Nuclear Many-Body Physics at High Energies:

from Fixed Target Experiments to the EIC

Ivan Vitev

T-2, Los Alamos National Laboratory

2

Motivation• Theoretical underpinnings of nuclear effects at high energy • Importance and experimental opportunities

Initial-state interactions and cold nuclear matter energy loss• A formalism to address many-body scattering in nuclear matter• Radiative energy loss in large nuclei: important regimes• Applications to DY, shortest radiation length in nature

Final-state interactions and medium induced photons• Induced photons, coherence effects, differences from gluons• Numerical results, smallness of the gluon bremsstrahlung• Other final-state effects. Jets in SDIS?

Conclusions

Outline of the Talk

I. The Origin of Nuclear Effects

A number of cold nuclear matter effects observed as modification of the experimentally measured inclusive cross sections

I.V., PLB (2003)

ασσ ANA =

B. Kopeliovich et al, PRC (2005)

J. Qiu, IV, PRL (2004)

Two schools of thought: parameterize (universal), compute (process-dependent).

SDIS

⇒

A

Dynamical Generation of Nuclear Effects

DY

An example illustrating the importance of these effects is the forward rapidity π0 suppression at RHIC

xF =x1 −x2 ≈x1

Type Effect

IS broadening Cronin

Coherent FS Shadowing

IS E-loss Forward xF suppression

FS E-loss Quenching of jets, inclusive spectra

Focused on soft multiplicities and the incoherent regime

II. Parton Energy Loss (Early Work)

ΔErad =c2EL

ωdNg

dωd2k⊥=

CRαs

π 2q⊥2

k⊥2 (k⊥ −q⊥ )

2

G. Bertsch et al, PRD (1982)

Essential physics is the transverse dynamics of the gluon and the color excitation of the quark

M 0 +M1

2=M0

2+ReM1

*M0 + 2 M1

2

“Medium induced” part

Challenges (2 of them)

An operator approach to multiple scattering in QCD

Coherence phases(LPM effect)

Color current propagators

( ) ( )( ) ( )( ) ( )( )( )

1

... ...2 1

2 222 2 2

1 1

1... 1... ...

10

1

- cos c

( )( )

2 s

1

o

njj i el

n ng g R s

n n

L zi

g ii i

e

n m n

i

m

m m

k kk n

n

n

l

mn

i

kk k

d z

z

d dd q q

N dN Ck k

dk d k dk d k d q

B z zC

σδ

σ

ω ω

α

π λ= +

∞ ∞+ +

+ += =

=

=⊥ ⊥

=

Δ

=

−

+

⎛ ⎞−⎜ ⎟

⎝ ⎠

⎡ ⎤= = ⎢ ⎥

⎢ ⎥⎣

Δ

Δ∑

⎦

⎡ ⎤× ⋅⎢ Δ⎣

−⎦

∫∑ ∑

∑ ∑

∫∏

∑ ⎥

Number of scatteringsMomentum transfers

( )

1

1...1

1 1

1 1

1 1

1 1

......2

......

....

†

.

†

.

ˆ

n

ni in

n

n

n

n

ng i i

i i

i ii i

i ii i

D D V V

dNk Tr A A

dk d k

A A

A AR

−

−

−

−

++

⊥

∝

= +

=

+

∑

∞ ∞∞

21( )

2 el qσ δ ⊥− 21( )

2 el qσ δ ⊥−2

eld

d q

σ

⊥

M. Gyulassy et al., NPB (2001)

Very general algebraic approach

7

• Predictions of this formalism tested vsparticle momentum, C.M. energy, centrality

• Nuclear modification factor

TNN

TAA

collTAA dpdd

dpdd

NpR

ησηση

//1

),( 2

2

⋅><

=

Leading Particle Quenching

IV, (2005)

A Note on PQCD Energy Loss Regimes in

CNM

ωdNsoft

dωd2k⊥~

q⊥2

k⊥2 (k⊥ −q⊥ )

2

ωdNhard

dωd2k⊥~1k⊥2

I.V., PRC (2007)

IS and FS E-losses are different

- Initial vs Final BC

CNM energy loss for quarks can be O(5%-10%) in a large (W, Au, Pb…) nucleus

For E<100 GeV IS and FS E-loss are quite similar. DY and SDIS - complementary

DY and the Determination of the Shortest Radiation Length

in Nature

B.W. Zhang, IV, B. Neufeld, in progress

At tree level for DY shadowing from coherent final-state scattering does not exist. Ideal to determine IS E-loss

One expects better accuracy in the large xF region at Femilab E906

RDY =B. dσ pA / dQ2dxF

A. dσ pB / dQ2dxF

X.N. Wang et al. PRL (2002)

Design parameters of EIC - center of mass energies: 20 GeV - 100 GeV

Reasonable reach for jets (high enough ET)

A. Accardi, NPA (2003)

CNM Quenching, Absorption, e.c.t.

Df2f

hff

2f

Af2f

hff

2f

D

h2

DIS

A

h2

DISM

(x)qΣe(z)(x)DqΣe

(x)qΣe(z)(x)DqΣe

dzdνσd

σ1

dzdνσd

σ1

υ)(z,R

Process - observable

Jet Cross Section and Jet Shapes

Direct access to the characteristics of the in-medium parton interactions

Phenomenological approaches focus exclusively on 1 point

IV, S. Wicks, B.-W. Zhang, JHEP (2008)

Jets in A+A at RHIC RAA for jet cross sections with CNM and final-state parton

energy loss effect are calculated for different R CNM effect contribute ~½ RAA jet at the high ET at RHIC

RAA – CNM effects, QGP quenching and R dependence in p+p

σ(R1)/σ(R2) in p+p – R dependence in p+p

σ(R1)/σ(R2) in A+A – QGP quenching and R dependence in p+p

IV, B.W. Zhang, PRL (2010)

Definition of the jet modification: includes additional 2D information

III. Motivation to Study Photon Emission

Strong interest, a number of interesting effects predicted: strong enhancement of photon production, negative photon ellipic flow, …

Induced photons B. Zakharov, JETP Lett.

(2004)

Sadly, most have not been observed

R. Fries et al., PRL (2003)

E

Rate

Hadron Gas Thermal Tf

QGP Thermal Ti

“Pre-Equilibrium”?

Jet Re-interaction √(Tix√s)S. Turbide et al., PRC (2005)

Photon vs Gluon Emission

Theoretical approaches developed to describe gluon emission cannot be directly generalized to photon radiation

Gluon radiative amplitude for single scattering of a fast on-shell quark:

Without three-gluon vertex, is photon emission a simple exercise ?

Derivation of Photon Emission

Virtual double scattering corrections vanish

Scattering in the medium: Yukawa

Photon Emission: Analytic Results

Two limits; interference is important Leading contribution is L-dependence, withnon-linear corrections with L Number of interactions <n> = 32/ qL

IV, B.W. Zhang, PLB (2008)

Photon Emission: Incoherent Limit

Recover the known incoherent results Very collimated emission in the direction of

the incoming and outgoing partons

Known double log result for photon number

θ =1

E2

μ 2L

λξ

J.Qiu ,IV, PLB (2003)

θ

θ :

1 GeV

E [GeV ]

Photon Emission: Numerical Results

In the QGP In a cold nucleus. Parameters constrained by shadowing, Cronin, forward Y (xF) suppression

(Im)Probablity for Medium-Induced Photon Observation

IV, B.W. Zhang, PLB (2008)

Suppression of photon bremsstrahlung is critical to explain RHIC data

RAA =

. dσ AA / dpTdyNbin. dσ

pp / dTdy

Possibly Interesting Features But …

By the same token it is unlikely that medium-induced photons will be a readily observable in e+A

Certainly a full calculation is needed to compare to fragmentation photons in SDIS

Suppression of the spectrum implies suppression of the angular distribution

IV, PLB (2005)ω =1 GeV ω =3 GeV ω =10 GeVIntensityscale

N.B. The calculation is for coherent FS gluon emission. Expect similar pattern for γ

ΔE rad LPM suppressed

dI rad

dω(ω)

dI rad

(dω)dr(r) → →

Summary Many-body nuclear effects at high energies can be

understood in terms of soft partonic interactions between the projectile and the target: Cronin, shadowing, IS and FS energy loss (forward rapidity, xF suppression)

Phenomenologically, these give consistent picture of cold nuclear matter (m.f.p.,momentum transfer)

Relation between IS and FS energy loss can be explored in DY and SDIS processes. For EIC the physics of jets should become accessible. These provide much more information in comparison to leading particles (already used at RHIC)

Medium induced photons from FSI derived. BH and LPM regime compared –strong suppression in the production rate, broad conical distribution.

Unfortunately the induced rate is small (confirmed at RHIC). Studies will be difficult (if at all possible). Quantitative studies needed

“In the abode of light are the origins of truth, and from the source of darkness are the origins of error.”

Thank you!

From the Dead Sea Scrolls

ALL credit for this witty slide goes tomy collaborator Ben-Wei Zhang