Dilepton production in statistical models

(1)

Dilepton production in statistical models

J. Manninen ¹

1

Frankfurt Institute for Advanced Studies

May 3, 2013

(2)

Outline

1 Introduction

2 Statistical hadronization model Freeze-out decay cocktail

3 Di-electron radiation

(3)

Introduction

Invariant mass spectrum of di-lepton pairs carry plenty of information

p+p well understood in terms of CFO cocktail

Deviations from cocktail in A+A: dynamics, energy loss, quarkonia melting, in-medium modication, QGP

Electromagnetic signals survive the evolution and are separable

→ oers windows to look into all stages of evolution

(4)

Statistical hadronization model

Statistical hadronization: counting the number of hadrons

Statistical Hadronization Model:

Statistical equilibrium:

a priori equal probabilities Boltzmann energy spectrum Resonant interactions

Include all resonances ≈ interactions

arXiv:0901.2909v2

All light (uds) hadron yields can be described in all collision systems Also the yields that are dicult to measure (η, ω, ρ ...)

Free parameters of the model:

T , γ and normalisation

(5)

Statistical hadronization model

Statistical model as an event generator

h N j i = (2J _j + 1)V ( 2π) ³

Z Z

γ _S ⁻ ⁿ

^s

e ^qp

²

⁺ ^m

²^j

^/ ^{T −µ·q}

^j

^/ ^T

− 1

× SF (m)d ³ pdm

Choose thermal parameters, calculate (once) hN j i as usual Sample for each event N _i :s from Poisson with hN _j i

Sample N _i hadrons (+momenta & masses) for each event Easy to implement geometrical / kinematic cuts

Easy to emulate clusters' dynamics

(6)

Statistical hadronization model Freeze-out decay cocktail

Cocktail at RHIC and LHC

Above SPS energies, mesons completely dominate the decay cocktail but baryons aect indirectly the cocktail composition (relative yields) + potentially strong in-medium modication of vector mesons

Hadron direct Dalitz other

π ⁰ - π ⁰ → γ e ⁺ e ⁻ -

η ⁰ - η ⁰ → γ e ⁺ e ⁻ η ⁰ → π ⁺ π ⁻ e ⁺ e ⁻ η ⁰ - η ⁰ → γ e ⁺ e ⁻ η ⁰ → π ⁺ π ⁻ e ⁺ e ⁻

ρ ⁰ ρ ⁰ → e ⁺ e ⁻ - -

ω ⁰ ω ⁰ → e ⁺ e ⁻ - ω ⁰ → π ⁰ e ⁺ e ⁻ φ ⁰ φ ⁰ → e ⁺ e ⁻ - φ ⁰ → η e ⁺ e ⁻ J/ψ J/ψ → e ⁺ e ⁻ J/ψ → γ e ⁺ e ⁻

ψ ⁰ ψ ⁰ → e ⁺ e ⁻ ψ ⁰ → γ e ⁺ e ⁻ -

D mesons - - D ^± → e ^± ν _e + X

B mesons - - B → e ^± ν _e + X

(7)

Mass dependent widths for the di-lepton sources

Example ρ ⁰ direct decay

Partial width : Γ ^{V →l}

⁺

^l

⁻

(m) = m ³ ₀

m ³ Γ ^{V →l}

⁺

^l

⁻

(m ₀ ) Total width : Γ ^tot (m) ≈ Γ ^ρ→ππ (m) = Γ ⁰ m ₀ ²

m ²

p

m ² − 4m ² π

q m ₀ ² − 4m ² π

₃

Branching fraction(ρ ⁰ → e ⁺ e ⁻ ) = Γ ^{V →l}

⁺

^l

⁻

( m)

Γ ^tot ( m)

(8)

But the clusters are moving

SHM does not tell anything about the clusters' distributions

Assumption: Clusters have Gaussian rapidity and p _T distributions Every p+p interaction produces always 2 equal mass clusters RHIC: t σ y and σ p

T

(means are set to zero)

LHC: σ _y and σ _p

_T

calculated from models

(9)

SHM transverse momentum spectra at 2.76 TeV

SHM: T=170MeV ; γ _S = 0.6 (p+p) γ _S = 0.95 (Pb+Pb) ; V 0 =70fm ³

In thermal equilibrium, energy is shared equally among available forms

⇒ In each event in the rest frame of the cluster M _clust = P

i E _i

Transverse momentum of the cluster in LAB frame is normally

distributed with h|~p _clust |i == M _clust and σ _p

_T

= M _clust / 2

(10)

Landau scaling in longitudinal direction

Projectile/Target dynamics spread the thermal distribution Random (Gaussian) boosts along z-axis σ ^y _clust ( √

s) = ln( √ s/2m p )

Boosts do not change the inv. mass of a correlated dilepton pair

(11)

Transverse momentum boosts and p T cuts

Light hadrons→ e ⁺ e ⁻

ALICE acceptance

(12)

Di-electron radiation

From p+p to A+A with Glauber model

Light (uds) hadron yields are scaled with N P

Heavy (cb) hadron yields are scaled with N _bin

Scaling works well at RHIC

May not be a good approximation at LHC

Model dependent extrapolation to A+A (especially semi-central)

(13)

Low invariant mass region at 2.76 TeV

Low invariant mass region is dominated by the freeze-out decay cocktail

T=170MeV ; γ _S = 0.6 ; V=2V ₀ γ _S = 0.95 ; V=380V ₀

(14)

SHM vs. PHSD at LHC 2.76 TeV

Cocktails agree well in p+p

ρ ⁰ enhanced due to nite length hadronic phase in PHSD

η 's involve dierent di-lepton channels

(15)

Statistical model vs. HSD transport calculations at RHIC

SHM agree very well with the hadronic transport model HSD at RHIC Au+Au

No evidence for prolonged hadronic radiation

(16)

Di-electron radiation from QGP in Pb+Pb 2.76 TeV

QGP dominates the M ∈ [M φ : M _J/ψ ]

over heavy avor radiation at LHC SHM insucient for A+A Di-electrons provide a unique window to

detect and study properties of QGP at LHC

(17)

Invariant mass spectrum in LMR in p+p √

s _NN =200 GeV

LMR can be understood well within the simple model

(18)

The PHENIX excess

(19)

Beyond standard cocktail contributions

X → K ¯ K → e ⁺ e ⁻ ν _e ν ¯ _e Hadron

f ₀ ( 980) K ⁺ K ⁻ K ⁰ K ¯ ⁰ -

f ₁ ( 1285) - - K ¯ Kπ

f 2 ( 1270) K ⁺ K ⁻ K ⁰ K ¯ ⁰ - f ₀ ⁰ ( 1350) K ⁺ K ⁻ K ⁰ K ¯ ⁰ - f ₁ ⁰ ( 1420) K ^∗+ K ⁻ + c.c K ^∗ ⁰ K ⁰ + c.c - f ₂ ⁰ ( 1525) K ⁺ K ⁻ K ⁰ K ¯ ⁰ - f ₀ ( 1500) K ⁺ K ⁻ K ⁰ K ¯ ⁰ - f ₁ (1510) K ^∗+ K ⁻ + c.c K ^∗ ⁰ K ⁰ + c.c - f 2 ( 1430) K ⁺ K ⁻ K ⁰ K ¯ ⁰ -

φ K ⁺ K ⁻ K ⁰ K ¯ ⁰ -

a ⁰ ₀ ( 980) K ⁺ K ⁻ K ⁰ K ¯ ⁰ -

K(892) ^± K ^± π ⁰ - -

K(892) ⁰ K ⁰ π ⁰ - -

(20)

Excited mesons and other exotic contributions EPJC71,1615

Exotic states may contribute to the PHENIX excess:

X → K ¯ K → e ⁺ e ⁻ ν _e ν ¯ _e

Upper limit estimate still below the PHENIX data

(21)

STAR measurement at 200 AGeV

STAR excess ≈ 2 with measured standard cocktail calculation Measurement of η, η', ρ ⁰ very challenging in A+A (QCD/pp ratios)

⇒ call for detailed dynamical modeling

(22)

ρ ⁰ broadening can explain the STAR excess PRC85,024910

Broadening of ρ ⁰ lifts the excess region in PHSD with factor of ≈ 2

Exotic states feed the same region PHENIX acceptance

(23)

Conclusion

SHM provides essentially parameter free calculational scheme to

study di-lepton radiation in p+p(¯p) collisions at ultra-relativistic

energies

(24)

back up slides

(25)

Correlated open heavy avour feed IMR

Heavy avor total cross sections Angular distribution of mothers Momentum distribution of mothers Decay form factors

Relative multiplicities (BRs)

Angular correlation of daughters

(26)

Extended SHM for open heavy avour production

Open heavy avor is assumed to be in relative chemical equilibrium Relative yields of 6 (18) lowest D (B) mesons evaluated within SHM

with T=170MeV ; γ _S ^hard =0.3 ; µ { B,S,Q} = 0

p+p: σ _¯ _cc ^tot (2.76TeV)=3.6mb (experimental data) (or γ _c ≈ 30) p+p: σ _¯ _bb ^tot (2.76TeV)=1/40 σ ^tot _¯ _cc (MC@ _s HQ)

Pb+Pb: σ _¯ _cc ^tot (2.76TeV)=N _bin σ _cc ^tot _¯ (2.76TeV) (also σ _bb ^tot _¯ )

LHCb ALICE T=170 MeV T=150 MeV

D∗+D0 2.20 ± 0.48 2.09 2.40 2.49

D0D+ 2.07 ± 0.37 2.08 2.37 2.25

D0Ds 7.67 ± 1.67 7.98 8.55

D∗+D+ 0.94 ± 0.22 1.00 0.99 0.90

D∗+Ds 3.48 ± 0.93 3.32 3.44

D+Ds 3.70 ± 0.84 3.37 3.81

(27)

Heavy avour rapidity distributions in p + p collisions

Probability to nd parton along the rapidity axis is dened by a triangle whose maximum is at y cm and goes to zero at

y = asinh(x ₁ √

s/2m _N ) & y = −asinh(x ₂ √

s/2m _N )

y _cm = atanh( ^x _x

¹₁

⁻ ₊ ^x _x

²₂

)

(28)

Di-electron radiation Heavy avour energy-loss and correlations

Heavy avour p T and energy loss PRC78,014904

pQCD: c and b quark cross sections & initial momentum

MC@ s HQ evolution: running coupling & improved infrared regulator HQ propagate in Heinz & Kolb hydro background

→ simultaneous R _AA and v ₂ @ RHIC (K _coll = 2 ; K _coll+rad = 0.6)

The model is in agreement with preliminary R AA of D mesons at LHC

(29)

Angular correlations of open heavy avor mesons at LHC (in)

p+p: π correlations among heavy avour mesons == hardest (up limit) central Pb+Pb: correlations are washed out == softest (low limit)

P corr ∼ R _AA ² < 10%

(30)

Dilepton production in statistical models