The photon spectrum in relativistic heavy ion collisions

QPT2017, Xi’an, July 21 – July 23 2017

Marco Ruggieri

UCAS, Beijing

Lanzhou University, Lanzhou

Plan of the talk

• Introduction: photons in RHICs

• Photons: neglecting the early stage

• Photons: production in the early stage

• Comparison with experimental data

• Conclusions

INTRODUCTION: PHOTONS IN HEAVY ION COLLISIONS

Photons in HICs Photons are produced during all the lifetime of the fireball in HICs. Leave the system indisturbed (low scattering rate): Bring information about the specific stage of the fireball lifetime that has produced them.

Pre-equilibrium stage •Prompt •Pre-eq quark-gluon scattering

Viscous qgp+hadron phase evolution •Thermal QGP •Thermal hadrons

Photons are good candidate for representing: •Thermometer of QGP [Heinz et al., PRL] •Clock of QGP [Liu et al., PRC79 (2009), Liu and Liu, PRC89 (2014)]

Some sources

Why photons from the medium? Why do we expect photons from the medium in RHICs, afterall?

(a)-(b)-(c)-(d) Different impact parameters

PHENIX

Why photons from the medium? Why do we expect photons from the medium in RHICs, afterall?

“Experimental” nucleon-nucleon contribution

Photon spectrum that we should measure if QGP does not produce photons. These photons would be produced solely by nucleon-nucleon scatterings during the overlap of the two colliding nuclei. No Glasma No QGP No Hadrons-from-QGP

Prompt photons g

PHENIX

Why photons from the medium? Why do we expect photons from the medium in RHICs, afterall?

(a)-(b)-(c)-(d) Different impact parameters

what we measure

what we would measure

Comparing

with

The difference has to come from the medium that is produced by the HICs, namely by the QGP and its byproducts.

Indication that QGP and its byproducts play a considerable role in photon production in RHICs

PHENIX

Photons from the medium

QGP photons •Pre-eq stage During Glasma-to-QGP evolution •Thermal QGP During thermal QGP evolution (i.e. before hadronization) Thermal hadronic photons During thermal hadron gas evolution

This is a very complicated problem

Pre-eq stage •Rate in pre-equilibrium phase is still under investigation [J. Berges et al., 1701.05064, McLerran et al., NPA 900 (2013), Kharzeev et al., 1206.1334]

•Photons from classical currents in the early stage [N. Tanji, PRD92 (2015)]

Thermal QGP •QGP is a strongly coupled system [C. Gale at al., 1409.4778, I. Iatrakis et al., 1609.07208]

As a matter of fact:

PHOTON PRODUCTION: NEGLECTING THE EARLY STAGE

Hydro + pQCD Fu-Ming Liu. et al., PRC79 (2009)

Emphasis on the medium and large pT spectrum, where pQCD rules.

Hydro: EPOS 3 Liu and Liu and Werner, 2015

Direct photon spectra well reproduced

Photons from holo-QCD Iatrakis et al., JHEP 1704 (2017)

VQCD2

VQCD1

GN

Electric conductivity

Lattice

Photon emission rate of a strongly coupled and thermalized QGP, computed by means of holographic QCD

SYM

PHOTON PRODUCTION IN THE EARLY STAGE

Initial condition, aka Glasma

Ba

z

x

y

Ea

System after the collision: Glasma vzc

vz-c

Transverse plane view of a nucleus

Fluctuating color charge density

Globally: color neutral Locally: color charge fluctuates x

y

CGC fields interact and form two sets of opposite effective color charges on the two nuclei

Before collision: Color Glass Condensate

B A

A B

IP-glasma+hydro J. F. Paquet et al., PRC93 (2016)

IP-Glasma initial condition B. Schencke et al., 2013

Pure gluon system CYM evolution

Hydro evolution Thermal photon emission

t 0.4 fm/c Switch to Hydrodynamics

No photon production

Glasma Instability The Glasma is affected by instabilities: •Classical instabilities: responsible for the turbulent behavior at late time •Quantum instabilities: responsible for early particle production Chiral anomaly offers one example of quantum instability:

ABJ anomaly Adler (1969), Bell and Jackiw (1969)

Warringa (2012)

The physics embedded in the ABJ anomaly equation is that even if at the initial time the system is dominated by classical gluon fields, the Glasma will eventually produce an axial current, hence dynamical quarks.

For homogeneous fields this instability can be related to the Schwinger effect [Warringa (2012)]:

Conduction current Movement of color charges

Displacement current Change of local dipole moment

Classical field equation

Already appeared in talks: X. G. Huang, D. Hou, F. Wang,……

Ez

Relativistic transport calculation M. R. et al., 1703.00116

Annihilation Compton

The idea: •Quarks and gluons are produced since the very beginning. •Quark-gluon scatterings produce photons. •Tune the rate to the AMY rate [Arnold, Moore and Yaffe (2001)]

Initial gluon field

QGP production Schwinger instability

See also Greco in this workshop

Photon spectrum: RHIC collisions

AFTm, with pre-eq.

w/out pre-eq.

AFTm: Abelian Flux Tube model, with early stage dynamics. Glauber: No early stage dynamics. System assumed to be thermalized at t=0.6 fm/c

AFTm and Glauber have: •Same multiplicity •Same eccentricity •Same QGP final spectrum Hence they correspond to the very same collision (system size, geometry, energy).

AFTm, early stage: AFTm, before thermalization time t=0.6 fm/c AFTm, late stage: AFTm, after thermalization time

M. R. et al., 1703.00116

In the pre-eq stage: Photons are produced by a bulk with large energy density Photon enhancement in agreement with Berges et al. (2017)

Comparison with BAMPS and PHSD

AFTm M. R. et al., 1703.00116 BAMPS Zhe Xu et al., 1612.05811 PHSD O. Linnyk et al., PRC92 (2015)

Main differences due to different quark production mechanism. BAMPS: initial state made of gluons; quarks are produced by inelastic QCD scatterings. AFTm: both quarks and gluons are produced during early evolution by the decay of gluon field.

QGP photons

Comparison with BAMPS and PHSD

Main differences due to different quark production mechanism. BAMPS: initial state made of gluons; quarks are produced by inelastic QCD scatterings. AFTm: both quarks and gluons are produced during early evolution by the decay of gluon field.

QGP photons

Uncertainty on the formation time of QGP

Direct photon spectra at RHIC

2) Hadrons gas from E. Bratkovskaya et al. [PRC92 (2015)]

1) Prompt photons from Paquet et al. [PRC93 (2016)]

Contributions added

A direct comparison with hydro has to be considered purely qualitative, because of: •Different early stage evolution (CYM versus Schwinger versus String breaking) •Different energy density profile (initial state fluctuations are important, Eskola et al. 2011)

Theoretical models agree fairly well with experimental data

Conclusions

• Photons are very interesting probes of the medium created in RHICs: because of their small scattering rate, they are measured as they are produced by the medium itself.

• No dark age for QGP if instability is considered

Pre-equilibrium q&g produce abundantly photons, comparable in number with those produced by equilibrated QGP during the whole fireball lifetime.

• Do we understand the photon spectrum in RHICs?

MaybeYes: taking into account the experimental data from PHENIX and STAR collaborations, theoretical calculations are able to reproduce them fairly well.

Open problem: photon v2

• Almost no theoretical calculation is able to reproduce the measured elliptic flow of photons.

Liu and Liu and Werner, 2015

Very nice result! But no other calculation based either on hydro or on transport is capable to reproduce these results. Why? More theoretical work is needed to understand the experimental data

about the photon v2. Delayed QGP? Non-flow? Magnetic field?

Io stimo più il trovar un vero, benché di cosa leggiera, che 'l disputar lungamente delle massime

questioni senza conseguir verità nissuna.

Thanks for your attention

Acknowledgements This work has been supported by:

CAS President International Fellowship Initiative (Grant No. 2015PM008) NSFC Projects (11135011 and 11575190)

Collaborators Vincenzo Greco Lucia Oliva G. X. Peng Salvatore Plumari Armando Puglisi Francesco Scardina

APPENDIX

Comparison with BMSS scenario

Berges et al., 1701.05064

Based on a kinetic description of the early time evolution, but: •Assuming a specific thermalization scenario [BMSS, Baier et al., Phys. Lett. B502 (2001)] •Large occupation gluon number, f1/as instead of a classical gluon field, in the early stage

For collisions at the LHC energy the relative contribution of the Glasma is smaller, because of the •Shorter lifetime of the early stage •Longer lifetime of the thermalized QGP

Hydro + pQCD: fluctuating ICs Eskola et al., 1210.3517 [nucl-th] and PRC83 (2011)

Fluctuating initial conditions affect the photon production rate:

Enhancement more important for: •Lower energy collisions •Less central collisions

Fluctuations enhance photon production

Field decay in 3+1D

Fields at midrapidity averaged on the transverse plane

Field decay timescale sets qgp formation time:

M. R. et al., in preparation

Timescale and quark abundance in agreement with: Lappi et al., PRL96 (2006) Scardina et al., PLB 724 (2013) M. R. et al., NPA 941 (2015)

QGP lifetime in fireball: •RHIC 5 fm/c •LHC 10 fm/c

QGP formation time in AFTm M. R. et al., private archive

Solid lines Chemical equilibrium for massless quarks and gluons

Au-Au 0-20% 200A GeV

Au-Au 20-40% 200A GeV

AFTm produces QGP: •Quickly •Almost equilibrated

QGP formation time in AFTm M. R. et al., private archive

Pb-Pb 0-20% 2.76A TeV

Pb-Pb 20-40% 2.76A TeV

How shiny is the early stage?

About 30% of QGP photons is produced in the first

0.6 fm/c

Lifetime of QGP in a RHIC fireball: approx 5-6 fm/c

In one/tenth of its lifetime, QGP produces 1/3 of the photons

it can produce in the full lifetime.

Early stage shines!

We can count how many photons come from the early stage, and compare with those produced during the full QGP lifetime.

In agreement with Berges et al., 1701.05064

Increasing impact parameter

Au-Au @ 200A GeV

Comparing RHIC and LHC M. R. et al., 1703.00116

We compare how many photons are produced by the AFTm relatively to Glauber:

photons AFTm

photons Glauber

LHC early stage is less shiny than the RHIC one, when both are compared with a thermal QGP.

Early stage lifetime •RHIC 0.6 fm/c •LHC 0.3 fm/c

Thermalized QGP lifetime •RHIC 5 fm/c •LHC 10 fm/c

Thermalized QGP at LHC gives more substantial contribution to photon production than the RHIC one.

Yield of pre-equilibrium

Direct photon spectra at LHC We can check how the pre-eq contribution affects photon spectrum:

The message Photons from pre-eq: •Early stage less important for collisions at LHC

2) Hadrons gas from E. Bratkovskaya et al. [PRC92 (2015)]

1) Prompt photons from Paquet et al. [PRC93 (2016)]

Contributions added

Hydro: does not consider photons in the early stage

QGP photon production rate M. R. et al., 1703.00116

Annihilation Compton

NLO processes give important contribution to the rate because of collinear singularities [Arnold, Moore and Yaffe (2001)]: AMY rate

We use a model function, F(T), tuned in order to reproduce the AMY rate at a given temperaure:

In the collision integral:

QGP photon production rate M. R. et al., 1703.00116

Annihilation Compton

AMY: Arnold, Moore and Yaffe, 2001

In the collision integral:

Fair agreement between AMY rate and the one implemented in our collision integral.

Enhanced cross sections

Transport gauged to hydro

Transport Hydro Description in terms of

parton distribution function Dynamical evolution governed

by macroscopic quantities

“bridge”

(.) Collision integral is gauged in each cell This assures that the fluid dissipates according to the desired value of h/s. (.) Microscopic details are not important The specific microscopic process producing h/s is not relevant, only macroscopic quantities are, in analogy with hydrodynamics.

Total Cross section is computed in each configuration space cell according to Chapman-Enskog equation to give the wished value of h/s.

M. R. et al., Phys.Lett. B727 (2013)

Photon spectrum: LHC collisions

AFTm, with pre-eq.

w/out pre-eq.

AFTm: Abelian Flux Tube model, with early stage dynamics. Glauber: No early stage dynamics. System thermalized at t=0.3 fm/c

AFTm and Glauber have: •Same multiplicity •Same eccentricity •Same QGP final spectrum Hence they correspond to the very same collision (system size, geometry, energy).

M. R. et al., 1703.00116

AFTm, early stage: AFTm, before thermalization time t=0.6 fm/c AFTm, late stage: AFTm, after thermalization time

The initial condition

Initial chromo-electric field: smooth in transverse plane

b=7.5 fm Ez

What we do We prepare a fireball such that: Has some classical color field dynamics Matches Glauber fireball at 0.6 fm/c: Has a pre-equil. evolution from t=0+

What we do not Prepare a more realistic initial condition (IP-Glasma, Schenke et al. 2013)

Eccentricity Multiplicity

Although a bit far from Glasma, picture arising agrees qualitatively (and to some extent quantitatively) with results obtained from Glasma+CYM when phsyical quantities are computed. Florkowski and Ryblewski, PRD 88 (2013)

M. R. et al., PRC 92 (2015)

Boltzmann equation for QGP In order to study the temporal evolution of the fireball we solve the Boltzmann equation for the distribution function f:

Field interaction Collision integral

Field interaction: change of f due to interactions of the QGP with a field (e.g. color-electric field).

Collision integral: change of f due to collision processes in the phase space volume centered at (x,p). Responsible for deviations from ideal hydro (non vanishing h/s).

In the collision integral: qqqq, qgqg, qgqg, gggg,…………

Boltzmann equation for QGP In order to permit particle creation from the vacuum we need to add a source term to the rhs of the Boltzmann equation:

Invariant source term: change of f due to particle creation in the volume at (x,p).

Invariant source term

Florkowski and Ryblewski, PRD 88 (2013) M. R. et al., PRC 92 (2015)

Invariant source term Field interaction

Field interaction

Link QGP distribution function and classical color field evolutions

We have to solve self-consistently Boltzmann and field equations