x)/ ū(x). σd σp + σn d¯p ≈ ≈1+. (16) σp σp ū p Calculations of the effect of nuclear corrections for deu- terium show they are small for the x range currently measured. It is known that the next-to-leading order QCD corrections to the Drell-Yan cross section are substantial, ap- proximately a factor of two (emphasizing the need for consistent Figure 5. Drell-Yan Feynman diagram and kinematic variables. use of hard scattering functions and parton distributions to the same order in αs ), but the corrections factors for the proton distributions gives the structure functions for scattering from a and neutron are very similar. The NUSEA results in Fig. 2 are neutron. based on a next-to-leading order calculation involving all quark In principle, the parity violating term F3 for charged current flavors, but the results are very close to what are obtained from neutrino scattering on an isoscalar target gives a good measure- the simple leading order formulae discussed here as long as the ment of the valence distribution while the F2 term from either actual xF distributions of the data are considered (i.e. whether neutral or changed current interactions measures the sum of xF  0. For example, the NA-51 data have < xF >≈ 0. ). valence plus sea. In practice, the valence distributions are larger than the sea distributions for x > 0.04 which magnifies the C. Global Fits errors in determining the sea in this way. A more substantive issue is that most of the high statistics neutrino experiments In major efforts, several groups have performed extensive are performed with heavy targets such as iron. One must deal systematic fits of parton distribution functions (pdf) to all with the nuclear corrections that, despite 30 years of study, are the available deep inelastic scattering and Drell-Yan data and still not well understood. Nuclear corrections must also be report error bars on the results. These include the Coordinated considered for the “neutron” data that are taken from results on Theoretical-Experimental Project on QCD (CTEQ); Martin, a deuterium target, often with the assumption that the nuclear Roberts, Sterling and Thorne (MRST); and the Neural Networks effects are small. Recent work relating short-range correlations PDF collaboration (NNPDF) (next-to-leading order to the size of the nuclear effects has led some to predict that the and next-to-next to leading order ). Analyses of W and Z nuclear effects in deuterium are larger than previously believed boson production at the LHC discussed below are influenced at higher x values. by the next-to-next to leading order corrections. The global fits are periodically updated as new data become available, so many B. Drell-Yan Reactions versions exist, usually with distinct labels such as CTEQ6 , CTEQ10 and CTEQ14. One challenge for all but A much more direct method to study the sea of antiquarks is the Neural Networks PDF collaboration is understanding the to use a hadron-induced reaction and detect a virtual photon. correlations inherent in their assumptions of a functional form to This is the diagram shown in Fig. 5 for the Drell-Yan process fit. The other challenge is incorporating the systematic errors of where a quark from the beam annihilates an antiquark in the the various data sets properly. There are often tensions between target or vice versa. Factorization theorems also have been the various data sets that are pointed out in the articles reporting proven for this reaction. The leading order cross section the fits, and options are explored emphasizing or deemphasizing can simply be written as one or another of the experimental results. When used in QCD calculations, these global fits are very successful in describing a dσ 8 π α2 Õ 2 wide variety of data from collider and fixed target experiments. = e [q(xb )q̄(xt ) + q̄(xb )q(xt )]. (15) dxb dxt 9 s x b xt q q Examples of the parton distributions extracted by CTEQ10 at two different scales are shown in Fig. 6. The integrals of xb and xt are the momentum fractions of the beam and target the flavor differences of the sea contributions from various partons participating in the reaction, and s is the square of the global fits and models are given in Table 1. Extending the center of mass energy of the beam and target. If an experiment integral down to x of 0 does require some care, so in Tab. 1 is performed, for example, with a proton beam that selects xb in it is generally cut off at some lower x value. For example, in the valence dominated region and xF = xb − xt  0, the first the CTEQ14 fit, d¯ − ū changes sign at x ∼ 0.006. The integral term dominates and the charge squared weighting and the fact in the CTEQ10 fit is relatively stable as the lower x limit is the uv (x) ∼ 2 dv (x) means the measurement is, by a factor of pushed down to, for example, 0.00001.  6 ∫x xmin xmax x ma x (d¯ − ū)dx Q2 Source Ref. distribution can be accessed in semi-inclusive deep inelas- mi n. (GeV2 ) tic scattering or with transversely polarized hadron beams 0.0 1.0 0.147 ±.026 4 NMC on transversely polarized nucleon targets. These are known 0.015 0.35 0.080 ± 0.011 54 NUSEA as the transversity distributions, δq(x, Q2 ). So far little data 0.0 1.0 0.118 ± 0.012 54 NUSEA on the tranversity distributions are available. Several groups 0.001 1.0 0.165 54 CT66nlo have been able to extract limited valence transversity distribu- 0.001 1.0 0.114 54 CT10nlo tions. Only Martin, Bradamante and Barone 0.001 1.0 0.116 2 CT10nlo 0.01 1.0 0.090 54 CT14nlo have obtained sea quark transversity distributions. They are 0.001 1.0 0.086 1 Stat. Mod. typically smaller than the valence distributions and within the 0. 1.0 0.13 ? Det. Bal. current error bars, consistent with 0. In a non-relativistic model, 0.02 0.345 0.108 54 Chiral Soliton δq(x, Q2 ) can be easily obtained by rotating ∆qi (x, Q2 ), but in 0.0 1.0 0.13 ± 0.07 ? Lattice a relativistic treatment of rotations this is no longer true. Table I. Integrals of (d¯ − ū) from xmin to xmax from experiment E. Parameterizing Parton Distributions (NMC and NUSEA) and from several global fits (CTEQ6.6, CTEQ10, CTEQ14), calculations (Lattice), and models (Statistical and Detailed Historically, the evolution of thinking about the sea generally Balance). The weak variation of the integral to the choice of scale took the following path. At high x, the valence quarks dominate, is illustrated with the CTEQ10 comparison at 2 and 54 GeV2. The and there was little experimental information about the sea. scales of the detailed balance and lattice calculations are not explicitly Based on the models of Regge theory at low x and quark reported in those references. counting rules at high x, for the valence quarks x f (x) was expected to be proportional to x 1/2 (1−x)2n−1 where the number D. Spin-Dependent Parton Distributions of spectator quarks, n, equals 2. A typical functional form for the global parton distribution fitting was x f (x) = C x α (1 − x)β With polarized beam and target, additional spin-dependent with C, α, and β as free parameters for each flavor. (Modern parton distributions are needed to fully characterize the nucleon fits of parton distributions find more general parameterizations response. With a longitudinal polarized lepton beam incident are required for high quality reproduction of the body of on a longitudinally polarized nucleon target, the asymmetry experimental data.) Based on the approximately constant of spin-antiparallel cross sections (σ 1/2 ) to spin-parallel cross photon-proton total cross sections at high energy, for the sea sections (σ 3/2 ) divided by the sum is x f (x) is approximately constant at low x and Q2. Since the existence of sea quarks imply at least a 5 quark Fock state, d 2 σ 1/2 − d 2 σ 3/2 g1 (x, Q2 ) the x f (x) at high x were expected to behave as (1 − x)2×4−1 , A(x, Q2 ) = = D[A1 + η A2 ] ≈ D , falling off rapidly at high x and being almost x independent d 2 σ 1/2 + d 2 σ 3/2 F1 (x, Q2 ) at low x. Again a similar functional form was assumed. A (17) recent global analysis confirms these expectations for nucleon parton distributions at low x and for the valence quarks at high 2y − y 2 x, but for the sea and glue at high x the agreement is only D= , (18) qualitative. It should be noted that there is still debate 2(1 − y)(1 + R) + y 2 about the quark counting rules for the pion parton distribution functions at high x and soft gluon summation seems to be p important. Q2 2(1 − y) On an isoscalar target η= , (19) E y(2 − y) νp F2 + F2νn = x u(x) + ū(x) + d(x) + d(x) ¯ + s(x) + s̄(x) ,   Õ Õ 2 g1 (x, Q2 ) = ei2 (q ↑ (x, Q2 ) − qi↓ (x, Q2 )) = ei2 ∆qi (x, Q2 ), (21) i i ep (20) F2 + F2en = 2 q ↑/↓ (x, Q2 )  where the are the quark helicity distributions. E is 5 2 the incident beam energy (for an experiment with the target x u(x) + ū(x) + d(x) + d(x) + [s(x) + s̄(x)]. (22) ¯ 18 5 at rest in the lab), D is the virtual photon polarization, and R is the ratio of the longitudinal to transverse cross section. IF the contributions of the strange quarks were small, the A2 is bounded by R which is small in the Callan-Gross limit average of the F2 ’s for neutrinos would be 18/5 times the F2 ’s and η is usually small, so A2 usually gives a relatively small for electromagnetic processes. When the data showed this contribution to A(x, Q2 ). The global analyses can then be approximate relation held for x > 0.1, it was concluded that extended to polarized structure functions, though the polarized the assumption of small strange quark contributions was valid. data are much sparser. (See for example Ref..) At low x, the experiments at HERA found a rising cross While not directly measurable in inclusive polarized lepton section showing that the glue must dominate for x below ∼0.01 scattering on a polarized target, the third twist-two parton and high Q2 as shown in Fig. 6. In that case, gluon splitting  7 where the quark has a fraction, z, of the momentum of the gluon. Pqq (z) is the probability a quark splits into a quark of momentum fraction z and a gluon. 1 2 Pqg (z) = (z + (1 − z)2 ) (25) 2 4 1 + z2 Pqq (z) = (26) 3 1−z F. Strange Quark Distributions Eq. 23 assumes that at low x (high energy) the strange quark mass is negligible. Information on the strange sea at low x values comes from W production at p + p colliders, LHC and RHIC. The formalism is exactly parallel to that of Drell-Yan production with the experimental difference that the neutrino from the leptonic W decay branches is not detected but inferred from missing energy. The results from ATLAS are also included in Fig. 9 below at their x value of maximum sensitivity, ∼ 0.023 at a scale of 1.9 GeV2 s + s̄ = 1.19 ± 0.07 (exp.) ± 0.02 (mod)+0.02 −0.10 (par), (27) 2d¯ where (mod) indicate uncertainties from model variation and (par) are from parameter variations. It indicates at such x values the effects of quark mass on gluon splitting are indeed small. To gain better sensitivity to the strange quarks, one can look for neutrino DIS events with two opposite sign muons in the final state. These were expected to arise mainly from the processes ν + s → µ− + c and then c → µ+ + νµ + s, (28) ν̄ + s̄ → µ+ + c̄ and then c̄ → µ− + ν̄µ + s̄. (29) Often it was assumed the strange quark distributions at higher x ¯ differing only by a scale factor. had the same shape in x as (ū+ d), In a leading order analysis by the NuTeV collaboration , the strange sea parton distributions were assumed to be ū(x) + d(x) ¯   s(x) = κν (1 − x)αν (30) Figure 6. CTEQ10 next-to-leading order parton distribution func- 2 tions at upper) Q2 = 2.5 GeV2 and lower) 54 GeV2. Note that the gluon distributions have been divided by a factor of 5. ū(x) + d(x) ¯   s̄(x) = κν− (1 − x)αν − (31) dominates the antiquark distributions and for a given flavor 2 ¯ Q2 ) ≈ s(x, Q2 ) ≈ s̄(x, Q2 ). ū(x, Q2 ) ≈ d(x, (23) κ=1 and αν = 0 would correspond to a SU(3) flavor symmetric sea. Typical fitted results for κν and κν− are 0.44 ± 0.06 ± 0.04 αs ∫ 1 dy and 0.45 ± 0.08 ± 0.07, respectively. The results are sensitive to ū(x, Q2 ) ≈ 2π x y the choice of the non-strange parton distributions. For example,  x x x  Q2 with GRV non-strange distributions, κν and κν− are 0.37 ± G(y)Pqg ( ) + ū(y)(δ(1 − ) + Pqq ( )) log 2 0.05 ± 0.03 and 0.37 ± 0.06 ± 0.06. y y y µ Thus, the higher x measurements of the strange sea, which. (24) chronologically came first, revealed a different picture, showing where G(y) is the gluon distribution. The splitting function that the strange quarks are suppressed relative to ū and d. ¯ Pqg (z) is the probability a gluon annihilates into a q q̄ pair Again, this is usually interpreted as due to the influence of  8 not too large, the most energetic (leading) hadron has a signifi- cant probability of containing a quark with the same flavor as the struck quark. This quark flavor retention was experimentally tested by the EMC collaboration in deep inelastic muon scatter- ing and is supported by models of fragmentation such as the Lund model. Several criteria for the regions of kinemat- ics where this assumption is valid have been proposed [49–51]. Semi-inclusive DIS results from HERMES for the differ- ence d¯ − ū were shown in Fig. 3 and were in agreement with the Drell-Yan results. This technique has been used by the HERMES and COMPASS collaborations to study the flavor dependence of the spin structure functions. Their results for polarized quark distributions are in reasonable agreement. Of course the fragmentation functions introduce new sources of uncertainty. There have been several global analyses including de Florian et al. , Leader, Sidorov and Stamenov , and Ethier, Sato and Melnitchouk. Fig. 8 illustrates the recent results from Ethier, Sato and Melnichouk. While the total spins carried by u and d quarks are well constrained, even the signs of the antiquark distributions are uncertain. Their result for the integral of the flavor difference in the sea quark spin ∫1 ¯ = 0.05 ± 0.08. This   distributions is 0 dx ∆ū(x) − ∆d(x) Figure 7. The results of NuTeV fits for xs− (x) = x(s(x) − s̄(x) at Q2 of 16 GeV2. The inner band is the uncertainly without including quantity will be discussed in the context of various models and that of the charm semi-leptonic branching ratio. The outer band is the calculations below. combined error. HERMES has also used semi-inclusive kaon production to study the unpolarized strange quark distribution. Consider the heavier strange quark mass at lower energies. Hadronic Q(x) = u(x) + ū(x) + d(x) + d(x) ¯ and S(x) = s(x) + s̄(x). For models would suggest that s(x) , s̄(x) since the mass of the scattering from an isoscalar target like deuterium, the number uds + u s̄ fluctuation (Λ + K + ) is lower than that of any system of inclusive DIS events N DI S , can be written in leading order with an s̄ quark in the baryon; thus they would have different x as dependences. In a next-to-leading order analysis ,the NuTeV d 2 N DI S (x) = 2 2 + 2 ,   collaboration found KU (x, Q ) 5 Q(x, Q ) 2 S(x, Q ) (34) dx dQ2 ∫ 1 dx x [s(x) − s̄(x)] = 0.00196 ± 0.00046 (stat.) where KU is a kinematic factor depending on the cross section 0 and one has assumed charge symmetry, u p = dn , d p = un , ± 0.00045 (syst.)+0.00148 −0.00107 (external). (32) ū p = d¯n and d¯p = ūn. + − The number of charged kaons produced, (N K = N K + N K ), The external error refers to uncertainties on external measure- is given by ments such as the charm quark mass and the charm semi- leptonic branching ratio. The fitted x dependence of this d 2 N K (x) analysis is shown in Fig. 7. The x dependence of the uncer- = KU (x, Q2 ) dx dQ2 tainty band is partially a consequence of the assumed functional  ∫ ∫  form. × Q(x) dz DQ K + S(x) dz DSK (z). (35) Another technique that is sensitive to the flavor of the quark is semi-inclusive deep inelastic scattering. Experimentally, If charge-conservation invariance is assumed in fragmentation, hadron production in deep inelastic scattering is observed to then there are only two functions describing the fragmentation factorize into scattering from an initial parton and fragmentation K = 4 D K (z) + D K (z) and D K ≡ 2 D K (z). If the involved. DQ u d s s as the struck quark jet forms color neutral hadrons. For a hadron, h, that carries a fraction, z (equals the energy of the hadron fragmentation functions are well enough known, these two divided by the energy of the virtual photon, both in the lab equations can be solved for S(x). frame), of the momentum of the struck quark Figure 9 shows the HERMES results for xS(x) compared to a CTEQ6 leading order fit for the strange distributions and  the sum of the light antiquark distributions, x ū(x) + d(x) ¯  dσ h Õ. = Ki qi (x, Q2 ) Dih (z), (33) Also shown are a neural network fit and a CTEQ6.5S-0 fit dx dQ2 dz where the shape of the S(x) is not constrained to be the same ¯i= f , f as that of the light quarks. The HERMES result has quite a where K is a kinematic factor containing the hard scattering different shape than the usual global fits, suggesting that there cross section. The expectation is that if z is sufficiently, but is little strange quark content for x > 0.1 and is more similar  9 Figure 9. x(s(x) + s̄(x)) obtained by HERMES from a leading order analysis of semi-inclusive kaon production on deuterium at a scale of 2.5 GeV2. The dotted black and blue lines are the CTEQ6L fits to (x(ū(x) + d(x) ¯ and x(s(x) + s̄(x)) respectively. The light blue dotted line is an CTEQ6.5s fit with a less constrained shape for the strange distributions relative to the light sea quarks. The blue band is the ± 1 σ band of the strange quark distributions of the NNPDF2.3 fit which does not ab initio impose a shape on the parton distributions. Note the ATLAS result of eq. (27) shown as the green band suggests that by x of 0.023 s + s̄ ∼ ū + d¯ at a scale of 1.9 GeV2. Figure 8. Spin-dependent parton distribution functions with 1 σ uncertainty bands at a scale of 1 GeV2 of Ethier, Sato and Melnitchouk strange quark densities with the multi-muon neutrino data are obtained from a self-consistent fit of parton distributions and not clearly understood. fragmentation functions. The combination of the HERMES and ATLAS data inspires a speculation that the strange quark distributions may be domi- to the neural network result in this x range. While this neural nated by gluon splitting while the light antiquark distribution network fit was not consistent with the W production results of may have a substantial non-perturbative Eq.(27), more recent NNPDF results including the ATLAS
piece. Fig. 10 shows the combination 0.18 x ū + d¯ − s − s̄ using CTEQ6l1 leading W and Z production data do approach 1 at x < 0.01 for the order light quark distributions and the HERMES S(x). Also ratio of strange to light sea. None of the semi-inclusive data shown is x(d¯ − ū) as determined from the Drell-Yan data (Fig. 2 were included in these unpolarized global fits. COMPASS also in a next-to-leading order analysis). The comparison is only has measured the charged kaon multiplicities from 160 GeV qualitative since it involves results from different scales and muon scattering on deuterium. Both the summed charged from leading order and next-to-leading order analyses. How- kaon multiplicities and the ratio of K + to K − multiplicities are ever, the shapes of the two distributions are remarkably similar distinctly different from the HERMES results, while they agree suggesting whatever the non-perturbative origin of the flavor for the ratio of charged pions in the region of overlap but asymmetry is also having a big effect on the total light quark not the sum. Guerrero and Accardi suggest that hadron sea at x & 0.07. This similarity may provide a clue that pion mass corrections may account for much of the discrepancy. degrees of freedom play a central feature in the explanation. If so, it is not yet known what effect this would have on the comparison of the polarized antiquark distribution results from G. Intrinsic Charm the semi-inclusive analyses. In an independent analysis, Borsa, Sassot and Stratmann analyze the kaon multiplicities Just as production of strange mesons can be used to measure with simultaneous variation of the parton distributions and the intrinsic strangeness in the nucleon, production of charm fragmentation functions and obtain strange quark densities is used to look for intrinsic c c̄ components of the nucleon, close to the NNPDF 3.0 set. Still, at the present time, the that is charm at non-perturbative scales that is not produced differences in the kaon multiplicities from these two semi- by QCD evolution. Indeed, higher than expected production inclusive DIS experiments and also the differences in inferred cross sections for charmed mesons in pp collisions led to the  10 ¯ − ū(x)) vs 0.18 ∗ x(d¯ + ū(x) − s(x) − s̄(x)) using Figure 10. x(d(x) NUSEA d¯ − ū evaluated at 54 GeV2 , and HERMES s + s̄, and CTEQ6l1 ū + d, ¯ evaluated at 2.5 GeV2. suggestion by Brodsky et al. of finite intrinsic charm. In neutral current deep inelastic scattering, the issue is to separate intrinsic charm contributions from the QCD process of photon-gluon fusion. The expectation is that due to the heavier charm quark mass, intrinsic charm would show up at high x. Experimentally, this has been studied by the EMC collaboration at CERN and the ZEUS and H1 experiments Figure 11. The upper graph shows the NUSEA d/ ¯ ū data compared at HERA by detecting multi-muon events. There is some to the hadron model calculation of Alberg and Miller and the tension between these data sets. New data at high x would statistical parton distribution fit of Bourrely and Soffer. The be very welcome. One recent analysis that also included lower plot shows d¯ − ū from NUSEA and HERMES along SLAC J/Ψ data places upper limits on the average x of intrinsic with an instanton model , chiral quark solition model , the meson cloud model of Alberg and Miller and the statistical parton charm of 0.5% and on the magnitude of the c c̄ component of distribution fit. less that 1%. A next-to-leading order analysis by the NNPDF collaboration finds that for x X0u − − ≈ X0d > X0d −  X0s > X0s , (39) Pauli principle could still lead to a flavor asymmetry here also. Lattice calculations of the disconnected diagrams with realistic ¯ > ū(x) and d(x) leading to the predictions that d(x) ¯ − ū(x) ≈ pion masses are only now reaching the point where this can be ¯ ∆ū(x) − ∆d(x). ¯ ū flattens out at about At high x, the ratio of d/ tested. 2.5 in their model. Their results are shown as the green bands A promising new technique to directly calculate parton in the upper panel of Fig. 11 and as the dashed-dot curve in the physics on the lattice is large-momentum effective theory lower panel of Fig. 11. [LMET] [82, 83]. First results on the flavor structure are Zheng, Zhang and Ma argue that the principle of detailed beginning to become available, and the systematic errors of balance in gluon splitting and recombination naturally leads to this new technique are being evaluated. Lin et al. report a sea quark asymmetry. For example, there are three ways a an asymmetry in the integral of (d¯ − ū) of 0.14 ± 0.05 and an |uuduūi can transition to a |uudgi but only two ways a |uudd di ¯ asymmetry in the integral of the polarized sea quark asymmetry, can transition to a a |uudgi. Assuming a statistical ensemble ∆ū − ∆d¯ of 0.24 ± 0.06. In a later conference proceedings, of Fock states and a normalization condition, they predict Lin reports numbers for the integral of d¯ − ū of 0.13 ± ∫1 ∫ 1 0.07 and 0.08 (∆ū − ∆d)dx ¯ = 0.14 ± 0.09. The error bars are ¯ − ū(x)) = 0.13, (40) dx(d(x) still sizable, but the first results might suggest ∆ū − ∆d¯ > d¯ − ū 0 as suggested by models where the number of colors is large but with no free parameters, in remarkable agreement with the they are 2 σ away from the global fit result for the polarized experimental result. In a slightly more general model , they difference of Ref. The second result of near equality predict flavor asymmetries for other octet baryon states and of the flavor and spin integrals is near the statistical model kaons. expectations. Another example of extremely promising work  12 the ratio of ūd̄ goes to 4 (much larger than what is seen so far ū+ d̄ in ∫ Fig. 2) and, indeed, ∫ 2s̄ goes to 1. They also predict that ¯ (∆ū − ∆d)dx = 3 (d¯ − ū)dx. In the first publication they 5 estimated the integrated antiquark difference to be 0.24 ± 0.1. In the second publication, they make assumptions about the x dependence of the parton distribution functions, fit the in- tegrated antiquark difference, and make predictions for the instanton contribution to the polarized distributions and the Drell-Yan asymmetry. The latter does not match the existing data very well. D. Hadron Models There is a long history of considering the impact of meson- baryon fluctuations on physical baryon properties. That a neutron could fluctuate into a proton and a π − is a simple Figure 13. Examples of recent lattice QCD results for isovector ¯ explanation of why the neutron charge density appears to antiquark parton spin distributions, (∆ū(x) − ∆d(x)), compared to the JAM15 global fit (blue). The magenta band is the LP3 lattice be positive in the center and negative at longer distances. calculations of Lin et al and the green band is the ETMC lattice Sullivan first considered the deep inelastic scattering from calculations of Alexandrou et al.. Only statistical errors are the pion cloud of the proton. In the late 1970’s and early 1980’s shown. Lin et al. note that the small x region, of primary interest chiral bag models showed that pion fields were required to for the sea quarks, can suffer additional systematics due to the limited preserve chiral symmetry at the bag boundaries. Thomas nucleon boost momentum. investigated the impact of the pion cloud on SU(3) breaking, essentially predicting d¯ − ū > 0 with about the right magnitude. comes from the publications of Alexandrou et al. also with Signal and Thomas extended the calculations to the strange physical values of the pion masses ( and references sea and, for example, Cao and Signal addressed the non- therein). In their most recent publication , they validate perturbative structure of the polarized sea. the methodology of the LMET approach and identify the It is easy to see that if the physical proton is made up of a remaining systematic effects. Examples of the current state bare proton and a bare nucleon plus pion cloud of the lattice work adapted from are shown in Figure 13. | p = α|p + β c1/2,0 |p π 0 + c−1/2,1 |n π + ,   There remain large uncertainties and some disagreement with the global fit results, for example in x(∆u − ∆d) (not shown) uū + d d¯   where the experimental errors are considerably smaller. In = α|uud + β c1/2,0 |uud + √ + c−1/2,1 |udd + u d¯ , another significant step, transversity parton distributions can 2 now be calculated. Based on these recent works, it is (42) anticipated that there should be rapid progress in reducing the lattice uncertainties in the next few years, and the lattice soon where c1/2,0 and c−1/2,1 are the isospin Clebsch- q may be providing extremely important insights. Gordan coefficients h1/2, 1/2, 1, 0|1/2, 1/2i = − 13 and q h1/2, −1/2, 1, 1|1/2, 1/2i = 23 respectively. The high en- C. Instantons ergy convention for the sign of Tz = 12 for the proton is used. In Instantons are topological, non-trivial, four-dimensional higher x regions where the gluon splitting generated sea might gluon field configurations that solve the U(1) problem and be negligible, this predicts d/¯ ū = 5, much higher than the contribute to path integrals in QCD. In the 1980’s a picture experimental ratio. If one adds a Delta resonance component of the QCD vacuum emerged as an dilute liquid of well local- " ized topological fluctuations. The small size of the instantons was given as the reason the chiral symmetry breaking scale γ c3/2,−1 |uuu + ūd was so large, ∼ 1 GeV, why pions are so light, and why glue- # balls are heavy. Early quenched lattice calculations gave uū + d d¯ some support to this picture. More recent lattice calculations + c1/2,0 |uud + √ + c−1/2,1 |udd + u d¯ (43) 2 suggest a much more complicated gluon structure, and in the end, lattice simulations should determine this. Forte and then the appropriate Clebsch-Gordan coefficients squared Shuryak showed that instanton-anti-instanton pairs con- 2 tribute to the isosinglet axial current in a polarized proton. The 3/2, m∆Z , 1, mZπ |1/2, 1/2 are 1/2, 1/3, and 1/6. If γ 2 were ’t Hooft effective Lagrangian couples ū R u L d¯R dL and also much larger than β2 and the gluon splitting generated sea were ū L u R d¯L dR , so the interaction with an instanton can change, negligible then ūd̄ = 1/2. However, this does not seem to be for example, a u L into a u R d¯R dR , creating an excess of d. ¯ reasonable physically. Peng et al. used the E886 results Dorokhov and Kochelev demonstrated that at large x and estimates that β2 ≈ 2 γ 2 to infer that β2 = 0.20 ± 0.04.  13 A distinctive feature of these pion models is that all the F. Quarks and Mesons antiquarks are contained in spin-zero pions and so cannot have a preferred orientation. Therefore, ∆ū = ∆d¯ = ∆ū − ∆d¯ = 0. An intermediate picture is to envision that the mesons couple On the other hand, since the nucleon and pion must be in a directly to the valence quarks. The coupling is governed by relative P wave to conserve parity and angular momentum, one similar isospin Clebsch-Gordan coefficients might expect the antiquarks to reveal the presence of orbital |u → β c1/2,0 |u π 0 + c−1/2,1 |d π + ,   angular momentum, for example, through a non-zero Sivers (44) function (for example, ). |d → β c−1/2,0 |d π 0 + c1/2,−1 |u π −.   (45) From here, one could add more baryon and meson states. Once vector mesons are included, the net spin of the antiquarks ¯ ū = 11/7, Here the isospin coupling would give a ratio of d/ can be non-zero. Similarly, with the inclusion of strange close to peak of the experimental results. baryons and mesons, one can try to calculate properties of the strange sea. The primary issues are where to truncate the hadronic expansion and how to properly include meson-nucleon G. Chiral Soliton Models form factors in frame independent manner that incorporates experimental input. Many of these issues have been handled In the limit of a large number of colors, large Nc , QCD by Alberg and Miller. Recent predictions of the Alberg becomes equivalent to an effective theory of mesons, and and Miller calculations in the context of chiral light front baryons appear as solitons. The calculations are typically perturbation theory are shown in Fig. 11. New data based on an effective action derived from the instanton vacuum expected soon at higher x should be decisive for this approach. of QCD [34, 111–113]. Numerical calculations of the x Clearly, if higher precision data confirm the rapid drop at x∼ dependence of d¯ − ū are shown in Fig. 11. At high x the ¯ ū is predicted to be 11/7 as in the pion+valence ratio of d/ 0.3, it will be inconsistent with this picture. quark picture discussed above. As in the instanton picture, there A further puzzle for a hadronic fluctuation description comes is a close connection between the unpolarized and polarized from leading proton and neutron production in deep inelastic isovector sea contributions with scattering at HERA where a nucleon with near beam velocity is detected at zero degrees. These data are often ¯ − ū(x) ≈ 3 ∆ū(x) − ∆d(x) ¯.   interpreted in terms of a pion-nucleon fluctuation, and indeed d(x) (46) 5 are used to extract the structure function of the pion (See, for example, Levman ). However the yield of leading protons In a similar approach Wakamatsu and Watabe obtain a is twice that of leading neutrons, in contrast to the expectation slightly more complicated relation between the antiquark flavor from the isospin Clebsch-Gordan coefficients above. In some and spin differences which they parameterize as models, Pomeron and isoscalar Reggeon exchange dominate over much of the measured region. ¯ [∆ū(x) − ∆d(x)] = 2.0x 0.12 [d(x) ¯ − ū(x)]. (47) E. Chiral Effective Theory H. Five-Quark Fock States Another approach uses chiral effective field theory. (See, for Brodsky et al. proposed a phase-space-inspired distribution example, which is extended to the strange quark sea in, for a five-quark Fock state in a proton at some low scale as for example, Wang et al. and references therein.) Thomas, Melnitchouk and Steffans showed that in chiral 5 !" 5 # −2 expansions of the moments of strange-quark distributions, the Õ Õ mi2 P(x1,... , x5 ) = N5 δ 1 − xi m2p − , (48) coefficients of leading non-analytic terms in the kaon mass i=1 i=1 xi are model independent and can only arise from pseudoscalar loops. Chiral effective theory starts with the most general where m p is the proton mass and mi is the mass of quark i. effective Lagrangian for the interaction of an octet of baryons The delta function ensures momentum conservation. They through pseudoscalar fields. These include the so-called “kaon were focused on c c̄ states. Chang and Peng extended rainbow,” “kaon bubble,” “hyperon rainbow,” “kaon tadpole,” this analysis to the lighter quarks, first by fitting the strange sea and Kroll-Ruderman diagrams. In reference the integral by evolving the distribution from an initial scale to the Q2 of of the leading non-analytic contribution to the integral of the HERMES results discussed above, and then determining ¯ − ū(x)) was estimated be about 0.2, most of which comes (d(x) the u and d quark sea using the combination ū + d¯ − s − s̄ from the pion-nucleon terms. For the strange sea, the integral based on the HERMES and NUSEA results. The results are of x(s(x) − s̄(x)) ranges from 0.4-1.1 ×10−3 to be compared sensitive at the 20-30% level to the choice of initial scale of 0.5 with the experimental number given in Eq. 32. or 0.3 GeV. Typical results fitting the 2014 HERMES analysis One novel consequence of this approach is that the parton and the NUSEA results gives probabilities of uū, d d, ¯ and s s̄ distributions contain a delta function contribution at x = 0, of 0.19, 0.31 and 0.11 respectively. The results are also quite implying that the total integral of s(x) or s̄(x) is experimentally sensitive to the choice of kaon fragmentation functions. They inaccessible. On the other hand the x weighted integral is well conclude the HERMES results do not exclude the existence of defined since the delta function contributions at x=0 vanishes. an intrinsic strange-quark component of the nucleon sea.  14 IV. Prospects for Future Work It is anticipated that the first new results, expected very soon, will be SeaQuest data of 120 GeV proton induced Drell-Yan measurements on hydrogen, deuterium and several nuclear targets. These data will extend the x range of ūd̄ to x of 0.4- 0.5 and will decisively confirm or refute the suggestion of a decrease in ūd̄ above x of 0.2, The Jefferson Lab 12 GeV upgrade will provide extremely high luminosity polarized deep inelastic and semi-inclusive deep inelastic data for x> 0.1, though at modest Q2. Figure 14 illustrates the projected sensitivity of the measurement of ∆ū − ∆d¯ from an approved CLAS-12 measurement(E12- 09-007). High statistics data will also be obtained in semi-inclusive kaon production. If the issues with hadron mass corrections can be satisfactorily understood, such data should lead to better strange quark distributions. RHIC experiments have accumulated data with a total luminosity of about 400 pb−1 with longitudinally polarized protons at ∼ 500 GeV center of mass energy and ∼ 85 pb−1 at Figure 14. Projected JLAB uncertainties for a semi-inclusive DIS 200 GeV center of mass energy. Final results for W production ¯ compared to HERMES and COM- measurement of x(∆ū − ∆d) and the spin carried by the sea quarks should be available PASS data, an early global fit , another chiral quark soli- soon and are expected to place better constraints on ∆ū and ton model and another meson cloud model. ¯ Runs in 2015 and 2017 focused on transversely polarized ∆d. protons and orbital angular momentum related to the Sivers V. Summary function. First results with 25 pb−1 , albeit with sizable statistical errors, are consistent with the expected sign flip of the Sivers While the large contribution to the sea resulting from gluon function between deep inelastic scattering and vector boson splitting is well described at low x, the non-perturbative features production. These will be considerably improved with of the sea are an essential aspect of proton structure that is still the 2017 data. For the next several years, RHIC’s focus will be not understood. The trend of the NUSEA data to suggest that on the beam energy scan. Further polarized proton running is ¯ ū decreases rapidly above x ∼ 0.2 and possibly becomes d/ not currently anticipated before 2021. less than 1 at higher x does not seem to be consistent with any The COMPASS experiment in 2017 acquired more semi- model. Admittedly, the error bars grow large at higher x. The inclusive DIS data. In 2018 they plan to continue pion-induced SeaQuest experiment should provide higher statistics Drell-Yan Drell-Yan to study the Sivers function of the valence quarks measurements in this x range in the very near future. Precise before the SPS shuts down in 2019-2020. They are propos- semi-inclusive DIS measurements at Jefferson Lab and W+/− ing a 2021 run with muons on a transversely polarized production at RHIC should sharpen the comparison of d¯ − ū deuterium target to improve the measurements of the transver- with the polarized sea ∆ū − ∆d. ¯ JLAB data should also shed sity distribution h1d and the nucleon tensor charge and trans- light on the third puzzle of the x dependence of the strange verse momentum distributions. In the longer term, plans are in sea distributions. High statistics LHC data will also contribute progress for a proton radius measurement and radiofrequency- significantly to constraining the sea quark distributions. At the separated hadron beams, for, among other physics, Drell-Yan same time it appears that lattice results may become decisive in measurements with beams of kaons and anti-protons. the near future. This combination of new experimental results and advances in theory give the authors confidence that the The impact of LHC data is already clearly seen in the origin of a non-perturbative sea of the proton can become a discussion of the strange quark sea. A recent study by Khalek et solved problem in the next few years. al. concludes that High-Luminosity LHC measurements, In addtion to the fundamental insight into hadron structure planned for the middle of the 2020’s, can reduce the parton provided by the proton sea, at the highest scales of discovery in distribution functions uncertainties by factors of 2-5 depending proton-proton colliders like the Large Hadron Collider, the cross on the x range and specific channels. sections for quark-antiquark coupling to new particles such as In the longer term, a high-luminosity polarized electron-ion heavy Z’s or W’s depend directly on these non-perturbative collider would provide definitive information about the flavor features of the antiquark distributions at higher x. If ū is indeed dependence of the spin of the quarks and gluons in the proton greater than d¯ at high x values, then Z 0 production is favored and their orbital angular momentum. The need for such a over W 0 production in a pp collider, while if d¯ is greater than facility was a major recommendation of the 2015 Nuclear ū, W 0 production is favored. Such considerations can affect Science Advisory Committee Long Range Plan. the production yield on the same order as factors of 2-4 in  15 luminosity of the LHC in the search for new physics. Acknowledgments The authors would like to thank Ian Cloët for many helpful discussions. This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, contract no. DE-AC02-06CH11357; and Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, project no. 2016-098-N0 and project no. 2017- 058-N0. R. D. Field and R. P. Feynman, “Quark Elastic Scattering as a Y. L. Dokshitzer, “Calculation of the Structure Functions for Source of High Transverse Momentum Mesons,” Phys. Rev. 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