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 combina- tion 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: Z Z 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] ). ■■■1 021001-1 ©2019 The Author(s) This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the article, journal citation, and DOI. 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 JPS Conf. Proc. 26, 021001 (2019) 021001-2 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; e0) 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 neu- trons, 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 prob- ability 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 correla- tions 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]. ■■■2 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 JPS Conf. Proc. 26, 021001 (2019) 021001-3 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 momen- tum 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 vi- olation 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 anti- quarks 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 nu- cleons 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.