In the QCD sector the PDFs limit our knowledge - transport PDFs to hadron-hadron cross-sections using QCD factorization theorem for short-distance inclusive processes where X=W, Z, D-Y, H, high-E T jets, prompt-γ and  is known to some fixed order in pQCD and EW in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^ pApA pBpB fafa fbfb x1x1 x2x2 X The central rapidity range for W/Z production AT LHC is at low-x (5 ×10 -4 to 5 ×10 -2 ) at 14 TeV (10 -3 to ) at 7 TeV The Standard Model is not as well known as you might think 7 TeV

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. Can be used as a luminosity monitor? PDF uncertainty is THE dominant contribution and most PDF groups quote uncertainties ~3-4% But we have to account for the difference between the central predictions of PDFs WHAT DO WE KNOW WELL? Last year I had been thinking that predictions were coming into better agreement CTEQ and MSTW predictions agreed well within their quoted uncertainties BUT new PDF sets have come on to the ‘market’ which show stronger disagreements.....

Let’s look at the modern PDFsets MSTW08 CTEQ66 HERAPDF1.0 NNPDF2.0 ABKM09 GJR08 Overall disagreement ~8% in W, Z cross- sections The PDF4LHC recommendation is to take the envelope of the NNPDF, MSTW, CTEQ predictions --even this may not be enough! Plots from G.Watt -MSTW

Why these disagreements? Firstly groups use different values of α S (M Z ), the effect of this can been seen on the figures A common value would bring some of the predictions into better agreement Secondly groups have different ways of accounting for heavy quark production And use different values of the heavy quark mass. Within any chosen scheme a change of quark mass from 1.4 to 1.65 GeV can change the W/Z cross-sections by ~2.5% Thirdly, different groups use different input data sets, e.g. the data used by CTEQ and MSTW are very similar and they do NOT include the latest most accurate HERA data which are used in HERAPDF1.0. Not only are these new (2009) data more accurate they also have a different normalisation This accounts for ~2.5% upward shift of the HERAPDF prediction Fourthly there are some differences in philosophy regarding choices of PDF parametrisation and theoretical/model prejudices which are imposed Let’s look more closely at some of these points

Results of the combination compared to the separate data sets This page shows NC e+ combined data HERA data reach low- x values even for Q 2 ~ 100 GeV 2

No HERA data Separate H1 +ZEUS New 2009 HERA Combined Z w 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 high scale, Q 2 ~M Z 2, the sea is driven by the gluon by g→q qbar splitting NOTE these predictions show uncertainty due to experimental errors only- model errors are not included- so the final uncertainties will be larger than shown. Impact of HERA data on the LHC- just one example Consider a PDF fit done under exactly the same conditions except for the HERA data which are/are not included

In practice we add to the experimental errors some estimate of model uncertainties and parametrisation uncertainties Compare to CTEQ66, including lepton decay distributions HERAPDF helps to ascertain where the uncertainties are really coming from CTEQ6.6 PDF predictions at 10 TeV ~5% error at central rapidity HERAPDF1.0 predictions at 10 TeV ~3% error at central rapidity

We must account properly for heavy quark production.: there are two extremes- Use only 3 massless parton flavours and calculate exact ME’s for heavy quark production (FFN method)- wrong at high scale since ln(Q 2 /m c 2 ) terms not resummed Consider all partons as massless except that charm and beauty turn on abruptly at their kinematic thresholds (ZMVFN) – WRONG at low scale near these thresholds A GMVFN (Genral-mass Variable Flavour Number Scheme) is supposed to give us the nest of both worlds.. BUT there are different ways to do this...ACOT, Thorne, FO-NLL ZMVFN gives the largest c-cbar contribution to F2 and FFN the smallest Plot from J Rojo NNPDF

The different HQ schemes certanily accounts for some of the difference between NNPDF2.0 (ZMVFN) and CTEQ/MSTW- if quarks are massive then charm production will be suppressed at threshold and the light quark densities will increase to compensate, when fitting low-scale DIS data- this in turn leads to slightly larger W/Z cross-sections. The same effect explains why a larger choice of charm mass leads to a larger W/Z cross-section I am also betting that the difference in HQ treatment explains the differnce in the ABKM result and those of MSTW/CTEQ since the ABKM HQ treatment is closest to a fully FFN treatment – where the charm parton is not only suppressed but non-existent!

H1 and ZEUS have also combined charm data recently And the HERAPDF1.0 gives a good description of these data –within its error band- The error band spans m c =1.35 (high) to m c =1.65 (low) GeV The data show some preference for higher charm mass than the standard choice m c =1.4 GeV

If we input the charm data to the PDF fit it does not change the PDFs significantly BUT After charm is input the χ2 profile vs the charm mass parameter gives m c = 1.57 ± 0.02 GeV Before charm is input the χ2 profile vs the charm mass parameter is shallow..

But the HERAPDF uses the Thorne General Mass Variable Flavour Number Scheme for heavy quarks as used by MSTW08 This is not the only GMVFN CTEQ use ACOT- χ NNPDF2.0 use ZMVFN These all have different preferred charm mass parameters, and all fit the data well when used with their own best fit charm mass Model and param. Errors included We have re-analysed the HERAPDF+F2c data using several different heavy quark schemes

We then use each of these schemes to predict W and Z cross-sections at the LHC (at 7 TeV) as a function of charm mass parameter If a fixed value of mc is used then the spread is considerable (~7%)- but if each prediction is taken at its own optimal mass value the spread is dramatically reduced (~2%) even when a Zero-Mass (ZMVFN) approximation has been used The PDFs MSTW08, CTEQ6.6, NNPDF2.0 do NOT use charm mass parameters at the optimal values- and this partly explains their differing predictions. Note NNPDF2.1 HAS now moved upwards –heavy quarks scheme now used

Are ratios better predicted? The W/Z ratio is YES- ~1% spread but the W+/W- ratio is NOT ~>5% and this shows up more strongly in the W and lepton symmetries Let’s look a bit more closely at these ratios

There is uncertainty in the strangeness sector that does not cancel out between Z and (W + + W - )… it was always there we just didn’t account for it Z = uubar + ddbar + ssbar +ccbar +bbar W + + W - ~ (udbar + csbar) + (dubar+scbar) YES this does translate to the Z/lepton ratio CTEQ6.5 pre 2008 MSTW08 CTEQ6.6 ZOOM in on Z/W ratio – there is fantastic agreement between PDF providers PDF uncertainty from the low-x gluon and flavour symmetric sea cancels out- and so do luminosity errors BUT there is somewhat more PDF uncertainty than we thought before 2008 (~1.5% rather than <1% in the central region) Now let’s look at ratios: Z/W ratio is a golden benchmark measurement (10TeV)

The biggest difference is MSTW08 to CTEQ66 The difference doesn’t look much until you home in on the discrepancy of the MSTW08 prediction to the CTEQ66 error band It exceeds my standard 10% scale Turns out to be~35% discrepancy! Where is it coming from?- compare W+ and W- distributions It looks like the W- agrees fairly well but the W+ is lower for MSTW We can trace this difference back to the different valence PDFs of CTEQ66 and MSTW08 But in the W asymmetry – there is NOT fantastic agreement (10 TeV)

We actually measure the decay lepton spectra- but dicsrepancies persist in the lepton asymmetry as well The illustration above is for 7 TeV comparing HERAPDF1.0 to MSTW08 and CTEQ66 NOTe the uncertainty band shown below the figures is absolute rather han fractional for these figures

Dominantly, at LO Aw= (u(x 1 ) dbar(x 2 ) – d(x 1 ) ubar(x 2 )) (u(x 1 ) dbar(x 2 ) + d(x 1 ) ubar(x 2 )) And at central rapidity x 1 = x 2 and ubar ~ dbar ~ qbar at small x So Aw~ (u – d) = (u v – d v ) (u + d) (u v + d v + 2 qbar ) x- range affecting W asymmetry in the measurable rapidity range at ATLAS (10TeV) Predictions for AW are different in the central region- because predictions for valence distributions at small-x are different Actually this LO approx. is pretty good even quantitatively The difference in valence PDFs you see here does explain the difference in A W between MRST and CTEQ As we move away from central rapidity: as x 1 increases (decreases) the larger (smaller) difference is weighted by larger (smaller) sea distributions at smaller x 2

Can we improve our knowledge of PDFs using ATLAS data itself? We actually measure the decay lepton spectra Generate pseudodata at 14TeV corresponding to 100pb -1 - using CTEQ6.6 HERAPDF1.0 MSTW2008 PDFs with full uncertainties Recent study with full detector simulation AND QCD di-jet background estimation ATL-Com-PHYS Input these pseudo-data to the HERAPDF1.0 fit…. 5-10% uncertainty K Lohwasser

This is the HERAPDF uv and dv BEFORE adding lepton asymmetry pseudo-data And this is what it looks like if we add the lepton asymmetry pseudo-data. Generate pseudo-data a la CTEQ6.6 central value with experimental errors from ATL-Com-PHYS LHC asymmetry data can measure valence distributions at x~0.005

Can we improve the situation with early LHC data? Generate 100 pb -1 W + /W - 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 dataAFTER including W data e+ rapidity spectrum and gluon PDF AFTER these pseudodata are included in the PDF fit Gluon PDF uncertainties are reduced Hep-ex:

W/Z production depends on q- qbar luminosity we can look at this at different scales

There have been updates which bring HERAPDF and NNPDF somewhat closer to MSTW

Look at the 90% CL plots where no PDF looks ‘outlandish’ These plots cover the whole range of scales for LHC Over much of the range there is agreement within 10% End lecture 8