Low x physics at hera
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The low- x Structure Function Data. Introduction. Brian Foster Bristol/DESY. Corfu Summer School, 4.9.01. Low- x physics at HERA. Other probes of QCD dynamics @ HERA. Diffraction and its connection with low- x DIS. Summary & Outlook. For low x , HERA ~ only game in town.

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Low- x physics at HERA

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Low x physics at hera

The low-x Structure Function Data

Introduction

Brian Foster

Bristol/DESY

Corfu Summer

School, 4.9.01

Low-x physics at HERA

Other probes of QCD dynamics @ HERA

Diffraction and its connection with low-x DIS

Summary & Outlook

Brian Foster - Corfu lectures


Where are we now

For low x, HERA ~ only game in town.

Where are we now?

Brian Foster - Corfu lectures


Qcd as a description of low x

QCD as a description of low x

Factorization - hard processes can be regarded as convolution

of “sub-process” cross section with probability to find

participating partons in target & probe - subsequent

hadronisation ~ independent process

For DIS can (normally) consider

virtual photon as d-function

=> s ~ f  swhere

s is sub-process cross section

f is parton dist. function,

satisfying f/ m ~ f P

(m = renormalisation scale,

Pis a splitting function)

Brian Foster - Corfu lectures


Qcd evolution

where are AP splitting functions

QCD evolution

In general Ps are perturbative expansions to particular

orders, keeping terms most important for particular regions:

Leading lnQ2 terms come, in axial gauge, from evolution

along parton chain strongly ordered in transverse momenta,

LO DGLAP sums up

terms - NLO sums

terms which arise when two adjacent

kts become comparable, losing factorlnQ2.

Brian Foster - Corfu lectures


Qcd evolution1

In small x region, leading terms in ln 1/x must be summed

independent of Q2. This is done by the BFKL equation.

LO

terms arise from strong x ordering

Generally, however, QCD coherence  angular ordering -

work in unintegrated f(x,kt2,m2) - 2 hard scales  more

complicated CCFM evolution equation. DGLAP/BFKL two

limits of angular ordering. DGLAP, q  kt/kl, q grows since kt

grows; in BFKL, q grows because kl  x falls.

QCD evolution

Brian Foster - Corfu lectures


Low x structure function data

Kinematics

e(k)

e'(k')

2

Q

Q2 = xys

g

*(q)

2

W

xP

p(P)

Low-x structure function data

 s = k+P=energy in the ep c.m.s.

Q2 = -(k-k')2 = -q2 =virtuality of the exchanged 

x = Q2/(2P•q)=fraction of proton momentum

carried by the struck quark

y = (P•q)/(P•k) =fraction of beam lepton energy

transferred to the photon

W 2 = ys ~ Q2/xenergy in the *p c.m.s.

Brian Foster - Corfu lectures


Bpt f 2 low q 2 from zeus

To reach lowest possibleQ2, some tricks needed!

As well as exquisite

understanding of

detector -

BPT F2(low Q2)from ZEUS

Brian Foster - Corfu lectures


F 2 low q 2 from zeus h1

ZEUS BPT dataAt lowQ2 , F2falls likeQ2

F2(low Q2)from ZEUS & H1

Brian Foster - Corfu lectures


F l from qcd fit from h1

Since =>

sr =F

sr ~F2 for small y,

æ

sr ~F2 - fory 1, so =

F2fit -

ç

-

F

F

F

(x,Q2)

ç

L

L

L

è

(x,Q2)

2

FLfrom QCDfitfrom H1

Brian Foster - Corfu lectures


F l from qcd fit from h11

FLfrom QCDfitfrom H1

Brian Foster - Corfu lectures


F l from qcd fit from h12

FLfrom QCDfitfrom H1

Brian Foster - Corfu lectures


Iii other probes of qcd dynamics forward p 0 @ h1

III: Other probes of QCD dynamicsForward p0 @ H1

Brian Foster - Corfu lectures


Forward jets @ h1

Forward jets @ H1

Brian Foster - Corfu lectures


Forward jets @ h11

Forward Jets @ H1

Brian Foster - Corfu lectures


Iv interpretation models

There are many parameterisations of the structure function

data on the market - some more deeply based on physics

others rather just convenient functional forms.

e.g. DL fit ;

wheree0 is “hard Pomeron”

SinceW 2 ~ Q2/x , and ,

Regge theory, which governs high-energys s relevant for lowx

IV. Interpretation & models

Brian Foster - Corfu lectures


Logarithms

Another model exploits the “double-logarithmic” limit of QCD:

Haidt, coming from a different direction, uses

Ball-Forte fit

Logarithms

Brian Foster - Corfu lectures


More logarithms

Erdmann uses

More Logarithms

Brian Foster - Corfu lectures


Nlo qcd fits

Several on the market - MRST, CTEQ essentially global NLO

QCD fits to all DIS data (HERA & fixed target) plus other

relevant channels; GRV attempts to generate structure functions

by evolution from “valence-like” gluon at very low Q . All give

excellent fits to the data, with many free parameters.

NLO QCD fits

GRV’98

CTEQ

Deviation of exp. data from CTEQ fit

Brian Foster - Corfu lectures


Pdfs with errors

Although using a subset (DIS) of the data, recently “home-grown”

pdfs appeared which give errors on fitted pdfs as well as the

correlations - e.g. Botje

PDFs with errors

Botje

Brian Foster - Corfu lectures


Nnlo pdf fitting

NNLO estimates for

the splitting fns. now

becoming available -

(Van Neerven&Vogt)

MRS, CTEQ groups

using them.

Some strange effects!

“Premature”

(K.Ellis, DIS2000)

NNLO PDF fitting

Brian Foster - Corfu lectures


Nnlo pdf fitting1

Thorne achieves

interesting improvements

by incorporating

ln(1/x) terms in splitting

fns after NNLO BFKL

using running coupling

BFKL eq.

NNLO PDF fitting

Brian Foster - Corfu lectures


F 2 its derivatives

ZEUS has very precise F2

data over 6 orders of

magnitudein (x, Q2).

What can it tell us?

Look at the log. derivative

since ~ LO gluon - most

sensitive to low-xdynamics

- fit x bins with form

F2 = A+B(ln Q2)+C(ln Q2)2

Plot derivative as fn. of x&

Q2in bins of constantW

F2 & its derivatives

Brian Foster - Corfu lectures


F 2 its derivatives1

Errors on F2

syst. +stat. in

quadrature

(correlations

ignored.

F2 & its derivatives

Brian Foster - Corfu lectures


F 2 its derivatives2

There is no turn-over at constant

Q2

One can look at

3-D surface of log. Slopes.

The fundamental point is that the precision and kinematic

range of the data is now opening up qualitatively new areas of

study. The question is - what does it mean?

F2 & its derivatives

Brian Foster - Corfu lectures


What is happening at low x

As x falls, as we have seen, the gluon radiation drives a strong

increase in parton density and hence increase inF2.

At some point, the number of partons becomes so large

that they cannot “fit” inside the proton and their

wave-functions overlap - this is known as parton saturation.

What is happening at low x?

Brian Foster - Corfu lectures


Dipole models

Recently, great deal of interest in dipole models & saturation.

L.T.

Breit,  mom.

prest

In principle offers unification of inclusive DIS, diffraction

+

1 g

exchange

2 g octet

exchange

2 g singlet

exchange

Diffraction

Dipole Models

Inclusive F2

Brian Foster - Corfu lectures


Dipole models1

Example of this type of model: Golec-Biernat & Wuesthoff predicts

-Q2s0

Dipole Models

Brian Foster - Corfu lectures


Fits to slopes

The Golec-Biernat&Wusthoff model does a reasonable

qualitative job - but so does QCD, and/or a variety of simple

parameterisations.

Fits to slopes

Brian Foster - Corfu lectures


Qcd fit pdfs

Although one can make QCD fit the logarithmic slopes, the

resultant pdfs, as we saw earlier, are strange to say the least!

ZEUS

prel..

ZEUS

prel..

QCD fit pdfs

Brian Foster - Corfu lectures


Qcd fit f l

But the predictedFLis even stranger!

ZEUS

prel..

QCD fit FL

Brian Foster - Corfu lectures


F 2 derivatives summary

The agreement of the data with dipole models and the saturation

concept is intriguing - are we seeing the first departure from

linear evolution in QCD? Clearly premature to draw this

conclusion - NLO QCD can also reproduce the data to the same

level - although at the cost of producing pdfs that are very

difficult to interpret in a sensible way.

The fundamental point is that the precision and kinematic range

of the data is now opening up qualitatively new areas of study.

Perhaps we are seeing a qualitatively new behaviour of QCD -

but we can’t be certain. One of the problems is that the

interesting “critical line” is down atQ2 ~ 1 GeV2 - we need to

measure at low x but higher Q2. - needs a higher energy than

HERA can achieve.

F2 derivatives - summary

Brian Foster - Corfu lectures


Diffraction

In diffraction, proton stays intact

In great majority of DIS events,

proton breaks up into hadrons +

“remnant” in forward direction

We saw that, in dipole models, there was an intimate connection

between DIS & diffraction. Is this borne out by the data?

Diffraction

Brian Foster - Corfu lectures


Diffraction1

The most basic measurement is the total cross section for

diffraction. Does it agree with our expectations?

}

GB

&W

No. It has sameW2dependence asstot - W0.4.

Contradicts optical theoremstot ~ Wa => sdiff ~ W2a; and

ifstot ~ g, sdiff ~g2; and Regge, from Pomeron traj. stot~ W0.16

Diffraction

Brian Foster - Corfu lectures


Diffraction2

What about the structure functions? The analogue to F2 is F2D

Diffraction

Brian Foster - Corfu lectures


Diffraction vector mesons

Note steep rise inW

dependence ofs -

indicative of hard

processes becoming

dominant.

The intimate link between diffraction & non-diffractive DIS

via dipole models & saturation also clearly applicable to vector

meson production.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Diffraction vector mesons1

Inset shows

fit with Wd.

For theJ/y, the charm mass seems to be large enough to

provide a hard scale even atQ2 = 0.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Diffraction vector mesons2

Fit to

measured

cross sections

with Wd.

For ther, theQ2provides a hard scale.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Diffraction vector mesons3

Fit to

measured

cross sections

with Wd.

For all vector mesons , Q2 + M2seems to be a common hard

scale.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Diffraction vector mesons4

For Q2 > 5 GeV2, lVM ~ 2* lDIS

Compare the W dependence for VM production and DIS.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

But the J/y wave

function needs to be

modelled so that

model dependence

enters extraction.

What else can we learn from VMs? Since J/y seems to always

be in the pQCD realm, we can in principle learn about proton

gluon distribution.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

By fitting cross-section t dependence we can look at

Pomeron trajectory.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

What is the appropriate hard scale in VM production?

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

VM production at high t.

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

J/y

f/r

f

Production s ratios BFKL prediction (Forshaw et al.)

y/r

r

2g

BFKL

Diffraction - vector mesons

Brian Foster - Corfu lectures


Low x physics at hera

Simplest final state in diffraction

Deeply virtual Compton scattering

Measures Re part of a QCD amplitude

Measures “skewed” parton distributions -

generalisation on normal proton pdf’s.

Brian Foster - Corfu lectures


Low x physics at hera

Data cf. QEDC only QEDC & DVCS MC

Deeply virtual Compton scattering

DVCS process clearly necessary - extract cross-section

Brian Foster - Corfu lectures


Low x physics at hera

Now cross section measured, can go onto to look at

interference etc.

Deeply virtual Compton scattering

Brian Foster - Corfu lectures


V summary outlook

The agreement of the data with dipole models and the saturation

concept is intriguing - are we seeing the first departure from

linear evolution in QCD? Clearly premature to draw this

conclusion - one of the problems is that the interesting “critical

line” is down at Q2~ 1 GeV2 - we want to measure at low x

but higher Q2.

This I guess will have to wait

for THERA, LHC ep option,

….? Is there something else

we can do “now”? Yes,

possibly. Running HERA

with nuclei rather than p

gives access to high-density

of partons at low x.

V Summary & Outlook

Brian Foster - Corfu lectures


Summary outlook

Many open questions -

and of course

this is not only important

to those

interested in QCD!

If we want to useW,Z

production at LHC as

lumi. monitor, we had better

understand smallxat HERA!

h

Summary & Outlook

Brian Foster - Corfu lectures


Summary outlook1

The quality & precision of the HERA data are driving studies

of low-x physics.

Watching the Herculean labours of the F2 experts extracting the

96-97 result tells me that we are nearing the end of the road for

improved precision in the standard inclusive F2 at low x -

from now one attention will turn to semi-inclusive(particularly

F2charm) and rare processes

Much theoretical help required (as always) to tell us where/how

to look

The connection between diffraction and DIS is certainly a very

interesting one that can throw much light on low-x physics.

It may well justify a “HERA-III” programme - but all

this will depend on TESLA!

Summary & Outlook

Brian Foster - Corfu lectures


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