HERA I - Preliminary H1 and ZEUS QCD Fit 28/03/08 A.Cooper-Sarkar, R.Devenish, C.Gwenlan, K.Nagano, J.Ferrando, Y.Ri, E.Tassi, J.Feltesse, A.Glazov, M.Klein, G.Li, B. Olivier, V.Radescu, E.Rizvi, V.Shekelian, Z.Zhang Choice of data set Central fit: choice of parametrization Central fit: choice of error treatment Central fit: choice of model assumptions Quality of fit to data PDFs plus experimental errors PDFs plus model uncertainties Comparison to older H1/ZEUS fits, comparison to CTEQ, MRST Model uncertainty investigations Model Variations

Preliminary QCD Fit to Combined H1-ZEUS HERA-I data A.Cooper-Sarkar, R.Devenish, C.Gwenlan, K.Nagano, J.Ferrando, Y.Ri, E.Tassi, J.Feltesse, A.Glazov, M.Klein, G.Li, B. Olivier, V.Radescu, E.Rizvi, V.Shekelian, Z.Zhang

QCD Fits of the preliminary combined data set presented at LP07 Input data sets : Published HERA I cross sections NC and CC e+, e- 1.5 < Q2 < 30000 GeV2 → 240 pb-1 1.5 With H1 NC MB (Q2 < 12 GeV2) moved up by 3.4 % after reanalysis of luminosity

Possible forms of PDF parametrization: H1 style Published H1 PDF2000 New H1-style parametrization optimised for combined data set Optimization means starting without D,E,F parameters and adding parameters until there is no further χ2 advantage PDFs: gluon, U=u+c, Ubar=ubar+cbar, D=d+s+b, Dbar=dbar+sbar+bbar Sea flavour break-up at Q0: s = fs*D, c=fc*U AU=(1-fs)/(1-fc)AD

Possible forms of PDF parametrization: ZEUS style ZEUS-JETS published New ZEUS-JETS optimized for combined data set PDFs: gluon, uv, dv, Sea= usea+ubar+dsea+dbar+s+sbar+c+cbar Sea flavour break-up at Q0: sbar = (dbar+ubar)/4, charm dynamically generated, dbar-ubar fixed to fit E866 data

Possible forms of PDF parametrization: ‘inbetween’ Original ‘inbetween’ parametrization Lim x→0 u/d →1 ‘inbetween’ parametrization optimized to combined data set Lim x→0 u/d →1 PDFs: gluon, uv, dv, Ubar=ubar+cbar, Dbar=dbar+sbar+bbar Sea flavour break-up at Q0: s = fs*D, c=fc*U AUbar=(1-fs)/(1-fc)ADbar Can also dynamically generate charm, but need to keep AUbar to ADbar relationship as here

Which look rather like the published ZEUS and H1 gluons respectively! For each of the old parametrizations, which have non-zero D parameter for the gluon, there are two minima: ‘straight’ gluon and ‘humpy’ gluon solution. Which look rather like the published ZEUS and H1 gluons respectively! For the H1/ZEUS combined data set the χ2 of the straight solution is always lower by about 10 χ2 points. For the H1 data set alone the ‘humpy’ gluon had the lower χ2, whereas for the ZEUS data set alone the ‘straight’ gluon had the lower χ2 This χ2 table compares humpy and straight gluon solutions for the old parametrizations and the straight solution for the new parametrizations: using a χ2 definition where all 47 systematic errors of the combined data set are added in quadrature. Table from J.Feltesse excellent agreement on all results in this talk 433.6

Choice of parameterization All parametrizations give an excellent χ2 /degree of freedom : Inbetween : 431.9/563=(573-10) H1 param : 434.7/563=(573-10) ZEUS_Jet : 433.6/562=(573-11) Chosen central parameterization : ‘optimized Inbetween’ Motivations : Less model dependence on B parameters than in H1 param. No need for an additional input (ubar-dbar) x distribution as in ZEUS-Jet param Most conservative errors. It is inspired by both H1 and ZEUS parameterizations. The two other parameterizations AND humpy solution for inbetween the are considered in the model variations

Choice of treatment of systematic errors Reminder: combining H1 & ZEUS cross-sections Full account taken of systematic uncertainties of H1 and ZEUS measurements, including correlations: 43 separate sources plus 4 ‘procedural uncertainties’ 44:   photoproduction assumed correlated in H1-ZEUS 45:  FL is set to 0 for Centre-of-Mass Energy shift 46:  Difference between "all relative" -- "global normalisations relative" treatement 47:  Extra 1% for y<0.02 NC data to take into account correlated HFS simulation   (based on hadronic energy scale correlations study)

47 systematic errors added to statistical quadratically χ2= 428.0 47 systematic errors treated by Hessian method χ2=553.1 43 original sources of systematic errors added to statistical quadratically and 4 procedural errors Offset χ2=476.7 Central values very similar, uncertainties largest for OFFSET method, we chose this because it is most conservative. Note there is not much difference between these different error treatments since systematic errors not so big Proposal that these χ2 values be made preliminary, all are for 563 degrees of freedom

Theoretical framework NLO DGLAP evolution Facttorisation and renormalisation scales Q2 Zero-mass variable flavour number heavy quark scheme Model assumptions Which will be varied to assess model uncertainty Q02 = 4 GeV2 input scale Q2min = 3.5 GeV2 minimum Q2 of input data fs = 0.33D strange sea fraction, means s=0.5d fc = 0.15U charm sea fraction, means c=0.176u mc=1.4 mass of charm quark mb=4.75 mass of beauty quark αs(Mz) = 0.1176 PDG2006 value Form of the parametrization: ‘in between’/ H1/ ZEUS-JETS/ ‘humpy’

PDF fit RESULTS let’s call it the HERA-I PDF Comparison to HERA combined data

Preliminary status requested HERA I - Preliminary H1 and ZEUS QCD Fit Preliminary status requested Blow up just three x values to see older ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF New HERA-I PDF fit predictions vs. H1/ZEUS combined data for NC e+p. Experimental uncertainties on the PDF fit predictions are included but can barely be be resolved.

Preliminary status requested HERA I - Preliminary H1 and ZEUS QCD Fit Preliminary status requested New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at low Q2. Experimental and model uncertainties on the PDF fit predictions are included but barely be resolved

Preliminary status requested HERA I - Preliminary H1 and ZEUS QCD Fit Preliminary status requested New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at high Q2. Experimental and model uncertainties on the PDF fit predictions are included but cannot be resolved

Preliminary status requested HERA I - Preliminary H1 and ZEUS QCD Fit Preliminary status requested New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at high Q2. Experimental and model uncertainties on the PDF fit predictions are included

HERA I - Preliminary H1 and ZEUS QCD Fit CC e+p (left) e-p (right) compared to older ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF.

PDF fit RESULTS PDFs: experimental and model errors Comparison to other PDFs

First consider experimental uncertainties HERA I PDFs New H1/ZEUS combined PDFs with experimental uncertainty bands from statistical errors plus 43 sources of systematics in quadrature plus 4 procedural systematics OFFSET

Now add 6 sources of model dependence mc 1.3 → 1.55 GeV variation of mass of c quark mb 4.3 → 5.0 GeV variation of mass of b quark fs 0.25→ 0.40 variation of strange sea fraction at Q0 fc 0.10→ 0.20 variation of charm sea fraction at Q0 Q02 2.0 →6.0 GeV2 variation of starting scale Qmin2 2.5→5.0 GeV2 variation of cuts on the data included

Now add 6 sources of model dependence HERA I PDFs HERA I PDFs New H1/ZEUS combined PDFs with total experimental uncertainty plus model uncertainty

Preliminary status requested Compare to previous ZEUS/H1 results Preliminary status requested HERA I PDFs Resolution of previous discrepancies, improvement in level of uncertainty

Compare to CTEQ and MRST analyses Do we want preliminary status for these?

Compare to CTEQ and MRST analyses: 2008 Note MSTW08 is as yet unpublished- I have a pre-release

Look at our results in more detail: vs Q2

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands AT THE STARTING SCALE Q20 = 4 GeV2

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands At Q2 =10 GeV2

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: AT Q20 = 100 GeV2 . Note how uncertainties are decreasing

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: AT Q20 = 10000 GeV2 . At scales relevant to LHC physics uncertainties are impressively small.

Checks between ZEUS and H1

Check analysis H1 Package ZEUS Package

Investigate model uncertainties

Include only variation of charm mass and beauty mass mc:1.35→1.5 GeV and mb: 4.3 →5.0 GeV This model dependence is invisible

Include only variation of strange fraction fs: 0.25 →0.40 Makes very little difference in the total Sea, but affects sea flavour break-up

Include only variation of charm fraction fc: 0.10 →0.20 A smaller effect than fs: makes very little difference in the total Sea, but affects sea flavour break-up

Include only variation of starting scale Q02: 2 → 6 GeV2 Has a small asymmetric effect on PDF ucertainties

Include only variation of minimum Q2 of fitted data Qmin2: 2 Include only variation of minimum Q2 of fitted data Qmin2: 2.5 → 5 GeV2 Has an even smaller asymmetric effect on PDF ucertainties

We illustrate some of the other choices as variations compared to our central value: αS(Mz) = 0.1156 → 0.1196 New H1 ‘optimized’ parametrization New ZEUS-JETS ‘optimized parametrization Old ‘in-between’ parametrization with ‘humpy’ gluon solution Use of massive variable flavour number scheme- cannot be checked by both ZEUS and H1 yet, so no preliminary request

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested Comparison of central fit plus total uncertainties to variations with αs(Mz)=0.1156 (left) and 0.1196 (right) Confirms what we’ve already seen-variation is outside the gluon error bands even when other model dependence is accounted.

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested Comparison of central fit plus total uncertainties to parametrization variation using: New H1 optimised parametrization Marginally outside normal error bands for valence even when other model dependence is accounted (but note this is at low x where valence isn’t very significant)

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested Comparison of central fit plus total uncertainties to parametrization variation using: New ZEUS-JETS optimised parametrization Inside error bands if other model dependence is accounted

Preliminary status requested HERA I PDFs HERA I PDFs Preliminary status requested Comparison of central fit plus total uncertainties to parametrization variation using: the ‘humpy’solution for the h1/zeus parametrization. At Q2=10 (left) and Q2=4 (right)GeV2 where the humpy structure is more visible. Marginally outside normal error bands for valence more than for gluon! even when other model dependence is accounted (but note this is at low x where valence isn’t very significant)

Finally we may be criticized for the use of a zero-mass scheme. Comparison of central fit plus total uncertainties to variation of heavy quark scheme: using massive variable flavour number scheme of Thorne. This cannot yet be checked by both H1 and ZEUS

Summary An immense amount of work has been done to resolve differences between ZEUS and H1 PDF fitting analyses Agreement has been reached on procedure AND Agreement has been reached on fit results We wish to make preliminary: Plots of the new HERA-I PDF fit compared to the new HERA-I combined data Plots of the PDFs: u-valence, d-valence, gluon and total Sea : U, D, Ubar, Dbar with experimental uncertainty bands and model uncertainty bands and additional plots showing variations NOT added into model uncertainty Plots of the PDFs in comparison to previous ZEUS and H1 analyses Plots of the PDFs in comparison to CTEQ6 and MRST04 analyses

EXTRAS: Questions asked by ZEUS and H1 already

Compare to previous ZEUS-JETS fit : with errors on both The extra data and reduction of systematics constrains gluon better at low-x, which by the momentum sum-rule constrains it better at high-x. Hence it is precise even without jets.

What would it look like with the parametrization uncertainty added in Illustration of the difference between using 6 or 7 sources of model uncertainty: On the right the 7th uncertainty from form of parametrization: h1 vs zeus-jet is added in.

How much of the change is data and how much is the parametrization: the plots below are ALL with the new combined data- parametrization make a large difference to the error estimate ZEUS-Jets Parametrization in between H1 parametrization Central values are really very similar- quite remarkable since ZEUS and H1 parametrizations are not- however the size of errors differs, with ‘in between’ being the most conservative

Other extras

Now in terms of ubar, dbar, sbar, cbar xubar xcbar xdbar xsbar ZEUS-Jets Parametrization in between H1 parametrization The similarity of these is perhaps even more remarkable given the different treatment of charm- clearly the fixed fraction fc=0.15 is about right compared to dynamical turn on at Q2=mc2

Compare to previous ZEUS and H1 analyses in a different style

And we could have added in Include only variation of αs (Mz): 0 And we could have added in Include only variation of αs (Mz): 0.1156 → 0.1196 (PDG2006) Looking at this uncertainty alone it affects only the gluon PDF

And if we add in the variation of αs (Mz) to the other 6 model uncertainties. I chose not to add this in since MRST(MSTW) and CTEQ both use fixed alphas and I want the public to compare ‘like with like’.

Comparison of central fit plus total uncertainties to variations with alphas=0.1156 (left) and 0.1196 (right) : U D plots

There is another model uncertainty that we could add in- the variation if one uses different forms of parametrization: H1 style newly optimized paremetrization and ZEUS-JETs style newly optimized parametrization. Looking at this uncertainty alone there is a small asymmetric effect, most visible in valence distributions.

Illustration of the difference between using 6 or 7 sources of model uncertainty: On the right the 7th uncertainty from form of parametrization: h1 vs zeus-jet is added in. There is excellent agreement with J Feltesse. I chose not to add this in because its not the same kind of variation as the others- varying our new parametrization to two others is not an ‘up and down’ variation!

Comparison of central fit plus total uncertainties to parametrization variation using: the ‘humpy’solution for the h1/zeus parametrization

NC e+p low and high Q2 from Enrico, only experimental errors

NC e-p high Q2 from Enrico, only experimental errors

CC e-p and e+p from Enrico, only experimental errors

Check analysis H1 Package ZEUS Package Gluon PDF

Check analysis H1 Package ZEUS Package u-valence

Check analysis H1 Package ZEUS Package d-valence