# Diffractive Dissociation of Alpha Particles as a Test of Isophobic Short-Range Correlations inside Nuclei

###### Abstract

The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering has a strongly “isophobic” nature. This surprising observation suggests short-range correlations between neighboring and nucleons in nuclear wavefunctions that are much stronger compared to or correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation of the isophobic nature of the EMC effect: the diffractive dissociation on a nuclear target of high energy nuclei to pairs of nucleons and with high relative transverse momentum, . The comparison of events with and events directly tests the postulated breaking of isospin symmetry. The experiment also tests alternative QCD-level explanations for the isophobic EMC effect. In particular it will test a proposal for hidden-color degrees of freedom in nuclear wavefunctions based on isospin-zero diquarks.

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^{†}preprint: SLAC-PUB-XXXXX

Diffractive dissociation of relativistic hadrons is an important tool for probing hadron structure. The fundamental quark-antiquark structure of the pion was tested at Fermilab by Ashery et al. Ashery:1999nq by observing 500 GeV pions dissociate into dijets on a nuclear target. Their work was motivated by theoretical studies of diffractive excitation in quantum chromodynamics Bertsch:1981py .

In this paper we propose an extension of the Ashery diffractive dissociation method to probe the fundamental structure of mesons, nucleons and nuclei. We shall show how one can probe phenomena such as the quark-diquark structure of baryons, short-range nucleon-nucleon correlations and QCD “hidden-color” Brodsky:1983vf degrees of freedom inside nuclei. The main goal is to test the “isophobic” nature of short-range correlations (SRCs) within nuclei reported by the CLAS collaboration at Jefferson Laboratory 2018Natur.560..617C . Isophobic SRCs could provide a solution to the long-standing problem observed in deep inelastic scattering (DIS) experiments of leptons on nuclei, which show nuclear structure that does not follow simple additive cross section behavior Aubert:1983xm , a phenomenon known as the “EMC effect” Norton:2003cb .

We also discuss how diffractive dissociation of heavy nuclei can test a new model for the isophobic nature of the EMC effect where short-range quark-quark correlations in heavy nuclei are dominated by color-singlet 12-quark configurations: the “hexa-diquark.” Formed out of nearest neighbor scalar diquarks, this multi-diquark model may also form strongly bound tetra-diquark valence quark states and thus may be visible in the MARATHON experiment at JLab Petratos:2000qp .

The EMC effect was first discovered in 1983 in DIS experiments over a wide range of nuclear targets as a strong distortion of the nuclear quark distributions in the domain of high momentum fraction: Bjorken scaling parameter values of . Recently the CLAS collaboration at Jefferson Laboratory compared nuclear parton distributions for a large range of nuclear targets and found, surprisingly, that the EMC effect has a strongly isophobic nature. One model for this behavior is to identify short-range correlations between neighboring and nucleons which are much stronger compared to or SRCs.

In fact there are two conventional models to explain the EMC effect, either a modification of the mean field inside nuclei or the short ranged (nearest neighbor) correlated nucleon pairing within the nucleus Weinstein:2010rt ; Cloet:2019mql . The CLAS results are in favor of the nucleon SRC model and the data show the highly isophobic nature previously mentioned; similar nucleons are much less likely to pair than proton-neutron pairs at a factor of 20 times higher than proton-proton and neutron-neutron pairs 2018Natur.560..617C ; Subedi:2008zz . A definitive experimental test of this model is highly desirable and the diffractive dissociation of alpha particles is a straightforward and robust way to measure it.

In an accompanying paper West:2019rw we suggest an alternative explanation for the EMC effect. We postulate that the isophobic nature is due to virtual quark and gluon dynamics underlying nuclear structure in terms of QCD short-distance degrees of freedom. The formation of a hexa-diquark, a charge-0, spin-0, baryon number-4, isospin-0, color-singlet intermediate state is proposed as an essential component of nuclear wavefunctions. Each in the hexa-diquark is a scalar diquark with color. The hexa-diquark is a strongly-bound color-singlet configuration, and it is thus a natural constituent of the nucleus in terms of QCD degrees of freedom. It may be related to color superconductivity models e.g. of Alford et al. Alford:1997zt as it could form from an analog of an isolated color-charged Cooper pair condensate in the core of the nucleus. A multi-diquark core, whether a strongly bound hidden-color state or a bosonic color-condensate, will allow heavier nuclei to form central multi-diquark structures as well. We discuss implications for nuclei therein.

In this work, we show that the diffractive dissociation of relativistic nuclei can provide a definitive test of the isophobic nature of short-range correlations in the nuclear wavefunction as well as a way to discriminate between nucleon-based and quark-based models for the EMC effect. Predictions made by light front holographic QCD Brodsky:2014yha may also be tested.

Light-front wave functions (LFWFs) Dirac:1949okn are the eigenfunctions of the light-front Hamiltonian of relativistic quantum field theories, encoding the properties of bound state systems such as hadrons or nuclei in QCD and atoms and molecules in QED. The LFWFs are frame independent and causal and they underlie a wide range of bound-state observables: form factors, structure functions, distribution amplitudes, generalized parton distributions, transverse momentum dependent distributions, weak decays, final state interactions, and more. Light-front holography provides a connection between anti-de Sitter space (AdS) in five dimensions and the physical spacetime dimensions of color-confining QCD Polchinski:2002jw .

Ashery developed a novel method to obtain the light-front wavefunction of the pion by measuring the diffractive dissociation of a relativistic pion into two jets upon a nuclear target, . The pion interacts with the nucleus with minimal momentum transfer. When the target is left intact, the two-gluon exchange contribution retains the color of the projectile (a color singlet for the pion) and gives an imaginary amplitude and an approximately constant diffractive cross section; this is characteristic of Pomeron exchange. To first approximation, the amplitude measures the second derivative of the pion light-front wavefunction Brodsky:1997de ; Frankfurt:1999tq ; Nikolaev:2000sh . The transverse impact parameter separation of the two quarks in the pion is inversely proportional to the relative transverse momenta. After the soft interaction, the two jets will have opposite transverse momenta and -, and their longitudinal momenta can be translated into the light front variable , with one jet having and the other . Therefore both the transverse and the longitudinal distributions can be obtained.

A key feature of the diffractive dissociation process is “color transparency:” When the pion dissociates to a quark and diquark at high relative transverse momenta, , the interaction on the nucleus is dominated by small-size color-singlet configurations Brodsky:1988xz . The pion is not absorbed and in fact interacts with each nucleon coherently Frankfurt:1993it .

This procedure can also be applied to other systems in order to obtain their constituent Fock states and light front wavefunctions. Let us consider other examples:

(1) Diffractive dissociation of a relativistic proton.

If the dominant Fock state configuration of the proton is three quarks , one will most often observe 3 jets: . However, if the proton is dominated by quark di-quark configurations , as predicted by light-front holography and other models, one will instead observe two jets , similar to pion dissociation. A subset of these events will also have jets when the dijet itself dissociates. Light-front holography also predicts that the quark-diquark relative orbital angular momentum in the proton has equal probability for and . This could be tested by using a polarized proton beam and measuring the angular correlation of the quark and diquark jets.

(2) Diffractive dissociation of relativistic nuclei to two nucleons, e.g. .

If the isophobic I=0 SRCs underly the EMC effect, one would observe , where the and have high relative transverse momenta. In contrast, the I=1 nucleon pairs produced in and events will have much smaller relative transverse momenta.

(3) Diffractive dissociation of relativistic nuclei to hidden color states.

On the other hand, if the particle is dominated by the hexa-diquark configuration, diffractive dissociation of the particle into multiple colored jets is the primary signature. One such result is two hexaquark jets (tri-diquarks), such as . These jets would be color singlet J=1 hexaquarks (similar to the quantum numbers of a deuteron) if one of the diquarks has spin or if the dissociation leads to nonzero orbital angular momentum . Signatures of the hexa-diquark and other diquark combinations include multiple colored jets with various combinations of diquarks, e.g. jets with and constituents. This would be a colored jet with a colored jet. At very small rates, the helium nucleus would dissociate into all diquarks with a colored jet signature. These are all quite distinct from correlation signatures.

(4) Diffractive dissociation of relativistic deuterium nuclei to hidden-color systems.

The deuteron is a J=1, I=0 color singlet bound state in QCD and will normally dissociate into states due to its weak binding energy. However, there are five different color-singlet combinations of the six quarks in its valence Fock state, including color-singlet hexaquarks such as , where the diquark has spin . The deuteron Fock state can also be matched to an isobar pair such as with . The weight of each configuration can be measured by diffractive dissociation, such as .

5) Diffractive dissociation of relativistic electromagnetic systems.

One could measure the light-front wavefunction of positronium and other atoms through diffractive dissociation of in-flight atoms. In this case, the Coulomb-photon exchange measures the first derivative of the positronium light-front wavefunction. It is possible to have minimal momentum transfer to the target, which is left intact. This would separate and measure the two most important Fock states in positronium, and . A non-perturbative analysis of these lightfront wavefunctions was performed in 2015 Wiecki:2014ola .

Coulomb dissociation of true muonium would be particularly interesting Brodsky:2009gx . The transition of its LFWF from

(1) |

is a primary experimental signature.

Several muon related experimental results may point to physics beyond the Standard Model. These include the anomalous magnetic moment of the muon Bennett:2006fi , lepton non-universality in B meson decays Ciezarek:2017yzh ; Aaij:2019bzx and possibly Higgs decays although early hints in the Higgs sector Khachatryan:2015kon appear to have gone away Sirunyan:2017xzt . The analysis and detection of true muonium Fock states may be of great interest for exploring solutions to these puzzles Lamm:2015fia .

## Acknowledgements

We thank J. D. Bjorken for helpful discussions. This work is supported in part by the Department of Energy, Contract DE–AC02–76SF00515. IS is supported by Fondecyt (Chile) grant No. 1180232 and CONICYT PIA/BASAL FB0821.

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