### Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism

We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function G

^{aμ, bν}_{22}due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to G^{aμ, bν}_{22}coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τ_{Z}gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τ_{Z}>> 1/Qs and τ - τ_{Z}>> 1/Qs (with Qs the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ - τ_{Z}>> τ_{Z}>> 1/Qs we end up with a result very different from kinetic theory and consistent with amore »- Publication Date:

- Grant/Contract Number:
- SC0004286

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 3; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Research Org:
- The Ohio State Univ., Columbus, OH (United States)

- Sponsoring Org:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Perturbative QCD; Quark-Gluon Plasma

- OSTI Identifier:
- 1506450

```
Wu, Bin, and Kovchegov, Yuri V.
```*Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism*. United States: N. p.,
Web. doi:10.1007/jhep03(2018)158.

```
Wu, Bin, & Kovchegov, Yuri V.
```*Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism*. United States. doi:10.1007/jhep03(2018)158.

```
Wu, Bin, and Kovchegov, Yuri V. 2018.
"Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism". United States.
doi:10.1007/jhep03(2018)158. https://www.osti.gov/servlets/purl/1506450.
```

```
@article{osti_1506450,
```

title = {Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism},

author = {Wu, Bin and Kovchegov, Yuri V.},

abstractNote = {We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function Gaμ, bν22 due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to Gaμ, bν22 coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τZ gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τZ >> 1/Qs and τ - τZ >> 1/Qs (with Qs the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ - τZ >> τZ >> 1/Qs we end up with a result very different from kinetic theory and consistent with a picture of “free-streaming” particles. Due to the approximations made, our calculation is too coarse to indicate whether the region (i) or (ii) is the correct one: to resolve this controversy, we shall present a detailed diagrammatic calculation of the rescattering correction in the φ4 theory in the second paper of this duplex.},

doi = {10.1007/jhep03(2018)158},

journal = {Journal of High Energy Physics (Online)},

number = 3,

volume = 2018,

place = {United States},

year = {2018},

month = {3}

}