Theory Uncertainties for Higgs Searches using Jet Bins

Transcription

1 heory Uncertainties for Higgs Searches using Bins Iain Stewart MI LBL Higgs Jamboree, Oct.0 Based On: arxiv:7.7 I.S. & F. ackmann (inut to LHC Higgs Xsec working grou for summer 0 recommendations, BNL accord ) arxiv: C.Berger, C.Marcantonini, W.Waalewijn

2 Outline Introduction: -bins in Higgs Searches heory Uncertainties & Correlations Using Fixed Order Calculations for Bins Exloiting Log Resummation for Bins

3 Use jet bins to maximize sensitivity backgrounds vary with # of jets H WW ν ν H WW νjj eg. large to background in H WW t t t H W W W W b b H ττ H γγ ν ν ν ν 95% CL limit on σ/σ SM 0-jet bin vetoes b-jets ALAS events 5 Ex. Obs. Ex. Obs. - - H γ γ H (.08 γ γ (.08 fb ) fb ) - - H WW H WW lνlν lνlν (.70 (.70 fb fb) ) - - W/Z H, W/Z H H, H bb bb (.04 (.04 fb fb) ) - - H τ τ H (.06 τ τ (.06 fb ) fb ) - - H ZZ H ZZ llll llll ( fb fb) ) - - H ZZ H ZZ llqq llqq (.04 (.04 fb fb) ) - - H ZZ H ZZ llν ν llν (.04 ν (.04 fb fb) ) Preliminary l/l Z veto E cuts >0/ miss - L dt ~.0-.3 fb, cut anti b-tag jet veto data H(60) # WW W+jets di-boson to Z+jets WW l s=7 ev l cut cut m ll CLs limits m H Figure 3: he exected (dashed) and observed (solid) cross section limits for the individual search nels, normalised to the Standard 6 - Model Higgs boson cross section, as functions of the Higgs boson CMS, s = 7 ev, L =.55 fb hese results use the rofile likelihood technique with 95% CL limitsint using the CL S construction. he searches for the Standard Model Higgs boson can also be interreted in the framewor Standard Model with a fourth generation of heavy fermions. he masses of the fourth-generatio tons and down-tye quark are set to a high value of 600 GeV. he mass difference between the generation u-tye and down-tye 4 quarks is fixed to 50 + ln(m H /5[GeV ]) for consistenc the electroweak recision measurements [7]. he systematic uncertainties related to the QCD PDF and α S uncertainties are assumed to be the same as the Standard Model case for the gluon rocess. o account for the missing 3 electroweak radiative corrections which can have a sizable i on the roduction cross section, an additional ±% systematic uncertainty is added linearly to the all theoretical uncertainty on the roduction cross section. he imact of a heavy fourth generat fermions on the signal roduction rates in the various channels are not homogeneous, for a reint tation of the searches for the Standard Model Higgs boson in this framework a secific combina therefore necessary. he result of this combination is illustrated in Fig. 7. With the aforemention of model arameters, Higgs boson mass hyotheses above 6 GeV are exected to be excluded 95% CL and a Higgs boson with mass in excess of 9 GeV and u to 593 GeV is excluded at th CL. Previous exclusion limits in this framework, set by evatron and LHC exeriments, are re Soft in [9, 8, 9]. "! ll cut m cuts

4 Gluon fusion: gg H Vector-boson fusion: qq qqh otal cross to NNLO section(see t Sally s talk) otal cross section to NNLO* at NNLO σ total PDF+α s uncertainty (see Joey s talk) σ total total 8% exclusive jet cross sections H + 0 jets H +jet H + jets sum is erturbative uncertainties σ 0 ± 0 σ ± σ ± σ total ± total My talk: i =? correlations=? Entries Data / MC erturbative uncertainty: % 000 Data SM (sys stat) ALAS Preliminary s = 7 ev, H WW lνlν - L dt =.70 fb WW WZ/ZZ/Wγ t t Single o Z+jets W+jets (data driven) H [50 GeV] N jets

5 Vetoing s : eg. H WW + 0 jets Search for jets and require jet evatron: cut LHC: cut 0 GeV 5 GeV <cut Soft Veto changes form of erturbation theory Even if hard signal rocess gg H contains no jets, jet veto affects cross section by restricting ISR hms t-channel singularities roduce Sudakov double logarithms σ( cut )=σ B 3α s cut σ ln 0 = + π m H H Perturbative corrections get large at small cut m H

6 Vetoing s : eg. H WW + 0 jets Search for jets and require jet <cut evatron: cut 0 GeV LHC: cut 5 GeV Soft Veto changes form of erturbation theory σ 0 + α s L + α sl α s L + α sl α s + α sl α sl +... L =ln cut m H + α s +...

7 σ total = cut dσ dσ d + d 0 d cut d σ 0 ( cut ) + σ ( cut O cut ) cut Added uncertainty from our ability to redict deendence ( large logs or article migration between bins ) ( Cancels when adding σ 0 and σ cut cut anti-correlated Extension to multile exclusive jet bins: σ 0 ( cut cut ),σ ( cut, cut ),σ ( cut, cut 3 ),... inclusive jet cross section H + jet cut ) How do we comute cut?

8 (A) Direct Exclusive Scale Variation? vary µ F,µ R in σ i s i consider σ 0 (µ), vary µ [m H /, m H ] to get 0 etc. uncertainties here are 0% correlated so that σ total = σ 0 + σ +... does not account for cut gets back its uncertainty total due to numerical cancellations can underestimate uncertainties σ total σ B +αs + α s + O(α3 s ) O σ ( cut ) σ B αs (L +L+) + α s (L4 +L 3 +L +L+) + O(α 3 s L6 ) large K-factor large logs large cancellation for for some range of cut σ 0 ( cut )=σ total σ ( cut ) L =ln( cut /m H)

9 For examle, at LHC for m H = 65 GeV and E cm =7eV σ total =(3.3 b) +9.5 α s + 35 α s + O(α3 s ) σ jet 30 GeV) = (3.3 b) 5. α s + 8 α s + O(α3 s ). Direct Exclusive Scale Variation: green lines 8 gg H +0 jet (NNLO) cancellation σ0( cut )[b] 6 4 E cm =7eV m H =65GeV µ = m H / µ = m H µ = m H /4 combined incl. unc cut All lots: MCFM for sectra, FeHiP for NNLO cross section, MSW dfs, anti-k jets with R=0.5

10 (B) Combined Inclusive Scale Variation IS, ackmann, arxiv:7.7 reat inclusive cross-section uncertainties as indeendent ( ) total,,,... For cut uncertainty use: cut = Proagate errors to get uncertainty for σ 0 ( cut )=σ total σ ( cut ) eg. {σ 0,σ } ( + total ) has anti-correlation σ total σ B +αs + α s + O(α3 s ) O σ ( cut ) σ B αs (L +L+) + α s (L4 +L 3 +L +L+) + O(α 3 s L6 ) treated as indeendent series large K-factor estimate for logs obtained from σ ( cut ) L =ln( cut /m H) large logs

11 re of Cross Sections For examle, at LHC for m H = 65 GeV and E cm =7eV cut dσ dσ d + d d cut d 0( cut ) + σ ( cut α s + O(α3 s ) σ total =(3.3 b) +9.5 α s + 35 α s + O(α3 s ) σ jet 30 GeV) ) = (3.3 b) 5. α s + 8 α s + O(α3 s ). Direct Exclusive Scale Variation L+) + α s (L4 +L 3 +L +L+) + O(α 3 s L6 ) ( cut green lines )=σ total σ ( cut Combined Inclusive Scale Variation red lines ) total and σ ( cut ) are largely indeendent in σ 0 can use indeendent scale variations 6 for ons σ total, σ 0 = total + σ0( cut )[b] heory Unc. in Higgs Searches Using Bins / gg H +0 jet (NNLO) E cm =7eV m H =65GeV µ = m H / µ = m H µ = m H / cut combined incl. unc. agree when cut is turned off these lots only vary µ R = µ F (varying µ F alone is quite small for Higgs) gg jet

12 Quite generic: same attern at evatron similar lots if we vary raidity cuts similar lots for other rocesses

13 0 s Continued Convergence (NLO to NNLO) Higgs + 0 s Continued excl. scale variation vs. Combined incl. scale variation direct excl. scale variation combined incl. scale variation Naive excl. scale variation vs. Combined incl. scale variation cl. scale 8 variation combined8 incl. scale variation 8 naiveexcl. scale variation combined incl. scale variation E cm =7eV 6 E cm =7eV 4 6 m H =65GeV 4 6 m H =65GeV E η jet 3.0 η jet cm = 7 ev 4 E cm = 7 ev m H = 65 GeV E cm NNLO = 7 ev 4 m H = 65 GeV E cm NNLO = 7 ev NNLO m H NLO = 65GeV NNLO m H NLO = 65 GeV NLO NNLO NLO NNLO NLO NLO cut cut cut cut FIG. : Fixed-order erturbative cut uncertainties for gg H + 0jetsatNLOandNNLO. he cut uerrowis fortheevatron and the lower row for the LHC with E cm =7eV. Ontheleft,theuncertaintiesareobtainedfromthenaivescalevariationin s σ 0 and correlations ( cut )betweenµ = m H e.g. /4andµ = m H cut Uncertainties and correlations. On = 30 GeV and NNLO the right, e.g. the atuncertainties cut = 30 are obtained GeV by and indeendently NNLO evaluating the scale uncertainties in σ total and σ ( cut )andcombiningtheminquadrature. (FortheLHCcasethedarkshadedNNLObands corresond to results in the to-left anel of Fig.. he naive scale variation band corresonds to the dashed green lines, and the total) combined =8.6% δ(σ inclusive uncertainty total )=8.6% band corresonds to δ(σ the solid total red)=8.6% δ(σ lines.) total )=8.6% σ0( cut )[b] Introduction Counting s at Fixed Order Resummation for Higgs + 0 s at NNLL+NNLO σ0( cut ) [b] (σ ) = 9% inclusive cross sections with these cuts, δ(σ 0 ) =.4% Introduction Counting s at Fixed Order Resummation for Higgs + 0 s at NNLL+N Higgs + 0 s Continued σ0( cut ) [b] Naive excl. scale variation vs. Combined incl. scale variation δ(σ ) = 9% δ(σ 0 ) =.4% σ0( cut ) [b] NNLO NLO ( = σ jet ) ( cut σ jet cut, jet ) ρ(σ cut. σ ) = +0% 0, σ ) = +0% (9) For convenience we adot the notation that cut is always used for the cutoff that determines the uer boundary of the jet bin under consideration, which gives the analog σ0( cut )[b] δ(σ ) = 9% 30 GeV,jet δ(σ 0 ) = 8% σ ( jet δ(σ 0 ) = 8% ρ(σ 0, σ ) = 64% 30 GeV) =(.00 b) [ 3.6 α s + O(α s) ]. (0) For σ = σ σ there is a sizeable cancellation between these α s terms. If we lower the cut to jet GeV then the logarithm increases and there is an almost exact cancellation with the 5.4α. In the to right ann (MI) heory Unc. in Higgs Searches Using Bins / 6 naive excl. scale variation σ0( cut ) [b] E cm = 7 ev m H = 65 GeV cut δ(σ ) = 9% ρ(σ 0, σ ) = 64% Frank ackmann (MI) heory Unc. in Higgs Searches Using Bins / 6 σ0( cut ) [b] combined incl. scale variation E cm = 7 ev m H = 65 GeV NNLO NLO cut Uncertainties and correlations e.g. at cut = 30 GeV and NNLO δ(σ total )=8.6% δ(σ ) = 9% δ(σ 0 ) =.4% ρ(σ 0, σ ) = +0% δ(σ total )=8.6% δ(σ ) = 9% δ(σ 0 ) = 8% ρ(σ 0, σ ) = 64% Frank ackmann (MI) heory Unc. in Higgs Searches Using Bins

14 other examles 5 σ( cut )[b] σ0( cut )[b] σ( cut )[b] σ0( cut )[b] gg + jet (NLO) gg H +0 jet (NNLO) 30 GeV jet EE cm cm =7eV m H H =65GeV µ µ = = m H H / / µ = m µ = m H µ = m H H /4 µ = m H /4 combined incl. unc. combined incl. unc cut gg H + jet (NLO) WW+0 jet jet GeV(NLO) cut σ( cut )[b] σ( cut )[b] gg H + jet (NLO) 30 GeV jet E cm =7eV m H =65GeV µ = m H / µ = m H µ = m H / cut gg H + jet (NLO) GeV jet combined incl. unc E cm =7eV 0.3 m 0. H uncertainties for background =65GeV E cm =7eV µ = E m H / 0 cm =7eV rocesses in jet-bins m 0. H =65GeV µ µ = m HW µ = m H / 0. µ µ = =m m H /4 W µ = m H combined µ = m W incl. / unc. 0. µ = m H / combined incl. unc. 00 combined incl. unc cut cut cut t anel), WW +0 jets (lower left anel), H + jet with jet 30 GeV lower right anel). Central values are shown by the blue solid curves, FIG. : Perturbative redictions for H +0 jets (uer left anel), WW +0 jets (lower left anel), H + jet with jet n dashed and dotted curves, and the result of combining indeendent 30 GeV jet σ (µ), indeendent σ = σ σ should be estimated the same way

15 choice of cuts δ(σ 0 )=.3% and δ(σ )=5.5%, which is eendent tainties for σin H) which quadrature, and σ,andaddingthem gives solid {σ total, red σ 0, σ curves, } is given by which rovide a eg. Numbers more realistic for estimate reflected reating for the the erturbative inclusive inching jet uncertainties of 30 GeV uncertainty. the green lines total, in Fig.,. (Note as unco, gives the solid red curves, which rovide a, m H = Using the result that from increasing A. A the d we range jet can 30 examine of scale variation total total 0 {σ total, σ 0, σ } is given by estimate for the erturbative uncertainty. GeV the or searately C = result from full A. uncertaintiesvarying A we can and examine correlation µ r and µ the matrix f doeswith not mitigate total 0,, andthis total roblem.) + he. 0 ( s ties of the ( )-jet bins in Higgs roduction. For the cuts in start and U.S. correlation Deartment with: matrix of En- analog of Eq. () for this examle would be with 0, δ(σ, and ) f0 ) δ ( f0 ) δ + total total he relative = uncertainties ( -FG0-94ER4088, s in Higgs Eq. roduction. (0) andvarying by the Forthe σthe scale =(0.85 cutsbyinfactors ± 0.49) + of b, two, corresonding we have f. (A3) s of the U.S. Deartment of En- relative unce ying the scale σ total by factors =(8.70 of ± σ 0.75) 0.6 two, tainties =(0.85 b, δ(σ.3% ) f0 ) and correlations δ ( for σ 0 and σ f0 ) directly follow from Eq. relative quantities f i and δ i,onegets C = total δ total we have σof ± 8.6%, + = nder -FG0-94ER4088, the grant DE-SC and by the 0.49) =( b, f8.8%, ± 5.5% corresonding 0.6) and + b, 0. 57%, and σ resectively. We le =(0.85 ± 0.49) b, corresonding σ 57% f 0 to relative = relative σ= 8.6%. tot uncertainties of 8.6%, and 8.8%, and 57%, resectively. We let 70 G =(0.85 ± 0.49) δ(x) uncertainties σ. (A3) + () δ(σ 0 ) = ( f nder the grant DE-SC and 0 ± 0.75) b, σ =(3.9 ± 0.6) δ(x) Similarly, b, denotetherelativeercentuncertaintyofthequan of 8.6%, the8.8%, correlation and coefficients 57%, δtotal + 0 δ ) 0 f, resectively. for 0 ( We let σ By treating tity b, denotetherelativeercentuncertaintyofthequantity x, corresonding all σ i as 0% andρ(x, y) the to correlated, σ 0 and σ following Similarly, fromthe Eq. correlation (A) are δ(σ ) correlation σuncer- tainties σ= 0 is coefficient σ forced to between the have f0 ) δ ( f0 ) δ he uncertainties and coefficients correlations = f for + σ =(0.85 δ(x) ± denotetherelativeercentuncertaintyofthequantity x, x, lowing for σ f 0 0 and σ, fol- direct α s ase of hree 0.49) b, corresonding to uncertaintieand the σ αa Bins of 8.6%, asmallerrelativeuncertaintythanσ 8.8%, andy. and quantities and ρ(x, A.Ayields ρ(x, from 57%, y) Eq. i resectively. (A) and correlation δare i,onegets [ coefficient We total let, as ] / between 70 ingev. Eq. (), x In ase of hree y) thecorrelationcoefficient between x comb δ(x) Bins denotetherelativeercentuncertaintyofthequantity of 8.6%, 8.8%, and 57%, resectively. We let 70 GeV. In and and since y. A.Ayields y. ita.ayields has to make[ uρ(σ for 0, σ total )= much + δ larger uncertainties σ as a functi eneralize Eq. a be () δ(x) x, toand denotetherelativeercentuncertaintyofthequan- used the case ρ(x, of y) in σthe correlation δ(σ σ as a func roagate get:. ρ(σ 0, σ total )= 0 )=8%, coefficient + δ δ ]( f 0 ), total / [ ρ(σ between xδ(σ )=3%, combined mine inc that is actually andtity y. A.Ayields x, inand current ρ(x, In y) addition theδ(σ correlationcoefficient between x combined in and y. A.Ayields ρ(σ 0 )=8%, 0 )=8%, to the cross δ ( f 0 ), σδ(σ, eneralize Eq. () to the case of ρ(σ 0, σ total + δ total )=0, 0 ) = ( ] δ / [ total sections in 0, σ total )=0.77, δ(σ δ(σ each ρ(σ )=3%, )=3%, jet abin, better we can estim nly thatneighboring is actually jet usedbins current will be [ δ also, σ )= 0.6 dash a better, ρ(σ est 0 ρ(σ consider, σ total 0, σ the total )=0.77 )=0.77 relative,, jet ( f f 0 ) δ total + ) ] / [ ρ(σ 0, σ )= + δ 0total, f, 0 ] totalfractions ρ(σ )= 0.50, ρ(σ, σ,)= 0.6 σ f 0 )= 0.6 = σ 0 mined /σ total,, by and ation to more than three jet bins ρ(σ dive u/ δ(σ 0 )=8%, σ /σ total, which 0, σ )= + δ δ total ( / f 0 ) + δ ( ( δ nly neighboring jet bins will be [ δ(σ ) f0 ) δ ( f0 = ] Alternatively, are we canoften use {σ / δ(σ total )=3%, used δ in exerimental dashed mined analyses. curve by( ated. u δ(σ 0 he )=8%, ρ(σerturbative 0 σ )= 0.50, σ )= 0.50 theory,, ( f 0 ) ation to more than three jet bins ρ(σ 0, σ + δ,f 0,f } as the total three f + indeendent quantities. f he tions following from Eq. () are [ δ(σuncertainties δ)=3%, and correlations () () ort lusive cross sections ρ(σ 0 σ, total σ total, σ)=0.77,, ρ(σ dashed curv ρ(σ )=0.77 where we, have only, σ ρ(σ shown )= 0.6,, σ )= 0.6 the nonzero, correlations. dive andwhen Not a lo ρ(σ where we have only shown the nonzero correlations. Note dive and a 0, σ )= 0.50 where for the we jet that σ 0, have fractions only shown follow the by nonzero standard and σ as well as and σ() correlations. error roagation bsolute uncertainties by total + δ ( haveortant Note a substantia earlie tive jet or consider by δ jet ρ(σfractions: that 0, σthat from σ)= 0.50 negative 0 and σ those 0 and in σ as correlation, σ Eq. well as well (). as σas heδ f ) ] ated. then [ ( f 0 ) ] / ( / [ δ(f lusive cross sections σ total, σ,, and σ general and σ because σ exressions f 0 bsolute uncertainties have have a of the jet-bin () substantial a substantial are given i by = i total /σ i., + δ ( 0 ) ( ρ(σ 0, σ total = + δ boundary when ortant theyield cut ear ross sections and event fractions where we have negative only negative in A. ρ(σ correlation because of the jet-bin they share, shown correlation A, 0 and, σ we )=0, while the nonzero because find ) δ ) δ f ] total / + δ ), 0 δ ( f 0 ), total, ρ(σ, σ total )=0, f 0 tive uncertainties by δ i = i /σ i. when the c where we share, have only while shown σ the 0 and correlations. of the jet-bin [ σ nonzero are uncorrelated. Noteboundary jet-v that σ 0 and σ are 0 and σ as well correlations. Note jet they] ross sections and share, while In as contrast, σ and and the σ σ naive have are uncorrelated. scale a substantial variation assumes jet that σ 0 andinσ contrast, well the naive and scale σ have variation a substantial assumes that all 30 that 30 GeV, f 0 = σ event fractions ρ(σ ρ(σ, 0 σ, σ total )=0, )=0, / 0 ρ(σ, δ(f yield a contro G a negative correlation In yield a cont negative correlation the cross the because contrast, 0 )=3%, [ δ(f sections cross because sections of the the naive jet-bin scale are of the 0% are jet-bin 0% boundary variation boundary correlated. they assumes )=33%, σ total that all the cross ρ(f 0, sections σ total )=0.4 are 0%, correlated. ρ(f Due, σ total they Due )= 0.6 the Due tojet-veto can- the tocan- cellations 0 andbetween σρ(f the, logar can f = share, σ ρ(σ, σ )= + δ ( while. σ(a) jet-veto log share, while 0 and σ cellations σ are uncorrelated. δ σ between are between the uncorrelated. the the erturbative erturbative f ) ] /, f 0 = σ ρ(σ, σ total )=0, 0, σ )= + δ total δ 0 ( f 0 ), [ σ total. (A4) f 0 f series, series, this series, this leads leads this to leads to t = In σ ρ(σ total contrast,. (A) In contrast, much the the much smaller naive he naive smaller scale relative 0,f, σ )= 0.80 )= + δ (. (3) (and variation uncertainties δ scale variation (and unrealistic) assumes f ) ] / Alternatively, we can use {σ total,f 0,f } as three indeenden. (A4) following from Eq. () are forthen f 0 assumes that and f that all 0 are σ total much he smaller relative (and uncertainties unrealistic) foruncertainties, f 0 and f all are with ourwith ou ix for the thefour crossquantities sections choice the cross sections choice are of cuts 0% are 0% of δ(σ cuts correlated. 0 )=.3% correlated. δ(σ 0 )=.3% and Dueδ(σ to Due and )=5.5%, the to the δ(σ can-cellations between reflected in the erturbative can- )=5.5%, which is h choice Comaring of cuts toδ(σ Eq. ( 0 )=.3% (), the use andof δ(σ jet )=5.5%, fractions with whichσ which total is en by ) ix for the four quantities inching the inching ofseries, the green ofthis the lines leads green Fig. to lines. in (Note duci reflected in the δ(f denominator 0 the ) ( = ( inching yields δ ) δ(f the total a nonzero green + δ ) ( 0 ) ( lines, = ) δ anti-correlation Fig.. Fig. (Note. (A5) ) f total + 0 for (Not

16 (C) Use Resummed Predictions to get Uncertainties this will allow us to include both tyes of uncertainties (correlated & uncorrelated) from methods (A) and (B)

17 How to Veto Central s Conventional: Algorithm Conventional: algorithm Search for jets and require jet evatron: cut 0 GeV LHC: cut 5 GeV Vetoes Search for jets and require < cut <cut Comlicated hase-sace restrictions Soft Soft jet jets Alternative: Event shae Alternative: Event Event shae Shae Measure beam thrust of each event Measure beam thrust for of each event cm = cm = k e ηk k e ηk = = Ek Ek z k k k z k k k Ek z k cm = k e ηk = k k and require cm < cm cut and require cm < cm cut Better suited to analytic calculations Better suited to analytic calculations Nice for higher order calculations Soft Soft Soft Frank ackmann (MI) Higgs Production with a Central Veto / 6 Frank ackmann (MI) Higgs Production with a Central Veto / 6

18 veto restricts ISR, gives double logs L =ln cut or L =ln cm cut m H LO Parton Shower NLO eg. MC@NLO is NLO+LL m H σ 0-jet = + α s L + α sl 4 + α 3 sl eg. Pythia is LL (+ tuning) + α s L + α sl 3 + α 3 sl α s n ( cut ) + α sl + α 3 sl α sl + α 3 sl α sn ( cut ) + α 3 sl α 3 sl α 3 s +... LL

19 veto restricts ISR, gives double logs L =ln cut or L =ln cm cut m H Calculation: LO NLO NNLL + NNLO m H NNLO σ 0-jet = + α s L + α sl 4 + α 3 sl α s L + α sl 3 + α 3 sl α s n ( cut ) + α sl + α 3 sl α sl + α 3 sl α sn ( cut ) + α 3 sl α 3 sl α 3 s +... LL NLL NNLL Berger et.al. two orders of summation beyond LL shower rograms

20 (C) Use Resummed Predictions to get Uncertainties this will allow us to include both tyes of uncertainties (correlated & uncorrelated) from methods (A) and (B) Idea: reweigh or POWHEG to NNLO for central values for cut (what you do now) resummed calculation has two sources of uncertainty, one is correlated with total, one gives given these as % errors for sectra in a MC samle to aly these errors for cm cut cut, reweigh

21 NNLL + NNLO calculation H gg µ H µ [Stewart, F, Waalewijn] B g µ B f S gg B µ S Λ QCD Soft dσ s = H gg (µ) d cm dt a dt b B g (t a,µ) B g (t b,µ) S gg Function describes at the scale Hard H gg hard virtual radiation µ H m H B cm t a + t b Beam B g virtual & real energetic ISR µ B cm m H Soft S gg B virtual & real soft radiation µ S cm B i (t, x) =,µ m H dξ ξ I ij(t, x/ξ) f j (ξ) logs give sensitivity to smaller scales Perturbation theory at each scale contributes to uncertainties

22 µ Small cut cm individual scale variations three searate scale variations µ H = µ H0 µ B and µ S give cut = SB (dominate for small cm cut ) with σ total µ H µ B µ S cm 0% correlated 80 0 σ( cm cut ) [b] δσ [%] E cm = 7 ev m H = 65 GeV cut cm cut cm µ H µ B µ S E cm = 7 ev m H = 65 GeV µ H µ B µ S

23 total. he full covariance matrix for {σ total, σ 0, σ }, C H = that is the analog of Eq. () but for the resummed result, is then C = C SB + C H, C SB = Htot H H0 H H SB SB C SB = 0 SB SB 0 SB SB C H = Htot Htot H0 Htot H Htot H0 H0 H0 H 0 SB SB, (34) Htot Htot H0 Htot H Htot H0 H0 H0 H, Htot H H0 H H where SB is obtained f µ B variations, and C SB he Hi are obtained fr Htot = H0 + H. bin shown by the darker by SB + H0, which is of C. 6 As an examle, consi NNLO, the inclusive cro 0.75) b and σ =(.5 gives δ(σ 0 )=5%, ρ(σ 0, σ total )=0.77, ρ(σ 0, σ )= 0.64 strict NNLL result. In Ref. [35] the nonsingular contributions were obtained for the sum of O(α s )+O(α s)cross-sectionsusing For σ 0 this corresonds FEHiP [8, 9]. Here we use a much higher statistics and thesectrum structure here

24 Small cut cm like small cut direct exclusive scale variation shown for NNLO & combined NNLL scale variations shown σ0( cm cut )[b] E cm =7eV m H =65GeV cut cm NNLL+NNLO R(MC@NLO) (excl. µ) NNLO (excl. µ) δσ0 [%] cut cm 30 E cm =7eV m H =65GeV NNLL+NNLO R(MC@NLO) (excl. µ) NNLO (excl. µ) logs are large, NNLL central value lower than NNLO reweigh MC@NLO to match NNLO value/uncertainty at 00GeV Central value is nearer NNLL. Uncertainty is only for norm. direct exclusive uncertainties here are too small (we discussed that...)

25 Small cut cm like small cut combined inclusive scale variation shown for NNLO & combined NNLL scale variations shown σ0( cm cut )[b] E cm =7eV m H =65GeV cut cm NNLL+NNLO R(MC@NLO) (incl. µ) NNLO (incl. µ) δσ0 [%] cut cm 30 E cm =7eV m H =65GeV NNLL+NNLO R(MC@NLO) (incl. µ) NNLO (incl. µ) NNLO band largely overlas NNLL result reweigh MC@NLO to match NNLO incl. uncertainties (full sectrum). Overlas nicely. his factor of two imrovement in uncertainty is what one would exect if a similar reweighing exercise is done for jet

26 Discussion Reweighing will reduce theory errors. Logical next ste. I have tables for LHC@ 7 ev, mh =65 GeV. (And evatron for many mh s because they already started the reweighing during the summer rush.) Other mh table s for the LHC are straightforward to roduce. ) Will you quote exerimental results/limits for exclusive jet cross section? (bkgnd+signal, signal) at Hadron level (corrected to erfect detector). ie. Quote exerimental results without any jet-bin bias from theory. (Useful to theorists for benchmarking.) I) Can you make a lot to show the effect of theory uncertainties? eg. quote what the result would look like with zero theory errors. his would be a strong motivation for theorists to do better, once they see clearly the laces they are loosing.

27 From CMS: CMS PAS HIG--04 0/08/ able 3: Summary of all systematic uncertainties (relative). his is just an indicative table, since the recise values deend on the final state and jet-bin. Source H qq gg non-z resonant to DY W + jets V(W/Z) W + W W + W W + W WZ/ZZ +γ Luminosity rigger efficiencies Muon efficiency Electron id efficiency Momentum scale E miss resolution counting Higgs cross section 5-5 WZ/ZZ cross section 3.0 qq WW norm. 5 gg WW norm. 50 W + jets norm. 36 to norm. 5 Z/γ + norm. 60 Monte Carlo statistics he uncertainty on the signal efficiency is estimated to be 0% and is dominated by the theoretical uncertainty in the jet veto efficiency determination. he uncertainty on the background estimations in the H W + W signal region is 5%, which is dominated by the statistical uncertainties of the background control regions in data.

28 heory Plans: A calculation of the Higgs + 0-jet cross section at one higher order (N3LL) is feasible. Only a missing loo calculation. his will hel reduce the erturbative uncertainty. Similar resummed calculations for Higgs + jet are already in rogress.

29 Backu

30 σ0( cut )[nb] W +0 jet (NLO) 0 0 W + jet (NLO) 0 30 cut E cm =7eV µ = m W µ =m W µ = m W / combined incl. unc σ( cut )[nb] W + jet (NLO) E cm =7eV cut W + + jet (NLO) jet 30 GeV µ = m W µ =m W µ = m W / combined incl. unc..5.5 σ( cut )[nb] 0.5 E cm =7eV jet 80 GeV µ = m W µ =m W µ = m W / combined incl. unc. σ( cut )[nb] 0.5 E cm =7eV jet, 30 GeV µ = m W µ =m W µ = m W / combined incl. unc cut cut

31 σ 0 = σ total σ, f 0 = σ 0, σ total σ = σ σ, f = σ σ total. total total 0 total total + ( ) ( ) 0 + relative uncertainties δ(σ 0 ) = f 0 δ(σ ) = δ total + ( f 0 ) δ ( f0 [ ) δ ( f0 ) f + ( ) δ ] f [ ( ) ] δ(f 0 ) = ( f 0 ) ( δ total + δ ), (A5) δ(f ) = δ total + ( f0 ) δ ( f0 ) δ f + f, correlation coefficients ρ(σ 0, σ total )= [ + δ δ total [ ρ(σ 0, σ )= + δ total δ ( f 0 ) ] /, ] / ( f 0 ) [ + δ ( δ f ) ] /, f 0 ( ) ρ(σ 0, σ )=0, ( ) ρ(σ, σ total )=0, ( ) ( ) [ ρ(σ, σ )= + δ ( δ f ) ] /. f 0 he relative uncertainties for f and f are ( [ ) ] / ρ(f 0, σ total )= + δ, δ total ( ρ(f 0,f )= + f 0 f ρ(f, σ total )= δ total δ(f ). δ δ total ) ( ) δtotal f 0 δ(f 0 )δ(f ), (A6)

32 Validation? Other otions? Drell-Yan airs from validation. l + Soft γ,z with a jet veto should be used for l + Soft l + 4 Directly P b measure P a beam thrust (imortant on its own). And UE is no harder than it is for H. P b P a b a P b X l Soft l Soft ell-yan roduction. dσ/dq(τ δ(dσ/dq) B cut ) [b/gev] [%] E cm = 7 ev Q = m Z (b) Drell-Yan near threshold. 0 no g scale unc. x PDF+α sing. NLO Soft s E NNLL 80 cm =.96 ev τ NLL B cut =0. P a 40 LL sing. NLO QτQ B cut Soft δ(dσ/dq) [%] (d) Dijet roduction near threshold. 0 P b P a b (c) Isolated Drell-Yan. Soft scale unc. PDF+α s no g 0 50 E cm =7eV x τb cut sing. NLO Q Soft (e) Isolated NNLL dijet roduction. a P b