Ultraperipheral collisions and low-x physics

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ Ul ape iphe al collisions and low-x physics © 2022 he Au ho Published e sion Lappi, Tuomas Lappi, T. (2022). Ul ape iphe al collisions and low-x physics. In DIS 2021 : P oceedings o he 28 h In e na ional Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s (A icle 003). S ich ing SciPos . SciPos Physics P oceedings. h ps://doi.o g/10.21468/SciPos PhysP oc.8.003 2022 SciPos Phys. P oc. 8, 003 (2022) Ul ape iphe al collisions and low-xphysics Tuomas Lappi1,2? 1Depa men o Physics, Uni e si y o Jy äskylä P. O. Box 35, 40014 Uni e si y o Jy äskylä, Finland 2Helsinki Ins i u e o Physics, P.O. Box 64, 00014 Uni e si y o Helsinki, Finland ?[email p o ec ed] P oceedings o he XXVIII In e na ional Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s, S ony B ook Uni e si y, New Yo k, USA, 12-16 Ap il 2021 doi:10.21468/SciPos PhysP oc.8 Abs ac Ul ape iphe al collisions a he LHC and RHIC o e he highes cu en ly a ailable en- e gy o pho on-nucleon and pho on-nucleus collisions. Thus hey a e a aluable ool o s udying he gluonic s uc u e o had ons and nuclei a small x. We discuss ecen heo e ical wo k owa ds unde s anding such exclusi e p ocesses a NLO accu acy in QCD pe u ba ion heo y. These heo e ical ad ances a e also immedia ely ele an o unde s anding he physics o deep inelas ic sca e ing a small x. We also discuss ex- pe imen al esul s in ul ape iphe al collisions, mos p ominen ly o exclusi e ec o meson p oduc ion. Copy igh T. Lappi. This wo k is licensed unde he C ea i e Commons A ibu ion 4.0 In e na ional License. Published by he SciPos Founda ion. Recei ed 20-07-2021 Accep ed 21-03-2022 Published 11-07-2022 Check o upda es doi:10.21468/SciPos PhysP oc.8.003 1 In oduc ion In he expec a ion o a new e a o high ene gy deep inelas ic sca e ing (DIS) expe imen s wi h he EIC [1], ul ape iphe al collisions o hea y ions [2]o e a way o s udy some o he same physical p ocesses a exis ing collide s. The elec omagne ic ield o a ully ionized hea y nucleus a eling a close o he speed o ligh can, using he Weizsäcke -Williams equi alen pho on app oxima ion, be unde s ood as a lux o high ene gy quasi- eal (Q2≈0) pho ons. The pho on lux and pola iza ion s uc u e can be calcula ed o a a he good accu acy. This makes i possible o s udy high ene gy pho on-nucleus, pho on-p o on and pho on-pho on collisions a he LHC and RHIC. He e, we will ocus on he small-xphysics and sa u a ion aspec s o hese collisions. We will i s desc ibe he dipole pic u e o DIS and he Colo Glass Condensa e (CGC) e ec i e heo y o QCD in he sa u a ion limi . We will hen discuss he compleme a y desc ip ion o exclusi e p ocesses using he collinea ac o iza ion app oach. We hen discuss some ecen expe imen al measu emen s in ul ape iphe al collisions, bo h o exclusi e ec o meson p o- duc ion and o o he UPC measu emen s. 003.1 SciPos Phys. P oc. 8, 003 (2022) 2 Dipole pic u e o DIS and he Colo Glass Condensa e ˆσ P γ∗z 1−z T =−∆T2 Figu e 1: The dipole pic u e o DIS. To unde s and he dipole pic u e o DIS, one should place onesel in he es ame o he a ge (o mo e accu a ely in he “dipole ame” [3]whe e he pho on ene gy is la ge han he i uali y, bu he a ge has mos o he collision ene gy). In such a ame he pho- on de elops a cloud o QCD Fock s a e componen s which, a high collision ene gy, hen in e ac ins an a- neously wi h he gluonic shockwa e o he a ge . The leading such QCD Fock s a e is a colo neu al qua k- an iqua k dipole, hence he e m “dipole pic u e”, see Fig. 1. The in o ma ion on he small-x, p edominan ly gluonic, deg ees o eedom o he a ge is con ained in he so called “dipole c oss sec ion.” Mo e p ope ly speaking he deg ee o eedom is he elas ic o wa d sca e ing ampli ude No a dipole o size Twhich, in eg a ed o e he ans e se plane, gi es he o al c oss sec ion: σdip(x, T) = 2Zd2bTN(x, T,bT);Zd2bTei∆T·bT. (1) The p edic i e powe o he dipole amewo k lies in he ac ha om his same deg ee o eedom one can calcula e c oss sec ions o a mul i ude o p ocesses: • The o al γ∗po γ∗Ac oss sec ion is ob ained by con olu ing he he dipole ampli ude by he squa e o he pho on- o-q¯ qwa e unc ion: σγ∗H o =|Ψ(γ∗→q¯ q)|2⊗σdip wi h ⊗≡Z1 0 dzd2 T. (2) • C oss sec ions o inclusi e di ac ion, on he o he hand, a e gi en by he squa e o he dipole ampli ude, Fou ie - ans o med om impac pa ame e o momen um ans e : dσγ∗H→X+H d =1 4π|Ψ(γ∗→q¯ q)|2⊗|N(∆T)|2. (3) • Exclusi e ec o meson c oss sec ions equi e, in addi ion o he pho on wa e unc ion, he ligh cone wa e unc ion o he ec o meson: dσγ∗H→V H d =1 4πΨ(γ∗→q¯ q)⊗N(∆T)⊗Ψ∗(q¯ q→V) 2. (4) • C oss sec ions o inclusi e pa icle p oduc ion in pp, pAand AA collisions a e exp essed in e ms o he Fou ie ans o m ( om he dipole size o he p oduced pa icle mo- men um) o he same dipole ampli ude. In he CGC [4]e ec i e heo y pic u e he small-xdeg ees o eedom o he a ge a e desc ibed in as a classical colo ield. The sca e ing ampli ude o a colo ed poin like p obe om such a ield is gi en by an eikonal ligh -like pa h o de ed exponen ial: he Wilson line (see Fig. 2) U(xT) = Pexpig Zdx−A+(xT,x−). (5) 003.2 SciPos Phys. P oc. 8, 003 (2022) The classical colo ield is adia ed om he la ge -xpa ons o he a ge . We do no , howe e , ca e abou he numbe o na u e o hese pa ons, bu only abou hei o al colo cha ge (see Re . [5] o ecen wo k epo ed a his con e ence). Thus he ampli ude o a colo neu al qua k-an iqua k dipole is gi en by he ace o a p oduc o a Wilson line a he ans e se coo dina e o he qua k and a conjuga e Wilson line a he posi ion o he an iqua k, he dipole ope a o N=1 Nc T D1−U†bT+ T 2UbT− T 2E. (6) One o he a ac i e ea u es o his o mula ion ollows om he ac ha he Wilson lines and hei p oduc s a e, by cons uc ion, SU(Nc) ma ices ha li e on a compac mani old. This na u ally leads o a bounded ampli ude N≤1 co esponding o gluon sa u a ion buil in o he o malism. A Figu e 2: High ene gy qua k in e ac - ing wi h classical gluon ield. In addi ion o p o iding an in ui i e pic u e o high ene gy sca e ing in he sa u a ion egime, he dipole pic u e is a s a ing poin o a sys ema ical pe u ba- i e expansion in weak coupling QCD. Highe o de co ec ions can be calcula ed by adding gluons o he pic u e, see Fig. 3. The classical gluon ield pic u e o he a ge p o ides a unique way o he calcula e he sca e ing ampli udes o highe Fock s a es. The phase space egion whe e a gluon is so gene a es a con i- bu ion ha is enhanced by a la ge loga i hm (Lead- ing Log (LL) ∼αsln1/x, Nex - o-Leading Log (NLL) ∼α2 sln1/x), which mus be abso bed in o a eno maliza ion o he a ge gluon ield. This leads o he BK/JIMWLK [6–8] eno maliza ion g oup e olu ion equa ions ha esum hese loga i hms. The pa o phase space o he one-gluon co ec ion ha is no enhanced by a loga i hm is hen a genuine NLO ∼αsco ec ion. Figu e 3: Adding a gluon o he dipole pic u e o DIS. The las yea s ha e seen signi ican ad ances in pushing his pe u ba i e expansion o he NLL and NLO le els. The NLO e sions o he BK [9]and JIMWLK [10,11]equa ions ha e been de i ed and complemen ed wi h collinea esumma ions needed o s abilize hem [12,13]. The o al DIS c oss sec ion o massless qua ks has been calcula ed [14–17], and used o ob ain a good desc ip ion o HERA o al c oss sec ion da a [18]. Di ac i e dije p oduc ion in DIS has also been add essed [19]. The phase space o p ope je s a small xis mo e limi ed a he EIC, bu hese calcula ions a e cu en ly being ex ended o he di ac i e s uc u e unc ions which ha e been measu ed a HERA and ce ainly will be accessible a he EIC. Simila ly one can also calcula e exclusi e elec op oduc ion o ligh ec o mesons [20]using a pa on dis ibu- ion ampli ude o desc ibe he meson. Exclusi e hea y qua konium p oduc ion is a pa icula ly impo an obse able o QCD, bo h because o he clean expe imen al signa u e [1]and be- cause he mass o he hea y qua k makes i possible o unde s and he physics o he bound s a e in a weak coupling pic u e. These calcula ions equi e i ual pho on wa e unc ions o massi e qua ks, which a e now g adually s a ing o become a ailable a NLO [21]. Signi ican ad ances in pushing he calcula ions o exclusi e qua konium p oduc ion o NLO in he dipole pic u e [22,23]ha e been epo ed a his con e ence [24]. Simul aneouly he e has been a lo o ela ed ac i i y o also mo e calcula ions o pa icle p oduc ion a o wa d apidi y in had on-ha don collisions o NLO accu acy, acing many o he same echnical issues as in DIS. 003.3 SciPos Phys. P oc. 8, 003 (2022) Con a y o he in ini e momen um ame pa onic pic u e o he a ge in collinea ac- o iza ion, in he dipole pic u e o DIS one is pe u ba i ely calcula ing he pa onic s uc- u e o he i ual pho on. The mos impo an heo y ing edien in hese calcula ions is he pho on ligh cone wa e unc ion (LCWF). The LCWF’s a e de ined as he coe icien s ψγ→q¯ q, ψγ→q¯ qg, ...o an expansion o he in e ac ing “d essed” pho on s a e in e ms o “ba e” Fock s a es: |γ∗〉D=|γ〉B+ψγ∗→q¯ q|q¯ q〉B+ψγ∗→q¯ qg |q¯ qg〉B+... (7) The Hamil onian pe u ba ion heo y calcula ions in ligh cone gauge and mixed longi udi- nal momen um– ans e se coo dina e space ha a e needed o calcula e he LCWF’s could be called he inal on ie o QCD pe u ba ion heo y. Pe haps as one o he las one-loop pe u - ba i e QCD esul s hey a e only now becoming ully a ailable, e.g. o he spli ing γ∗ T,L→q¯ q wi h massless qua ks [15–17],γ∗ L→q¯ qand soon γ∗ Twi h qua k masses [21]. Simila calcula- ions o he q→qg LCWF’s, needed o had onic collisions, a e also ad ancing. I is impo an o ealize ha he e is no “CGC” e ec i e heo y in ol ed in he LCWF’s hemsel es; hey a e pu ely pe u ba i e undamen al quan i ies desc ibing he elemen a y e ices. The LCWF’s a e, howe e , c ucial ing edien s o CGC calcula ions o expe imen al obse ables. As discussed abo e, calcula ing exclusi e ec o meson c oss sec ions equi es, in addi ion o he pho on LCWF and he dipole ampli ude, a LCWF o he ec o meson. Typically in he phenomenological li e a u e one has used simple LCWF pa ame iza ions i o lep onic decay wid hs, such as he Boos ed Gaussian o LC-Gaus pa ame iza ions [25]. Imp o ing he p ecision he e equi es, howe e , a mo e sys ema ical app oach. One op ion is o s a om a non ela i is ic po en ial model wa e unc ion and ans o m i in o ligh cone coo dina es (see e.g. [26]). One can also use he non ela i is ic limi in a mo e sys ema ical way by expanding a ound he limi o la ge qua k mass. This non ela i is ic QCD (NRQCD) app oach exp esses he bound s a e p ope ies in e ms o uni e sal long dis ance ma ix elemen s, which can be aken om e.g. decay wid h da a and hen used o p oduc ion c oss sec ions. This is a commonly used app oach o inclusi e qua konium p oduc ion, and is now also becoming a ailable o exclusi e DIS [22,24]. An app oach ha is close o he high ene gy limi om he s a is o di ec ly sol e he bound s a e p oblem on he ligh cone, using a phenomenological (e.g. AdS-mo i a ed) con ining po en ial. S a ing om Re . [27], he e has been a sys ema i- cal p og am o de elp a se o ec o meson LCWF’s om such an app oach, cons ained by a b oad se o qua konium spec oscopic da a. 3 Collinea ac o iza ion o exclusi e p ocesses Exclusi e p ocesses can also be add essed om he poin o iew o collinea ac o iza ion. He e one o ganizes pe u ba ion heo y o be able o esum la ge loga i hms o he i uali y Q2 by DGLAP o ERBL eno maliza ion g oup equa ions. Fo exclusi e ec o meson p oduc ion in ul ape iphe al collisions Q2≈0, bu one can a gue ha he cha monium mass p o ides a ha d enough scale o he o malism o be applicable. Thus he goal is o use pho op oduc ion da a o de e mine he ini ial condi ions o he e olu ion owa ds highe Q2. The collinea and small-x o malisms sha e a common egion o alidi y. To ge an in ui i e pic u e o hei ela ion we can s a om he dipole pic u e and go o he pe u ba i e dilu e limi . The dipole ampli ude is an elas ic ampli ude, wi h a colo neu al ou going s a e. Thus one exchanges acuum quan um numbe s wi h he a ge , i.e. a “pome on” exchange. The simples such s a e in a pe u ba i e se up is a 2-gluon exchange in he elas ic ampli ude, co esponding o he squa e o a single gluon exchange inelas ic ampli ude, see Fig. 4. Thus, o leading o de in he dilu e limi , he dipole ampli udes should be p opo ional o he gluon 003.4 SciPos Phys. P oc. 8, 003 (2022) dis ibu ion. A mo e ca e ul calcula ion yields he esul [28]: σdip( T) = π2 Nc αs(µ2)x g(x,µ2) T2(8) Figu e 4: Dipole ampli ude in he wo gluon exchange app oxima ion. Fo highe o de s in pe u ba ion heo y his es- ima e is clea ly no enough. To ea exclusi e p o- cesses p ope ly in pe u ba i e QCD one needs o in- oduce he concep o Gene alized Pa on Dis ibu ion (GPD). The GPD is a one-body ope a o desc ibing he gluon (o qua k) con en o he a ge as measu ed in an o -diagonal ansi ion wi h a ha d ex e nal scale, see Fig. 5. In e ms o equa ions one w i es he sca - e ing ampli ude as a con olu ion A∼Z1 −1 dxCg(x,ξ)Fg(x,ξ) +X q=u,d,s Cq(x,ξ)Fq(x,ξ)φV M . (9) He e Cg/q(x,ξ)a e pe u ba i ely calculable coe - icien unc ions desc ibing he elas ic pho on-pa on sca e ing. The ec o meson wa e unc- ion φV M is, in cu en phenomenological applica ions, ypically aken o be ully non ela i is- ic, so ha i is jus a cons an p opo ional o he lep onic decay wid h o he meson. The pa onic con en o he a ge is desc ibed by he GPD’s Fg/q(x,ξ). The GPD’s a e collinea dis ibu ions. This means ha one keeps ack o he explici dependence on he longi udinal momen um ac ions x+ξ,x−ξ, bu he ans e se momen um only appea s as a eno - maliza ion scale. One is hus wo king in a kinema ical egime whe e he ans e se momen a ci cula ing in he diag am a e s ongly o de ed. In p inciple he GPD’s a e independen quan- i ies ha a e ela ed o he con en ional pa on dis bu ions only in ce ain limi . Howe e , based on some ela i ely gene al assump ions, in he small-xlimi hey can be ela ed o he PDF’s by he “Shu ae ans o m” [29], which is commonly used in phenomenological appli- ca ions o ex ac he gluon PDF om exclusi e da a. Cq/g Fq/g φV M (x−ξ)P+ (x+ξ)P+ Figu e 5: Exclusi e ec o meson am- pli ude in he GPD o mula ion Taking his app oach o NLO accu acy in a phe- nomenologically easonable way has been a mul i- yea esea ch p og am [30,31]. The NLO co ec ions a e la ge and s ongly dependen on he ac o iza ion scale, e en o he ex en ha hey can change he sign o he ampli ude. Howe e , a e a lo o wo k o s a- bilize he pe u ba i e expansion, one is now in a posi- ion o use exclusi e ec o meson da a o ex ac he gluon dis ibu ion om da a a NLO accu acy [32]. The exclusi e da a is no ye included in global PDF i s, bu he ools now seem o be se ling in o place o do so. 003.5 SciPos Phys. P oc. 8, 003 (2022) 4 Exclusi e ec o meson measu emen s Measu emen s o exclusi e ec o meson c oss sec ions ha e been a mains ay o he UPC p o- g am a he LHC (see e.g. [33–36]) and a RHIC. Ini ially he c oss sec ions ha e been s a is ics limi ed, bu as he LHC luminosi y g ows, hey a e cons an ly ge ing mo e de ailed and di - e en ial, helping o di e en ia e be ween heo e ical models. As an example o ecen de elopmen s is he ALICE measu emen [37]o he cohe en γ+A→J/Ψ+Ac oss sec ion as a unc ion o he momen um ans e . One hing ha is ema kable abou his measu emen is he access o ex emely small alues o ans e se momen a: he esul s a e epo ed in a ange o − ∼0.0005...0.1GeV2. These alues a e ex- ac ed om he ans e se momen a o he J/Ψdecay lep ons, since he ecoil nucleus canno be measu ed. The EIC will ha e good acess o la ge | | alues ha a e ele an o imaging he p o on, bu ob aining a compa able esolu ion a small | |will be a majo challenge. Gen- e ally he epo ed -dis ibu ion is s eepe han expec ed om heo y. Quan i a i ely such a de elopmen would be expec ed om sa u a ion, which should make he impac pa ame e p o ile la e . Howe e , he speci ic sa u a ion model [38]compa ed o he expe imen al da a by ALICE is no s eep enough o desc ibe i well. The cohe en c oss sec ion, whe e he a ge does no b eak up in he in e ac ion, mea- su es he gluon densi y in he ans e se plane a e aged o e he con igu a ions o he a ge . Complemen a y in o ma ion abou he gluonic s uc u e can be ob ained by simul aneously measu ing he incohe en c oss sec ion, whe e he a ge b eaks up in o a ela i ely low in- a ian mass colo neu al sys em, sepa a ed om he ec o meson by a apidi y gap. In he Good-Walke pic u e he incohe en c oss sec ion measu es he luc ua ions o he gluon densi y, wi h he alue o he momen um ans e ela ed o he ans e se leng h scale o hese luc ua ions. A ull unde s anding o he small-xgluonic s uc u e o he a ge equi es measu emen s and calcula ions o bo h cohe en and incohe en p ocesses. A challenge in sepa a ing cohe en and incohe en p ocesses wi h a nuclea a ge is ha he ypical momen um ans e in he egion whe e hey a e bo h impo an is qui e small, meaning ha he ecoil nucleus disappea s down he beampipe wi hou being de ec ed. The nuclea b eakup p ocess i sel is also no well unde s ood heo e ically. The LHC expe imen s sepa a e he con ibu ions by i ing he o al -dis ibu ion o a linea supe posi ion o em- pla es o di e en p ocesses. A he EIC one will y o e o nuclea b eakup e en s using o wa d de ec o s, bu doing his accu a ely enough o ge a cohe en signal a highe will be challenging [1]. 5 O he UPC measu emen s Exclusi e ec o meson p oduc ion has been he i s channel o ocus on in ul ape iphe al collisions, p esumably because i is he easies one o igge on. Now, howe e , he p og am is ex ending o mo e inclusi e eac ions. A ecen in iguing example is he s udy [39]by he CMS collabo a ion o he angula dependence o di ac i e pho on-nucleus dije e en s. He e one measu es he dije angula co ela ion in ϕ=ϕQT,PT, he angle be ween he sum QT=pT1+pT2and di e ence PT=1 2pT1−pT2o dije momen a, whe e pT1,pT2a e he ans e se momen a o he je s. This obse able p o ides access o he he physics o gluon angula momen um, h ough he gluon ans e se momen um dis ibu ion (TMD). Such p ocesses will be a majo pa o he physics p og am o he EIC, howe e , in a much mo e limi ed kinema ical phase space. Ano he sligh ly mo e exo ic a enue o he audience o his con e ence is he s udy o wha could be e med “non-QCD inal s a es”. A pho on-pho on in e ac ion in an ul ape iph- 003.6 SciPos Phys. P oc. 8, 003 (2022) e al collision p o ides he highes ene gy pho on-pho on collisions cu en ly a ailable. One applica ion a e he i s measu emen s o a e bu con en ional QED p ocesses. Fo example he STAR measu emen [40]o angula modula ions in γ+γ→`+`−con i ms QED p edic- ions o he pola iza ion s uc u e and kT-dependence o he pho on lux, also se ing as a no maliza ion check o QCD s udies. The di ec measu emen o Ligh -by-ligh sca e ing by ATLAS [41]p o ides no only a di ec es o a highly supp essed one-loop e ec o QED, bu a way o sea ch o new axion-like pa icles. As a i s example o an in e es ing QCD analysis in inclusi e pho on-media ed p ocesses, he ATLAS collabo a ion has epo ed p elimina y esul s on inclusi e dije p oduc ion in pho on- nucleus collisions [42]. This analysis is un o una ely s ill no inalized and published. I i eaches a good enough le el o accu acy, i would se e as a heo e ically con olled and sen- si i e p obe o small-xgluon dis ibu ions [43]. As discussed in he ea lie sec ions, a high ene gy he pho on s a e also has an impo an had onic componen , which becomes impo an in high ene gy sca e ing. In he absence o a ha d scale, i.e. o pho op oduc ion and wi hou hea y qua ks, his means ha e ec i ely he pho on s a s o ac like a ρ-meson. One can hen see i as a ligh e e sion o a p o on, and use hea y-ion-like analysis echniques ha ha e ound new a eas o applica ion in smalle colli- sion sys ems, p o on-nucleus and high mul iplici y p o on-p o on collisions. The a che ypical such analysis is o look o “ low” s uc u es in azimu hal mul ipa icle co ela ions ha , a leas in a hea y ion e en , a e caused by hyd odynamical inal s a e in e ac ions. The ATLAS collabo a ion has pe o med p ecisely such an analysis [44], di iding pho on-nucleus e en s in o mul iplici y classes. In he high mul iplici y e en sample one iden i ies a cos2ϕs uc u e ha could be in e p e ed as he signal o inal s a e in e ac ions, a iny d ople o qua k gluon plasma c ea ed in a pho on-induced collision. 6 Conclusions The majo pa o his con ibu ion has discussed ecen ad ances in small-x heo y in he gluon sa u a ion egime. We ha e a gued ha he e has been a sys ema ical push o mo e o NLO accu acy in pe u ba i e weak coupling calcula ions o DIS and o he dilu e-dense p ocesses. To consis en ly include he e ec s o gluon sa u a ion, hese calcula ions a e p e e ably pe - o med in a mixed longi udinal momen um- ans e se coo dina e space. The in e ac ion wi h he a ge is desc ibed by eikonal sca e ing ampli udes, Wilson lines. Simul aneously, also in he complemen a y collinea ac o iza ion pic u e he desc ip ion o exclusi e eac ions and hei connec ions o inclusi e ones has been mo ing o NLO accu acy, including in phenomeno- logical applica ions. While a lo o his heo y de elopmen is mo i a ed by he EIC physics p og am, we do no need o wai o he EIC o exci ing new measu emen s. The LHC and RHIC ha e a g owing and e sa ile p og am o pho on-media ed ul ape iphe al collisions ha add esses he same physics opics. Ul ape iphe al collisions each highe collision ene gies han he EIC will, bu only in ol e quasi- eal pho ons. Thus hey equi e a hea y qua k o a je o s ay in he weak coupling egime. The EIC will add o his a le e a m in Q2 ha u n new kinds o obse ables in o pe u ba i e p obes o gluons in o dina y ba yonic ma e . Thus he e is a s ong complemen a i y be ween he ul ape iphe al and EIC p og ams. 003.7 SciPos Phys. P oc. 8, 003 (2022) Acknowledgemen s This wo k has been suppo ed by he Eu opean Resea ch Council unde g an no. ERC-2015- CoG-681707, by he EU Ho izon 2020 esea ch and inno a ion p og amme, STRONG-2020 p ojec (g an ag eemen No 824093) and by he Academy o Finland, p ojec 321840. The con en o his a icle does no e lec he o icial opinion o he Eu opean Union and espon- sibili y o he in o ma ion and iews exp essed he ein lies en i ely wi h he au ho s. Re e ences [1]R. Abdul Khalek e al., Science Requi emen s and De ec o Concep s o he Elec on-Ion Collide : EIC Yellow Repo ,a Xi :2103.05419. [2]A. J. Bal z, The Physics o Ul ape iphe al Collisions a he LHC, Phys. Rep . 458, 1 (2008), doi:10.1016/j.phys ep.2007.12.001. [3]A. H. Muelle , Pa on Sa u a ion-An O e iew,a Xi :hep-ph/0111244. [4]F. Gelis, E. Iancu, J. Jalilian-Ma ian and R. Venugopalan, The Colo Glass Condensa e, Ann. Re . Nucl. Pa . Sci. 60, 463 (2010), doi:10.1146/annu e .nucl.010909.083629. [5]A. Dumi u, H. Män ysaa i and R. Paa elainen, Impac pa ame e dependence o colo cha ge co ela ions in he p o on,a Xi :2105.08503. [6]I. Bali sky, Ope a o expansion o high-ene gy sca e ing, Nucl. Phys. B 463, 99 (1996), doi:10.1016/0550-3213(95)00638-9. [7]Y. V. Ko chego , Small-x F2s uc u e unc ion o a nucleus including mul iple pome on exchanges, Phys. Re . D 60, 034008 (1999), doi:10.1103/PhysRe D.60.034008. [8]A. H. Muelle , A Simple de i a ion o he JIMWLK equa ion, Phys. Le . B 523, 243 (2001), doi:10.1016/S0370-2693(01)01343-0. [9]I. Bali sky and G. A. Chi illi, Nex - o-leading o de e olu ion o colo dipoles, Phys. Re . D 77, 014019 (2008), doi:10.1103/PhysRe D.77.014019. [10]I. Bali sky and G. A. Chi illi, Rapidi y e olu ion o Wilson lines a he nex - o-leading o de , Phys. Re . D 88, 111501 (2013), doi:10.1103/PhysRe D.88.111501. [11]A. Ko ne , M. Lublinsky and Y. Mulian, Jalilian-Ma ian, Iancu, McLe an, Weige , Leonido , Ko ne e olu ion a nex o leading o de , Phys. Re . D 89, 061704 (2014), doi:10.1103/PhysRe D.89.061704. [12]E. Iancu, J. D. Mad igal, A. H. Muelle , G. Soyez and D. N. T ian a yllopoulos, Resumming double loga i hms in he QCD e olu ion o colo dipoles, Phys. Le . B 744, 293 (2015), doi:10.1016/j.physle b.2015.03.068. [13]B. Ducloué, E. Iancu, A. H. Muelle , G. Soyez and D. N. T ian a yllopoulos, Non-linea e o- lu ion in QCD a high-ene gy beyond leading o de , J. High Ene gy Phys. 04, 081 (2019), doi:10.1007/JHEP04(2019)081. [14]I. Bali sky and G. A. Chi illi, Pho on impac ac o in he nex - o-leading o de , Phys. Re . D83, 031502 (2011), doi:10.1103/PhysRe D.83.031502. 003.8