A probabilistic QCD picture of diffractive dissociation and predictions for future EICs Anh Dung Le Based on: ADL, Mueller & Munier, PRD 103 (2021) 054031 ADL, Mueller & Munier, ar iv:2103"100## ADL, arXi!:2103"0$$24 Presen%ed at RPP2021 MO I!A ION + A QCD pi.%ure for diffra.%ion and partonic le!el + Predic%ions a% /u%ure ele.%ron-ion colliders (EICs) 4'ser!a'le of interes%: Rapidity-gap distribution! Diffraction at #ERA$ A large angular ga& obser!ed( Large ra&idity ga& (LRG) 2 CON E" ) 3" DIS in dipole 6odel and diffra.%ion 33" Diffra.%i!e disso.ia%ion of oniu6: a proba'ilis%ic ,CD &ic%ure 333" Diffra.%ive disso.ia%ion a% /u%ure EICs 3 QCD dipole *odel for DI) 7ir%ual photon probes nu.leus !ia a quark-an%iquar9 .olor single% dipole (oniu6) Dipole /a.%oriza%ion: Proba. of the splitting virtual photon → dipole :;: momen%um frac%ion of &hoton carried b) quar9 (or an%i8uark)] 4 Diffractive dissociation of virtual p+oton 2!ol!ed s%a%e 'y Q-D radiati!e e6issions Photon disso.iated to a se% o/ &arti.les (X) > angular gap in de%e.%ors =u.leus ke&% in%ac% 5 Diffractive dissociation of onium 6 Color dipole evolution: )oft-gluon e*issions I0 I0 r Large N 1 ?igh-ra&idi%) e!olu%ion I . I 2 r 2 Transverse position rk r2 space I1 I1 Large nu6'er o/ colors (N.) li6i%: gluon ≃ ;ero1si;e quar91an%i8uark pair @ one1gluon e6ission ≃ (1A 2) di&ole bran.hing (L4; soH1gluon a&&roI.) Boos%ing to high rapidi%y B: 1 Bran.hing re&ea%ed (and inde&enden%) → 'ran.hing &ro.ess 1 Coc9 s%ate of oniu6 is a se% of di&oles wi%h random si;es {r9F A random num'er densi%) n(r9) Each event recorded in a detector corresp. to a realization of this density 7 "uclear sca-ering of oniu* (I/$ S&*atri0 ele*ent Chosen fra*e$ Nucleus boosted to Y 0 Total rapidity Y Onium of size r evolved to )&matri0 ele*ent$ verlap I"#$% r’ - For a particular configuration: &-'atri( ele'ent for the nuclear scattering of a dipole r) average over all dipole configurations of the oniu' at rapidity 8 "uclear sca-ering of oniu* (III/$ Balits2%&3ovchegov evolution e4uation &cattering a'plitude T"r*#% = 1 – S"r*#% obeys the BK evolution e0uation - Initial conditions: 9 "uclear sca-ering of oniu* (II/$ Cross&sections Total cross-section: 1i2ractive cross-section: !nelastic cross-section: Rapidity-gap distribution: .uilding block: &"#$% 10 )cattering of s*all onia$ Probabilistic picture Interesting regime: niu' 'uch s'aller than the nuclear saturation 'o'entu' 5&"#%: Recall: verlap I Scattering proba. of each dipole in the oniu' Fock state is s'all → T"r)% = (, - S(r)%% << 1 niu'-nucleus overlap: For a given realization of the onium Foc3 state: Su' of all diagrams in 6hich 7 dipoles in the Fock state interact with the nucleus 8ando' variables Proba. of pic3ing diagrams with k dipoles interacts Average weights: k ... 11 Cross-sections in probabilistic picture Total cross-section: 1i2ractive cross-section: !nelastic cross-section: Need of 6eights w3 9alculation of the overlap I 12 Model for oniu* evolution (I/$ Mean-field appro0i*ation niu' evolve to Mean-field evolution + a rando' set of dipoles A!erage o!er man) reali;a%ions a% B: → mean num'er densi%) → %)&i.al value for %he si;e of %he larges% dipole 3ni%ial oniu6 0 Line of e!olu%ion o/ %he %)&ical larges% di&ole 1eterministic evolution 13 :arge dipole sizes &'all dipole sizes Model for oniu* evolution (II/$ 5arge&dipole fluctuation !ntroducing a minimal stochastic e2ect: one <uctuation > 3ni%ial small oniu6 0 ;'plitude T solves B/ e0uation representing for nucleus boosted to Y$ :arge-dipole niu' evolved to <uctuation Overlap of front from fluctuation and =ain front gives negligible overlap nucleus gives main contribution to I 14 As%*ptotics of diffraction: 6antitative results from the *odel (I/ Exchange 6eights: Events involving many participating dipoles are not rare@ ?ith: Nuclear saturation mo'entu': 15 )ome re*arks 1i2ractive cross-section for a minimal gap Y$ 8apidity-gap distribution: ?ith: Nuclear saturation mo'entu': 16 "iffraction at electron-ion colliders 17 Diffractive sca-ering at photon level 1i2ractive cross section with 'ini'al gap Y$ : Rapidity gap distribution: .K evolution of T and Ain Kernel K: Initial conditions: + Fixed coupling: + + Running coupling: + (parent dipole presc.) (Balitsky presc.) 18 Choices of 2ine*atics Kinematics accessible at BNL-!"# and LHeC: ● Rapidity: Y & '( )* (x B C(,$-D, 5(,$-E* resp.) ● +,oton -irtuality: .² & ) 0 )* GeV² 19 Result (178/$ Diffractive sca-ering with a *ini*al gap Diffractive cross section: %*: minimal rapidity gap 20 Result (278/$ Rapidity gap distribution (%*: rapidity gap) 21 Conclusions Onium – nucleus: i. 1erivation of parameter-free e(pressions of diffractive cross section and rapidity gap distribution at asy'ptotics. ii. A large nu'ber of color singlet e(changes is i'portant for diffraction. Virtual photon – nucleus: iii. Running-coupling and fi(ed coupling lead to rather di2erent gap distributions. iv. Fe gap distributions in fi(ed coupling case agree 0ualitatively with the prediction in the oniu'-nucleus case =easure'ent of rapidity gap distributions at future EI9s is i'portant for microscopic understanding of diffraction> 22.