Status of parton distributions and impact on the Higgs

Status of parton distributions and impact on the Higgs Daniel de Florian Dpto. de Física - FCEyN- UBA Higgs Hunting 0 Paris - July 8

Introduction to PDFs Summary of available fits Comparison of PDFs Impact (and issues) on Higgs Cross section : gg channel for inclusive cross section g t, b H g

PDFs Main ingredient of any high-energy observable in Hadronic Colliders dσ = ab dx a non-perturbative parton distributions dx b f a (x a,µ F )f b (x b,µ F ) dˆσ ab (x a,x b,q,α s (µ R)) +O m Λ Q perturbative partonic cross-section f a (x a ) X f b (x b ) Partonic cross-section: expansion in α s (µ R) dˆσ = α n s dˆσ (0) + α n+ s dˆσ () +... Expression relies on factorization theorem : HT, mass corrections, etc. not trivial

PDFs are universal! Include all observables where pqcd is under control : each one helps to constrain a combination of pdfs at certain kinematics Fixed target : lp and DY HERA Tevatron Process Subprocess Partons x range l ± {p, n} l ± X γ q q q, q, g x 0.0 l ± n/p l ± X γ d/u d/u d/u x 0.0 pp µ + µ X uū, d d γ q 0.05 x 0.35 pn/pp µ + µ X (u d)/(uū) γ d/ū 0.05 x 0.35 ν( ν) N µ (µ + ) X W q q q, q 0.0 x 0.5 ν N µ µ + X W s c s 0.0 x 0. ν N µ + µ X W s c s 0.0 x 0. e ± p e ± X γ q q g,q, q 0.000 x 0. e + p ν X W + {d, s} {u, c} d, s x 0.0 e ± p e ± c cx γ c c, γ g c c c, g 0.000 x 0.0 e ± p jet + X γ g q q g 0.0 x 0. p p jet + X gg,qg,qq j g,q 0.0 x 0.5 p p (W ± l ± ν) X ud W, ū d W u,d,ū, d x 0.05 p p (Z l + l ) X uu,dd Z d x 0.05 MSTW

Traditional approach PDFs obtained by global fit : χ minimization ansatz for PDFs at µ 0 with initial set of parameters xf(x, µ 0)=Ax α ( x) β function(x) 00 parameters evolve PDFs to relevant scale Q using DGLAP f i (x, µ F ) d ln µ F = j P ij (x, α s (µ F )) f j (x, µ F ) Splitting functions known up to NNLO Vogt, Moch, Vermaseren χ 500000 data points Calculate observable and χ minimum? yes χ = no N (T i E i ) i= δe i Hessian provides estimate of uncertainties result : best fit χ (a) = χ χ 0 = X i,j H ij δa i δa j + provide 40/50 pdfs to compute uncertainties for any observable

Neural Network approach Construct a set of MonteCarlo replicas of the original data set where the replicas fluctuate about central data Split data sets into training and validation sets Fit to the data replicas obtaining PDF replicas PDFs generated using a neural net to find the best fit. Eliminates largely dependence on parameterization. Still includes pre-processing factor to constrain kinematic limits f(x, µ 0)=Ax α ( x) β NN(x) Statistical definition of mean value and standard deviation F { } F for { } observable F[{q}] = N rep N rep k= F[{q (k) }], σ F = ( N rep ( N rep k= NNPDF, Ball et al ) ) ( F[{q (k) }] F[{q}] ) / be used for the determination of central values and un N rep = 0 or 00

set order data α s (M Z ) uncertainty HQ MSTW 008 NNLO global fitted (+ external variations) Hessian (dynamical tolerance) GM-VFN (ACOT +TR ) Martin, Stirling,Thorne, Watt CT NLO global combined HERA external (several values & older fit) Hessian (dynamical tolerance) GM-VFN (SACOT-X) CTEQ, Lai et al. NNPDF. new NNLO global combined HERA external (several values & recent fit) Monte Carlo (pdf replicas) GM-VFN (FONLL) NNPDF, Ball et al. AB(K)M NNLO DIS+DY(f.t.) fitted Hessian FFN +matching Alekhin, Blümlein, Klein, Moch (G)JR NNLO DIS+DY(f.t.)+ some jet fitted Hessian FFN (VFN massless) Glück, Jimenez Delgado, Reya HERA PDF NNLO only DIS HERA external Hessian GM-VFN (ACOT +TR ) H & Zeus collaborations Each group one provides a number of sets to compute central values and pdfs, pdf+coupling uncertainties

µ F =ŝ (a) Ratio to MSTW 008 NLO (68% C.L.) (c) (c) Ratio to to MSTW 008 008 NLO NLO (68% (68% C.L.) C.L.) (e) (e) O (68% C.L.) C.L.). 5.05 5.. 5 5.05.05 5 5! q (qq) luminosity at LHC ( W Z MSTW08 NLO CTEQ6.6 - gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) MSTW08 NLO MSTW08 CTEQ6.6NLO CTEQ6.6 CT CT NNPDF. NNPDF. Luminosities LHC @ 7 TeV plots from G.Watt CT NNPDF. - - 0 80 40 0 M H 80 (GeV) 40 M H (GeV) tt tt s = 7 TeV) NLO - - s / s s / s s / s Three GG luminosity global fits at LHC in ( s reasonable = 7 TeV), G " g + agreement 4/9! (q+q) GG luminosity LHC ( s = 7 TeV), G " g + 4/9! (q+q) but deviations sometimes as large as q. q. MSTW08 NLO 5 MSTW08 CTEQ6.6NLO uncertainties 5 (not well understood why!) CTEQ6.6 CT CT NNPDF. NNPDF..05 - (b) Ratio Ratio to to MSTW 008 008 NLO NLO (68% (68% C.L.) C.L.) (d) (d) Ratio to to MSTW 008 008 NLO NLO (68% (68% C.L.) C.L.) (f) (f) O (68% (68% C.L.) C.L.).. 5 5.05.05 5 5.. 5 5.05.05 5 5.. 5 5.05! q (qq) luminosity at LHC ( MSTW08 NLO MSTW08 HERAPDF.0 NLO HERAPDF.0 GJR08 GJR08 W Z - - - - gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) MSTW08 NLO MSTW08 HERAPDF.0 NLO HERAPDF.0 GJR08 GJR08 0 80 40 0M H 80 (GeV) 40 M H (GeV) tt tt - - - s / s s / s s / s s / s much bigger differences for q non-global pdfs! GG luminosity at LHC ( s = 7 TeV), G " g + 4/9! (q+q) GG luminosity at LHC ( s = 7 TeV), G " g + 4/9! q(q+q ) MSTW08 NLO MSTW08 HERAPDF.0 NLO HERAPDF.0 GJR08 GJR08 s = 7 TeV) -

PDF4LHC recommendation for Higgs @ NLO Compute uncertainties using global MSTW & CT & NNPDF Obtain the envelope of all 68% c.l. bands : NLO uncertainty supplemented with α s (M Z )=±0.00 (±0.00) at 68% (90%) c.l. Envelope to partially account for TH uncertainties (assumptions) Take the ratio of NLO-envelope to MSTW-NLO and rescale band at NNLO.05 PDF4LHC at work different values of α s (m Z ) exact pdf+α s uncertainties NLO NNPDF.0 CTEQ6.6 MSTW008nlo PDF4LHC recipe R 3.8.6.4 rescaling factors lower curves = upper limit of uncertainty bands LHC HIGGS XS WG 0 R.5.4.3. NNLO-QCD (PDF+! s 68% C.L.)*rescaling factor normalized to MSTW008nnlo LHC HIGGS XS WG 0. 5.8.6 LHC 7 TeV normalized to MSTW008 pdf+α s 68% C.L. 0 50 00 50 300 350 400 450 500 m H (GeV).4. different values of! s (m ) Z exact PDF+! s uncertainties Tevatron LHC 7 TeV LHC 4 TeV 0 50 00 50 300 350 400 450 500 M H [GeV] 0.7 0.6 Tevatron LHC 7 TeV LHC 4 TeV LHC 7 TeV 0.5 0 50 00 50 300 350 400 450 500 M H [GeV]

PDF4LHC at work : NNLO with MSTW and NNPDF NNLO supports PDF4LHC prescription : stability from NLO CTEQ NNLO coming soon

Of course, any time there is a prescription/recommendation there should be criticism! Baglio, Djouadi, Godbole ABM&JR Uncertainties might be substantially underestimated by PDF4LHC prescription : use all available sets Example: ABM + JR @ Tevatron ABM vs MSTW at 60 GeV 0% (>5 sigma) M H (GeV) ABM [8] [9] JR [] MSTW08 [] HERAPDF [] 0.438 ± 0.066.380 ± 0.076.593 ± 0.09.68 ± 0.046.47.05 ± 0.05.0 ± 0.06.09 ± 0.078.65 ± 0.038.055 5 04 ± 0.047 85 ± 0.055.060 ± 0.07.4 ± 0.034 7 0 0.78 ± 0.04 0.770 ± 0.050 33 ± 0.067 68 ± 0.03 00 5 0.677 ± 0.038 0.67 ± 0.045 3 ± 0.06 ± 0.09 0.700 30 0.588 ± 0.034 0.589 ± 0.04 0.79 ± 0.058 0.75 ± 0.06 0.65 35 0.53 ± 0.03 0.58 ± 0.037 0.647 ± 0.054 0.666 ± 0.04 0.54 40 0.449 ± 0.08 0.456 ± 0.034 0.576 ± 0.050 0.59 ± 0.0 0.479 45 0.394 ± 0.05 0.403 ± 0.03 0.54 ± 0.047 0.57 ± 0.00 0.44 50 0.347 ± 0.03 0.358 ± 0.08 0.46 ± 0.044 0.47 ± 0.08 0.377 55 0.306 ± 0.00 0.38 ± 0.06 0.43 ± 0.04 0.4 ± 0.07 0.336 60 0.7 ± 0.09 3 ± 0.04 0.37 ± 0.039 0.378 ± 0.06 0.300 65 0.40 ± 0.07 0.53 ± 0.0 0.335 ± 0.036 0.34 ± 0.04 0.69 70 0.3 ± 0.05 0.6 ± 0.00 0.30 ± 0.034 0.307 ± 0.03 0.4 75 0 ± 0.04 0.03 ± 0.09 0.74 ± 0.03 0.78 ± 0.0 0.7 80 0.69 ± 0.03 ± 0.07 0.48 ± 0.030 0.5 ± 0.0 5 85 0.5 ± 0.0 0.64 ± 0.06 0.5 ± 0.08 ± 0.0 0.76 90 0.36 ± 0.0 0.48 ± 0.05 0.05 ± 0.07 0.07 ± 0.0 0.59 00 ± 0.009 0. ± 0.03 0.70 ± 0.04 0.7 ± 0.009 0.3 Potentially big concern for Higgs exclusion limits Why so different Higgs cross sections? : gluons and coupling constant

One big issue: coupling constant affects cross-section strong correlation with pdfs World average : PDG (S. Bethke) α s (M Z )=4 ± 0.0007 uncertainty most probably larger but not more than 0.00

One big issue: coupling constant affects cross-section strong correlation with pdfs World average : PDG (S. Bethke) α s (M Z )=4 ± 0.0007 uncertainty most probably larger but not more than 0.00 What about pdf sets? partially responsible for the disagreement NNLO! S (M Z ) values used by different PDF groups Bethke 009 (" PDG 0) 68% C.L. PDF MSTW08 HERAPDF.0 GJR08/JR09 Closed symbols: NNLO Open symbols: NLO 0. 0.5 0. 0.5 0.3! S (M Z ) MSTW CTEQ NNPDF PDF4LHC recommendation : use for each fit the corresponding and consider uncertainty ABM NLO 0.0 +0.00 0.005 0 ± 0.009 ± 0.0006 0.79 ± 0.006 (G)JR 0.45 ± 0.008 NNLO 0.7 ± 0.004 0.35 ± 0.004 0.4 ± 0.000 Results from global fits agree with world average, large differences with non-global DIS only-fits prefer smaller coupling? Challenged by recent analyses: only BCDMS? Thorne and Watt : Dis-only fits spoil gluon behavior at large x Jets stabilize result towards world average NNPDF-Thorne, Watt HERA also finds large value 0.76 α s (M Z ) α s (M Z )=±0.00 (±0.00) at 68% (90%) c.l. only experimental errors NNPDF-MSTW

ABM claims wrong use of NMC data as responsible for both gluons and coupling d σ dx dq 4πα xq 4 [ y y ] / +R(x, Q F (x, Q ), ) F R and higher-twist ABM : Use cross section instead of. Wrong procedure reproduce features from other global fits (and Higgs cross section) Thorne,Watt TW tried using different versions of NMC data and find small effect for gluon and coupling NNPDF finds also very small effect Ratio to MSTW 008 NNLO.08.06.04.0 8 6 4 Gluon distribution at Q = M H = (65 GeV) Cut W < 0 GeV Cut Q < 5 GeV Cut Q < GeV Use R 990 for NMC Cut NMC (x < 0.) Cut all NMC data Fix! (M ) = 0.3 S Z Input xg > 0, no jets NNLO PDF (68% C.L.) MSTW08 - - y = 0 at 7 TeV LHC y = 0 at Tevatron x Issue still remains open : Lack of jet data might be main responsible?

JETS Interesting exercise by R.Thorne and G.Watt (0) Check how well PDFs reproduce jet Tevatron data CDF Run II inclusive jet data using kt algorithm (76 points) χ /N pts. < 3 within 90% C.L. D# Run II inclusive (data points before systemat NLO PDF (with NLO ˆσ) µ = p T / µ = p T µ =p T MRST04.06 (0.59) 4 (0.3) 4 (0.3) MSTW08 0.75 (0.30) 0.68 () (4) CTEQ6.6.5 (0.4).66 (0.0).38 (4) CT.03 (0.3).0 ().8 (4) NNPDF. 0.74 () (0.5).3 (0.69) HERAPDF.0.43 (0.39) 3.6 (0.66) 4.03 (.67) HERAPDF.5.6 (0.40) 3.05 (0.66) 3.80 (.66).6 (0.5). () 3.6 (.) GJR08.36 (0.3) 4 (0.3) 0.79 (0.36) no jet Data / Theory.8.6.4. 0.6 0.4 0. 0 JET 0.0 < y < 0.4 NNLO PDFs, data points MSTW08,! = 48,! = 33 D0 RunII p JET T (GeV) only central predictions (no band comparison) better agreement with New HERAPDFs JET < y <. Message from TW : only global analysis provide accurate distributions and uncertainties No acceptable description of jet data from non-global sets

JETS PV: Any PDF should reproduce jet data if being used for Higgs Closest observable to Higgs in terms of Luminosity, kinematics and power of coupling! g jet g t, b H g jet g

JETS PV: Any PDF should reproduce jet data if being used for Higgs Closest observable to Higgs in terms of Luminosity, kinematics and power of coupling! g jet g t, b H g jet g Now, jets are not so trivial! Jets at NNLO? use NLO or NLO +Threshold corrections soft corrections are small (few %), depend on definition of threshold Sizable scale dependence (TH uncertainty) Owens, Kidonakis DdeF, Vogelsang Comparison subtle because of large correlations in systematic uncertainties Dijet more complicated (no NNLO-threshold corrections available) Run I vs Run II tension in data not using Run II jets up to 0% change in gluon at large x Thorne, Watt

Conclusions Everything looks pretty solid and coming LHC data will help to constrain PDFs much better! PDFs play a role in setting exclusion limits for Higgs, but limit can not depend of pdf set used We know recent examples (e.g. MRST-06 vs MSTW-08) where TH improvements produced considerable change in PDFs (and Higgs cross section) Do not expect such big modification in the future. But to be safer, I would recommend try PDF4LHC prescription with larger uncertainty to leave room for possible TH/EXP improvements (mostly on jets!)

Example: MSTW 008 vs MRST 006 Ratio to MSTW 008 NNLO.08.06.04.0 8 6 4-5 4 Gluon distribution at Q = GeV -4 MSTW 008 NNLO (90% C.L.) MRST 006 NNLO Stirling (009) - 4 - x Tevatron 006 analysis did not provide a reliable estimate of uncertainties in large x gluon distribution due to issue in parametrization (DIS to MS scheme transformation) Do not expect such a big modification in the future

Some questions/comments/conclusions So far, only experimental errors considered Some TH (assumptions) uncertainties estimated by envelope prescription Baglio et al α TH s = ±0.00 might be incorporated directly on the analysis central values MSTW : 0.7 NNPDF : Coupling constant and World average : mixing of perturbative orders #-decays (N3LO) Quarkonia (lattice) $ decays (NLO) DIS F (N3LO) DIS jets (NLO) World average PDG (S. Bethke) α s (M Z )=4 ± 0.0007 e + e jets & shps (NNLO) electroweak fits (N3LO) e + e jets & shapes (NNLO) 0. 0. 0.3! s (" Z) PDF4LHC recommendation α s (M Z )= only EW & tau (N3LO) α s (M Z )=0.09 ± 0.003 ±0.00 (±0.00) at 68% (90%) c.l.

(a) PDFs provide sets obtained with different values 0.5 Vertical of error Inner: PDF αonly s bars (M Z ) (pb) " H (c) (pb) " H NNLO gg#h at the LHC ( 7 6 5 4 3 9 (d) NLO gg#h at the LHC ( s = 7 TeV) for M = 80 GeV H NNLO gg#h at the LHC ( s = 7 TeV) for M = 80 GeV 5.8 H 0. 7 5.6 7 0. 5.4 6.5 6.5 5. 0. source 6 of discrepancy at LHC but not enough 5 90% C.L. PDF 6 at Tevatron 0.09 (pb) " H 5.5 5 4.8 4.6 4.4 Vertical error bars Inner: PDF only Outer: PDF+! S s = 7 TeV) for M H 68% C.L. PDF = 0 GeV MSTW08 HERAPDF.0 GJR08/JR09 Closed symbols: NNLO Open symbols: NLO 0. 0.5 0. 0.5 0.3! S (M Z MSTW08 68% C.L. PDF CTEQ6.6 CT MSTW08 NNPDF. HERAPDF.0 HERAPDF.0 ) (c) (b) (pb) " H (e) (d) 0.3 7 6 0.6 5 0.4 4 0. 3 0. 0.6 0.4 0. 9 Sizable effect in uncertainties NNLO NNLO gg#h gg#h at the at the Tevatron LHC ( ( s s = = 7.96 TeV) TeV) for Mfor = M0 = GeV 80 GeV (pb) " H 0.6 0.08 5.5 0.07 5 0.06 0. 0.5 0. 0.5 0.3! S (M Z Vertical error bars Inner: PDF only Outer: PDF+! S 90% 68% C.L. PDF MSTW08 HERAPDF.0 GJR08/JR09 0. 0.5 0. 0.5 0.3 Z Z H Closed symbols: NNLO Open symbols: NLO NLO 90% C.L. PDF 68% C.L. PDF MSTW08 MSTW08 HERAPDF.0 HERAPDF.0! S (M ) ) NNLO NNLO gg#h gg#h at the at the Tevatron LHC ( ( s s = = 7.96 TeV) TeV) for Mfor = M80 = GeV 40 GeV Results in better agreement when evaluated at same value: coupling main 0.4 Outer: PDF+! S GJR08/JR09 Closed symbols: NNLO Open symbols: NLO H H H )

Some issues: Selection of data which observables (no prompt photon) incompatible data sets (W lepton asymmetries) open bins/combined data (Hera) Weights for some experiments enhance the relevance of some data set enhance some parton distribution reduce effect of inconsistent data sets Aesthetic requirements unphysical behavior of pdfs at x=0 and : penalty terms Theoretical issues Uncertainties HQ treatment and masses Parametrization of pdfs Selection of factorization/renormalization scales TH improvements for some observables (resummation) Solution of evolution equations and precision (speed!) α s from fit or external value? which value/uncertainty? what is sigma in a global fit? χ =?

Future HERA PDF can include Tevatron and LHC data idate NNLO fit (compared to CT. NLO.8 PRELIMINARY Ratios of central CT. PDFs µ = GeV g u ub d CT. with NNLO (CT. NNLO)/(CT.).6.4. db sc from P. Nadolsky 0.6-5 -4 0.0 0.0 0.05 0. 0. 0.5 rences between NLO and NNLO sets are compara x ABM : includes Tevatron jets and improvement in HQ thresholds NNPDF. will soon include LHC data (W lepton asymmetry)