Parton Distribution Functions for the LHC

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1 Parton Distribution Functions for the LHC Present Status & Uncertainty determination Alberto Guffanti Niels Bohr International Academy & Discovery Center Niels Bohr Institute - Copenhagen Ph. D. course on Particle Physics Phenomenology NBI Copenhagen October 4, 011

2 What are Parton Distribution Functions? Definition - Factorization Consider a process with one hadron in the initial state D(x,Q ) According to the Factorization Theorem we can write the cross section as dσ = 1 dξ x a 0 ξ D a(ξ,µ )d ˆσ a ξ, ŝ 1 µ, α s(µ ) + O Q p A. Guffanti (NBIA & Discovery Center) PDFs@LHC / 46

3 What are Parton Distribution Functions? Definition - DGLAP equations The initial condition cannot be computed in Perturbation Theory (Lattice? In principle yes, but...)... but the energy scale dependence is governed by DGLAP evolution equations ln Q qns (ξ, Q ) = P NS (ξ, α s ) q NS (ξ, Q ) Σ ln Q (ξ, Q Pqq P ) = qg Σ (ξ, α g P gq P s ) gg g (ξ, Q )... and the splitting functions P can be computed in PT and are known up to NNLO (LO - Dokshitzer; Gribov, Lipatov; Altarelli, Parisi, 1977) (NLO - Floratos, Ross, Sachrajda; Gonzalez-Arroyo, Lopez, Yndurain; Curci, Furmanski, Petronzio, 1981) (NNLO - Moch, Vermaseren, Vogt, 004) A. Guffanti (NBIA & Discovery Center) PDFs@LHC 3 / 46

4 Problem Faithful estimation of errors on PDFs Single quantity: 1-σ error Multiple quantities: 1-σ contours Function: need an "error band" in the space of functions (i.e. the probability density P[f ] in the space of functions f (x)) Expectation values are Functional integrals F[f (x)] = Df F[f (x)]p[f (x)] A. Guffanti (NBIA & Discovery Center) PDFs@LHC 4 / 46

5 Problem Faithful estimation of errors on PDFs Single quantity: 1-σ error Multiple quantities: 1-σ contours Function: need an "error band" in the space of functions (i.e. the probability density P[f ] in the space of functions f (x)) Expectation values are Functional integrals F[f (x)] = Df F[f (x)]p[f (x)] Determine a function from a finite set of data points A. Guffanti (NBIA & Discovery Center) PDFs@LHC 4 / 46

6 Proper Fitting avoiding Overlearning A. Guffanti (NBIA & Discovery Center) 5 / 46

7 Proper Fitting avoiding Overlearning A. Guffanti (NBIA & Discovery Center) 5 / 46

8 Proper Fitting avoiding Overlearning A. Guffanti (NBIA & Discovery Center) 5 / 46

9 Proper Fitting avoiding Overlearning A. Guffanti (NBIA & Discovery Center) 5 / 46

10 Proper Fitting avoiding Overlearning A. Guffanti (NBIA & Discovery Center) 5 / 46

11 Proper Fitting avoiding Overlearning Need a redundant parametrization to avoid parametrization bias. Need a way of stopping the fit before overlearning sets in to avoid fitting statistical noise. Need a reliable error estimation. A. Guffanti (NBIA & Discovery Center) PDFs@LHC 5 / 46

12 DATA SET SELECTION A. Guffanti (NBIA & Discovery Center) 6 / 46

13 Choice of Dataset Global vs. Restricted dataset Restricted set Analyses HERAPDF: use only HERA DIS data AB(K)M/JR: use Fixed target DIS, HERA and Drell-Yan data Focus on the most precise dataset(s) Avoid possible incompatibilities Limited flavour separation Neglect important constraints (gluon at medium/large-x) Global Analyses CTEQ-TEA/MSTW/NNPDF: HERA DIS, Fixed target DIS and Drell-Yan, Vector Boson and Inclusive jet production at colliders Focus on completeness Reliable flavour separation Possible data incompatibilities A. Guffanti (NBIA & Discovery Center) 7 / 46

14 Choice of Dataset Which data constrain which PDFs H1, ZEUS: F e± p (x, Q ) BCDMS: F µp (x, Q ), F µd (x, Q ) NMC: F µp (x, Q ), F µd (x, Q ), F µn SLAC: F µp (x, Q ), F µd E665: F µp (x, Q ), F µd (x, Q ) F µp (x,q ) (x,q ) CCFR, NuTeV, CHORUS: F ν( ν)p,3 (x, Q ) q, q at all x (x, Q ) g at moderate and small x E605, E70, E866: pn µ µ + X q, (g) E605: Drell-Yan p, n asymmetry ū, d CDF: W rapidity asymmetry u/d ratio at high-x CDF, D0: Inclusive jet data g at high-x CCFR, NuTeV: Dimuon data s, s sea A. Guffanti (NBIA & Discovery Center) PDFs@LHC 8 / 46

15 ] NNPDF.1 Dataset [ GeV T / p / M Q NNPDF.1 dataset NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H ZEUSFC H1FC DYE605 DYE886 CDFWASY CDFZRAP D0ZRAP CDFRKT D0RCON OBS Data set Deep Inelastic Scattering F d /F p NMC-pd F p NMC, SLAC, BCDMS F d SLAC, BCDMS σ ± NC HERA-I, ZEUS (HERA-II) σ ± CC HERA-I, ZEUS (HERA-II) F L H1 σ ν, σ ν CHORUS dimuon prod. NuTeV F c ZEUS (99,03,08,09) F c H1 (01,09,) x data points -1 1 Drell-Yan & Vector Boson prod. dσ DY /dm dy E605 dσ DY /dm dx F E866 W asymm. CDF Z rap. distr. D0/CDF Inclusive jet prod. Incl. σ (jet) CDF (k T ) - Run II Incl. σ (jet) D0 (cone) - Run II A. Guffanti (NBIA & Discovery Center) PDFs@LHC 9 / 46

16 PDF PARAMETRIZATION A. Guffanti (NBIA & Discovery Center) / 46

17 PDF parametrization Theoretical Requirements - QCD Sum Rules Valence Sum Rules 1 0 [u(x, Q ) u(x, Q )]dx =, 1 0 [d(x, Q ) d(x, Q )]dx = [s(x, Q ) s(x, Q )]dx = 0 A proton has net quantum numbers of up and 1 down quarks. Momentum Sum Rule 1 a=q, q,g 0 xf a (x, Q )=1 Momenta of all partons must add up to the proton momentum. A. Guffanti (NBIA & Discovery Center) PDFs@LHC 11 / 46

18 PDF parametrization Theoretical Requirements - Positivity of Observables Cross-sections must be positve Tipically realized imposing PDF positivity... but remember: PDFs are not Probability Density Functions (nor are they observables) No probabilistic interpretation beyond Leading Order Might result in excessive constraints on PDFs. 4 3 NNPDF.0 CTEQ6.6 MSTW 008 ) 0 xg (x, Q x A. Guffanti (NBIA & Discovery Center) PDFs@LHC 1 / 46

19 PDF parametrization Standard Approach (CTEQ-TEA/MSTW/ABKM/HERAPDF) Introduce a simple functional form with enough free parameters q(x, Q )=x α (1 x) β P(x; λ 1,...,λ n ). "Theoretically motivated"-form x 0 : q x a 1 - Regge-like behaviour x 1 : q (1 x) a - quark counting rules P(x; λ 1,...,λ n): affects medium x, just a convenient functional form A. Guffanti (NBIA & Discovery Center) PDFs@LHC 13 / 46

20 PDF parametrization Standard Parametrization Parton Distributions Combination xu v (x, Q )=A u x η 1 (1 x) η (1 + u x + γu x) xd v (x, Q )=A d x η 3 (1 x) η 4(1 + d x + γd x) xs(x, Q )=A S x δ S (1 x) η S(1 + S x + γs x) x (x, Q )=A x η (1 x) η S+ (1 + γ + δ x ) xg(x, Q )=A g x δg (1 x) ηg (1 + g x + γg x)+a g x δ g (1 x) η g x(s + s)(x, Q )=A + x δ S (1 x) η + (1 + S x + γs x) x(s s)(x, Q )=A x δ (1 x) η (1 + x/x 0 ) 9 parameters A. Guffanti (NBIA & Discovery Center) PDFs@LHC 14 / 46

21 PDF parametrization The NNPDF Approach - Neural Networks Neural Networks are non-linear statistical tools. Any continuous function can be approximated with neural network with one internal layer and non-linear neuron activation function. Efficient minimization algorithms for complex parameter spaces. They provide a parametrization which is redundant and robust against variations. A. Guffanti (NBIA & Discovery Center) PDFs@LHC 15 / 46

22 PDF parametrization Neural Networks... just another basis of functions Multilayer feed-forward networks Each neuron receives input from neurons in preceding layer and feeds output to neurons in subsequent layer Activation determined by weights and thresholds ξ i = g j ω ij ξ j θ i Sigmoid activation function g(x) = e βx A. Guffanti (NBIA & Discovery Center) PDFs@LHC 16 / 46

23 PDF parametrization Neural Networks... just another basis of functions Multilayer feed-forward networks Each neuron receives input from neurons in preceding layer and feeds output to neurons in subsequent layer Activation determined by weights and thresholds ξ i = g j ω ij ξ j θ i Sigmoid activation function A 1--1 NN: ξ (3) 1 (ξ(1) g(x) = e βx 1 )= 1 () 1 + e θ (3) 1 ω 11 1+e θ() 1 ξ(1) 1 ω(1) 11 ω () 1 1+e θ() ξ(1) 1 ω(1) 1 A. Guffanti (NBIA & Discovery Center) PDFs@LHC 16 / 46

24 PDF parametrization NNPDF.1 Parametrization Parton Distributions Combination NN architechture Singlet (Σ(x)) = (37 pars) Gluon (g(x)) = (37 pars) Total valence (V (x) u V (x)+d V (x)) = (37 pars) Non-singlet triplet (T 3 (x)) = (37 pars) Sea asymmetry ( S (x) d(x) ū(x)) = (37 pars) Total Strangeness (s + (x) (s(x)+ s(x))/) = (37 pars) Strange valence (s (x) (s(x) s(x))/) = (37 pars) 59 parameters A. Guffanti (NBIA & Discovery Center) PDFs@LHC 17 / 46

25 PDF UNCERTAINTIES A. Guffanti (NBIA & Discovery Center) 18 / 46

26 PDF Uncertainties The Hessian Method The figure of merit to be minimized in the fit is the fully correlated χ χ = N dat (D I T I ({a})) (cov) 1 (D IJ J T J ({a})) I,J=1 where D k and T k are the data and theory values for each data point Important to properly accout for correlated uncertainties. Special care needed for normalization uncertainties (in general multiplicative uncertainties). [R. D. Ball et al., arxiv:091.76] A. Guffanti (NBIA & Discovery Center) PDFs@LHC 19 / 46

27 PDF Uncertainties Normailization Uncertainties m-cov R(e + e - ) CELLO 1987 Dashed line: data below 36 GeV Solid line: all data D Agostini 1994 A. Guffanti (NBIA & Discovery Center) PDFs@LHC 0 / 46

28 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ 30 χ {a i } > 0 χ 0 a i0 a i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 1 / 46

29 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ {a i } χ χ 0 χ 68% χ =1 N X a i a a + i0 i a i A. Guffanti (NBIA & Discovery Center) PDFs@LHC / 46

30 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ M N M! a i N 500 A. Guffanti (NBIA & Discovery Center) PDFs@LHC 3 / 46

31 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ a i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 4 / 46

32 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ χ χ 0 χ 0 a i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 5 / 46

33 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ χ χ 0 χ 0 a i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 6 / 46

34 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ χ χ 0 χ 0 a i χ T χ A. Guffanti (NBIA & Discovery Center) PDFs@LHC 7 / 46

35 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ χ χ 0 χ 0 a i χ T χ A. Guffanti (NBIA & Discovery Center) PDFs@LHC 8 / 46

36 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ χ χ 0 χ χ 0 a i a i0 a + i a i χ T χ A. Guffanti (NBIA & Discovery Center) PDFs@LHC 9 / 46

37 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] 40 Eigenvector 4 40 Eigenvector BCDMSp BCDMSd H1a H1b ZEUS NMCp NMCr CCFR CCFR3 E605 CDFw E866 D0jet CDFjet 0 BCDMSp BCDMSd H1a H1b ZEUS NMCp NMCr CCFR CCFR3 E605 CDFw E866 D0jet CDFjet distance 0 distance T A. Guffanti (NBIA & Discovery Center) PDFs@LHC 30 / 46

38 PDF Uncertainties The Hessian Method Used by most PDF fitters (CTEQ, MSTW, ABKM, HERAPDF). Given an observable which depends on a set of parameters {z} X({z}) =X 0 + z i i X({z}) the variance is given by σ X = σ ij i X j X with σ ij being the covariance matrix in parameter space. Diagonalization: choose the z i as eigenvectors of σ ij with unit eigenvalues so that σ X = X Relies on linear error propagation, i.e. Gaussian approximation A. Guffanti (NBIA & Discovery Center) PDFs@LHC 31 / 46

39 PDF Uncertainties The Hessian Method [P. Nadolsky, CTEQ School 009] -dim (i,j) rendition of N-dim () PDF parameter space a j u l p(i) contours of constant global u l : eigenvector in the l-direction p(i): point of largest a i with tolerance T s 0: global minimum z l p(i) u l diagonalization and T s rescaling by s 0 0 the iterative method a i Hessian eigenvector basis sets (a) Original parameter basis z k (b) Orthonormal eigenvector basis χ T N {a i } T N {z i } A. Guffanti (NBIA & Discovery Center) PDFs@LHC 3 / 46

40 PDF Uncertainties The Hessian Method [P. Nadolsky, CTEQ School 009] -dim (i,j) rendition of N-dim () PDF parameter space X zm (b) Orthonormal eigenvector basis X = X z m = X = 1 X N i=1 X (+) i X ( ) i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 33 / 46

41 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] -dim (i,j) rendition of N-dim () PDF parameter space X ϕ Y (b) Orthonormal eigenvector basis cos ϕ = X Y X Y = 1 4 X Y N i=1 X X (+) i Y X ( ) i Y (+) i Y ( ) i A. Guffanti (NBIA & Discovery Center) PDFs@LHC 34 / 46

42 PDF Uncertainties Multidimensional error Analysis [P. Nadolsky, CTEQ School 009] χ a i χ A. Guffanti (NBIA & Discovery Center) PDFs@LHC 35 / 46

43 PDF Uncertainties The Monte Carlo Method Used by NNPDF (and old Fermi and Alekhin sets). Generate N rep Monte Carlo replicas of the data (Monte Carlo in the space of parameters is not a smart idea, because of flat directions) Fit a set of PDFs to each replica, the ensemble of replicas gives the probability density in the space of PDFs You get a set of N rep replicas, compute central values, standard deviations, correlations as you would do for any Monte Carlo ensemble: F[{q}] = 1 N rep F[{q (k) }] N rep k=1 N rep σ F = N rep 1 (F[{q}] F[{q}] ) A. Guffanti (NBIA & Discovery Center) PDFs@LHC 36 / 46

44 PDF Uncertainties The Monte Carlo Method in practice Generate artificial data according to distribution N O (art)(k) i =(1 + r (k) N σ sys N) O (exp) i + p=1 r (k) p where r i are univariate (gaussian) random numbers σ i,p + r (k) i,s σi s Validate Monte Carlo replicas against experimental data (statistical estimators, faithful representation of errors, convergence rate increasing N rep) O(00) replicas needed to reproduce correlations to percent accuracy A. Guffanti (NBIA & Discovery Center) PDFs@LHC 37 / 46

45 PDF Uncertainties Hessian vs. Monte Carlo Q: Are the two methods equivalent? A: Hessian and MC method give the same results in the linear error propagation approximation Fit vs H1PDF000, Q = 4. GeV Q: Nice, but what about in the real world? A: arxiv: , pg. 41 Q: Wait a minute, you assumed gaussian errors... A: arxiv: , pg. 4 xg(x) x [S. Glazov and V. Radescu] A. Guffanti (NBIA & Discovery Center) PDFs@LHC 38 / 46

46 PDF Uncertainties Hessian vs. Monte Carlo Q: Are the two methods equivalent? A: Hessian and MC method give the same results in the linear error propagation approximation Fit vs H1PDF000, Q = 4. GeV Q: Nice, but what about in the real world? A: arxiv: , pg. 41 Q: Wait a minute, you assumed gaussian errors... A: arxiv: , pg. 4 xg(x) x [S. Glazov and V. Radescu] A. Guffanti (NBIA & Discovery Center) PDFs@LHC 38 / 46

47 PDF fits status A. Guffanti (NBIA & Discovery Center) 39 / 46

48 The present status of PDF fits The PDF sets Matrix ABKM09 CT JR09 HERAPDF1.5 MSTW08 NNPDF.1 Dataset Pert. Heavy α S Param. Uncert. Order Flavours DIS (FT, HERA) NLO FFN fitted 6 indep. PDF Hessian Drell-Yan (FT) NNLO (BMSN) Polynomial ( χ = 1) (5 param.) DIS (FT, HERA) LO GM-VFNS external 6 indep. PDF Hessian Drell-Yan (FT, Tev) NLO (S-ACOT) Polynomial ( χ = 0) Jets (Tevatron) (6 param.) DIS (FT, HERA) NLO FFN fitted 5 indep. PDF Hessian Drell-Yan (FT) NNLO VFN Polyinom. ( χ = 1) Jets (Tevatron) (15 param.) NLO GM-VFNS external 5 indep. PDF Hessian DIS (HERA) NNLO (TR) Polnom. ( χ = 1) (14 param.) DIS (FT, HERA) LO GM-VFNS fitted 7 indep. PDF Hessian Drell-Yan (FT, Tev) NLO (TR) Polynom. ( χ 5) Jets (HERA, Tev) NNLO (0 param.) DIS (FT, HERA) LO GM-VFNS external 7 indep. PDF Monte Carlo Drell-Yan (FT, Tev) NLO (FONLL) Neural Netw. Jets (Tevatron) NNLO (59 param.) A. Guffanti (NBIA & Discovery Center) PDFs@LHC 40 / 46

49 The present status of PDF fits PDFs... a family portrait At the starting scale ( GeV )... NNPDF.1 LO, Q = GeV xσ/ xg/5 xt 3 xv S + xs NNPDF.1 NLO, Q = GeV xσ/ xg/5 xt 3 xv S + xs NNPDF.1 NNLO, Q = GeV xσ/ xg/5 xt 3 xv S + xs - xs - xs - xs x x x -1 A. Guffanti (NBIA & Discovery Center) PDFs@LHC 41 / 46

50 The present status of PDF fits PDFs... a family portrait At the starting scale ( GeV )... NNPDF.1 LO, Q = GeV xσ/ xg/5 xt 3 xv S + xs NNPDF.1 NLO, Q = GeV xσ/ xg/5 xt 3 xv S + xs NNPDF.1 NNLO, Q = GeV xσ/ xg/5 xt 3 xv S + xs - xs - xs - xs x x x and at the typical EW scale (0 GeV ) NNPDF.1 LO, Q 4 = GeV NNPDF.1 NLO, Q 4 = GeV NNPDF.1 NNLO, Q 4 = GeV xσ xg xσ xg xσ xg xt 3 xv S xt 3 xv S xt 3 xv S 1 xs - xs 1 xs - xs 1 xs - xs x x x -1 A. Guffanti (NBIA & Discovery Center) PDFs@LHC 41 / 46

51 The present status of PDF fits Comparison between Parton Luminosities When trying to understand differences between PDF sets it is useful to look at parton luminosities Φ ij (M X )= 1 s 1 τ x 1 x 1 f i (x 1, M X )f j (τ/x 1, M X ) gg: Ratio to MSTW 008 NLO (68% C.L.) gg luminosity at LHC ( s = 7 TeV) MSTW08 NLO CTEQ6.6 CT NNPDF M H (GeV) tt s / s Ratio to MSTW 008 NLO (68% C.L.) gg luminosity at LHC ( s = 7 TeV) MSTW08 NLO HERAPDF1.0 ABKM09 GJR M H (GeV) tt s / s qq: Ratio to MSTW 008 NLO (68% C.L.) Σ q(qq) luminosity at LHC ( s = 7 TeV) MSTW08 NLO CTEQ6.6 CT NNPDF.1 W Z - -1 s / s Ratio to MSTW 008 NLO (68% C.L.) Σ q(qq) luminosity at LHC ( s = 7 TeV) MSTW08 NLO HERAPDF1.0 ABKM09 GJR08 W Z - -1 s / s A. Guffanti (NBIA & Discovery Center) PDFs@LHC 4 / 46

52 The present status of PDF fits Comparisons to LHC data Predictions for LHC Standard Candles compared to LHC data σ(w + )B(W + -> l + ν) [nb] NLO LHC 7 TeV, VRAP NNLO MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 α s = 0.119, 0.10 α s = 0.119, 0.117, CMS + ATLAS average, 36 pb σ(w - )B(W - -> l - ν) [nb] NLO LHC 7 TeV, VRAP NNLO MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 α s = 0.119, 0.10 α s = 0.119, 0.117, CMS + ATLAS average, 36 pb σ(z 0 )B(Z 0 -> l + l - ) [nb] NLO LHC 7 TeV, VRAP NNLO MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 α s = 0.119,0.10 α s = 0.119, 0.117, CMS + ATLAS average, 36 pb σ(ttbar) [pb] LHC 7 TeV, HATHOR, mt = 17 GeV LHC average σ(ttbar) = pb MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 NLO NNLO ( σ(w + ) + σ(w - ) ) / σ(z 0 ) LHC 7 TeV, VRAP NLO NNLO MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 α s = 0.119,0.10 α s = 0.119, 0.117,0.114 σ(w + ) / σ(w - ) LHC 7 TeV, VRAP NLO NNLO MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 α s = 0.119,0.10 α s = 0.119, 0.117,0.114 σ(ttbar) / σ(z -> l+l-) LHC 7 TeV, HATHOR + VRAP, mt = 17 GeV MSTW08 MSTW08 NNPDF.1 NNPDF.1 ABKM09 NLO NNLO.4 CMS + ATLAS average, 36 pb CMS measurement, 36 pb CMS measurement (36 pb -1 ) LHC data will soon be precise enough to distinguish between different predictions. A. Guffanti (NBIA & Discovery Center) PDFs@LHC 43 / 46

53 The present status of PDF fits Introduction W lepton asymmetry 1. data the LHC. W!µ, at Z!µµ LHCb Motivation 3. Z!"" 4. Outlook 5. Conclusions Dataset W and Z at LHCb 1. Introduction LHCb. W!µ, Z!µµ 3. Z!"" 4. Outlook 5. Conclusions Motivation LHCb: Measurements extended up to!l = 4.9 Dataset ATLAS + CMS Z n AlW = σ(pp W + l + νl ) σ(pp W l ν l ) + l + ν ) + σ(pp W + l ν ) σ(pp W LHCb l l X, pre ex Motivation Dataset LHCb ATLAS: muon charge asymmetry (31pb 1 ) [ArXiv:13:99] CMS: muon charge 8%asymmetry of Z within W (36pb 1 ) [ArXiv:13:3470] LHCb acceptance 17% (16%) of W+ (W-) within LHCb acceptance 4 LHCb Important for PDF constrains 18 Guffanti of Z A.within (NBIA & Discovery Center) 17% (16%) PDFs@LHC of W+ 44 / 46

54 The present status of PDF fits Introduction W lepton asymmetry 1. data the LHC. W!µ, at Z!µµ LHCb Motivation 3. Z!"" 4. Outlook 5. Conclusions Dataset W and Z at LHCb 1. Introduction LHCb. W!µ, Z!µµ 3. Z!"" 4. Outlook 5. Conclusions Motivation LHCb: Measurements extended up to!l = 4.9 Dataset ATLAS + CMS Z n AlW )d (x, M ) d(x, M )u (x, M ) u(x1, MW 1 W W W )d (x, M ) + d(x, M )u (x, M ) u(x1, MW LHCb 1 W W W X, pre ex Motivation Dataset LHCb ATLAS: muon charge asymmetry (31pb 1 ) [ArXiv:13:99] CMS: muon charge 8%asymmetry of Z within W (36pb 1 ) [ArXiv:13:3470] LHCb acceptance 17% (16%) of W+ (W-) within LHCb acceptance 4 LHCb Important for PDF constrains 18 Guffanti of Z A.within (NBIA & Discovery Center) 17% (16%) PDFs@LHC of W+ 44 / 46

55 The present status of PDF fits First contstraints on PDFs from LHC Q = M W, ratio to NNPDF Q = M W, ratio to NNPDF NNPDF NNPDF.1 1. NNPDF.1 + CMS 5 GeV cut + ATLAS 1. NNPDF.1 + CMS 5 GeV cut + ATLAS xubar xd x x - -1 ATLAS and CMS data compatible with data included in global analysis The provide important constraint to PDFs in the small medium-x region Significant uncertainty reduction for light (anti-)flavour distributions A. Guffanti (NBIA & Discovery Center) PDFs@LHC 45 / 46

56 The present status of PDF fits... the data we would love to have from the LHC Medium- and large-x gluon Prompt photons Inclusive Jets t-quark distributions (p, y) (?) Light flavour separation at medium- & small-x Low-mass Drell-Yan High-mass W prduction Z rapidity distribution W (+jets) asymmetry Strangeness & Heavy Flavours W + c Z + c, γ + c Z + b A. Guffanti (NBIA & Discovery Center) PDFs@LHC 46 / 46

NNPDF: Neural Networks, Monte Carlo techniques and Parton Distribution Functions

NNPDF: Neural Networks, Monte Carlo techniques and Parton Distribution Functions Alberto Guffanti Albert-Ludwigs-Universität Freiburg on behalf of the NNPDF Collaboration: R. D. Ball, L. Del Debbio (Edinburgh,