1E.C. AschenauerStony Brook Student Seminar, February 2010

Stony Brook Student Seminar, February 2010 1

The new kid on the blockThe Electron Ion Collider

E.C. Aschenauer


The Standard Model

E.C. Aschenauer

QED: Theory of the Electromagnetic InteractionQCD: Theory of the Strong Interaction


A reminder of Quantum Electro-Dynamics (QED)

E.C. Aschenauer

Theory of electromagnetic interactions Exchange particles (photons) do not carry electric

charge Flux is not confined: V(r) ~ 1/r, F(r) ~ 1/r2

Coupling constant (α): Interaction StrengthIn QED: αem = 1/137

√α √α

Feynman Diagram: e+e- annihilation

Vem (r) =−q1q2

4πε0r=αem

r

http://www.americanscientist.org/articles/00articles/dzierbacap7.html


Vs (r) =43α s

r+ kr

Quantum Chromo-Dynamics (QCD) - 1973

E.C. Aschenauer

Theory of strong (nuclear) interactions Three colour charges: red, green and blue Exchange particles (gluons) carry colour charge and

can self-interact Flux is confined: V(r) ~ r, F(r) ~ constant

q

qq

qg

√α√α

αs = strong coupling constant ≈ 0.3

long range force ~ r

gluons can self-interact - more vertices are allowed

~1/r at short range



Features of Quantum Chromo-Dynamics

E.C. Aschenauer

Confinement

At large distances, the effective coupling between quarks is large, resulting in confinement (V(r) ~ r)

Free quarks are not observed in nature

Asymptotic freedom

At short distances, the effective coupling between quarks decreases logarithmically

Under such conditions, partons appear to be quasi-free

0.2 fm 0.02 fm 0.002 fm


QED vs QCD

E.C. Aschenauer

Potentials:

long range aspect of Vs(r) leads to quark confinement and the existence of nucelons

QED QCD

Charges electric (2) colour (3)

gauge bosons γ g (8)

charged? no yes

coupling strength

αem = e2/4π ≈ 1/137 αs ≈ 0.3

Vs (r) =43α s

r+ krVem (r) =−

q1q2

4πε0r=αem

r



Stony Brook Student Seminar, February 2010

Deep Inelastic Scattering

E.C. Aschenaue

r

7

( , )E k( ', ')E k

q 2 2 2( ')Q q k k 'E E 2

2

Qx

Mv

hEz

Important kinematic variables:

cross section:

DF FF

( ) )( () ~ hf f

hf

f

d zdx Dz q

2tp

Photon:Photon:

Hadron:Hadron:

Quark:Quark:

The structure of the proton – simple view

E.C. Aschenuer


Quark splitsinto gluonsplitsinto quarks …

Increasing resolution (large angle scattering = large Q2)

Increasing resolution: we see “small” partons How do the quarks behave at low-x

E.C. Aschenaue

r


Deep Inelastic Scattering

( , )E k( ', ')E k

q

Important kinematic variables:

cross section:

DF FF2

~'

Ld

d dEW

1 2 1 22( )

p p i ig q s q p qsF gs pF gW q

ε ε

1 2 3 4

1 1 1( ) ( ) ( )

6 2 2r s t u s u s tb b b b

Spin 1

'E E

hEz

Photon:

Hadron:

Quark:

2tp

Collider:

Q2 =−q2 =−(k−k')2 =2EeEe'(1+cosΘe)

x =Q2

sy


“Structure Function” & quark densities

E.C. Aschenaue

r

11

Strong increase of sea quarks towards low x

Density increases with Q2

more partons by magnified view

F2(x)=e2x(q(x)+q(x))quark density

Dynamic creation of quarks at low x


d2empNC

dxdQ2 =2παem2 Y+

xQ4 (F2 −y2Y+

FL ±Y−Y+

xF3)

Measure Glue through DIS

E.C. Aschenauer

small x

large x

q(x, Q2 )+ q(x,Q2 ) g(x,Q2 ) q(x, Q2 )−q(x,Q2 )

Observation of large scaling violations

Gluon density dominates


What do we know till know

E.C. Aschenauer

F2=C(Q2)x-lQ2 = 1GeV 0.2fmEM proton radius: 0.9fm

gp

Transition, Why, How?

x<0.01 HERA: =−ln ∂F2 / ∂ ln x

Does the rise of F2 set in at the same Q2 for nuclei?

eRHIC: =−ln∂F2 / ∂ lnx


d2empNC

dxdQ2 =2παem2 Y+

xQ4 (F2 −y2Y+

FL ±Y−Y+

xF3)

FL: measures glue directly

FL ~ αs G(x,Q2) requires √s scan Q2/xs = y

⇒ G(x,Q2) with great precision

E.C. Aschenauer


Parton Saturation

E.C. Aschenauer

at small x linear evolution gives strongly rising g(x) BK/JIMWLK non-linear evolution

includes recombination effects saturation

Dynamically generated scale Saturation Scale: Q2

s(x) Increases with energy or decreasing x

Scale with Q2/Q2s(x) instead of x and Q2

separately as~1 as << 1 Question:What is the relation between saturationand the soft regime? Confinement?

HERA (ep):

Despite high energy range: F2, Gp(x, Q2) only outside the

saturation regimeRegime where non-linear QCD

(saturation phenomena) matter

(Q < Qs) not reached, but close

Only way in ep is to increase √s

EIC (eA): Instead extending x, Q reach

increase Qs

Pocket formula for nuclei

Remember: Q2 > Qs2 ⇒ α s =α s(Q

2 )

Q2 < Qs2 ⇒ α s =α s(Qs

2 )

Qs2 (x, A) ~ Q0

2 A

X⎛⎝⎜

⎞⎠⎟

1/3


The Nuclear Enhancement Factor

E.C. Aschenauer

Enhancing Saturation effects: Probes interact over distances L ~ (2mnx)-1

For probes where L > 2RA (~ A1/3), cannot distinguish between nucleons in the front or back of of of the nucleus.

Probe interacts coherently with all nucleons. Probes with transverse resolution 1/Q2 (<< Λ2

QCD) ~ 1 fm2 will see large colour charge fluctuations.

This kick experienced in a random walk is the resolution scale.

Simple geometric considerations lead to:

Nuclear Enhancement Factor:

Enhancement of QS with A: ⇒ non-linear QCD regime reached at significantly lower

energy in e+A than in e+p


Probing Saturation regime

HERA (ep) energy range higher G(x,Q2) very limited reach of the saturation regime

eRHIC (eA) will probe deeply into the saturation region

E.C. Aschenauer


d2empNC

dxdQ2 =2παem2 Y+

xQ4 (F2 −y2Y+

FL ±Y−Y+

xF3)

F2: for Nuclei

E.C. Aschenauer

Assumptions: 10GeV x 100GeV/n

√s=63GeV Ldt = 4/A fb-1

equiv to 3.8 1033 cm-2s-1

T=4weeks; DC:50% Detector: 100% efficient

Q2 up to kin. limit sx Statistical errors only

Note: L~1/A


Diffractive physics: ep vs eA

E.C. Aschenauer

xIP = mom. fraction of pomeron w.r.t. hadron

HERA/ep: ~20% of all events are hard diffractive Diffractive cross-section σdiff/σtot in e+A ? Predictions: ~25-40%? Diffractive structure functions

FLD for nuclei and p extremely sensitive

Exclusive Diffractive vector meson production: dσ/dt ~ [xG(x,Q2)]2 !!

Distinguish between linear evolution and saturation models

?

Curves: Kugeratski, Goncalves, Navarra, EPJ C46, 413

ddt t=0

(γ * A→ MxA) ~α 2 GA(x,Q2 )⎡⎣ ⎤⎦

2

DIS: Diffraction:


How to measure coherent diffraction in e+A ?

Beam angular divergence limits smallest outgoing Qmin for p/A that can be measured

Can measure the nucleus if it is separated from the beam in Si (Roman Pot) “beamline” detectors pTmin ~ pAθmin

For beam energies = 100 GeV/n and θmin = 0.08 mrad:

These are large momentum kicks, much greater than the binding energy (~8MeV) Therefore, for large A, coherently

diffractive nucleus cannot be separated from beamline without breaking up

E.C. Aschenauer

species (A)

pTmin (GeV/c)

d (2) 0.02Si (28) 0.22Cu (64) 0.51In (115) 0.92Au (197) 1.58U (238) 1.90

Need to rely on rapidity gap

method simulations look good high eff. high purity

possible with gap alone ~1% contamination ~80% efficiency

depends critical on detector hermeticity

improve further by veto on breakup of nuclei (DIS) Very critical

mandatory to detect nuclear fragments from breakup

n: Zero-Degree calorimeter p, Afrag: Forward

Spectrometer New idea: Use U instead of

AU


Measure the Gluon Form Factor

E.C. Aschenauer

RA = 1.2A1/3fmElastic scattering on full nucleus long wavelength gluons (small t)

Expectation for 1M J/y

Requirement:Momentum resolution < 10MeVgreat t resolutionNeed to detect nuclei break-upproductsdetect e’ in FED

Basic Idea:Studying diffractive exclusive J/y productionat Q2~0 Ideal Probe:large photo-production cross sectiont can be derived from e,e’ and J/ y 4-momentum


Important to understand hadron structure: Spin

E.C. Aschenauer

SqDq

DG

Lg

SqLq

dq1Tf

SqDq

DG

Lg

SqLq dq1Tf

Is the proton spinning like this?

“Helicity sum rule”

12h= P, 12 |J QCD

z |P, 12 = 12q

∑ Sqz+Sg

z+ Lqz

q∑ +Lg

z

total u+d+squark spin

angular momentum

gluonspin Where do we go with

solving the “spin puzzle” ?

N. BohrW. Pauli


How to measure Quark Polarizations

E.C. Aschenaue

r

27

3/ 2 (~ )q x

rSγ* +

rSN =

32

N qSS

1/ 2 (~ )q x

rSγ* +

rSN =

12

N qSS

Virtual photon g* can only couple to quarks of opposite helicity

Select q+(x) or q-(x) by changing the orientation of target nucleon spin or helicity of incident lepton beam

', ','||

', '

1 e h e he h

B Te h e h

N L N LA

P P N L N L

', ',', 1 / 2 3 / 2

|| ', ',1 / 2 3 / 2

~e h e h

e he h e hA

Asymmetry definition:qq q

inclusive DIS: only e’ info used semi-inclusive DIS: e’+h info used


How to measure DS and DG

E.C. Aschenauer

DG: Indirect from scaling violation

g1@eRHIC

Integrated Lumi: 5fb-1


Polarised quark distributions

E.C. Aschenaue

r

29

Correlation between detected hadron and struck qf

“Flavor – Separation”Inclusive DIS:

Semi-inclusive DIS:

( )u d u d s s

( , , , , , )u d u d s s

A PQdddddddddddddddddddddddddddd

Extract Dq by solving:

1, 1, 1, 1, 1,( ( ), ( ), ( ), ( ), ( ))Kp p d d dA A x A x A x A x A xπ π

dddddddddddddd( , , , , , 0)

u d u d s sQ

u d su d s

dddddddddddddd

In LO-QCD:

A1h(x,Q2 , z) =

1/2h −3/2

h

1/2h + 3/2

h~C

eq2q(x,Q2 )Dq

h(z,Q2 )

eq'2 q'(x,Q2 )Dq'

h (z,Q2 )q'∑q∑ q(x,Q2 )

q(x,Q2 )2( , , )h

qP x Q z MC

DF

FF

( ) )( () ~h

f

f

f

h

fq xd z d D z


Measured Asymmetries

E.C. Aschenaue

r

30

Proton

Deuterium

1 ~ 0 ( )KA K us

statistics sufficient for 5 parameter fit

( , , , , , 0)u d u d s s

Qu d su d s

dddddddddddddd


Polarized Quark Densities

E.C. Aschenaue

r

31

good agreement with NLO-QCDPolarised opposite to proton spin

Du(x) > 0

First complete separation of pol. PDFs without assumption on sea polarization

Polarised parallel to proton spin

Dd(x) < 0

Du(x), Dd(x) ~ 0

No indication for Ds(x) < 0

In measured range (0.023 – 0.6)

0.002 0.043u 0.054 0.035d 0.028 0.034s


Polarized Quark Distributions

E.C. Aschenauer

DSSV: arXiv:0904.3821

eRHIC: 10GeV@250GeV at 9 fb-1

X

0.2

-0.8

0.

0.8DSSV: Global Analysis of world data


The Gluon Polarization

E.C. Aschenauer

28

x

RHICrange

0.05· x · 0.2can be extended a bit by changing

√s to 64GeV & 500GeV

small-x0.001< x < 0.05

large-xx > 0.2

Dg(x) very small at medium x best fit has a node at x ~ 0.1 huge uncertainties at small x

Dg(x) small !?g(x) dx

0.

1

∫ = −0.084@10GeV 2Need to enlarge x-range

*g p D0 + X


Beyond form factors and quark distributions

E.C. Aschenauer

Generalized Parton Distributions

Proton form factors, transverse charge & current densities

Structure functions,quark longitudinalmomentum & helicity distributions

X. Ji, D. Mueller, A. Radyushkin (1994-1997)

Correlated quark momentum and helicity distributions in transverse space - GPDs


How to access GPDs?

E.C. Aschenauer

30

quantum number of final state selects different GPDs: theoretically very clean DVCS (g): H, E, H, E VM ( , , ): r w f H E info on quark flavors PS mesons ( , )p h : H E ~

~ ~

~

ρ0 2u+d, 9g/4

ω 2u-d, 3g/4f s, g

ρ+ u-d

J/ψ g

p0 2Du+Ddh 2Du-Dd

J

qz =

12

xdx H q + E q( )−1

1

⎛⎝

⎞⎠t→ 0

J q

z =12

qq∑ + Lq

z

q∑

12=J q

z + J gz =

12

qq∑ + Lq

z

q∑ + J g

z


Proton Tomography

[M. Burkardt, M. Diehl 2002]

FT (GPD) : momentum space impact parameter space:

probing partons with specified long. momentum @transverse position b

T

polarized nucleon:

[x=0]

from lattice

d-quarku-quark

E.C. Aschenauer


DVCS @ eRHIC

E.C. Aschenauer

dominated by gluon contributions Need wide x and Q2 range to extract GPDs Need sufficient luminosity to bin in multi-dimensions


EIC Scope - QCD Factory

e-

e+

p

Unpolarized andpolarized leptons4-20 (30) GeV

Polarized light ions (He3) 215 GeV/u

Light ions (d,Si,Cu)Heavy ions (Au,U)50-100 (130) GeV/u

Polarized protons50-250 (325) GeV

Electron accelerator RHIC

70% e- beam polarization goalpolarized positrons?

Center mass energy range: √s=28-200 GeV; L~100xHera

e-

Mission: Studying the Physics of Strong Color Fields

E.C. Aschenauer


The Relativistic Heavy-Ion Collider @ BNL

RHICBRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

v = 0.99995⋅c = 186,000 miles/sec

E.C. Aschenauer


EIC: one solution eRHIC @ BNL

E.C. Aschenauer

STAR

PH

EN

IX

2 x 200 m SRF linac4 (5) GeV per pass5 (4) passes

Polarized e-gun

Beamdump

4 to 5 vertically separatedrecirculating passes

Cohere

nt

e-c

oole

r

5 mm

5 mm

5 mm

5 mm

20 GeV e-beam

16 GeV e-beam

12 GeV e-beam

8 GeV e-beam

Com

mon

vacu

um

ch

am

ber

Gap 5 mm total0.3 T for 30 GeV

eRHICdetector

MeRH

IC

dete

ctor

10-20 GeV e x 325 GeV p 130 GeV/u Au

possibility of 30 GeV @low current operation

MeRHICeRHIC with

CeC

p (A) e p (A) e

Energy, GeV250 (100

)4

325 (125)

20 <30

>

Number of bunches

111 166

Bunch intensity (u) , 1011 2.0

0.31

2.0 (3)

0.24

Bunch charge, nC

32 5 32 4

Beam current, mA

320 50 42050 <10

>

Normalized emittance, 1e-6 m, 95% for p / rms for e

15 73 1.2 25

Polarization, % 70 80 70 80

rms bunch length, cm

20 0.2 4.9 0.2

β*, cm 50 50 25 25

Luminosity, x 1033, cm-2s-1

0.1 -> 1 with CeC

2.8


A typical High Energy Detector

E.C. Aschenauer

Particle types: neutrinos (missing energy) muons m hadrons , , p K p

quarks, gluons jets electrons, photons, p0

charged particles

beam pipeRough Classification track detectors for charged particles

“massless” detectors gas detectors solid state detectors

magnet coil(solenoid, field || beam axis)

Calorimeter for energy measurement electromagnetic

high Z material (Pb-glas) absorber (mostly Fe)

flux return yoke + active material

hadronic heavy medium (Fe, Cu, U)

+ active material


Detector Requirements from Physics

E.C. Aschenauer

ep-physics the same detector needs to cover inclusive (ep -> e’X), semi-

inclusive (ep -> e’hadron(s)X) and exclusive (ep -> e’p ) preactions

large acceptance absolutely crucial (both mid and forward-rapidity) particle identification is crucial

e, p, K, p, n over wide momentum range and scattering angleexcellent secondary vertex resolution (charm)

particle detection to very low scattering angle around 1o in e and p/A direction

in contradiction to strong focusing quads close to IP small systematic uncertainty (~1%/~3%) for e/p polarization

measurements very small systematic uncertainty (~1%) for luminosity

measurement eA-physics

requirements very similar to epchallenge to tag the struck nucleus in exclusive and diffractive reactions.difference in occupancy must be taken into account


First ideas for a detector concept

E.C. Aschenauer

Dipol3Tm

Dipol3Tm

Solenoid (4T)

ZDC

FPD

FED// //

Dipoles needed to have good forward momentum resolution Solenoid no magnetic field @ r ~ 0

DIRC, RICH hadron identification p, K, p high-threshold Cerenkov fast trigger for scattered lepton radiation length very critical low lepton energies


MeRHIC Detector in Geant-3

E.C. Aschenauer

Stony Brook Student Seminar, February 2010 40E.C. Aschenauer

and Summary

EIC many avenues for

further important

measurements and

theoretical developments

we have just explored the tip of the iceberg

you are here

Lq,g

DsDg

Dutot , Dd

tot

spin sum rule

Knowledge about

Gluons in p /A

Come and join us

Stony Brook Student Seminar, February 2010 41E.C. Aschenauer

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1E.C. AschenauerStony Brook Student Seminar, February 2010