Studies of PDF uncertainties for the measurement of the mass of the W boson at the LHC Stefano Camarda (DESY) October 21, 2014 October 21, 2014 Stefano Camarda 1
PDF uncertainties on m W ATL-PHYS-PUB-2014-015 “Studies of theoretical uncertainties for the measurement of the mass of the W boson at the LHC” Introduction Theory predictions and PDF uncertainties Event selection and methodology W polarization and PDF uncertainties Charm-initiated W production and PDF uncertainties Detector effects and summary of PDF uncertainties Parton shower uncertainties Conclusions Points of discussion for a coherent treatment of PDF uncertainties between ATLAS and CMS October 21, 2014 Stefano Camarda 2
Introduction The extraction of m W from the p ℓ T spectrum, is likely to be limited by theoretical uncertainties. This study addresses PDF uncertainties, and non-perturbative QCD uncertainties related to the parton shower model We need not only a precise estimation of PDF and other theoretical uncertainties, but also a roadmap to control and reduce them, by mean of precise experimental measurements of alternative observables The idea is to perform a breakdown of the physical mechanisms behind the PDF uncertainties, and estimate which are the most relevant sources of uncertainties. By pointing out the largest uncertainties, the idea is to provide a pattern to reduce them, rather than a precise estimation to be used in our measurement October 21, 2014 Stefano Camarda 3
Introduction PDF uncertainties for the extraction M W from p ℓ T at the Tevatron are 9 MeV (CDF) and 11 MeV (D0) It has been suggested in Eur. Phys. J. C 69 (2010) 379397 [Krasny, Dydak, Fayette, Placzek, Siodmok, ’10] that PDF uncertainties in proton-proton collisions could be larger than in proton-antiproton collisions for 1st quark generation effect: u and d PDF uncertainties on W boson polarisation 2nd quark generation effect: strange-quark PDF uncertainty on charm-initiated W boson production 3rd quark generation effect: bottom quark mass uncertainty in the extraction of non pertubative parameters from p Z T The idea of this study is to estimate such effects with standard tools for theory predictions and Monte Carlo, and get feedback from the theory community Are we missing something important? Do we need better, additional theoretical predictions to estimate these effects? October 21, 2014 Stefano Camarda 4
Introduction - disclaimer The emphasis is on tracking the physical sources of the uncertainties, we are not estimating the uncertainties to be used in the measurement This is not the ATLAS final word on PDF and PS uncertainties for the W mass, and on theory uncertainties We are considering in this study: u and d valence and sea PDF uncertainties Strange PDF uncertainties PS uncertainties, assuming they can be extrapolated from the measurement of p Z T to the modelling of p W T Detector effects on the muon momentum resolution We are not considering in this study: Gluon PDF uncertainties in all-order resummation (gluon PDF is varied only at NLO) Heavy flavour masses in the matrix-element calculations Differences in the heavy flavour content of W and Z production when propagating PS uncertainties from p Z T to p W T Any QED FSR, and NLO EW effect Detector effects on the measurement of the hadronic recoil October 21, 2014 Stefano Camarda 5
Theory predictions EW scheme G µ -scheme: with G F , M Z , M W as inputs from PDG 2012, α and θ W calculated at tree level Γ Z and Γ W measured value from PDG 2012 CKM from PDG 2012, but V tx = 0, no top in the initial state Theory predictions and tools MCFM W+j production at LO O( α s ), which is the real part of W inclusive calculation at NLO finite width, leptonic decay, spin correlations CuTe differential W p T at NNLL with matching corrections at O( α s ) (NLO+NNLL) zero width approximation no decay of the W APPLGRID: Fast PDF convolution Need to combine the two codes, MCFM and CuTe, to get a realistic prediction of the lepton p T spectrum October 21, 2014 Stefano Camarda 6
CuTe Infrared Safety from the Collinear Anomaly [Becher, Neubert, Wilhelm ’11] The factorisation scale is set to µ = q ∗ + q T , with q ∗ ∼ 1 . 82 GeV The non-perturbative scale q ∗ ∼ e − C /α s ( m V ) protects the processes from receiving large long-distance hadronic contributions Allows to calculate the derivative of p W , Z for p T → 0 with T perturbative QCD One additional non perturbative parameter Λ NP = 0 . 6 GeV introduce a gaussian smearing for hadronic non-pQCD effects Public C++ code, very fast October 21, 2014 Stefano Camarda 7
Theory predictions - benchmark [pb/GeV] [pb/GeV] - + 6 pp W ; s = 7 TeV 6 pp W ; s = 7 TeV 10 10 → → 5 5 10 10 + - W W 4 4 T 10 T 10 /dp /dp 3 3 σ σ 10 10 d d 2 2 10 10 CuTe CT10nlo CuTe CT10nlo 10 10 MCFM CT10nlo MCFM CT10nlo NLO (fixed order) NLO (fixed order) Ratio Ratio 1.02 1.02 1 1 0.98 0.98 0 20 40 0 20 40 - + W p W [GeV] p [GeV] T T Perfect agreement between the two codes, at fixed order O( α s ), zero width, no decay. October 21, 2014 Stefano Camarda 8
Theory predictions - combination Reweighting function defined as r ( p T ) = NLO+NNLL NLO The reweighing is applied, in the range 0 . 1 < q T < 150 GeV, outside this range the weight is set to 0 [pb/GeV] [pb/GeV] - + CuTe; pp W CuTe; pp W → → 5 10 5 10 NLO (fixed order) NLO (fixed order) NLO+NNLL NLO+NNLL T T 4 /dp /dp 10 4 10 σ σ d d 10 3 3 10 2 10 2 10 10 10 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 - + W p W [GeV] p [GeV] T T Ratio Ratio - 1.6 + CuTe; pp W 1.6 CuTe; pp W → → NLO+NNLL NLO+NNLL 1.4 1.4 NLO NLO 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 - + W p W [GeV] p [GeV] T T October 21, 2014 Stefano Camarda 9
CKM decomposition of the reweighting function The NLO+NNLL/NLO ratio has a significant dependence on the flavour of the quarks initiating the W -boson production process: heavy quarks result in a harder p W T spectrum and a harder ratio between resummed and fixed order predictions The reweighting function is decomposed in terms of the CKM matrix: 6 × 2 functions are the NLO+NNLL/NLO ratios evaluated by setting to 0 all the CKM matrix except the V xy term, separately for W + and W − Reweighting function Reweighting function 1.6 1.6 1.4 1.4 1.2 1.2 1 1 - + CuTe; pp W CuTe; pp W → → V V 0.8 0.8 ud ud V V us us 0.6 V V 0.6 ub ub V V cd cd 0.4 0.4 V V cs cs V V cb cb 0.2 0.2 0 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 + - W p W [GeV] p [GeV] T T October 21, 2014 Stefano Camarda 10
Theory predictions - benchmark 4 4 [pb/GeV] 10 [pb/GeV] 10 - + pp W ; s = 7 TeV pp W ; s = 7 TeV → → + - 3 W 3 W 10 10 T T /dp /dp σ σ d d 2 2 10 10 CuTe CuTe MCFM+CuTe MCFM+CuTe NLO+NNLL NLO+NNLL Ratio Ratio 1.05 1.05 1 1 0.95 0.95 0 20 40 0 20 40 + - W W p [GeV] p [GeV] T T Good agreement at NLO+NNLL after reweighting. PDF uncertainties reproduced at high p T , at low p T CuTe has larger PDF uncertainties. In CuTe the factorisation scale is set to µ = q ∗ + q T , with q ∗ ∼ 1 . 82 GeV, → CuTe is sensitive to larger PDF uncertainties associated with the low x region. In MCFM prediction, the factorisation scale is set to 80 GeV. October 21, 2014 Stefano Camarda 11
Dedicated PDF set A dedicated PDF set has been produced to study the PDF uncertainties for M W extraction from p l T Simple setup which allows breakdown of uncertainties, not intended for final estimate of PDF uncertainties NLO Fit to HERA I data Starting scale Q 2 0 = 1 . 7 GeV 2 charm mass m c = 1 . 38 GeV bottom mass m b = 4 . 75 GeV top mass m t = 3 . 5 TeV → 5 flavour strange fraction r s = s / ¯ d = 1 13p parametrisation 26 hessian variations 4 model variations: m c = 1 . 32 , 1 . 44, r s = 0 . 72 , 1 . 25 Total of 30 variations October 21, 2014 Stefano Camarda 12
PDF at the starting scale ) 2 2 ) 2 2 ) 2 2 ) 2 2 2 Q = 1.7 GeV 2 0.4 Q = 1.7 GeV 2 Q = 1.7 GeV 2 Q = 1.7 GeV (x,Q 0.8 (x,Q (x,Q (x,Q MW-NLO exp+mod MW-NLO exp+mod MW-NLO exp+mod MW-NLO exp+mod 0.5 0.5 MW-NLO exp MW-NLO exp MW-NLO exp MW-NLO exp V 0.7 V 0.35 u d xu xd x x 0.6 0.3 0.4 0.4 0.25 0.5 0.3 0.3 0.4 0.2 0.3 0.15 0.2 0.2 0.1 0.2 0.1 0.1 0.1 0.05 0 0 0 0 -3 -3 -3 -3 10 -4 10 10 -2 10 -1 1 10 -4 10 10 -2 10 -1 1 10 -4 10 10 -2 10 -1 1 10 -4 10 10 -2 10 -1 1 x x x x ) Q 2 = 1.7 GeV 2 ) Q 2 = 1.7 GeV 2 ) Q 2 = 1.7 GeV 2 ) 1.6 Q 2 = 1.7 GeV 2 2 2 2 2 xg(x,Q 3 (x,Q 1.6 xs(x,Q 0.6 )(x,Q MW-NLO exp+mod MW-NLO exp+mod MW-NLO exp+mod MW-NLO exp+mod 1.4 MW-NLO exp MW-NLO exp MW-NLO exp MW-NLO exp 2.5 Σ 1.4 d x + 0.5 u 1.2 2 )/( 1.2 s x(s+ 0.4 1 1.5 1 1 0.8 0.8 0.3 0.5 0.6 0.6 0.2 0 0.4 0.4 -0.5 0.1 0.2 0.2 -1 0 0 0 -4 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 1 10 10 10 10 1 10 10 10 10 1 10 10 10 10 1 x x x x Blue band: experimental (hessian) uncertainties Red band: experimental uncertainties plus model variations, r s and m c October 21, 2014 Stefano Camarda 13
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