QCD based EMC Effect Model: Diquark Structures in Nuclear Matter

Jennifer Rittenhouse West Berkeley Lab & EIC Center @JLab Postdoctoral Fellow 3rd International Workshop on Quantitative Challenges in EMC & SRC Research 25 March 2021 EMC effect: Distortion of nucleon structure functions in nuclei

F x x Q2 q x q x 2( B) ≡ ∑ B f ( f( ) + f¯( )) f Volume 123B, number 3,4 PHYSICS LETTERS 31 Ma rch 1983 Volume 123B,number 3,4 PHYSICSLETTERS 31 March 1983 • Predicted in The vahdlty of thesecalculations can be tested by beddedIn nucleiF They( xmayB )differ from the fre e nu- 2 extractingthe ratio ofi the I fre e i nucleonI structure I i I / ~func- Data cleon case not only due to kinematicalsmearing caused tions F~/F~ from1,4 the lion and hydrogendata of the completeby the Fermi motiondisagreement of the nucleonsin the nucleus Theory EMC. Applying, for example,the smearingcorrection but also due to other effects. 13 with theoryInforma tion about the size of theseeffects andfa their ctors for the ~3proton and the neutronas given by influe nceon the structurefunctions has beenobtained Bodek and Rltchle (table 13 of ref. [8]), one///,"";i gets a by the EuropeanMuon Collaborationfrom extensiveratio whmh is very different from the one obtained =,-, ~2 12 muon scatteringexperiments using targetsof hquid it_ with the deuteriumN data [3]. It fa lls from a value of I • hydrogen[2], deuterium[3] and of iron [4]. Apa~1.15 rt atx = 0.05 to a value of ~0.1 atx = 0.65 which Why should quark + i/,,// from the different targetsthe sameapparatus has been is evenbelow the quark-modellowe r////..' bound of 0.25. 11 used for all measurements. N behaviorThe measurements - confinedwith hydrogen inand deuteriumA directK way to check the correctmnsdue to nu- ...... , targetsallow the determinationof the structure func-clear effects is to comparethe deuteronand iron data nucleonstions for fre e nucleons.at QCDThe proton energy structurefunction for they should be influe nce dslmdarly by the neutron 10 F~ has beenextracted from the hydrogendata alone. content of these09 nuclei. The iron data are the fina l scalesThe neutron ~200structure MeV functionF~ - hasbe been soobtained combineddata sets for the four muon beam energies by a combinedtreatment of the hydrogenand the 09 of 120,200, 250 and 280 GeV; the deuteriumdata affecteddeuterium data. when This then nucleons determinesthe ratio F~/Fp 08 which, for la rge x, representsthe ratio of the d- andhave u- been obtainedwith a single beam energyof 280 embeddedquark distributions. inIn thisnuclei? procedure,corrections GeV. The ratio of the i measuredI i nucleon ! i structure i i 08 0 02 O~ 06 X have beenapplied to take into accounteffects duefunctions to for iron F2N(Fe) = gg*1 wuFe 2 and for deutermm the nucleonmotion in the deuteronwhich is a loosFN(D) e ly = Fig.{F~ 1. D, Theoretical ne,therpredlcnons corrected for the for Fermi Fermi motion motion, correc- I I [ I I I 1 bound p-n system.In the kinematicalrange covered tion of the nucleonstructure function F N for Iron. Dotted 02 04 06 X has beencalculated point by point. For this compari- by the data (0.03 ~gluon which distributions could rected fortail the include non-lsoscalarlty d.Triple-dot-dashed of line56Fe Same assumingauthors, momen- that The iron data are correctedfor the non-lsoscalarltyof 26Fe, both data setsare not correctedfor Fermi motion. The full be extractedfrom the high A target data, providedthe one neutron tum balancestructure always functionby aA - 1 behaves nucleus.The hke last F~ two = curves (1 curve is a hnear fit FN(Fe)/FN(D) = a + bx which resultsin knew how to calculatethe correctionsdue to nuclear shouldnot be understoodas predictionsbut as an indication structure functions - 0.75x)FP.of the sensitivity This givesof the a correction calculationsto of several ~+2.3%assumptions at x aslopeb=-052_+ 0.04 (stat.) -+ 0.21(syst) The shaded effects which are different in this casesince the nu- = 0.65 andwhich of arele s only s than poorly 1% known. forx < 0.3. The Q2 range, area indica te sthe effect of systematmerrors on this slope. becomecleonsin the distorted nucleusare packed much tighter together than in the deuteron. which ~s limite d by the extent of the deuteriumdata, If thesecorrections covered all effects causedby as thedifferent “THEto calculate for RATIO eachthe x-value, deuteriumOF THEvarying corrections NUCLEON from [7] 9 ~< areSTRUCTURE Q2 simply ~< 27 tlon FUNCTIONS of the two dataFN FORsetswill IRON not changeAND DEUTERIUMthe slope of “ quark structureof nuclei and were completelyunder- GeV 2 fortransferred x = 0.05to over the heavy11.5 ~< nucleus Q2 < case. 90 GeVDepending 2 for xon the observedx-dependence 2 of the ratio but can only The European Muon Collaboration, J.J. AUBERT et al. 1983 stood, they certainly should be applied to the deep= m-0.25 upthe to way 36 the~Q2 nucleus ~< 170wave GeV function2 forx IS calculated,= 0.65. and move it up or down by up to sevenpercent. The dif- elastic scatteringdata before these are comparedwith W~thm on the the hmlts assumptions of statisticalmade on and the momentum systematmtall errors and fe re nceFN(Fe)-FN(D) however ,s very sensitweto the predictionsof QCD. This appearsto be desirable the momentumbalance, the results[8-10], shown in no slgmficantQ2 dependenceof the ratm F~(Fe)/ the relatwe normahsatlon. EMC & SRCas workshop, the Alta re lll-P a25 rls lequations March [5]2021 in their original fig. 1, differ by severalpercent, 2 but show in each case Jennifer Rittenhouse West form require an inte gra tionfrom x to 1 (If they areFN(D) not isa observed.similar globalThe behavtour. x-dependenceThe ratioof of the the Q2structure aver- The result is m completedisagreement with the modified to allow an x rangeup to x = A [6]) andaged the ratiofunction is shownF A infor fig.a nucleus 2 wherewith the mass errornumber barsA areand of calculationsdlustrated an fig. 1. At high x, where an commonlyused parametrizatlonsof the quark andstatistical theonly. sum ofFor the a frestraight e nucleon linestructure fit of the functions form for enhancementof the quark distributionscompared to gluon distributionsare boundedto zero at x = 1. proton and neutronweighted with the corresponding the fre e nucleoncase is predicted,the measuredstruc- Up to now only those correctionsdue to the motionFN(Fe)/FN(D) nucleon numbers = a + bx[Z , F~ + (A - Z) F~] is rising with x ture function per nucleonfor ~ron ~s smaller than that of the nucleonsin the nucleushave beencalculated. forx >~ 0.2. The value of this ratio is about 1.2-1.3 For these calculationsit is commonto view the nucleusone gets at for x =the 0.65 slope and incre a s e srapidly to higher valuesofx. for the deuteron.The ratio of the two is fa lhng from as a collection of slowly moving nucleonsweakly bound In terms of quarks this means[9,10] that in a nucleus ~1.15 atx = 0.05 to a value of ~0.89 atx = 0.65 to each other with their inte rna lproperties unchanged b = -0.52 the + quark 0.04 distributions (statistical)+are enhanced0.21 (systemattc).at high x and ex- while it is expectedto rise up to 1.2-1.3 at this x comparedto the fre e nucleoncase. The methodsused The systematmtend fa r beyonderror x has= 1, beenthe kinematiccalculated lunit by being distort-x = A value. mg the measuredF N valuesby the individua l system- We are not aware of any publisheddetailed predic- 276 atm errors of the data sets,calculating the correspond- tion presentlyavailable which can explain the behav- mg slope for each error and adding the differences tour of these data. However there are severaleffects quadratically.The possibleeffect of the systematic known and discussedwhich can changethe quark dis- uncertaintieson the slope is lndma te dby the shaded tributionsm a high A nucleuscompared to the fre e area m fig. 2. Uncertalntmsm the relative normahsa- nucleoncase and can contributeto the observedef-

277 Proposed QCD model: Diquark formation across nucleon pairs

Diquark formation across N-N pairs in nuclei

Valence quarks in neighboring nucleons can bind together: donates up quark + donates down N1 N2 quark with spins anti-aligned:

[ud] 1 b c b c ψa = ϵabc (u ↑ d ↓ − d ↑ u ↓ ) 2

1. Binding energy ~148 MeV - adapted from http://fafnir.phyast.pitt.edu/particles/ energetically favorable

2. The QCD color factor - a measure of strength of strong force potential V(r) - it is attractive - diquark is bound

Diquark formation sticks pairs of nucleons together - it creates short-range correlations!

EMC & SRC workshop, 25 March 2021 4 Jennifer Rittenhouse West Diquark binding energy: Hadronic hyperfine structure

Spin-spin interaction affects hadron mass:

3 1. M m a σ σ m m (baryon) = ∑ i + ′∑ ( i ⋅ j)/ i j i=1 i

(de Rujula, Georgi & Glashow 1975, Gasiorowicz & Rosner 1981, Karliner & Rosner 2014)

Effective masses of light quarks are found using Eq.1 and fitting to measured baryon masses:

b b b b mu = md ≡ mq = 363 MeV, ms = 538 MeV

Binding energy of [ud] :

B.E. mb mb mb M ± [ud] = u + d + s − Λ = 148 9MeV “Diquark Formation from Nucleon-Nucleon Interactions I: Nuclear Matter,” JRW, arXiv:2009.06968

EMC & SRC workshop, 25 March 2021 5 Jennifer Rittenhouse West Quark-quark potential in QCD: V(r) calculation

• The invariant QCD Lagragian: SU(3)C

1 μνa a μ ℒ = − F Fμν + Ψ¯ f iγ Dμ − m Ψf 4 ( )

a a a where covariant derivative Dμ = ∂μ − igsAμt acts on quark fields, t are the 3x3 traceless Hermitian matrices (e.g. the 8 Gell-Mann matrices), gs 2 gs N the strong interaction coupling, αs ≡ . 1 4π • The QCD potential for states in representations R and R′ is given by: 2 gs v a a v V(r) = tR ⊗ tR u d 4πr ′ • To calculate for a , use the definition of the scalar , v V(r) 3c × 3c C2(R) a a , the quadratic Casimir operator, to find: v tR tR = C2(R) 1

2 N gs 1 2 V(r) = ⋅ ⋅ C (Ri) − C (R) − C (R′) 4πr 2 ( 2 2 2 ) • Diquarks combine 2 fundamental representation quarks into an anti- fundamental, : 3C ⊗ 3c → 3C

2 2 gs V(r) = − ⟹ Diquark is bound! 3 4πr

EMC & SRC workshop, 25 March 2021 6 Jennifer Rittenhouse West Complementary Model: Novel color-singlet HEXADIQUARK in the core of A>3 nuclei

Hexadiquark (HdQ) color-singlet in A≥4 nuclei

Ref: JRW, S.J.Brodsky, G. de Teramond, I.Schmidt, F.Goldhaber, arXiv:2004.14659 Nuclear Physics A

• 4 nucleus proposed to He ψ | ud ud ud ud ud ud contain a novel color HdQ⟩ = [ ][ ][ ][ ][ ][ ]⟩ singlet state

• 6 scalar diquarks strongly [ud] 1 b c b c bound together to form a ψa = ϵabc (u ↑ d ↓ − d ↑ u ↓ ) color singlet 2

• Fermi statistics upon quark Quark indices a, b, c = 1, 2, 3 are color indices in exchange, Bose statistics the fundamental representation. SU(3)C upon diquark exchange Diquarks are in the anti-fundamental representation:

3C ⊗ 3c → 3C

EMC & SRC workshop, 25 March 2021 8 Jennifer Rittenhouse West Hexadiquark wavefunction

The HdQ is a JP = 0+, I = 0 object which is a component of the 4He nuclear wavefunction:

|α C u ud d ud u ud d ud ⟩ = pnpn ( [ ])1C( [ ])1C( [ ])1C( [ ])1C⟩ + C ud ud ud ud ud ud HdQ ([ ][ ])6C([ ][ ])6C([ ][ ])6C⟩

All quantum numbers of the HdQ and the 4He ground state are identical: Q=2, B=4, I=0, J=0

Important: HdQ requires 2 correlated neutron- proton pairs. The effect of the HdQ is “isophobic” because [ud] diquarks form only across n-p pairs in the quark-diquark nucleon structure approach.

NB: The HdQ does not act in 3He, 3H -

“QCD hidden-color hexadiquark in the core of nuclei,” JRW, Brodsky, de Teramond, Goldhaber, Schmidt, Nucl.Phys.A 1007 (2021), arXiv:2004.14659 EMC & SRC workshop, 25 March 2021 9 Jennifer Rittenhouse West Diquark formation across N-N pairs: 3He and 3H

SRC prediction for MARATHON experiment:

Scalar [ud] diquark formation in A=3 nuclei for 3-valence quark internal structure:

3H : n − p ⟹ [ud][ud][ud] × 2 n p n n n − n ⟹ [ud][ud] + valence ⟹ 75 % − , 25 % −

3He : n − p ⟹ [ud][ud][ud] × 2 n p p p p − p ⟹ [ud][ud] + valence ⟹ 75 % − , 25 % −

For nucleons in quark-diquark internal structure:

3H : u [ud] + u [ud] + d [ud] ⟹ 100 % n − p

3He : d [ud] + d [ud] + u [ud] ⟹ 100 % n − p

EMC & SRC workshop, 25 March 2021 10 Jennifer Rittenhouse West Diquark formation implications: SeaQuest Antimatter Asymmetry

Antimatter asymmetry in the quark sea of protons Excess of d¯ quarks over u¯!

• Gluons produce quark-antiquark pairs in nucleons.

• uu¯ and dd¯ pairs form in equal amounts • Binding energy of spin-0 [ud] diquarks is ~148 MeV

• For protons with valence u (assuming the proton has quark-diquark structure) the d from gluon-to-dd¯ can be captured into a [ud] diquark

• Leaves a d¯ quark behind - excess d¯ in proton

• Predicts excess of u¯ in the neutron sea

• SpinQuest prediction: d¯ carries all the spin of the proton for the 5-quark Fock state: ud ud ud d¯ [ ][ ][ ] from Wired magazine, 28 February 2021

EMC & SRC workshop, 25 March 2021 11 Jennifer Rittenhouse West Fin!

Jennifer Rittenhouse West Berkeley Lab & EIC Center @JLab Postdoctoral Fellow 3rd International Workshop on Quantitative Challenges in EMC & SRC Research 25 March 2021