brian foster - corfu lectures 1 low-x physics at hera brian foster bristol/desy corfu summer school,...

Brian Foster - Corfu lectures

1

Low-x physics at HERABrian Foster

Bristol/DESY

Corfu Summer

School, 4.9.01

The low-x Structure Function Data

Other probes of QCD dynamics @ HERA

Diffraction and its connection with low-x DIS

Summary & Outlook

Introduction


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Where are we now?

For low x, HERA ~ only game in town.


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QCD as a description of low x

Factorization - hard processes can be regarded as convolutionof “sub-process” cross section with probability to find participating partons in target & probe - subsequenthadronisation ~ independent process

For DIS can (normally) consider virtual photon as -function=> f where is sub-process cross section f is parton dist. function, satisfying f/f P (renormalisation scale, P is a splitting function)


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QCD evolutionIn general Ps are perturbative expansions to particularorders, keeping terms most important for particular regions:

0 0

)()( )(1

ln2

),(n

n

m

nm

nm

ns

s xPxx

AxxP

)(nPwhere are AP splitting functions

Leading ln Q2 terms come, in axial gauge, from evolution along parton chain strongly ordered in transverse momenta,

Q2ý k2t;n ý k2t;nà1ý . . .LO DGLAP sums up (ës lnQ2)n terms - NLO sums

terms which arise when two adjacent ës(ës lnQ2)nà1kts become comparable, losing factor ln Q2.


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QCD evolutionIn small x region, leading terms in ln 1/x must be summed independent of Q2. This is done by the BFKL equation.LO (ës ln1=x)n terms arise from strong x ordering

x ü xn ü xnà1ü . . .Generally, however, QCD coherence angular ordering -work in unintegrated f(x,kt

2,m2) - 2 hard scales morecomplicated CCFM evolution equation. DGLAP/BFKL two limits of angular ordering. DGLAP, kt/kl, grows since kt grows; in BFKL, grows because kl x falls.


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Low-x structure function datae(k) e'(k')

*(q)

p(P)

xPW2

Q2

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 momentumcarried by the struck quark

y = (P• q)/(P• k) = fraction of beam lepton energytransferred to the photon

W 2 = ys ~ Q2/ x energy in the *p c.m.s.

Q2 = xys

Kinematics


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BPT F2 (low Q2) from ZEUSTo reach lowest possible Q2 , some tricks needed!

As well as exquisiteunderstanding ofdetector -


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F2 (low Q2) from ZEUS & H1ZEUS BPT data At low Q2 , F2 falls like Q2


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FL from QCD fit from H1Since => 2 (x,Q2) FL (x,Q2)

Y

y2r =F r ~F2 for small y,

r ~F2 - for y 1, so = FL 22

4

2 y

YxQr

F2

fit - FL


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FL from QCD fit from H1


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FL from QCD fit from H1


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III: Other probes of QCD dynamicsForward 0 @ H1


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Forward jets @ H1


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Forward Jets @ H1


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IV. Interpretation & modelsThere are many parameterisations of the structure functiondata on the market - some more deeply based on physicsothers rather just convenient functional forms.Since W 2 ~ Q2/ x , and ,Regge theory, which governs high-energy s relevant for low x

)()(2 WWF TL

e.g. DL fit ; where 0 is “hard Pomeron”

2,1,0

222 )(),(

ii

ixQfQxF 0)(),( 222

xQfQxF cc


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

Ball-Forte fit 20

22 lnln)/1ln()/48(exp),( QxQxF

Haidt, coming from a different direction, uses

)/1ln()/ln(41.0),( 20

20

22 QQxxQxF


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More LogarithmsErdmann uses )(222

2 )/ln()(),(x

QxaQxF


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NLO QCD fitsSeveral 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.

GRV’98

Deviation of exp. data from CTEQ fit

CTEQ


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PDFs with errorsAlthough 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 Botje


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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)


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NNLO PDF fitting

Thorne achieves interesting improvements by incorporatingln(1/x) terms in splitting fns after NNLO BFKL using running coupling BFKL eq.


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F2 & its derivativesZEUS has very precise F2 data over 6 orders of magnitude in (x, Q2). What can it tell us?

Look at the log. derivative

since ~ LO gluon - most sensitive to low-x dynamics - fit x bins with form F2 = A+B(ln Q2)+C(ln Q2)2

Plot derivative as fn. of x &Q2 in bins of constant W

22

lnQ

F


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F2 & its derivatives

22

2 ln2ln

QCBQ

F

Errors on F2

syst. +stat. inquadrature (correlations ignored.


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F2 & its derivativesThere is no turn-over at constant Q2

One can look at3-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?


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What is happening at low x?

As x falls, as we have seen, the gluon radiation drives a strongincrease in parton density and hence increase in F2. At some point, the number of partons becomes so largethat they cannot “fit” inside the proton and their wave-functions overlap - this is known as parton saturation.


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Dipole ModelsRecently, great deal of interest in dipole models & saturation.

prest Breit, mom.L.T.

In principle offers unification of inclusive DIS, diffraction

Inclusive F2

1 gexchange

2 g octetexchange

+2 g singletexchange

Diffraction


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Dipole ModelsExample of this type of model: Golec-Biernat & Wuesthoff predicts

1ln1ln),(

2

200

20

2

02

200

02*

Q

Q

x

x

Q

Q

x

x

Q

Q

x

xQxp

-Q20


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Fits to slopesThe Golec-Biernat&Wusthoff model does a reasonable qualitative job - but so does QCD, and/or a variety of simple parameterisations.


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QCD fit pdfsAlthough one can make QCD fit the logarithmic slopes, theresultant pdfs, as we saw earlier, are strange to say the least!

ZEUS prel..

ZEUS prel..


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QCD fit FL

But the predicted FL is even stranger!

ZEUS prel..


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F2 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 rangeof 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 at Q2 ~ 1 GeV2 - we need to measure at low x but higher Q2. - needs a higher energy than HERA can achieve.


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DiffractionIn great majority of DIS events,proton breaks up into hadrons +“remnant” in forward direction

In diffraction, proton stays intact

We saw that, in dipole models, there was an intimate connectionbetween DIS & diffraction. Is this borne out by the data?


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DiffractionThe most basic measurement is the total cross section for diffraction. Does it agree with our expectations?

}GB&W

No. It has same W2 dependence as tot - W0.4. Contradicts optical theorem tot ~ W => diff ~ W2; andif tot ~ g, diff ~g2; and Regge, from Pomeron traj. tot~ W0.16


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DiffractionWhat about the structure functions? The analogue to F2 is F2

D


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Diffraction - vector mesonsThe intimate link between diffraction & non-diffractive DISvia dipole models & saturation also clearly applicable to vector meson production.

Note steep rise in Wdependence of -indicative of hardprocesses becomingdominant.


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Diffraction - vector mesonsFor the J/, the charm mass seems to be large enough toprovide a hard scale even at Q2 = 0.

Inset showsfit with W.


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Diffraction - vector mesonsFor the , the Q2 provides a hard scale.

Fit tomeasuredcross sectionswith W.


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Diffraction - vector mesonsFor all vector mesons , Q2 + M2 seems to be a common hard scale.

Fit tomeasuredcross sectionswith W.


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Diffraction - vector mesonsCompare the W dependence for VM production and DIS.

For Q2 > 5 GeV2,VM ~ 2* DIS


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Diffraction - vector mesons What else can we learn from VMs? Since J/ seems to alwaysbe in the pQCD realm, we can in principle learn about protongluon distribution.

But the J/ wave function needs to be modelled so thatmodel dependence enters extraction.


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Diffraction - vector mesons

By fitting cross-section t dependence we can look atPomeron trajectory.


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Diffraction - vector mesons What is the appropriate hard scale in VM production?


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Diffraction - vector mesons VM production at high t.


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Diffraction - vector mesons Production ratios BFKL prediction (Forshaw et al.)

J/

2gBFKL

/

/


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Deeply virtual Compton scattering Simplest final state in diffraction

Measures Re part of a QCD amplitude

Measures “skewed” parton distributions -generalisation on normal proton pdf’s.


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Deeply virtual Compton scattering Data cf. QEDC only QEDC & DVCS MC

DVCS process clearly necessary - extract cross-section


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Deeply virtual Compton scattering

Now cross section measured, can go onto to look at interference etc.


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V Summary & OutlookThe 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 waitfor 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.


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Summary & Outlook

Many open questions -and of coursethis is not only important to thoseinterested in QCD!

If we want to use W,Zproduction at LHC aslumi. monitor, we had betterunderstand small x at HERA!


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Summary & Outlook

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

Watching the Herculean labours of the F2 experts extracting the96-97 result tells me that we are nearing the end of the road forimproved precision in the standard inclusive F2 at low x -from now one attention will turn to semi-inclusive (particularlyF2

charm) and rare processes

The quality & precision of the HERA data are driving studiesof low-x physics.

The connection between diffraction and DIS is certainly a veryinteresting one that can throw much light on low-x physics.It may well justify a “HERA-III” programme - but allthis will depend on TESLA!

brian foster - corfu lectures 1 low-x physics at hera brian foster bristol/desy corfu summer school,...

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brian foster corfu lectures

h1 slide

fit f

independent of q

lowx physics

f f p renormalisation

exchanged x

strong x