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 electron-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 photon probes nucleus via a quark-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 particles (X)
~ angular gap in detectors
Nucleus kept intact
5 Diffractive dissociation of onium
6 Color dipole evolution: Soft-gluon 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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