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QCD Based EMC Effect Model: Diquark Structures in Nuclear Matter

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QCD Based EMC Effect Model: Diquark Structures in Nuclear Matter 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 ~<x < 0.65) these correctionsare line Few-nucleon-correlation-modelof Frankfurtand Strlk- • son only mandata [9]. points Dashed withline . Collective-tube-modela total systematmof errorBerlad etle al. s s Fig. 2, The ratio of the nucleon structure functionsF N mea- Diquarksmallerthan formation 3% [3]. gives [10] Solidline Correction accordmgto Bodekand Rltchle than 15% have beenused. The iron data have been cor- sured on tron and deuteriumas a function ofx = O2/2M,-,v. In a similar way the nucleonstructure function and [8]. Dot-dashedline . Sameauthors, but no high momentum - 56 a mechanismthe fre e nucleonquark andby 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 l equationsMarch [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<j 2. M(meson) = m1 + m2 + a (σ1 ⋅ σ2)/m1m2 (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.
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