From HERA to eRHICA. Caldwell, Max-Planck-Institut f. Physik

eRHIC vs. Other DIS Facilities

eRHIC

DIS

eRHIC would cover a kinematic range which has already been measured …

• Wide range of A

• High luminosity

• Polarized beams

• Full acceptance det

• 3D structure of

nuclear matter

• Spin structure

• QCD dynamics in

much greater detail

Special eRHIC feature

Detector feature

Physics

The physics program is broad and extremely interesting

Optimized detector design will make a big difference in the physics which can be accessed. Towards Bjorken’s FAD.

See:I.~Abt, A.~Caldwell, X.~Liu and J.~Sutiak,arXiv:hep-ex/0407053

Selected HERA results

There are many physics topics addressed by HERA which I will not cover:

• electroweak• searches for BSM physics• precision tests of QCD (S, heavy quark production, jet rates, …)• all the results from HERMES and HERA-B

Instead, I will focus on the unique aspects of HERA collider physics, which is the small-x physics, and also discuss the high-x end. We will see what eRHIC could add

Cross sections measured over wide kinematic range ! Precise determination of PDFs in context of NLO DGLAP.

Inclusive cross sections

Blue: total error < 4% Red: total error > 4%

Dominated by statistical uncertainty

Dominated by syst uncertainty

ZEUS 1997 F2 measurement

y=1

y=0.

01

Structure function data used to parametrize parton densities in proton. Impressive precision achieved.

From Pumplin, DIS05

There are signs that DGLAP (Q2

evolution) may be in trouble at small x (negative gluons, high 2 for fits).

How well do we understand the small-x physics ? So far, no theory which predicts the x-dependence of cross sections (PDFs). Guided by data.

But all is not well …

High y cross sections

The data can be fit consistently with NLO DGLAP by H1 assuming no gluon saturation. The turn-over is due the negative contribution from FL. MRST, CTEQ have trouble fitting the H1 low Q2 data consistently at NLO DGLAP.

Note the turn-over of the cross section with decreasing x at small x in the H1 data.

€

σ r =2πα 2Y+

xQ4

⎛

⎝ ⎜

⎞

⎠ ⎟

−1d2σ

dxdQ2 = F2(x,Q2) −y2

Y+

FL (x,Q2) ⎡

⎣ ⎢

⎤

⎦ ⎥

In QPM: hadron is made up of quarks with zero PT

σL=0

€

FL =Q2

4π 2α

⎛

⎝ ⎜

⎞

⎠ ⎟σ L

FL =α S4πx2 dz

z3

16

3F2 + 8 eq

2(1− x z∑ )zg ⎡ ⎣ ⎢

⎤ ⎦ ⎥

x

1∫

Expected to dominate at small-x

QCD radiation introduces quark PT, σL0

LO pQCD

Helicity conservation

We will make an FL measurement at HERA in 2007 …

Measuring FL

€

σ r =2πα 2Y+

xQ4

⎛

⎝ ⎜

⎞

⎠ ⎟

−1d2σ

dxdQ2 = F2(x,Q2) −y2

Y+

FL (x,Q2) ⎡

⎣ ⎢

⎤

⎦ ⎥

Small Q2, ignore F3

For best sensitivity, maximize lever arm (y-range)

€

FL (x,Q2) =σ r (x,Q

2,y1) −σ r (x,Q2,y2)

f (y2) − f (y1)

f (y) = y2

Y+

y2/Y+

σr

10

F2

F2-FL

Expected precision on FL HERA:

eRHIC cannot push the small-x limit, but should provide much more accurate FL measurements. Could be crucial in understanding the physics of gluons.

FL: eRHIC vs. Other DIS Facilities

eRHIC

DIS

FL measurement from eRHIC+HERA

FL measurement from eRHIC+fixed target

eRHIC is in an optimal energy range to extract FL via cross section comparisons to previous experiments.

x<0.01 measure universal structure of QCD radiation.

x>0.1 measure hadronic structure. Non-perturbative boundary conditions. Eventually get these from the lattice ?

The behavior of the rise with Q2

Below Q2 0.5 GeV2, see same energy dependence as observed in hadron-hadron interactions. Observe transition from partons to constituent quarks in data. Distance scale 0.3 fm ??

Hadron-hadron scattering energy dependence (Donnachie-Landshoff)

eRHIC could probe this region with high precision (with the right detector)

Probing the parton-hadron transition

eRHIC

ALLM parametrization

Extremely precise measurements possible in this interesting region

Diffraction - the big surpriseLarge diffractive cross section came as a surprise:

Still no understanding from a pQCD approach.

Diffraction1. There is a large diffractive cross section, even in DIS (ca. 20

%)2. The diffractive and total cross sections have similar energy

dependences. Data suggests simple physics – what is it ?

Key detector issues:• Need to guarantee proton intact. • Cover full W range• Good MX resolution

Experience: measuring scattered proton gives cleanest measurements, but acceptance limited in PT,xL.

Notes on diffractionMeasurements have been performed with and without measuring the outgoing proton

With proton• can measure t • clean elastic sample• small acceptance (%)

Without proton• no t measurement • proton dissociation into low mass state difficult to estimate• large acceptance

Ideal: measure the outgoing proton with large acceptance. Will be easier at eRHIC because of the smaller EP, but needs detailed discussions with accelerator experts !

• Exclusive Processes (VM and DVCS)

VM Clean process - has been

measured for many different vector mesons differentially in many variables - wealth of information

€

TG (b) =1

2πBGe

−b 2

2BG

BG=4 GeV-2 corresponds to an rms impact parameter of 0.56 fm. smaller than the proton charge radius of 0.870 [PDG] …

eRHIC should aim to perform these measurements with the best possible precision (detector requirements)

Curves from dipole model analysis of Kowalski, Motyka, Watt Hep-ph 0606272

There is limited data on cross sections at high-x and high Q2

BCDMS has measured F2 up to x=0.75

H1, ZEUS have measured F2 up to x=0.65

Small-x is not the only frontier …

x

Q2

The PDF’s are poorly determined at high-x. Sizeable differences despite the fact that all fitters use the same parametrization xq(1-x). Is it possible to check this ?

HERA high-x

• At high Q2, scattered electron seen with 100% acceptance

• For not too high x, measure x from jet:

• For x>xEdge, measure

€

d2σ

dxdQ2

€

d2σ

dxdQ2 dxxEdge

1∫

HERA Kinematics

No jet foundJet found

Results99-00 e+P

Red line is expectation from CTEQ6D

99-00 e+P

Good agreement with CTEQ6D in previously measured region. Data tend to lie above expectations at highest x.With the right detector, eRHIC could make precision measurements at high-x !

Limited by MC generator

Measurements close to x=1 possible with good precision !

eRHIC with 100 pb-1 and FAD

HERA eRHIC

1. Precise scan of the transition region between partonic & hadronic behavior. Something changes there - can we understand it ? Need acceptance in electron direction.

2. Make precision measurements at high-x to understand the valence quarks. Need acceptance in proton direction.

3. Make FL a highlight of the program - much more direct access to gluon density than via F2 scaling violations. Needs high precision measurements - good resolution, small systematics. Note: FL can also be derived from comparison with HERA, fixed target.

4. Focus on clean, high acceptance diffractive and elastic scattering measurements. Needs high efficiency rejection of proton dissociation and high acceptance proton spectrometer.

Physics Picture

b ~ 0.2 fm/sqrt(t) t=(p-p‘)2

Exclusive processes yield matter profile of hadron.

r

b

r ~ 0.2 fm/Q (0.02 – 2 fm for 100>Q2>0.01 GeV2) transverse size of probe. Scan across transition from partons to hadrons !ct ~ 0.2 fm (1/2MPx) (<1 fm to 1000‘s fm).

For x<0.01, ct>10 fm. Study universal features of QCD radiation (short time scale fluctuations).

For x>0.1, ct<1 fm. Study proton structure (long times).

*

ct

Big picture

eRHIC would allow a precise 3D mapping of nuclear structure at different distance scales, permitting the study of the transition from partonic constituents to hadrons.

The short time-scale fluctuations of QCD which became visible at HERA could be studied in much greater detail, and with different targets. More input needed for theoretical understanding.

Both topics are fundamental, and need new data for a deeper understanding.