Low-x and PDF studies at LHCSept 2008

A M Cooper-Sarkar, Oxford

At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs)

How do PDF Uncertainties affect SM physicsW/Z production, Higgs profuction

How do PDF uncertainties affect BSM physics?-sometimes it will only affect precision e.g. Z’ in high-mass Drell-Yan-sometimes it will compromise discovery e,g, contact interactions in highET jet

production

What measurements can we make at LHC to improve the PDF uncertainty?

Do we even understand QCD a small-x?

• First pp collisions in Sep 2008 s = 10 TeV • Spring ’09 s = 14 TeV at Low luminosity • L= 1 fb-1/year (1032cm-2s-1)• End ’09 s = 14 TeV at High luminosity • L= 10 fb-1/year (1033 cm-2s-1)

Process (nb) Ev./10fb-1

W e 15 ~108

Z e+ e 1.5 ~107

t tbar 0.8 ~107

jets

(pT>200 GeV)

100 ~109

LHC is W, Z, top … factory

Large statistics for SM processes

• SM precision physics (EW, top-,b-physics, multijets…)

• Big potential for new physics (Higgs, Extra Dimensions, SUSY…)

So when is it all going to happen?

The Standard Model is not as well known as you might think

pA

pB

fa

fb

x1

x2

XThe central rapidity range for W/Z production AT LHC is at low-x

(5 ×10-4 to 5 ×10-2)

particularly in the QCD sectorand particlarly in the non-perturbative part of the QCD sector

At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs

Pre HERA Post HERA

ZEUS data

Look at predictions for W/Z rapidity distributions Pre- and Post-HERA

Why such an improvement

?

It’s due to the improvement in the low-x gluon

At the LHC the q-qbar which make

the boson are mostly sea-sea

partons at low-x And at Q2~MZ2 the sea is driven

by the gluon

It may at first sight be surprising that W/Z distns are sensitive to gluon parameters BUT our experience is based on the Tevatron where Drell-Yan processes can involve valence-valence parton interactions. At the LHC we will have dominantly sea-sea parton interactions at low-xAnd at Q2~MZ2 the sea is driven by the gluon- which is far less precisely determined for all x values

Not just statistical improvement. Each experiment can be used to calibrate the other since they have rather different sources of experimental systematics

• Before combination the systematic errors are ~3 times the statistical for Q2< 100

• After combination systematic errors are < statistical

• → very consistent data input HERAPDFs use Δχ2=1

Recent development: Combining ZEUS and H1 data sets

This is post HERA but just

one experiment

(ZEUS)

This is post HERA using the

new (2008) HERA combined

PDF fit

However there is still the possibility of trouble with the

formalism at low-x

MRST PDF

NNLO corrections small ~ few%NNLO residual scale dependence < 1%

W/Z production have been considered as good standard candle processes with small theoretical uncertainty.

PDF uncertainty is THE dominant contribution and most PDF groups quote uncertainties <~5% (but note HERAPDF ~1-2%)

BUT the central values differ by more than some of the uncertainty estimates. Experimental errors are now very small- but how about model uncertainty?Some differences are not just choices, massless heavy quark treatments won’t do.

PDF set σW+ BW→lν

(nb)σW- BW→lν (nb) σz Bz→ll (nb)

ZEUS-2005 11.87±0.45 8.74±0.31 1.97±0.06

MRST01 11.61±0.23 8.62±0.16 1.95±0.04

HERAPDF 12.13±0.13 9.13±0.15 2.01±0.025

CTEQ65 12.47±0.47 9.14±0.36 2.03±0.07

MRST04 11.74 8.71 1.97

CTEQ61 11.61±0.56 8.54±0.43 1.89±0.09

Can we improve the situation with early LHC data

Generate data with 4% error using CTEQ6.1 PDF, pass through ATLFAST detector simulation and then include this pseudo-data in the global ZEUS PDF fit (actually use the decay lepton spectra) Central value of prediction shifts and uncertainty is reduced

e+ rapidity spectrum and gluon PDF BEFORE these data are included in the PDF fit

BEFORE including W data AFTER including W data

e+ rapidity spectrum and gluon PDF AFTER these pseudodata are included in the PDF fit

Gluon PDF uncertainties are reduced

The uncertainty on the W+ W- and Z rapidity distributions are all dominated by gluon PDF uncertainty BUT there is cancellation of this uncertainty in the ratio

ZW = Z/(W+ + W-)

the PDF uncertainty on this ratio is ~1% and there is agreement between PDFsets

cteq66 HERAPDF0.1 Mrst04(1)

But the same is not true for the W asymmetryAw = (W+ - W-)/(W+ + W-)the PDF uncertainty on this ratio is reduced compared to that on the W rapidity spectra within any one PDF setBUT there is not good agreement between PDF sets- a difference in valence PDFs is revealed

Dominantly, at LO Aw= (u dbar – d ubar) (u dbar + d ubar)

And ubar = dbar = qbar at small x So Aw~ (u – d) = (uv – dv) (u + d) (uv + dv + 2 qbar )

Actually this pretty good even quantitatively

The difference in valence PDFs you see here explains the difference in AW

x- range affecting W asymmetry in the measurable rapidity range

uv – dvcteq65

mrst04

mrst04cteq65

Generate data with 4% error using MRST04 PDF and then include this pseudo-data in the global ZEUS PDF fit (actually use the lepton asymmetry data)

The PDF uncertainty of the valence distributions is improved by the input of such data and the central value can be changed

MRST04pseudodata ZEUS-S prediction

BEFORE including Ae pseudo-data

AFTER including Ae pseudo-data

ATLAS/CMS LHC Aw data can measure valence distributions at x~0.005

CTEQ6.5MSTW08

But what about the formalism at LOW-X ?: LHC will be a low-x machine (at least for the early years of running)

And note: even conventionally our knowledge of PDFs is decreases as x < 10-4

Q2=10

Q2=10000

Note CTEQ in general bigger uncertainties…but NOT for low-x gluon where more flexible parametrization of MSTW08 gives larger errors

But what about the formalism at LOW-X ?: LHC will be a low-x machine (at least for the early years of running)

Is NLO (or even NNLO) DGLAP good enough?

The QCD formalism may need extending at small-x

MRST03 is a toy PDF set produced without low-x data

MRST02

MRST03

200k events of W+- -> e+- generated with MC@NLO using MRST03 and MRST02

Reconstructed Electron Pseudo-Rapidity Distributions (ATLAS fast simulation)

6 hours running

Reconstructed e-Reconstructed e+

If something is very different about low-x behaviour it will show up in the our measurable rapidity range

But the TOY PDF is unlikely to be realistic - a better way cold be to look at pt spectra for W and Z production

Pt spectra show PDF differences, but also show differences in modelling – e.g. PYTHIA/HERWIG differences

Probably needs more sophisticated treatment e.g. RESBOS.

There has been an interesting recent calculation of how lack of pt ordering at low-x may affect the pt spectra for W and Z production at the LHC (See hep-ph/0508215)

MW(fit)

< pT(W) >

Same pattern

Pt spectra are also used to measure MWRaw dMW from PDF uncertainties as of today, when using pt(e), is ~20 MeV

So we’d better be sure we’ve got the calculations for Pt spectra right

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

MRST2002NLO ALEKHIN02NLO

d

(W- )/

dy /

d(W

+)/

dy

yW

x1=0.52 x2=0.000064

x1=0.006 x2=0.006

How to probe down to really low-x experimentally? Well the kinematics are such that it’s bound together with probing to higher-x.

We had hoped to learn about valence PDFs (d/u )at high-x by looking at the W-/W+ ratio at large rapidity, but this is bound up with our knowldege of low-x

LHCB kinematics

So it’s better to look at the PDF uncertainty on the total Drell-Yan cross-sections

Improvement with LHCb measurements

And this will feed into PDFs

Moving on to BSM physics

Tevatron jet data were originally taken as evidence for new physics—

i

These figures show inclusive jet cross-sections compared to predictions in the form (data - theory)/ theory

Theory CTEQ6M

Today Tevatron jet data are considered to lie within PDF uncertaintiesAnd the largest uncertainty comes from the uncertainty on the high x gluon

Theory MRST2002

SM + structure function uncertainty band

Mc = 2 TeV

2XD + structure function uncertainty band

4XD + structure function uncertainty band

Up to ~50% at high mass :

Enough to lose sensitivity to higher compactification scales

S.Ferrag

MJJ (GeV)

d/dM (a.u)

Such PDF uncertainties in the jet cross sections compromise the LHC potential for discovery of any new physics which can written as a contact interaction E.G. Dijet cross section has potential sensitivity to compactification scale of extra dimensions (M

c)

And what consequences might this have?

Can we know the high-x gluon better?

mrst01mstw08

There is newer Tevatron Run-II jet data in the latest PDF fits but no very striking improvement in the high-x gluon uncertainty- is there further hope from HERA jets?

Note there is now new Tevatron Run-II jet data

But it does not make MUCH difference to the

level of PDF uncertainties

Can we know the high-x gluon better?

And how might this impact on LHC high-ET jet cross-sections?

HERA now completed second stage of operation (HERA-II)HERA-II projection shows significant improvement to high-x PDF uncertainties

And will we be able to use LHC data itself to improve the situation?

Recently grid techniques have been developed to NLO cross-sections in PDF fits (e.g ZEUS-JETs fit)

This technique can be used for LHC high-ET jet cross-sections

Use data at lower PT and higher η-where new physics is not expected

Pseudo-data has been generated up to PT= 3 TeV for pseudo rapidity ranges

And then used in a global PDF fit to assess the impact of ATLAS data on PDFs

Impact of increasing statistics

Impact of decreasing experimental

systematic uncertainty

Impact of decreasing experimental correlated systematic uncertainty

Challenging!

Can we decrease Jet Energy Scale systematic

to 1%?

1 year (10 fb-1)

ATLAS TDR

But not all BSM physics is strongly compromised: e.g PDF Uncertainty in High-mass Drell-Yan- won’t stop us seeing Z’s

dominant

Gluons dominant

7 – 9 % Uncertainty

d-Valence dominant

Sea dominant

Different mass ranges have different contributions to the PDF uncertainty

And how do PDF uncertainties affect the Higgs discovery potential?- not too badly

g

g

Ht

q

q

W/Z

W/Z

W/Z

H

S Ferrag

Summary

PDF uncertainties impact significantly on

Precise W/Z cross-sections, hence on use of these as luminosity monitor

(however Z/W ratio is a golden calibration measurement)

High Et jet cross-sections, hence on discovery of new physics which can be written in terms of contact interactions

PDF uncertainties should not obscure discovery of

Higgs in mass range 100-1000 GeV

High mass Z’ in mass range 150-2500 GeV

Measurements from LHC itself may improve knowledge of

Gluon PDF at low-x (W prodn) and high-x (high ET jets/direct photon)

Low-x / high-x valence PDFs ( W asymmetry)

Low-x partons/ Low-x theory (low-mass Drell-Yan)

extras