Recent developments in QCD global analyses of proton s PDFs Marco Guzzi in collaboration with the CTEQ-TEA (CT) group

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1 Recent developments in QCD global analyses of proton s PDFs Marco Guzzi in collaboration with the CTEQ-TEA (CT) group XLV International Symposium on Multiparticle Dynamics

2 Intro Investigation of the structure of the nucleon crucial for a multitude of high-energy physics programs. Interpretation of eperimental measurements at hadron colliders relies on the precise knowledge of fundamental QCD parameters and Parton Distribution Functions (PDFs) of the proton. Discrimination of New Physics signals at the LHC crucially depends on precise knowledge of PDFs Global QCD analysis of PDFs is a vast topic, I ll focus on: basic facts, brief overview of the current status of modern PDFs, aspects of the CT14 analysis. selected CT14 recent results.

3 Making a long story short... Parton distribution functions (PDFs) of the proton are essential ingredients of factorization theorems in QCD: The general structure of the inclusive cross section for high-energy collisions involving hadron-hadron, lepton-hadron beams, or hadron targets, is a convolution product of long-distance non-perturbative contributions (PDFs) and short-distance infrared-safe perturbatively calculable quantities (hard scatterings cross sections). For Drell-Yan process in the collinear limit we have (Collins Soper Sterman (1984), (1985)) σ(h 1 h 2 l + l + X) = 1 1 dξ 1 dξ 2 f h1 a(ξ 1, α s (µ R ), µ R, µ F )f h2 b(ξ 2, α s (µ R ), µ R, µ F ) a,b 1 2 ˆσ ab ( 1, ( ) 2 Λ 2 ; α s (µ R ), Q, µ F, µ R ) + O ξ 1 ξ 2 Q 2, (1) ( ) Λ O 2 Q are subleading terms: higher twists, target corrections,... 2

4 Complicated objects The formal definition of PDFs in QCD, contains all the complications of real life : UV regulator in DR, gauge invariance Collins (2011) dw w f (0) j/h (ξ) = P ψ (0) 2π e iξp+ j (0, w, 0 T )W (w, 0) γ+ 2 ψ(0) j (0) P c, that is for quarks, where the Wilson-line factor is w ] W (w, 0) = P [e ig0 dy A + 0 (0)α (0,y,0 T )t α. (3) (2) Similarly to the case of renormalization scheme, a set of rules has to be provided in order to define the PDFs when a cross section calculation is performed, e.g. MS scheme.

5 Scale dependence In the collinear picture, the use of RG invariance tells us how to predict scale dependence or evolution of PDFs by renormalization group equations (RGE s) once the initial conditions are given. Parton evolution is obtained in terms of integro-differential equations known as DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi) equations d f i (, µ R, µ F ) d log µ F = j=q q,g 1 ( ) dy y P ij y ; α s, µ R, µ F f j (y, µ R, µ F ), (4) The evolution kernels or splitting functions P ij are known at 3-loop for the unpolarized case. Moch, Vermaseren, Vogt (2004)

6 Universal objects Gluons, quarks and antiquarks are the known constituents of the proton. Their distributions as a function of and generic scale µ, at which partons are probed, are universal quantities that do not depend on the specific hard process under consideration. Differently from hard-scattering cross sections, the analytic structure of the PDFs cannot be predicted by perturbative QCD, but has to be determined by comparing standard sets of cross sections, such as Eq. 1, to eperimental measurements by using a variety of analytical and statistical methods. For this reason PDFs are data-driven quantities.

7 PDFs for the LHC in the NNLO QCD era The increasing accuracy of the current data and LHC run I unprecedented energies, pushed the high-energy physics community towards a new realm of precision calculations: Enormous progress in perturbative NNLO QCD calculations (e.g. unitarity based methods ), semi-automated calculations of multi-leg NLO processes, NLO calculation of comple multi-leg processes such as for the production of vector boson plus 5 jets (e.g. W + 5 jets; H+3 jets), Understanding of jets substructure theoretical progress in the combination of the fied-order results with a parton shower codes, rapid developments of very sophisticated tools for phenomenology such as: HERAFITTER platform, (see H. Pirumov talk), META and MC-H PDFs (see A. Buckley talk), LHC run II: net challenge for precision

8 STATUS

9 Unpolarized collinear PDFs at NLO, NNLO in QCD: Recent ( ) determinations including LHC run I data: CTEQ TEA = CT, CT14 (Hessian method) MMHT = MSTW, MMHT14 (Hessian method) NNPDF = NNPDF3.0 (MC sampling and neural networks) ABM = ABM12LHC (Hessian method) Other recent determinations not including LHC data HERA2.0 (Hessian method) CTEQ-Jlab = CJ12 fit (Hessian method) JR (Hessian method) In the past years, a lot of efforts have been put in organizing a sistematic library to access all PDFs with an organic C++ interface: Etremely important tool for hadron collider phenomenology.

10 Different methodologies Methodologies for PDF determination vary among recent PDF analyses: smaller/larger/different data sets considered, heavy-flavor treatment (GMVFN, FFN,), different values/treatment of α s (M Z ), different parametrizations for input PDFs at Q 0,... differences in central predictions and error estimate A couple of eamples with pre LHC PDFs:

11 Results for F c 2 (, Q2 ) in DIS at NLO/NNLO At NNLO and Q m c : S-ACOT-χ FFN(N f = 3) without tuning It is close to other NNLO schemes S-ACOT-χ predictions are for a physically motivated rescaling variable ζ = (1 + 4m 2 c/q 2 ). Dependence on the form of ζ is also reduced F 2 c,q LH PDFs Q 2 GeV, m c 1.41 GeV Scale dependence long dash: S ACOT Χ NLO solid: S ACOT Χ NNLO short dash: FFNS NNLO Nf 3 MSTW08 NNLO Χ FONLL C Χ From: M.G., Nadolsky, Lai, Yuan, PRD (2012)

12 Other eamples of pre LHC determinations LHC 13 TeV, NNLO, α S (M )=0.118 Z Gluon - Gluon Luminosity NNPDF2.3 CT MSTW08 Gluon luminosity at the LHC 13 TeV. From PDF4LHC , JPG (2015) M X ( GeV ) 3 Z-boson production: p T spectrum LHC 8 TeV. From Malik and Watt JHEP (2014)

13 PDF4LHC: Comparisons and Benchmarking The PDF4LHC Working Group: performing thorough benchmark studies of PDFs and of predictions at the LHC making recommendations for a standard method of estimating PDFs + α s (MZ 2 ) uncertainties at the LHC through a combination of the results from different individual groups. Forthcoming PDF4LHC LHC run II PDF recommendations arxiv:. with more recent etensive comparisons between CT14, NNPDF3.0, MMHT14, ABM12LHC, HERA

14 Recent efforts in comparisons/benchmarking 2 2 NNLO, Q = 0 GeV ) [ref] NNPDF3.0 CT14 MMHT14 ) / g (, Q 2 g (, Q ) [ref] 2 ) / u (, Q NNPDF3.0 CT14 MMHT NNLO, Q = 0 GeV 1 Comparison of PDFs at Q2 = 2 GeV 2 between the NNPDF3.0, CT14 and MMHT14 sets at NNLO, with α s (M 2 Z ) = From PDF4LHC (July 2015) u (, Q

15 SOME RECENT ANALYSES

16 2 2 ) Constraints on the gluon at low from LHCb g δg/g PROSA NLO FFNS fit µ f 2 = GeV 2 HERA DIS HERA DIS + LHCb abs HERA DIS + LHCb norm Impact of heavy-flavour production cross sections measured by the LHCb eperiment on parton distribution functions at low Zenaiev et al., PROSA Collaboration EPJC 2015 (More in Achim Geiser s talk) = 4 GeV g (, Q NNPDF3.0 NLO α s = no LHCb D,D data 0 +- with LHCb D,D data (wgt) 0 +- with LHCb D,D data (unw) Charm production in the forward region: constraints on the small- gluon and backgrounds for neutrino astronomy Gauld, Rojo, Rottoli, Talbert, (2015)

17 Procedures for the combination of the PDFs into the future PDF4LHC ensemble Possible methods for the construction of the combined PDF4LHC ensemble: Meta-parametrizations + MC replicas + Hessian data set diagonalization J. Gao, P. Nadolsky JHEP (2014) (Gao, Huston, Nadolsky) Unweighting/compression of Monte-Carlo replicas G. Watt, R. Thorne, ; R. Ball et al., ; S. Forte, G. Watt, A compression algorithm for the combination of PDF sets Carrazza, Latorre, Rojo, Watt, (2015) (more in Andy Buckley s talk)

18 PDF s backbone: new high precision HERA data Measurements of lepton-proton deep-inelastic-scattering (DIS) reaction data from H1 and ZEUS coll. at HERA are the most important data sets in PDFs determination. H1 and ZEUS H1 and ZEUS σ r, NC 2 i Bj = , i=21 Bj = , i=20 Bj = , i=19 Bj = , i=18 Bj = , i=17 Bj = , i=16 Bj = , i=15 Bj = , i=14 Bj = , i=13 Bj = , i=12 HERA NC e p 0.4 fb 1 HERA NC e + p 0.5 fb 1 s = 318 GeV Fied Target HERAPDF2.0 e p NLO HERAPDF2.0 e + p NLO σ r, NC 2 i Bj = , i=21 Bj = , i=20 Bj = , i=19 Bj = , i=18 Bj = , i=17 Bj = , i=16 Bj = , i=15 Bj = , i=14 Bj = , i=13 Bj = , i=12 HERA NC e p 0.4 fb 1 HERA NC e + p 0.5 fb 1 s = 318 GeV Fied Target HERAPDF2.0 e p NLO HERAPDF2.0 e + p NLO 3 2 Bj = 0.005, i=11 Bj = 0.008, i= Bj = 0.013, i=9 Bj = 0.02, i=8 Bj = 0.032, i=7 3 2 Bj = 0.005, i=11 Bj = 0.008, i= Bj = 0.013, i=9 Bj = 0.02, i=8 Bj = 0.032, i=7 Bj = 0.05, i=6 Bj = 0.08, i=5 Bj = 0.13, i=4 Bj = 0.05, i=6 Bj = 0.08, i=5 Bj = 0.13, i=4 Bj = 0.18, i=3 Bj = 0.18, i=3 1 Bj = 0.25, i=2 1 Bj = 0.25, i=2-1 Bj = 0.40, i=1-1 Bj = 0.40, i=1-2 Bj = 0.65, i=0-2 Bj = 0.65, i= Q 2 / GeV Q 2 / GeV 2 Recent: New combined data and HERA2.0 PDFs released ariv: (More in Iris Abt s talk)

19 The need for precision /pb S /TeV Inclusive Higgs production Xsec for gluon-gluon fusion at N 3 LO, Anastasiou, Duhr, Dulat, Herzog, Mistlberger, PRL (2015). Significantly reduced the scale dependence of the Higgs cross section PDF and α s uncertainties become the dominant remaining theoretical uncertainty.

20 The CT14 global QCD analysis New results from the CTEQ-TEA group: S. Dulat, T.J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, C.-P. Yuan arxiv:

21 What s new in CT14 NNLO PDFs CT14 differs from CT PDFs in several respects: new HERA data: Combined HERA charm production measurements (F (c) 2 ) measurements of the longitudinal F L (, Q 2 ) in DIS neutral currents new Tevatron data: Tevatron Run 1 CDF and D0 inclusive jet data are dropped, old D0 data (0.75 fb 1 ) superseded by the new D0 (9.7 fb 1 ) W -electron rapidity asymmetry data. LHC 7 TeV run I data included ATLAS and LHCb W and Z production, ATLAS, CMS and LHCb W -lepton charge asymmetry, ATLAS and CMS inclusive jet data. CT14 has 2995 data points

22 CT14 Data sets ensemble I ID# Eperimental data set N pt χ 2 e χ 2 e/n pt S n 1 BCDMS F p BCDMS F2 d NMC F2 d /F p NMC σ p red CDHSW F p CDHSW F p CCFR F p CCFR F p NuTeV νµµ SIDIS NuTeV νµµ SIDIS CCFR νµµ SIDIS CCFR νµµ SIDIS H1 σr b Combined HERA charm production HERA1 Combined NC and CC DIS H1 F L

23 CT14 Data sets ensemble II ID# Eperimental data set N pt χ 2 e χ 2 e/n pt S n 201 E605 Drell-Yan process E866 Drell-Yan process, σ pd/(2σ pp) E866 Drell-Yan process, Q 3 d 2 σ pp/(dqd F) CDF Run-1 electron A ch, p Tl > 25 GeV CDF Run-2 electron A ch, p Tl > 25 GeV DØ Run-2 muon A ch, p Tl > 20 GeV LHCb 7 TeV 35 pb 1 W /Z dσ/dy l LHCb 7 TeV 35 pb 1 A ch, p Tl > 20 GeV DØ Run-2 Z rapidity CDF Run-2 Z rapidity CMS 7 TeV 4.7 fb 1, muon A ch, p Tl > 35 GeV CMS 7 TeV 840 pb 1, elec. A ch, p Tl > 35 GeV ATLAS 7 TeV 35 pb 1 W /Z cross sec., A ch DØ Run fb 1 elec. A ch, p Tl > 25 GeV CDF Run-2 inclusive jet production DØ Run-2 inclusive jet production ATLAS 7 TeV 35 pb 1 incl. jet production CMS 7 TeV 5 fb 1 incl. jet production

24 Aspects of the CT14 analysis PDFs are parametrized at init scale Q 0 = 1.3 GeV. large- data not included to avoid large non-perturbative contributions (W > 3.5 GeV) more fleible parametrizations for gluon, d/u at large, both d/u and d/ū at small, and strange ( s = s) PDFs. Non-perturbative parametrization employing Bernstein polynomials P a (): f a () = a 1 (1 ) a 2 P a () This reduces the correlation among its coefficients. CT14: 28 shape parameters, while CT has 25. S-ACOT-χ NNLO for the heavy flavor treatment NNLO calculations for DIS, DY, W, Z cross sections, for the jet cross sections and DIS charged currents we only use the NLO calculation but with NNLO PDF.

25 Aspects of the CT14 analysis: α s (M Z ) central value of α s (M Z ) = has been assumed in the global fits at NLO and NNLO, but PDF sets at alternative values of α s (M Z ) are provided. CT14 prefers α s (M Z ) = at NNLO (0.117 ± at NLO) at 90 % confidence level (C.L.). Uncertainties from the global QCD fits are larger than those of the data from LEP and other eperiments included into the world average Chin.Phys.C (2014). CT14 α s (M Z ) central is consistent with the world average value.

26 CT14: DGLAP evolution CT14 NNLO CT14 NNLO 0.8 g,q 5 u 0.8 g,q 5 f,q at Q = 2 GeV d f,q at Q = 0 GeV u d 0.2 s bar u bar d bar 0.2 d bar u bar s bar The CT14 PDFs u, u, d, d, s = s, and g, evolved up to Q = 2 GeV and Q = 0 GeV.

27 CT14 vs CT at NNLO 90% C.L. Ratio to reference fit CT14NNLO Ratio to reference fit CT14NNLO g(,q) Q =0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO d(,q) Q = 0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO Ratio to reference fit CT14NNLO Ratio to reference fit CT14NNLO u(,q) Q = 0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO u(,q) Q = 0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO ATLAS, CMS 7 TeV W/Z prod. d-quark increased by 5% at D0 ele charge asy data d highly reduced at 0.1 and u moderately increased.

28 CT14 d(, Q)/u(, Q) ratios d(,q)/u(,q) d(,q)/ u(,q) Q = GeV, 90% c.l. CT14 NNLO CT NNLO CJ12 NLO Q =2 GeV, 90% c.l. CT14NNLO CTNNLO Ratio to reference fit CT14NNLO (s+ s)/( u+ d) d/u at Q = 2 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO Q =2 GeV, 90% c.l. CT14NNLO CTNNLO fb 1 D0 charge asy reduction of the central ratio at > 0.1, new parametrization form increased uncertainty at < 0.05 s reduction at > 0.01 smaller ratio (s + s)/(ū + d). The SU(3)-symmetric asymptotic solution at 0 is still allowed in CT14: bigger unc. 5.

29 CT14 NNLO: agreement with data 5.40 Correlations 90 at LHC 8 TeV 9.00 Correlations 90 at LHC 13 TeV Total of 2947 data points from 33 eperiments χ 2 = 3252 at the best fit CT14 NNLO, χ 2 /N pt = 1.. Data and theory are in reasonable good agreement for most eperiments (net slides) Σ W in nb Σ z in nb CT NNLO CT14 NNLO Σ W in nb Correlations 90 at LHC 8 TeV CT NNLO CT14 NNLO Σ W in nb Σ W in nb Σ z in nb CT NNLO CT14 NNLO Σ W in nb 2.05 Correlations 90 at LHC 13 TeV CT NNLO CT14 NNLO Σ W in nb W /Z Correlations plots CT14 vs NNLO

30 CT14 NNLO: agreement with data d 2 σ/dp T dy [pb/gev] A l CMS, s=7 TeV, L=5.0 [fb] -1, R= P T [GeV] y < 0.5 ( 4 ) 0.5 < y < 1.0 ( 3 ) 1.0 < y < 1.5 ( 2 ) 1.5 < y < 2.0 ( 1 ) 2.0 < y < 2.5 ( 0 ) ATLAS, s=7 TeV, [pb] DATA 20 CT14, 68% C.L η l d 2 σ/dp T dy [pb/gev] Muon charge asymmetry ATLAS, s=7 TeV, L=37 [pb] -1, R=0.6 y 0.3 ( 12 ) 0.3 y < 0.8 ( 9 ) 0.8 y < 1.2 ( 6 ) 1.2 y < 2.1 ( 3 ) 2.1 y < 2.8 ( 0 ) 2.8 y < 3.6 ( -3 ) 3.6 y < 4.4 ( -6 ) 0 00 P T [GeV] CMS, s=7 TeV, L=4.7 [fb] P T > 25 GeV CT14, 68% C.L η µ Inclusive jet production and W lepton charge asymmetry at the LHC 7 TeV

31 CT14 NNLO: agreement with data A µ LHCb, s=7 TeV, 35 [pb] P T > 20 GeV CT14, 68% C.L η µ Electron charge asymmetry D0, L=9.7 fb CT14 NNLO CT14 NNLO CT NNLO -0.6 CTEQ6.6 NLO E e T > 25 GeV, E T,miss > 25 GeV η e 1.0 dσ W ± c d Η l pb CT14 unshifted data cosφ PDF Correlations of dσ W ± c)/d Η with CT14 PDFs at Q=0 GeV CMS 7 TeV, cross section of W ± c s quark p T,l 25 GeV gluon Η l W + c is not included in the fit (theory available only at NLO)

32 CT14 NNLO: agreement with data Total inclusive t t cross section at NNLO in QCD with Top++, (Czakon, Mitov, CPC 2014) pp t t (pb), PDF unc., α s = TeV 8 TeV 13 TeV 68% C.L. (Hessian) % 3.9% % 3.5% % 2.7% 68% C.L. (LM) +4.8% 4.6% +2.9% 2.9% pp t t (pb), PDF+α s 7 TeV 8 TeV 13 TeV 68% C.L. (Hessian) +5.5% 4.6% +5.2% 4.4% +3.6% 3.5% 68% C.L. (LM) +5.1% 4.7% +3.6% 3.5% CMS data DiffTop appro NNLO LHC 7 TeV, m t GeV central, CT14NNLO PDF unc. 68 CL ATLAS data DiffTop appro NNLO LHC 7 TeV, m t GeV central, CT14NNLO PDF unc. 68 CL data theory data theory p t T GeV p t T GeV Appro NNLO p T spectrum for the final state top-quark with DiffTop (M.G., Lipka, Moch, JHEP 2015)

33 Post CT14 analysis: ongoing/future work impact of the new HERA II recent combined DIS measurements impact of t t inclusive and differential cross section on...

34 Conclusions LHC unprecedented energies brought us in a new precision era A lot of efforts are ongoing to pin down PDFs uncertainties which still remain among the major sources of systematical theory uncertainties Things will be very interesting when many missing NNLO Xsecs will be consistently included in the net PDF iteration. Several future LHC programs for discovery of new physics interactions strongly depend on our knowledge of proton structure. THANK YOU!

35 Backup

36 In global PDF fits a large number of iterations of the theory calculation programs (NLO, NNLO) is required to evaluate cross sections: some of these computations are CPU time consuming! Advanced tools have been developed to have theory calculations on grids: etremely fast! FastNLO and APPLgrid

37 CT14 vs CT at NNLO 90% C.L. Ratio to reference fit CT14NNLO Ratio to reference fit CT14NNLO d(,q) Q = 0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO s(,q) Q = 0 GeV, 90% c.l. CT14NNLO CTNNLO/CT14NNLO

38 Definitions of the covariance matri arxiv: , appendi in R. Ball et al., arxiv: χ 2 = {ep.} N pts 1 s 2 k=1 k D k T k ({a}) N λ α=1 2 λ α β kα + K e λ 2 α α=1 The eperimental correlated systematic errors β kα are often published as percentages. It can be taken to be a percentage of the theoretical prediction T k ( truth ) or the eperimental datum D k. 1. Eperimental (D) prescription: normalize all β kα to D k 2. T (T 0 ) prescription: normalize luminosity & other multiplicative errors to (fied) T k, additive errors to D k 3. Etended T (T 0 ) prescription: normalize all errors to (fied) T k The methods are numerically equivalent if T k is close to D k. Additive (multiplicative) errors are to be normalized to T k (D k ) to avoid/reduce biases. The available eperimental data usually do not specify if the errors are additive or multiplicative.

39 Kinematics: LHC 7 TeV 7 TeV LHC parton kinematics 9 1,2 = (M/7 TeV) ep(±y) 8 Q = M 7 WJS20 M = 7 TeV 6 M = 1 TeV Q 2 (GeV 2 ) M = GeV M = 0 GeV y = HERA fied target

40 Kinematics: LHC 14 TeV LHC parton kinematics 9 1,2 = (M/14 TeV) ep(±y) 8 Q = M M = TeV WJS M = 1 TeV Q 2 (GeV 2 ) M = 0 GeV y = M = GeV HERA fied target