EMC Effect and Color Fluctuations in Nucleons

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Proceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018) Downloaded from journals.jps.jp by Deutsches Elek Synchrotron on 11/15/19 Proc. 8th Int. Conf. Quarks and Nuclear Physics (QNP2018) JPS Conf. Proc. 26, 021001 (2019) https://doi.org/10.7566/JPSCP.26.021001

EMC Eﬀect and Color Fluctuations in Nucleons

Mark Strikman1 1Physics Department, Penn State University, University Park, PA 16802, USA E-mail: [email protected] (Received April 3, 2019)

We outline recent developments in the experimental studies of the EMC effect which suggest that the proton - neutron short range correlations (SRC) play dominant role in the EMC effect. In combination with experimental evidence that the SRC are predominantly nucleonic these observations lead to even more stringent restrictions on the theoretical models than the ones which were discussed in the analyses of the nineties. It appears that only class of models where nucleons in SRCs are strongly deformed only in rare large x configurations does not contradict to the data. A mechanism of such deformations related to fluctuations of the interaction strength is outlined. The results of the global analysis of the centrality dependence of the jet production data in proton and deuteron–nucleus colli- sions at the LHC and at RHIC are presented. They appear to confirm the theoretical expectation that configurations of a proton with a large-x parton, xp > 0.1, have a smaller than average size and hence could be relevant for the explanation of the EMC effect. KEYWORDS: EMC effect, proton - nucleus scattering, LHC, RHIC

1. Introduction

Measurements of the eighties of the deep inelastic scattering of muons and electrons off nuclei: l + A → l + X, have established that at large x ≥ 0.4 the eA cross section significantly deviates from the sum of the cross sections of scattering off individual nucleons. This effect was first reported by the European Muon Collaboration and hence it is usually referred to as the EMC effect. There are many examples in nuclear physics when cross section of scattering off a nucleus is not described by the impulse approximation. A nontrivial aspect of the DIS process is that the EMC effect at x ∼ 0.5 cannot be described in any quantum mechanical model of nuclei where it consists only of nucleons - depletion of the EMC ratio, σ(eA)/σ(eD), in these models is much smaller than the observed effect. Indeed in the impulse approximation one can write the parton (quark, gluon,...) 2 density of nucleus, fA(x, Q ) as a convolution of the nucleon parton density and the light cone density ρN α α/ matrix A ( ) where A is the light cone fraction of nucleus momentum carried by a nucleon. The proof [1, 2] relies only on the validity of the two sum rules in the many nucleon approximation: the baryon charge and momentum conservation sum rules: ∫ ∫ A 1 A ρ(α)dα/α = A, ρ(α)dα = 1. (1) 0 A 0 Hence the EMC effect unambiguously requires presence of non -nucleonic degrees of freedom in nuclei.

2. A-dependence of the EMC eﬀect

At x ≥ 0.2 the essential longitudinal distances in the correlator of the e.m. currents determining the γ∗A cross section become smaller than the average internucleon distance (for details see [2] ).

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Therefore one expects that the deviations from the additivity of the cross section should be determined by the local two-nucleon density of the nucleus, leading to an approximate factorization of F2A [3]:

F A(x, Q2) 2 − 1 = r(A)ϕ(x, Q2), (2) 2 2 ZF2p(x, Q ) + NF2n(x, Q ) where we deﬁne normalization of ϕ(x, Q2) so that r(A = 2) = 1 and ϕ(x, Q2) is expected to be independent of A. This factorization is consistent with the SLAC and Jlab data. In principle, one may have to treat separately two nucleon eﬀects due to pn and pp short-range correlations (SRC) . However the data indicate that probability of pp SRC is much smaller than of pn SRC. The relative probabilities of the SRCs were measured in (e, e′) scattering at x ≥ 1.4, Q2 = 1.5 ÷ 3 GeV2:

2 σ(eA)/σ(e2H) = a (A). (3) A 2

Therefore one expects that

R(A) ≈ a2(A). (4) For heavy nuclei where the number of protons is significantly smaller than the number of neutrons, one needs to take into account dominance of the pn pairs and hence the presence of an equal number for protons and neutrons with momenta above Fermi surface, leading in particular p to a = (A/2Z)a2(A), and to the expectation that for heavy nuclei the strength of the EMC effect de- 2 p pends primarily on a2 and not on the number of neutrons. These expectations agree with the data, see [4] and references therein. Further analysis is necessary to quantify how strongly the data constrain possible relatively small contribution from the scattering off low momentum nucleons not belonging to SRCs and of pp and nn SRCs.

3. Models of the EMC eﬀect

3.1 Constraints on the models Soon after the first observation of the EMC effect, numerous models of the effect were proposed. Over the years a number of constraints on the models were found, some of them theoretical, some experimental which are difficult to satisfy in most of the classes of the models. The strongest ones come from requirements that • Model should satisfy the baryon charge and momentum sum rules which follow from the probability conservation. • No significant (≥ 2%) enhancement of the antiquarks at x = 0.1 ÷ 0.2 is allowed [5]. • The Q2-dependence of the magnetic form factor of bound nucleons with small momenta is very close to that of free nucleons [6, 7]. • Two nucleon SRCs are present in nuclei with a large probability ∼ 20%. They are predominantly proton - neutron ones and have a small (≤ 10%) admixture of non-nucleonic degrees of freedom. • A-dependence of the EMC effect is consistent with A- dependence of short - range pn correlations in nuclei measured in the large Q2 A(e,e’) reactions at x > 1.4. • The maximal strength of the EMC effect for Z=N nuclei is ≈ 10% and it is reached for x ∼ 0.6. • The EMC effect in heavy nuclei depends more strongly on the number of protons than on the number of neutrons [4].

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3.2 Pion and binding models One of the first suggestions for the explanation of the EMC effect came from the meson models of nucleon forces [8]. In these models pions carry a finite fraction of the nucleus momentum, ηπ, leading to a suppression by a factor [2]

ηπnx R(x) = 1 − , (5) (1 − x)

n for F2N(x) ∝ (1 − x) for large x. In the Jlab kinematics n ∼ 2, leading to ηπ(A > 40) ≥ 0.05 to fit the EMC effect. Numerical studies in these models find that pions carry typical light-cone fractions απ ∼ 0.15, leading to an enhancement of antiquark distribution in nuclei at small x:q ¯A(x = 0.1)/q¯N(x = 0.1) ∼ 1.1 ÷ 1.2. Numerical calculations with different effective repulsion have shown that one can reduce the effect, though the shape of the απ distribution remains the same, see discussion in [2]. Hence the experimental limit [5] on the deviation ofq ¯A/q¯N ratio from one implies that pions could be responsible only for a very small fraction of the EMC effect.

3.3 Binding models It was suggested early on that the EMC effect could be due to the nuclear binding. It is due to violation of the baryon charge conservation in the nonrelativistic approach, as well as the momentum conservation, see [9] for a detailed discussion. An ad hoc renormalization of the nuclear spectral function to remove the violation of the baryon sum rule allows to reproduce the EMC effect due to violation of the momentum conservation. To fix this problem one has to add other constituents(pions?, heavier mesons?) to restore the momentum sum rule, generating problems with description of antiquarks in nuclei discussed in section 3.2.

3.4 Exotic constituents It was suggested in a number of papers that the EMC eﬀect is due the presence of non-nucleonic components in the nucleus wave function – 6 (12) quark clusters, ∆-isobars. Obviously, one needs to introduce such components with a probability Pex > 1−RA even if one assumes that these components have the zero support at x ≥ 0.5. In practice these models end up with Pex ∼ 20%. Such a large exotic probability in combination with nucleonic SRC probability of 20% is very diﬃcult to accommodate in the nuclear phenomenology.

3.5 Mean field models In a number of the models it is assumed that the EMC effect originates from scattering off nucleons with average momenta. For example, the nuclear model was proposed in which mean scalar and vector fields couple to the quarks in the nucleon leading to modification of quark distribution in nuclei, see [10] and references therein. It is assumed in these models that effect does not depend on the nucleon momentum. These models also neglect presence of the SRC in nuclei and do not address the observed correlation between the probability of SRC in nuclei and the EMC effect. Also, it is assumed in the models that one can neglect scattering of the mesonic fields in spite of the fact that these fields carry significant energy and thus scattering off these fields should lead to the enhancement of antiquarks in nuclei. Also in these models (when treated as quantum field theory models) one faces the Landau pole – the zero charge effect– for pretty low virtualities. Overall, at the moment there seems to be no viable alternative to the scenarios where the EMC effect is associated with modifications of rare quark-gluon configurations selected by hard probe, and which become larger with increase of the bound nucleon momentum.

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4. How nuclear medium modiﬁes nucleon breathing

The dynamical mechanism addressing these constrains was proposed in [3]. It is based on idea that hard scattering off quarks selects at x ≥ 0.5 rare quark-gluon configurations in bound nucleons and that the deformation of the bound nucleon WF is enhanced for such rare configurations. The mechanism is based on two fundamental and well established properties of QCD: (a) large x configurations in nucleon have size significantly smaller than average, (b) interaction of a hadron in a small size configuration with a hadron target is much weaker than in an average configuration. In [2,3] the expressions were derived for the reduction of the probability of the configurations in bound nucleons which interact with strength much smaller than average: 4⟨U⟩ ⟨δ⟩ = 1 + , (6) ∆E where ⟨U⟩ is the expectation value of the potential acting on a nucleon in the nucleus, ∆E = MN∗ − MN ∼ 400 ÷ 600MeV is characteristic energy of excitation of the nucleon. Thus for heavy nuclei a maximal suppression is of the order 15 ÷ 20% with the dominant contribution originating from the scattering off the pn SRCs. One can use equations of motion to derive the dependence of the suppression on the momentum 2 of the bound nucleon [3]. In the lowest order in k /mN∆E neglecting term ∝ ϵA/∆E one finds

2k2 δ(k) = 1 − . (7) mN∆E Eq.7 including the binding term can be written in a compact form if one substitutes k2 in Eq.7 by ∆ 2 = 2 − − 2, m mN (pA prec) (8) where prec is the four momentum of the A-1 nucleon recoil system in the process in which a nucleon was removed from the nucleus. The possibility to rewrite Eq.6 in this form was ﬁrst pointed out in [11].

5. Evidence for the x-dependent nucleon size

Two tests were suggested to test the explanation of the EMC effect discussed in the previous section. One is the study of the bound nucleon parton distribution using tagged structure functions (e+2H → e + backward nucleon + X) [3]. Modifications are predicted to be large for nucleon momenta > 0.3 GeV/c (cf. Eqs. 7,8). Experiments aiming to test this prediction are underway at Jlab. The second test aiming to find out whether nucleon configurations with large x quarks have a smaller than average size was to study number of wounded nucleons in a hard pA scattering as a function x of the parton in the proton involved in the collision [3]. It was possible to perform the test using data on centrality dependence of the hard dijet production at the LHC and RHIC [12, 13]. Analysis was done in the color fluctuation model where one takes into account that in the proton - nucleus high energy interaction proton remains in a frozen configuration during passing the nucleus interacting with a fixed strength, σ, with the∫ probability of a given∫ strength given by probability σ σ σ = σ σ σ = ⟨σ⟩ ≡ σhN distribution, Ph( ) which obeys the sum rules Ph( )d 1 and Ph( ) d tot where ⟨σ⟩ is the configuration-averaged (total) cross section. The variance of the distribution divided by the mean squared, ωσ, is given by the optical theorem [14,15],

⟨ ⟩ dσ(h+p→X+p) 2 2 dt ωσ = ( σ / ⟨σ⟩ − 1) = . (9) dσ(h+p→h+p) dt t=0

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Distribution over the number of nucleons involved in the inelastic interactions is given by ∫ ( ) ∫ [ ] [ ] σ σ ν σ σ A−ν A ⃗ in( )T(b) in( )T(b) σν = dσP (σ) db 1 − , (10) p ν A A ∫ ∫ = ∞ ρ , ρ ρ ⃗ = where T(b) −∞ dz (z b) and is the nuclear density distribution normalized such that (r) dr A. σin(σ) is the inelastic cross-section for a configuration with the given total cross-section, which following Refs. [16,17] is taken to be a fixed fraction of σ. In the limit of no color fluctuation effects, Pp(σ) = δ(σ − ⟨σ⟩), and Eq. 10 reduces to the Glauber model expression. Using a Monte Carlo version of Eq. 10 (which includes nucleon - nucleon correlations in nuclei) and the models for the dependence of the hadron production on ν developed by the ATLAS (LHC) and PHENIX (RHIC) collaborations we studied dependence of rate of the jet production as a function of xp - light cone fraction of the nucleon momentum carried by the quark involved in the collision. First, we analyzed the ATLAS pPb data [18] at the highest values of experimentally studied xp [12]. Next, we performed [13] a global analysis of the ATLAS data [18] and the PHENIX dAu data [19]. We demonstrated that both sets of data are well described by the assumption that the average strength of the interaction is reduced by the x-dependent factor

λ(xp) = σ(xp)/ ⟨σ⟩ . (11)

In spite of very different collision energies and different kinematics (forward jets at the LHC and central jets at RHIC) values of λ(xp) were found to be pretty close, which is highly non-trivial. Our analysis finds that for fixed xp the suppression of the interaction strength is stronger at lower energies, consistent with expectation from QCD that cross-sections of the scattering of small configurations off nucleons grow faster with energy than for average configurations. A faster growth of the cross section of the interaction of nucleons in small configurations is coded in the energy dependence of PN(σ). We find that most of the residual difference between two sets of λ(xp) appears to be due to this effect

[13], see Fig.1.

N M

)

(

)

(

¨ ¦

Fig. 1. Extracted values of λ(xp) as a function of xp at RHIC and LHC energies (solid points), with ﬁts to an exponential function in xp shown as dashed lines to guide the eye. The shaded bands are a prediction for λ(xp) at each energy using the results at the other energy as input.

σ Using the parameterization for√ PN( ) at the lower, fixed–target energies given in Ref. [17], we λ ∼ . ≈ . = find that (xp 0 5) 0 38 at s 30√ GeV. At these lower energies, the large-xp quarks are thus localized in an area of transverse size λ(xp) ≈ 0.6 smaller than that in the average configuration,

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leading to significantly larger nonperturbative transverse momenta in these configurations than in the average configurations.. Since nucleons in configurations with large-x partons are weakly interacting and the strength of the interaction at fixed x falls at lower energies, it is natural to expect that such configurations interact very weakly with other nucleons at the energy ranges relevant for nuclei. In the bound nucleon wave function, such weakly interacting nucleon configurations are strongly suppressed, see discussion in section 4. Thus, this picture suggests a natural explanation for the observed suppression of nuclear parton density for partons in the EMC effect region.

6. Conclusions

Current data on the probability and the A-dependence of the SRCs led to tight constrains on the origin of the EMC effect. In the surviving class of the models one expects presence of the strong EMC effect in the deep inelastic scattering off high momentum nucleons. The critical tests of this expectation will be possible in the deep inelastic scattering off the deuteron in which momentum of the spectator nucleon is tagged. It is expected that the suppression of the large x quark distribution in fast nucleons should be proportional to the nucleon off-shellness and may also depend on the direction between the momentum of the struck nucleon and the virtual photon momentum (polarization). The study of the jet production appears to support the mechanism of suppression as due reduction of the strength of interaction of quark - gluon configurations in nucleons containing large x quarks. Further studies of jet production processes are necessary to separate the gluon and quark contributions at x ∼ 0.1 ÷ 0.2. Acknowledgments M.S.’s research was supported by the US Department of Energy Office of Science, Office of Nuclear Physics under Award No. DE-FG02-93ER40771.

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