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, arXiv:2103.10088 ADL, arXiv:2103.07724

Presented at RPP2021 MOTIVATION

@ A QCD picture for diffraction and partonic level

@ Predictions at future -ion colliders (EICs)

Observable of interest: Rapidity-gap distribution! Diffraction at HERA: A large angular gap observed!

Large rapidity gap (LRG) 2 CONTENTS

I. DIS in dipole model and diffraction

II. Diffractive dissociation of onium: a probabilistic QCD picture

III. Diffractive dissociation at future EICs

3 QCD dipole model for DIS

Virtual probes nucleus via a -antiquark color singlet dipole (onium)

Dipole factorization: Proba. of the splitting virtual photon → dipole

[z: momentum fraction of photon carried by quark (or antiquark)]

4 Diffractive dissociation of virtual photon

Evolved state by QCD radiative emissions

Photon dissociated to a set of (X)

~ angular gap in detectors

Nucleus kept intact

5 Diffractive dissociation of onium

6 Color dipole evolution: Soft- emissions

x0 x0 r Large N 1 High-rapidity evolution x c x 2 r 2 Transverse position rk r2 space x1 x1

Large number of colors (Nc) limit: gluon ≃ zero-size quark-antiquark pair ⇒ one-gluon emission ≃ (1→ 2) dipole branching

(LO; soft-gluon approx.)

Boosting to high rapidity Y: - Branching repeated (and independent) → branching process

- Fock state of onium is a set of dipoles with random sizes {rk} → random number density n(rk)

Each event recorded in a detector corresp. to a realization of this density 7 Nuclear scattering of onium (I): S-matrix element

Chosen frame: Nucleus boosted to Y 0 Total rapidity Y Onium of size r evolved to

S-matrix element:

Overlap I(Y0) r’ - For a particular configuration:

S-matrix element for the nuclear scattering of a dipole r’

average over all dipole configurations of the onium at rapidity

8 Nuclear scattering of onium (III): Balitsky-Kovchegov evolution equation

Scattering amplitude T(r,Y) = 1 – S(r,Y) obeys the BK evolution equation

- Initial conditions:

9 Nuclear scattering of onium (II): Cross-sections

Total cross-section:

Diffractive cross-section:

Inelastic cross-section:

Rapidity-gap distribution:

Building block: S(Y0) 10 Scattering of small onia: Probabilistic picture

Interesting regime: Onium much smaller than the nuclear saturation momentum QS(Y):

Recall:

Overlap I Scattering proba. of each dipole in the onium Fock state is small → T(r’) = (1 – S(r’)) << 1

Onium-nucleus overlap:

For a given realization of the onium Fock state:

Sum of all diagrams in which N dipoles in the Fock state interact with the nucleus Random variables Proba. of picking diagrams with k dipoles interacts

Average weights: k ... 11 Cross-sections in probabilistic picture

Total cross-section:

Diffractive cross-section:

Inelastic cross-section:

Need of weights wk

Calculation of the overlap I

12 Model for onium evolution (I): Mean-field approximation

Onium evolve to Mean-field evolution = a random set of dipoles Average over many realizations at Y:

→ mean number density

→ typical value for the size of the largest dipole Initial onium 0 Line of evolution of the typical largest dipole Deterministic evolution

13 Large dipole sizes Small dipole sizes Model for onium evolution (II): Large-dipole fluctuation

Introducing a minimal stochastic effect: one fluctuation !

Initial small onium 0

Amplitude T solves BK equation

representing for nucleus boosted to Y0

Large-dipole Onium evolved to fluctuation

Overlap of front from fluctuation and Main front gives negligible overlap nucleus gives main contribution to I 14 Asymptotics of diffraction: Quantitative results from the model (I)

Exchange weights:

Events involving many participating dipoles are not rare!!

With:

Nuclear saturation momentum:

15 Some remarks

Diffractive cross-section for a minimal gap Y0

Rapidity-gap distribution:

With:

Nuclear saturation momentum:

16 Diffraction at electron-ion colliders

17 Diffractive scattering at photon level

Diffractive cross section with minimal gap Y0 :

Rapidity gap distribution:

BK evolution of T and σin

Kernel K: Initial conditions: + Fixed coupling: +

+ Running coupling: +

(parent dipole presc.)

(Balitsky presc.) 18 Choices of kinematics

Kinematics accessible at BNL-EIC and LHeC:

● Rapidity: Y = 6, 10 (x ≈ 2x10-3, 5x10-5, resp.)

● Photon virtuality: Q² = 1 – 10 GeV²

19 Result (1/3): Diffractive scattering with a minimal gap

Diffractive cross section:

Y0: minimal rapidity gap

20 Result (2/3): Rapidity gap distribution

(Y0: rapidity gap)

21 Conclusions

Onium – nucleus:

i. Derivation of parameter-free expressions of diffractive cross section and rapidity gap distribution at asymptotics.

ii. A large number of color singlet exchanges is important for diffraction.

Virtual photon – nucleus:

iii. Running-coupling and fixed coupling lead to rather different gap distributions.

iv. The gap distributions in fixed coupling case agree qualitatively with the prediction in the onium-nucleus case

Measurement of rapidity gap distributions at future EICs is important for microscopic understanding of diffraction!

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