PDF studies at ATLAS HERA-LHC workshop 2007 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 BSM physics? high ET jets..contact interactions/extra dimensions How do PDF Uncertainties affect SM physics What measurements can we make at ATLAS to improve the PDF uncertainty?

HERA and the LHC- transporting PDFs to hadron-hadron cross-sections QCD factorization theorem for short-distance inclusive processes where X=W, Z, D-Y, H, high-ET 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 ^ pA pB fa fb x1 x2 X Knowledge of the PDFs is vital

What has HERA data ever done for us? Z Pre-HERA W+/W-/Z and W+/- → lepton+/- rapidity spectra ~ ± 15% uncertainties ! Why? Because the central rapidity range AT LHC is at low-x (5 10-4 to 5 10-2) NO WAY to use these cross-sections as a good luminosity monitor Lepton+ Lepton-

W+ W- Z Lepton+ Lepton- Post-HERA W+/W-/Z and W+/- → lepton+/- rapidity spectra ~ ± 5% uncertainties ! Why? Because there has been a tremendous improvement in our knowledge of the low-x glue and thus of the low-x sea

Pre-HERA sea and glue distributions Post HERA sea and glue distributions

How to constrain gluon-PDFs at LHC single Z and W± Production MRST PDF NNLO corrections small ~ few% NNLO residual scale dependence < 1% W± Symmetric W+- diff. cross section Theoretical uncertainties dominated by PDFs note that central values differ by more than the MRST estimate of the error To improve the situation we NEED to be more accurate than this:~3% Statistics are no problem we are dominated by systematic uncertainty PDF Set ZEUS-S CTEQ6.1 MRST01 (nb)

At y=0 the total uncertainty is ~ ±6% from ZEUS ~ ±4% from MRST01E From LHAPDF eigenvectors At y=0 the total uncertainty is ~ ±6% from ZEUS ~ ±4% from MRST01E ~ ±8% from CTEQ6.1 ZEUS to MRST01 central value difference ~5% To improve the situation we NEED to be more accurate than this:~4% BUT different PDF sets give somewhat different estimates of both the central values and the uncertainties of the W spectra

The uncertainty on the W/Z rapidity distributions is dominated by –- gluon PDF dominated eigenvectors Both low-x and high-x 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-x And at Q2~MZ2 the sea is driven by the gluon- which is far less precisely determined for all x values

So finally- can we improve our knowledge of PDFs using ATLAS data itself? W/Z production have been considered as good standard candle processes insensitive to PDF uncertainties……? This is true WITHIN a PDFset ( see Thorne’s talk) generator level But how about comparing PDFsets? We actually measure the decay lepton spectra Generate with HERWIG+k-factors (checked against MC@NLO) using CTEQ6.1M ZEUS_S MRST2001 PDFs with full uncertainties from LHAPDF eigenvectors At y=0 the total uncertainty is ~ ±6% from ZEUS ~ ±4% from MRST01E ~ ±8% from CTEQ6.1 ZEUS to MRST01 central value difference ~5% To improve the situation we NEED to be more accurate than this:~4% electron positron ATLFAST electron positron

Study of the effect of including the LHC W Rapidity distributions in global PDF fits by how much can we reduce the PDF errors 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 Central value of prediction shifts and uncertainty is reduced BEFORE including W data AFTER including W data AMCS, A. Tricoli (Hep-ex/0509002) Lepton+ rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF AFTER these data are included in the fit Lepton+ rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF Specifically the low-x gluon shape parameter λ, xg(x) = x –λ , was λ = -.199 ± .046 for the ZEUS PDF before including this pseudo-data It becomes λ = -.181 ± .030 after including the pseudodata

The uncertainty on the W/Z rapidity distributions is dominated by –- gluon PDF dominated eigenvectors and there is cancellation in the ratios AW = (W+ - W-)/(W+ + W-) ZW = Z/(W+ + W-) Remaining uncertainty comes from valence PDF related eigenvectors Well Known? Gold plated? We will measure the lepton asymmetry generator level Within each PDF set uncertainty in the lepton asymmetry IS LESS than in the lepton rapidity spectra, e.g about 2% for the asymmetry at y=0, as opposed to about 4% for the lepton rapidity spectra themselves (using MRST2001 PDFS) However the PDF sets differ from each other more strikingly- MRST01and CTEQ6.1 differ by about 13% at y=0! But this is an opportunity to use ATLAS measurements to increase knowledge of the valence PDFs at x~0.005 - see AMCS February06 SM session ATLFAST

Because the uncertainties in W+,W- and Z spectra are all coming from the gluon PDF there is cancellation in the ratios AW = (W+ - W-)/(W+ + W-) ZW = Z/(W+ + W-) Remaining uncertainty comes from valence PDF related eigenvectors Well Known? Gold plated? We will actually measure the lepton asymmetry Uncertainty in the lepton asymmetry IS LESS than in the lepton rapidity spectra, e.g about 4% for the asymmetry at y=0, as opposed to about 8% for the lepton rapidity spectra themselves (using CTEQ6.1M PDFS)

BUT Compare CTEQ and MRST PDF predictions for the W asymmetry- AW = (W + - W -)/(W + + W -) In the measurable rapidity range Look closely at y~0 MRST is 25% different from CTEQ mrst02 cteq61 W This difference persists in the lepton asymmetry, Al = (l+ - l-)/(l+ + l-), Though it is diluted to ~13% -but surely we could see that? lepton Not so gold-plated when you compare predictions from different PDF sets – But this is an opportunity to use ATLAS measurements to increase knowledge of the valence PDFs at x~0.005 - see AMCS February06 SM session

Where does this difference come from? Dominantly, at LO Aw= (u d – d u) (u d + d u) And u = d = q at small x ( I will return to this..it can be challenged) So Aw~ (u – d) = (uv – dv) (u + d) (uv + dv + 2 q ) Actually this pretty good even quantitatively – Make this simple LO calculation using the CTEQ and the MRST PDFs at Q2=MW 2 and x~0.006 (corresponding to zero rapidity) and you’ll find that it DOES explain the Aw difference between MRST and CTEQ. - let’s see the evidence

CTEQ6.1 uv MRST02 Q2=Mw2 uv – dv Q2=Mw2 dv x- range affecting W asymmetry in the measurable rapidity range MRST and CTEQ uv – dv distributions are significantly different : at Q2=MW2 and x~0.006 CTEQ: uv=0.17, dv=0.11, uv-dv=0.06 MRST: uv=0.155, dv=0.11,uv-dv=0.045 Q2=Mw2

CTEQ6.1 dbar MRST02 dbar-ubar ubar Evidence that dbar = ubar for both PDFs at small-x at Q2=MW2 and x~0.006 MRST and CTEQ dbar=ubar=0.7 So Aw=0.06/(0.28+1.4) = 0.036 CTEQ Aw=0.045/(0.265+1.4) = 0.027 MRST…pretty close!

But perhaps we need to look more closely at the tiny difference in dbar-ubar– look at MRST and CTEQ dbar-ubar on a scale blown up by x10 Could this play a role? Without approximations..but still LO, Aw = d (uv-dv) +dv Δ d (uv+dv+2d) -2dΔ –dvΔ Where Δ=dbar-ubar=0.016 for CTEQ Aw = 0.7x(0.06) + 0.11x0.016 0.7X(1.68) – 2x0.7x0.016-0.11x0.016 And Δ=0.010 for MRST AW=0.7x(0.045) + 0.11x0.011 0.7x(1.665) – 2x0.7x0.011-0.11x0.011 The terms involving the difference of ubar and dbar are simply too small to matter compared to the terms involving the valence difference.

So for the time being I have mocked up some lepton asymmetry data to follow the prediction of MRST04 with 4% errors and no scatter (!) Compare to the predictions of ZEUS-S. What if we input these data to the ZEUS-S fit? The PDF uncertainty is improved by the input of such data – the uncertainty on AW is reduced from ~8% to ~5% at y=0 (this improvement is spread amongst the valence parameters, not in any one parameter) -- but the fit is unable to describe the MRST pseudodata unless the valence params are extended. The valence parametrisations at Q20 become xuv = Au xau (1-x)bu(1+du √x + cu x) , xdv = Ad xad (1-x)bd (1+dd√x + cd x)- 16 rather than 14 parameters are needed to fit MRST pseudodata MRST02 pseudodata ZEUS-S prediction

Conclusion we have valence PDF discrimination, and will be able to measure valence distributions at x~0.005 on proton targets for the first time …………………….. Data on the low-x valence distributions comes only from the CCFR/NuTeV data on Fe targets. The data extend down to x~0.01, but are subject to significant uncertainties from heavy target corrections in the low-x region. HERA neutral current data at high-Q2, involving Z exchange, make valence measurements on protons- but data are not yet very accurate and also only extend down to x~0.01 Current PDFs simply have prejudices as to the low-x valence distributions - coming from the input parametrisations. The PDF uncertainties at low x do not actually reflect the real uncertainty (horse’s mouth- Thorne) LHC W asymmetry can provide new information and constraints in the x region 0.0005 < x <0.05

Example of how PDF uncertainties matter for BSM physics– Tevatron jet data were originally taken as evidence for new physics-- Theory CTEQ6M i These figures show inclusive jet cross-sections compared to predictions in the form (data - theory)/ theory Today Tevatron jet data are considered to lie within PDF uncertainties And the largest uncertainty comes from the uncertainty on the high x gluon

Mc = 2 TeV, no PDF error Mc = 2 TeV, with PDF error Such PDF uncertainties the jet cross sections compromise the LHC potential for discovery. E.G. Dijet cross section potential sensitivity to compactification scale of extra dimensions (Mc) reduced from ~6 TeV to 2 TeV. (Ferrag et al) Mc = 2 TeV, no PDF error Mc = 2 TeV, with PDF error 2XD 4XD 6XD SM

Gluon fractional error HERA now in second stage of operation (HERA-II) substantial increase in luminosity possibilities for new measurements And it could get much better… Gluon fractional error x HERA-II projection shows significant improvement to high-x PDF uncertainties relevant for high-scale physics at the LHC  where we expect new physics !!

Inputting data to a PDF fit needs a prediction for the cross-section which can be easily obtained analytically –true for DIS inclusive cross-section. But many NLO cross-sections can only be computed by MC and can take 1-2 CPU days to compute. This cannot be done for every iteration of a PDF fit. Recently grid techniques have been developed to include DIS jet cross-sections in PDF fits (ZEUS-JETs fit)

This technique has been extended to LHC high-ET jet cross-sections Use data at lower PT and higher η-where new physics is not expected T. Carli Dan Clements, Glasgow Claire Gwenlan, Oxford

Effect Of Increased Statistics on PDF Fits Increase 10×statistics Gluon Fractional Error Gluon Fractional Error Increasing the statistics from 1fb-1 to 10fb-1 has little effect on improving the constraining of PDFs at ATLAS. Dan Clements- DIS2006 –Structure Functions and Low x WG

Such PDF uncertainties on the jet cross sections compromise the potential for discovery. E.G. Dijet cross section potential sensitivity to compactification scale of extra dimensions (Mc) reduced from ~6 TeV to 2 TeV. (Ferrag et al) Mc = 6 TeV, no PDF error The reduced uncertainties can then be used in background calculations for new physics signals

Summary At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs) PDF uncertainties affect discovery physics Higgs cross-sections high ET jets..contact interactions/extra dimensions Investigate ‘standard candle’ processes are not SO insensitive to PDF uncertainties We can make measurements at ATLAS which will improve the PDF uncertainty

LHC is a low-x machine (at least for the early years of running) Low-x information comes from evolving the HERA data Is NLO (or even NNLO) DGLAP good enough? The QCD formalism may need extending at small-x BFKL ln(1/x) resummation High density non-linear effects etc. (Devenish and Cooper-Sarkar, ‘Deep Inelastic Scattering’, OUP 2004, Section 6.6.6 and Chapter 9 for details!) Thorne will talk about this

MRST have produced a set of PDFs derived from a fit without low-x data –ie do not use the DGLAP formalism at low-x- called MRST03 ‘conservative partons’. These give VERY different predictions for W/Z production to those of the ‘standard’ PDFs. Z W+ W- MRST02 W+ Z W- MRST03

Differences persist in the decay lepton spectra and even in their ratio and asymmetry distributions Reconstructed Electron Pseudo-Rapidity Distributions (ATLAS fast simulation) 200k events of W+- -> e+- generated with HERWIG 6.505 + NLO K factors Reconstructed e- Reconstructed e+ 6 hours running MRST02 MRST03 MRST02 MRST03 h h Reconstructed e+- e- Asymmetry Reconstructed e- / e+ Ratio MRST02 MRST03 h MRST02 MRST03

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)

The values of cross section of the process moves in the range 0 – 10% of the cross section obtained with CTEQ6ll depending on the cuts and PDFs used The shape of distributions of kinematic quantities of Z boson and its secondaries seems to be very similar at the current(very preliminary) level of investigation. This has to be confirmed/disconfirmed by more quantitative analysis. There are differences between the shapes of distributions of kinematic quantities of Z boson and its secondaries obtained with Herwig/Jimmy and Pythia.

Physics Motivations for Z+ b-jet Measurement of the b-quark PDF Process sensitive to b content of the proton (bb->Z @ LHC is ~5% of entire Z production -> Knowing σZ to about 1% requires a b-pdf precision of the order of 20% Differences in total Z+b cross-section from current PDFs are of the order of 5% Pt b (MeV/c)

Conclusions II Z+b measurement in ATLAS will be possible with high statistics and good purity of the selected samples with two independent tagging methods We will have data samples to control systematic errors related to b-tagging at the few-% level over the whole jet Pt distribution b-tagging efficiency Mistagging: from W+jet The measurement of Z+b should be more interesting at LHC than at Tevatron: Signal cross-section larger (x80), and more luminosity Relative background contribution smaller (x5)

Now study PDF effects < pT(W) > Same pattern dMW(fit) ~no correlation RMS(yW) Set#

Summary Raw dMW from pdf uncertainties as of today, when using pT(e), is ≥50 MeV However, measuring pT(Z) with 10 fb-1, gives  dpT(W) ~ 3 MeV  dMW(fit) ~ 1 MeV (slope)  2.5 MeV (residuals, from y(W) distortions) ~ 2.7 MeV This is obtained using pT(e), and should be true a fortiori when using MT(W), which is less sensitive to pT(W) Are pdf’s trustworthy to this level (i.e should we believe the correlation so blindly?) Next time : check if the correlation is preserved to this level with ResBos uncertainty from missing higher orders (vary Qren, Qfac in MCatNLO)

extras

And how do PDF uncertainties affect the Higgs discovery potential? q W/Z H g H t S Ferrag

Standard Model side: Theoretical Uncertainties Generator level MC@NLO: s computed by 100 GeV bin 200 GeV < invMass< 2500 GeV Sources of uncertainties: -Factorisation and Renormalisation scales 1/p * m t < m < p* m t -PDFs: CTEQ6 Energy scale variation 40 CTEQ6 pdfs S. Ferrag Invariant mass(GeV) Fully simulation level: Sample Zee M>150: 5114

So for the time being I have mocked up some lepton asymmetry data to follow each of the predictions of CTEQ6.1, MRST02 and ZEUS-S with 4% errors and no scatter (!) . In the plots below each of these pseudodata sets are compared to the predictions of ZEUS-S Cteq6.1 pseudodata ZEUS-S prediction MRST02 pseudodata ZEUS-S prediction ZEUS-S pseudodata ZEUS-S prediction It is clear that the MRST pseudodata do not agree with the ZEUS PDF prediction even within PDF errors What if we input these data to the ZEUS-S fit?

But it is possible that dbar and ubar could be more different for other PDFs CTEQ MRST Alekhin There are many difference between these PDF sets so I have made two toy PDFs (based on ZEUS-S) in which the only difference is dbar-ubar as x → 0. Standard dbar-ubar = 0.24 x0.5 (1-x)9 at Q20 ~ 7 GeV2 and Extreme dbar-ubar = 0.005x-0.16(1-x)13 (1+100x) at Q20 ~ 7 GeV2 ZEUS standard ZEUS extreme ALL with E866 dbar-ubar data superimposed

Clearly even this more extreme difference in dbar-ubar has had no visible impact on the lepton asymmetry The basic reason is that dbar and ubar are themselves quite large ~ O(1) at x=0.006 and Q2=MW2- since they have evolved from small values at low Q2 BUT The difference dbar-ubar has become relatively negligible - O(10-2) because it does NOT evolve – we could only see it if we could measure at the sub percent level of accuracy- W lepton asymmetry from ZEUS extreme Dbar-ubar W lepton asymmetry from ZEUS standard Dbar-ubar dbar dbar-ubar . A large difference in dbar-ubar at Q2=MW2 would involve putting it in as similarly large at the starting scale Q2~ 7 GeV2 –incredible fine tuning For ZEUS- extreme

How to constrain PDFs at LHC We can improve our knowledge on PDF’s at LHC measuring the vector boson production: photons, W’s, and Z’s Direct g production: (LO contributions) Compton: (~90%) Annihilation: (~10%) W production: (main contributions) Z production: (main contributions) At the EW scale we will have dominantly sea and gluon parton interactions at low-x And at Q2~M2W/z the sea is driven by the gluon which is far less precisely determined for all x values

Jet and photon are back to back How to constrain gluon-PDFs at LHC direct g production (Ivan Hollins, Birmigham Univ.) Typical Jet +  event Jet and photon are back to back Sensitive to PDF differences: CTQE6L-MRST01E ~ +16-18% disagreement on Jet and g PT distributions At this stage the aim is to establish the degree to which signal can be seen (photon identification, fake photon rejection etc.): g selection efficiency >91% Investigate methods for reducing background

Prompt photon cross-sections may also be amenable to this treatment –compare photon pt and η distributions for Cteq61 up and down eigenvector 15 -emphasizing the uncertainties in the high-x gluon (PT > 330 GeV) Ivan Hollins Birmingham

2) Differences I saw between pdf sets Plots are for photon distributions only ~700k events in each ~ 100fb-1 at 330 GeV Plots look only at the shape, no comparison made to absolute numbers  - distributions for MRST2004 and Cteq61. PT > 330 GeV  PT At ~350 GeV,  = 0, xT~0.05 Is this caused by High x uncertainly in the quark Mid x uncertainty in the gluon A v large uncertainly in the high x gluon? A poor LO cal?