pdfs at the lhc: lessons from run i and preparation for run ii

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Parton Distributions at the LHC Run II!Lessons from Run I and preparation for Run II

Juan Rojo!STFC Rutherford Fellow!

Rudolf Peierls Center for Theoretical Physics!University of Oxford!

! ATLAS Standard Model Workshop!

LAPP, Annecy, 05/02/2015

Juan Rojo ATLAS SM Workshop, LAPP Annecy, 07/02/2015

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Parton Distributions!status Feb 2015


Parton Distributions and LHC phenomenology

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2) Very large PDF uncertainties (>100%) for new heavy particle production

Supersymmetric QCD1) PDFs fundamental limit for Higgs boson characterization in terms of couplings

3) PDFs dominant systematic for precision measurements, like W boson mass, that test internal consistency of the Standard Model


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PDF sets at the dawn of LHC Run II


Data Theory Methodology

NNPDF3.0 arxiv:1410.8849

DIS Fixed Target DY Jets Top quarks LHC DY

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NNLOapprox for jets APPLgrid/aMCfast/FastNLO for LHC data EW corrections FONLL for heavy quarks

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Closure testing validation Artificial Neural Nets Monte Carlo replicas Bayesian reweighting

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MMHT14 arxiv:1410.3989

DIS Fixed Target DY Jets Top quarks LHC DY

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No LHC jets at NNLO APPLgrid/FastNLO EW corrections TR for heavy quarks Deuteron corrections

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Hessian eigenvectors More flexible param (Cheb polynomials) MC and Hessian RW Dynamic tolerance

!CT14

preliminary

DIS Fixed Target DY Jets LHC DY

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No LHC jets at NNLO APPLgrid/FastNLO Estimate of scale vars ACOT for heavy quarks

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Hessian eigenvectors More flexible param MC and Hessian RW Fixed tolerance

!ABM12

arxiv:1310.3059

DIS Fixed Target DY LHC DY

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Fixed-Flavor N for DIS VFN for LHC Fitted

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Hessian eigenvectors No tolerance

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HERAPDF2.0 preliminary

HERA-I and HERA-II !

Different HQ schemes RT default for HQ

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Hessian eigenvectors Model and param uncertainties MC representation also

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PDF sets at the dawn of LHC Run II


ATLAS CMS LHCb

NNPDF3.0 arxiv:1410.8849

2010 7 TeV incl jets 2.76 TeV incl jets

2010 W, Z rap dist, W pt 2011 high-mass DY

7 & 8 TeV ttbar xsecs !

2011 7 TeV incl jets 2011 W asy

2011 7 TeV Drell-Yan 2011 7 TeV W+charm 7 & 8 TeV ttbar xsecs

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2010 W rap 2011 Z rap

MMHT14 arxiv:1410.3989

2010 7 TeV incl jets 2.76 TeV incl jets

2010 W, Z rap dist 2011 high-mass DY


2011 7 TeV incl jets 2011 W asy

2011 7 TeV Drell-Yan 2010 Z rap


2010 W rap 2011 Z rap

CT14 preliminary

TBD TBD TBD

ABM12 arxiv:1310.3059

!2010 W, Z rap dist

! 2011 W asy 2010 W rap 2011 Z rap

HERAPDF2.0 preliminary

None None None

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PDF benchmarking


In 2012, a extensive benchmark comparison was performed between NNPDF2.3, CT10, MSTW08, ABM11 and HERAPDF1.5!

Reasonable agreement between the three global PDF sets, with some important exceptions, like the gluon in the Higgs region or the large-x quarks, relevant for searches!

ABM systematically different from global sets: softer large-x gluon, harder small-x quarks. Understood from different treatment of heavy flavours. N.B. comparisons performed for common value of αS(MZ)!

HERAPDF1.5 affected by very large uncertainties due to the reduced dataset (no constrains from hadronic data)!

2012 Benchmarks, arXiv:1211.5142

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PDF benchmarking


2012 Benchmarks, arXiv:1211.5142

In 2012, a extensive benchmark comparison was performed between NNPDF2.3, CT10, MSTW08, ABM11 and HERAPDF1.5!

Reasonable agreement between the three global PDF sets, with some important exceptions, like the gluon in the Higgs region or the large-x quarks, relevant for searches!

ABM systematically different from global sets: softer large-x gluon, harder small-x quarks. Understood from different treatment of heavy flavours. N.B. comparisons performed for common value of αS(MZ)!

HERAPDF1.5 affected by very large uncertainties due to the reduced dataset (no constrains from hadronic data)!

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PDF comparisons made easy: APFEL-Web

http://apfel.mi.infn.it/

Comparing different PDF sets is now really easy thanks to the new APFEL-Web online PDF plotter!

Just log in, select the PDF sets that you want to compare, the plotting settings, and have fun!!

Bertone, Carrazza, J.R. 13


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Benchmarks Revisited

Juan Rojo ATLAS SM Workshop, LAPP Annecy, 07/02/2015 [GeV]XM210 310

Rat

io

0.80.850.9

0.951

1.051.1

1.151.2

1.251.3

Gluon-Gluon, luminosity

NNPDF30_nnlo_as_0118MMHT2014_nnlo_as_0118CT10_nnlo_as_0118

= 1.30e+04 GeVSG

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with

APF

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Web

[GeV]XM210 310

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Quark-Antiquark, luminosity

NNPDF30_nnlo_as_0118MMHT2014_nnlo_as_0118CT10_nnlo_as_0118

= 1.30e+04 GeVS

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These benchmarks are now being revisited in the context of the PDF4LHC updated recommendations for Run II!

Improved agreement between global sets for some crucial processes, like gg Higgs, but still important differences i.e. in large-x antiquarks, crucial for searches!

Also the PDF4LHC prescription for the PDF+αS

combined uncertainty has been simplified (addition in quadrature, common αS value for all sets )!

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ABM vs global PDF fits


NNPDF, arXiv:1303.1189

Thorne, arXiv:1402.3536 The predictions of the ABM sets are systematically

different from those of the global PDF fits, even once the different value of αS(MZ) is accounted for!

These differences are understood due to the combination of a Fixed-Flavor Number scheme used to fit DIS data (not suitable at high Q2) and the use of a limited dataset without jet data!

NNPDF2.3 DIS+FFN reproduces well ABM11 predictions, but worse quality of fit to HERA data!

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PDF fits in ATLAS


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PDF fits in ATLAS: pros and cons


Pros Cons

Allows detailed validation of PDF-sensitive measurements before data released, in particular the covariance matrix and the correlated systematics

Might delay the availability of the data for global PDF fitters

Internal tests of the consistency of measurements in terms of PDF constraints, for instance, top data should constrain gluon at large-x, but not quarks

One should be careful not to sell an interpretation paper (a QCD fit done within ATLAS, based on ATLAS data) as an actual ATLAS measurement

Useful comparisons of the predictions between different PDF sets, which provide guidance for the global fits, and motivation to include new data

Sometimes unclear when and how the theory calculations used in an ATLAS fit (applgrid, K-factors) will be available to the PDF fitters

Essential to extract fundamental SM parameters from data, i.e. the strong constant, top mass or W mass

PDF fits based on ATLAS data are by no means exclusive of ATLAS, other groups as well can do them (ie NNPDF)

Develop and maintain a solid PDF expertise in the collaboration, which in turn ensures that relevant PDF-sensitive measurements will be carried out in ATLAS

Could be dangerous to assume that fits based on HERA and ATLAS data only are competitive with global fits

!IMHO, it is really excellent that ATLAS performs PDF fits, and these activities should be encouraged within the collaboration - but the scope and limitations of such fits should be also clear

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The ATLAS strangeness determination


! First PDF determination performed in ATLAS:

excellent measurement and very nice QCD analysis, that illustrates the potential of the W and Z rapidity distributions to constrain strangeness!

What would be my interpretation of this analysis? A QCD analysis of HERA and ATLAS W,Z data shows that this measurement is sensitive to the strange PDF, with preference for a symmetric strange sea.!

And what would be an incorrect interpretation? ATLAS has measured the strange sea to be symmetric!

A PDF fit within ATLAS is very useful, but one should never forget that in a global fit, different datasets pull in different directions, and in addition that different PDF fitting methodologies might change the conclusion!

The NNPDF2.3 paper showed that a fit only with ATLAS and HERA data has very large uncertainties, and that is possible to fit at the same time ATLAS W,Z and neutrino data

NNPDF re-analysis based on identical dataset

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Towards an ATLAS global fit


! The wealth of PDF-sensitive measurements from ATLAS suggest that an ATLAS global fit might be feasible:

starting with the usual backbone of HERA data, ATLAS data can be used for quark flavour separation (W,Z, low and high-mass Drell-Yan, …), gluons (jets, photons, top quarks, Z and W pt), even for the photon PDF!

Useful to test internal consistency of all the ATLAS datasets, their cross-correlations, important information for global PDF fits. i.e. do jet and top data pull in the same direction for gluon? do all DY datasets pull in the same direction for strangeness?!

With available data, such ATLAS global fit is still far from being competitive compared with global fits, as the NNPDF3.0 HERA+ATLAS fit shows!

But with more data, and including Run II, the scenario could be different …

“ATLAS Global fit” based on NNPDF3.0

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Stress Tests of QCD Theory with PDF fits


In addition to quantifying the constraints on PDFs of new ATLAS data, many interesting PDF studies could be performed with the aim of testing advanced QCD theory at the LHC. Some examples:!

Determination of the strong coupling constant and its running in the TeV range! Validate higher order calculations, i.e. NNLO for jets and top pair differential. Fit quality improved?! High-energy resummation in a joint fit of ATLAS and HERA data, deviations from DGLAP?! Threshold resummation, and impact on Higgs production?! Determination of the intrinsic charm content of the proton! PDF fits with parton shower effects, specific PDFs for NLO event generators

aMCfast

To maximise the physics output of PDF fits in ATLAS, essential to optimise the interface between HERAfitter (used for PDF fits in ATLAS) and the relevant theory codes that implement some of the above features

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Some additional questions …


Q1 Should ATLAS PDF fits include also data from other experiments, and become a global fit?!No, ATLAS PDF fits should be restricted to the interpretation of their own data only, with the usual HERA backbone. Individuals can pursue more global fits, but these should take place outside ATLAS!!Q2 Should ATLAS, given that it is experimental collaboration, stop doing PDF fits, which are interpretation papers?!No, interpretation papers can and should be pursued within ATLAS, just as is done for Higgs couplings or BSM searches, no reason why not doing it for SM measurements!!!Q3 Should ATLAS PDF fits estimate model and parametrisation variations?!Yes, this is really essential due to the reduced dataset. Else, the quoted PDF uncertainties would be completely unrealistic e.g. the Hessian HERAPDF2.0 uncertainties are similar to those of global fits ….!!Q4 Should ATLAS not pursue some measurements (and their interpretation) in cases where theory is not precise enough, like Z+1 jet or inclusive jets, where NNLO effects are important?!No, ATLAS should do the measurements of these important processes as accurately as possible, and then it is up to us theorists to keep the pace. Perhaps the Z high pT data can be used in PDF fits only in 3 years from now, but the data will be already available!!Q5 Should we worry about TMD PDFs or TMD factorisation for precision measurements of Run II?!No, in the current state-of-the-art of TMD fits, tuning Monte Carlo generators is probably enough, no obvious improvement if a different theory framework, like TMDs, is used

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ATLAS data in !Global PDF fits


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The PDF fitter’s wish-list for ATLASProcess Run I Run II

Inclusive Jets2011 7 TeV published but data not available

2012 8 TeV not yetExplore Constrains on large-x gluon and quarks

Dijets 2011 7 TeV published but data not available 2012 8 TeV not yet

Explore Constrains on large-x gluon and quarks

Test NLO and NNLO QCD calculations

Inclusive photons

2011 7 TeV published (no cov mat) 2012 8 TeV not yet

Explore Constrains on medium-x gluon

Ratios to reduce scale dependence?

Top quark production

2011 7 TeV diff distributions available 2012 8 TeV not yet

Differential distributions competitive with jets? Need fast interface to NNLO calculation

Constrain gluon at large-x

W,Z + jets 2011 7 TeV available 2012 8 TeV not yet

Explore Impact on gluon PDF

Ratios of W and Z for quark flav separation

Inclusive W,Z 2010 rap dists available 2011 rap dist should follow soon

Constrain quark flavor separation and strangeness Limited by systematics?

High-mass DY 2011 7 TeV availableExplore

Antiquarks at large-x Test NNLO QCD and NLO EW calculations!

All these processes are of course very important for PDF studies, and should be pursued with high-priority at Run II. Let me concentrate here on some less obvious possibilities ….!

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Cross section Ratios between 7, 8 and 14 TeV!The staged increase of the LHC beam energy provides a new class of interesting observables: cross section ratios for different beam energies!

!!These ratios can be computed with very high precision due to the large degree of correlation of theoretical uncertainties at different energies!

Experimentally these ratios can also be measured accurately since many systematics, like luminosity or jet energy scale, cancel partially in the ratios!

These ratios allow stringent precision tests of the SM, like PDF discrimination!

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Mangano, J. R., 12


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Juan Rojo NIKHEF Theory Seminar, Amsterdam, 22/01/2015

ATLAS: Gluon from 7 TeV / 2.76 TeV jet xsecsCMS: Drell-Yan 8 TeV / 7 TeV ratio

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Czakon, Mitov, Mangano, J. R., 13

Top Quark pair production: Excellent PDF discrimination

) Z

( MS_ 0.112 0.113 0.114 0.115 0.116 0.117 0.118 0.119 0.12

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ABM11CT10HERAPDFMSTW2008NNPDF2.3

LHC 8 over 7 TeV

effects like value of top mass largely cancel in the ratio

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Cross section Ratios between 8 and 13 TeV!The ratios of cross-sections, inclusive or differential, between 13 TeV and 8 TeV, should be one of the highest priorities in the first months of Run II data taking!

Allows to perform precision physics even if some systematics, like luminosity, are still large, since they can be cancelled, for instance forming suitable double ratios, e.g., for top production!

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Should be a useful ingredient for global PDF fits!!

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Mangano, J. R., 12

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Heavy Quark production!By now well stablished that top quark production can be used to constrain the large-x gluon PDF!Thanks to the NNLO calculation, now also differential data can be used for fits!However, it is less appreciated that charm and bottom production can be used to constrain the gluon, this time at small-x. And the top NNLO calculation can be also applied here.!LHCb data most sensitive, but ATLAS should also provide a competitive measurement. Important to explore at Run II. Provide full covariance matrix, breakup of systematics (not currently available)


x 6<10 5<10 4<10 3<10 2<10 1<10

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NNPDF3.0

NNPDF3.0 + LHCb D0 data (wgt)

NNPDF3.0 + LHCb D0 data (unw)

=0.118s_NNPDF3.0 NLO

Gauld, J. R., Rottoli, Sarkar, Talbert, in prepsimilar studies by the HERAfitter group

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Jets in NNLO global fits! The recent calculation of the gluon-gluon channel

NNLO jet cross sections is an important milestone towards the exact inclusion of jet data in NNLO PDF fits!

Large O(20-25%) enhancements wrt NLO results, if the scale used μ=pT,leading (pT of leading jet)!

Perturbative convergence improved if the jet μ=pT is used instead: smaller K-factors!

On the other hand, the gg channel is small at medium and large pT at the LHC energies!

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Juan Rojo SMatLHC14, Madrid, 09/04/2014

! While full NNLO result becomes available, approximate

NNLO results can be derived from the improved threshold calculation: reasonable approximation to exact at large pT and central region, breaks down at small pT!

Assume same K-factor holds for other partonic channels!

Carrazza and Pires, arXiv:1407.7031

NNLO threshold !De Florian et al, arXiv:1310.7192

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Jets in NNLO global fits! We can therefore compute approximate NNLO K-factors using the threshold approximation!

Comparison with exact gg NNLO can determine for which values of jet pT and η the NNLOthres calculation can be trusted!

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Juan Rojo SMatLHC14, Madrid, 09/04/2014

! At NNLO, the numerical value of χ2 depends sizeably on definition, “experimental” vs “t0”!

Will be very interesting to revisit these issues for the ATLAS 2011 jet data!

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Percentage difference between exact and approx ggJet data included in NNPDF3.0 at NNLO

χ2 NLO (exp) χ2 NLO (t0) χ2 NNLO (exp) χ2 NNLO (t0)

At medium pT and non-central rapidities, most of ATLAS data cut from the NNLO NNPDF3.0 fit. Should be better with 2011 jets!

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PDF fits at NLO+PS accuracy


! NLO+PS is current standard for LHC event simulation, and improves in many directions over fixed-order

NLO results: improved pert. behaviour, direct relation with measured quantities, less need for kin cuts …!

Using NLO+PS calculations in global PDF fits should have many important applications, like for the W mass among others, and is now technically possible thanks to aMCfast, the fast interface to MadGraph5_aMC@NLO based on the applgrid library!

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aMCfast: Bertone, Frixione, Frederix, J.R., Sutton,!arXiv:1406.7693 (for NLO), NLO+PS in preparation

! One crucial aspect to

explore is the role of the PDF used by the MC shower, since this is fixed even in the fast NLO+PS grid!

Quite small effect in most observables, except extreme kinematics like forward rapidities!

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aMCfast: Bertone, Frixione, Frederix, J.R., Sutton,!arXiv:1406.7693 (for NLO), NLO+PS in preparation

! One crucial aspect to

explore is the role of the PDF used by the MC shower, since this is fixed even in the fast NLO+PS grid!

Quite small effect in most observables, except extreme kinematics like forward rapidities!

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!With such tools, one could include directly the Z pT

distribution into global fits, which is not possible at fixed-order NLO!

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! QED and electroweak corrections are essential for precision LHC phenomenology: W and Z

production, W mass determination, WW boson pair production, TeV scale jet and top quark pair production, searches for new W’, Z’ bosons!

Consistent inclusion of electroweak effects require PDFs with QED corrections and a photon PDF !

NNPDF2.3 QED: first-ever determination of the photon PDF from LHC data!

Neglecting photon-initiated contributions leads to systematically underestimating theory errors in crucial BSM search channels!

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PDFs with QED corrections

( GeV )llM500 1000 1500 2000 2500 3000 3500

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WW production @ LHC 8 TeV

High-Mass Drell-Yan High-Mass WW prod


NNPDF 13

At Run II, some interesting EWK measurements that have been proposed to constrain the photon PDF!

For instance, the triple differential measurement of Drell-Yan cross-sections in invariant mass, rapidity and lepton transverse momentum allows to neatly disentangle photon PDF effects from other EWK effects!

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Pinning down the photon PDF


Boughezal et al, arXiv:1312.3972

Also the measurement of WW production at low transverse momentum and high invariant masses should provide direct constraints on the photon PDF!

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PDF uncertainties !at the LHC made easy


x-510 -410 -310 -210 -110 1

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Compressed Monte Carlo PDFs! Motivation: provide a practical implementation of the PDF4LHC recommendation, easy to use by

the experiments and computationally less intensive that the original prescription!

Having a single combined PDF sets (even with large number of eigenvector/replicas) would already be useful since widely-used tools like MadGraph5_aMC@NLO, POWHEG or FEWZ provide the PDF uncertainties without any additional cost!

But this is not true for all theory tools used at the LHC, so there is still a good motivation to be able to use a combined PDF set with a small number of eigenvectors/replicas!

Two approaches: META-PDFs (Gao and Nadolsky) and Compressed MC PDFs (CMC-PDFs)!

CMC-PDFs based on the Monte Carlo statistical combination of different PDF sets, followed by a compression algorithm to end up with a reduced number of replicas


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The Monte Carlo combination has a robust statistical interpretation, and in many cases leads to similar results, with somewhat smaller uncertainties, compared to the original PDF4LHC envelope.

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Basic strategy !

The MC combination of PDF sets is easy, but number of MC replicas still too large!

Compress the original probability distribution to one with a smaller number of replicas, in a way that all the relevant estimators (mean, variances, correlations etc) for the PDFs are reproduced

! The compression is applied at Q = 2 GeV,

though the results are robust wrt other choices!

Various options about how the error function to be minimised can be defined, ie., to reproduce central values add a term

! The algorithm also minimises the Kolmogorov distance

between the original and compressed distributions

! Same for variances, correlations and higher

moments!

At the end, optimal choice decided by the resulting phenomenology

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Gaussian vs non-Gaussian! Even if the original PDF sets in the combination are approximately Gaussian, their combination in general will

be non-Gaussian, and linear propagation might not be adequate!

Working in Gaussian approximation might not be reliable: i.e. skewness is not reproduced in the compression (despite central values and variances are) unless we explicitly include it in the minimised figure of merit

Juan Rojo PDF4LHC pre-Meeting, 16/01/2014

Skewness included

Skewness excluded

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LHC Phenomenology ! The ultimate validation is of course to check that the compressed set reproduces the original

combination for a wide variety of observables!

We have tested a very large number of processes, both at the inclusive and differential level and always found that Nrep=20-30 replicas are enough for phenomenology

Compression also works for fully differential distributions!

Tested on a large number of processes: jets, Drell-Yan, WW, W+charm, Z+jets, ….!

Calculations use fast NLO interfaces:!

1. aMCfast/applgrid for MadGraph5_aMC@NLO!

2. applgrid for MCFM/NLOjet++!

Very flexible to redo validation for any other compressed set


CMC-PDFs: Carrazza, Latorre, J.R. Watt, in prep

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Correlations ! Agreement between original and CMC-PDFs also holds at the level of cross-section correlations !Not an accident: selecting replicas at random fails to reproduce the correlation accurately enough

Cor

rela

tion

coef

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1<

0.5<

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Correlation Coefficient for ttbar

= 40repN

Reference

Compressed

Random (68% CL)

Correlation Coefficient for ttbar


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MC2Hessian ! For many important applications, a linearised Hessian version of Monte Carlo sets, based on

orthogonal eigenvectors, would be useful!

A MC2Hessian algorithm would allow to use NNPDF and CMC-PDF sets for profiling, as nuisance parameters, construct sets with reduced number of eigenvectors for specific applications like W mass ….!

…. while keeping also the crucial possibility of testing for the potential deviations from Gaussianity of the underlying probability distribution, quantifying the range of validity of linear approximation!

Various options possible, for example a la Meta-PDF, fit a functional form to each of the MC replicas


! But this is subject to the usual functional bias. ! A more robust choice is to use also MC replicas as linear expansion basis:

! The eigenvectors can then be determined from the a χ2 defined in the space of PDFs:

Covariance Matrix in the space of PDFs

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MC2Hessian - Preliminary results!

Preliminary results validate this strategy: it is possible to efficiently construct a Hessian representation of NNPDF3.0, or in general of any MC PDF set!

In particular, the CMC-PDFs will also be available in a Hessian representation


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! The comparison between the original

MC representation of a PDF set and its Hessian representation allow to determine the range of validity of the latter!

For instance, in important cases like BSM searches at high-mass, it is know that the Gaussian approximation is not adequate

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Summarising …


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Summary and discussion!

ATLAS has already provided a number of high-quality measurements for PDF fits, which provide important constraints in global PDF analysis ….!

… with many more to come still from Run I, and many new opportunities will open at Run II!!

PDF fits within ATLAS are highly valuable: validate crucial aspects of the measurement like the correlated systematics, test new theory calculations and tools, understand PDF impact of measurements and provide guidance for global fits ….!

… but it should also be clear that their scope is limited, and they are not meant to be alternative to global fits. Variants of NNPDF3.0 already explore the potential of an ATLAS global fit!

Many interesting physics opportunities not only in terms of PDF constrains from ATLAS data, but also for tests of QCD theory at the LHC!

We are making easier the estimation of PDF uncertainties at the LHC Run II: combine different PDF sets into a single compressed set, using a Hessian representation of MC sets, PDF sets with combined PDF+αS uncertainties, …If you have additional requests to make your life easier, just let us know!!


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Summary and discussion!

ATLAS has already provided a number of high-quality measurements for PDF fits, which provide important constraints in global PDF analysis ….!

… with many more to come still from Run I, and many new opportunities will open at Run II!

PDF fits within ATLAS are highly valuable: validate crucial aspects of the measurement like the correlated systematics, test new theory calculations and tools, understand PDF impact of measurements and provide guidance for global fits ….!

… but it should also be clear that their scope is limited, and they are not meant to be alternative to global fits. Variants of NNPDF3.0 already explore the potential of an ATLAS global fit!

Many interesting physics opportunities not only in terms of PDF constrains from ATLAS data, but also for tests of QCD theory at the LHC!

We are making easier the estimation of PDF uncertainties at the LHC Run II: combine different PDF sets into a single compressed set, using a Hessian representation of MC sets, PDF sets with combined PDF+αS uncertainties, …If you have additional requests to make your life easier, just let us know!


Thanks a lot for your attention!

and now time for discussion…

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Material for Discussion


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Comparison with Meta-PDFs!

To compare with the available Meta-PDFs in LHAPDF6, we have produced compressed sets based on MSTW08, CT10 and NNPDF2.3!

Reasonable agreement found for central values and variances, except perhaps small- and at large-x!

Need to redo the comparison when the two approaches use NNPDF3.0, MMHT14 and CT14


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The combined PDF set! Since there is reasonable agreement between CT10, MMHT14 and NNPDF3.0, the resulting

combined distribution is in general Gaussian, but there are also important cases where the non-gaussianity of the combined PDFs is substantial

x 5<10 4<10 3<10 2<10 1<10

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Gluon PDF, x=0.1, Q=100 GeVhisto1

Entries 100Mean 0.8887RMS 0.0151

NNPDF3.0CT10MMHT14MCcompPDFs

Gluon PDF, x=0.1, Q=100 GeV

! It is possible to have smoother distributions by increasing the number of replicas for each set, but

this does not seem to be required by phenomenology!

For typical applications using Nrep=100 for each of the three PDF sets is enough!

Note that in general, the combination of Gaussian distributions is not a Gaussian itself


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Compression as a mathematical problem! The goal now is to compressed the combined set of Nrep=300 replicas to a smaller subset, in a way

that this subset reproduces the statistical properties of the original distribution! Mathematically, this is a well-defined problem:

compression is finding the subset that minimises the distance between two probability distributions

! Many equally good minimisations possible,

so choice of minimisation algorithm not crucial (similar to the travelling salesman problem)!

Mathematically well-posed problem, with a number of robust solutions!

1. Kolmogorov distance!

2. Kullback-Leibler entropy!

3. …..!

Optimal choice determined by the requirements of the problem at hand, in this case LHC phenomenology


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Results of the compression! To gauge improvements due to compression, compare various contributions to the error function in

the best compression and in randoms selection with the same number of replicas

! Substantial improvements as

compared to random compressions, typically by one order or magnitude or more!

Compression is also able to successfully reproduce higher moments like skewness or kurtosis!

Similar improvements for the correlations and the Kolmogorov distances

Horizontal dashed line: !

lower limit of 68%CL range for random compressions with Nrep=100


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Results of the compression

Juan Rojo PDF4LHC Meeting, 03/11/2014

! For example, for Nrep=40 replicas the compressed and the original PDFs are virtually identical

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! As expected, for a very small number of replicas (10 in this case) agreement is much worse

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The compressed PDF set! Since there is reasonable agreement between CT10, MMHT14 and NNPDF3.0, the resulting

combined distribution looks typically Gaussian

! On average, the same number of replicas from each of the three sets is selected in the compressed

set, a further demonstration that the algorithm is unbiased

Replicas0 50 100 150 200 250 300

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CMC-PDF NLO - 25 replica distribution

NNPDF3.0 CT10 MMHT149 replicas 8 replicas 8 replicas


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Compressing native MC sets! The compression algorithm can of course be also used in native MC sets, like NNPDF. We have

shown that starting from NNPDF3.0 with Nrep=1000 replicas we can compress down to 40-50 replicas maintaining all relevant statistical properties

! Central values and variances well reproduced, but also, non-trivially, also higher moments and

correlations!

Sets with Nrep=1000 replicas are still useful for other applications, like Bayesian reweighting

All plots done with the APFEL Web plotter


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Phenomenology ! The ultimate validation is of course to check that the compressed set reproduces the original PDF

combination for a wide variety of LHC observables!


!NNLO cross-sections:!

gg->H with ggHiggs!

tt with top++!

W,Z with Vrap


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Phenomenology ! The ultimate validation is of course to check that the compressed set reproduces the original

combination for a wide variety of observables!


!NLO inclusive cross sections with MCFM!

H VBF!

WW!

WH


pdfs at the lhc: lessons from run i and preparation for run ii

Education

tev incl jets

tev w charm

lhc jets

lapp annecy

tev ttbar xsecs

z rap dist

tev drellyan2010 z rap

z rap herapdf2