W/Z production with 2b at NLO

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1 W/Z production with b at NLO Laura Reina Eugene, September 9 Motivations: main background to W H/ZH associated production; single-top production; H/A + b b and other signals of new physics; t t production; several non-standard model signatures. New studies: Wb b/zb b at NLO, b massive (F. Febres Cordero, L. R., D. Wackeroth) W + b-jet, FNS and 5FNS merged at NLO (J. Campbell, K. Ellis, Outlook F. Febres Cordero, F. Maltoni, L. R., D. Wackeroth, S. Willenbrock)

2 Wb b/zb b production at NLO, some history... V partons (-loop massless amplitudes) (Bern, Dixon, Kosower (97)) p p, pp V b b (at NLO, FNS, = ) (Campbell, Ellis (99)) p p, pp V b + j (at NLO, 5FNS) (Campbell, Ellis, Maltoni,Willenbrock (5,7)) p p, pp Wb b (at NLO, FNS, ) (Febres Cordero, L.R., Wackeroth (6,9)) p p, pp Zb b (at NLO, FNS, ) (Febres Cordero, L.R., Wackeroth (8,9)) p p, pp W + b-jet (at NLO, 5FNS+FNS with ) (Campbell, Ellis, Febres Cordero, Maltoni, L.R., Wackeroth, Willenbrock (8))

3 Wb b/zb b production with full effects q q LO Feynman diagrams: W b b q q q Wb b q W b b Subprocesses at LO: Wb b: q q Wb b Zb b: q q Zb b and Zb b: gg Zb b q q Zb b gg Zb b

4 Including O(α s ) corrections { ˆσ ij NLO (x, x, µ) = αs(µ) fij LO (x, x ) + α } s(µ) π fnlo ij (x, x, µ) ˆσ LO ij (x, x, µ) + δˆσ NLO ij (x, x, µ), δˆσ NLO ij = ˆσ virt ij + ˆσ real ij. Virtual Corrections: consist of one-loop diagrams interfered with corresponding LO amplitude Wb b: one subprocess, q q Wb b Zb b: two subprocesses, q q Zb b and gg Zb b Real Corrections: consist of tree level diagrams with one extra parton Wb b + k: two subprocess, q q Wbb + g and q( q)g Wb b + q ( q ) Zb b + k: three subprocesses, q q Zb b + g, gg Zb b + g and q( q)g Zb b + q( q)

5 W/Z + b-jets Febres Cordero, L.R., Wackeroth (6-9) We use the k T jet algorithm with and study two cases: Inclusive Cross Section: events with two (b + b) or three (b + b + j) jets resolved contribute to the cross section. Exclusive Cross Section: only events with two (b + b) jets resolved contribute to the cross section. Same convention used by MCFM (used to obtain the results for = ). b-jet kinematical cuts: Transverse momentum of the b-jets: p t > p t, min (5-5 GeV) for both b and b jets. Pseudorapidity: η < η max (-.5) for both b and b jets. PDF: for LO results we use -loop evolution of α s and CTEQ6L, while for NLO results -loop evolution of α s and CTEQ6M.

6 Tevatron: summary of LO and NLO total cross sections massive and massless calculation, setting µ r = µ f = M V + (V = W, Z). Cross Section, Wb b (pb) [ratio] = (pb) [ratio] σ LO.[-].8[-] σ NLO inclusive.[.5].5[.5] σ NLO exclusive.6[.].8[.] Cross Section, Zb b (pb) [ratio] = (pb) [ratio] σ LO.[-].7[-] σ NLO inclusive.[.5].6[.5] σ NLO exclusive.75[.].[.7]

7 Tevatron: scale dependence and theoretical uncertainty at NLO 5 LO NLO inclusive NLO exclusive 5 LO NLO inclusive NLO exclusive (pb) (pb) cuts: p t > 5 GeV η < µ = M w / +.5 µ f /µ cuts: p t > 5 GeV η < µ = M Z / +.5 µ f /µ Wb b: Tevatron (PRD 7 (6) 7) Zb b: Tevatron (PRD 78 (8) 7) Bands obtained by varying both µ R and µ F between µ / and µ (with µ = + M V / (V = W, Z)). LO scale uncertainty %. Inclusive NLO scale uncertainty %. Exclusive NLO scale uncertainty %.

8 Wb b, scale dependence: LO vs NLO and massless vs massive (pb) 5 NLO massless NLO massive LO massless LO massive Inclusive case µ = M w / +.5 µ/µ (pb) 5 NLO _ massive qq initiated _ qg+qg initiated cuts: p t > 5 GeV η <.5 µ/µ σ (pb).5..5 NLO Inclusive NLO Exclusive σ = σ NLO - σ NLO * (σ LO / σ LO ) = = (pb) Exclusive case NLO massless NLO massive LO massless LO massive µ = M w / +.5 µ/µ (pb) NLO _ massive qq initiated _ qg+qg initiated cuts: p t > 5 GeV η <.5 µ/µ cuts: p t > 5 GeV η < µ = M w / +.5 µ/µ (PRD 78 (8) 7)

9 Zb b, scale dependence: LO vs NLO and massless vs massive (pb) cuts: p t > 5 GeV η < NLO massless NLO massive LO massless LO massive.5.5 µ/µ (pb) 5 NLO _ massive qq initiated gg initiated qg initiated Inclusive case µ = M Z / +.5 µ/µ σ (pb).6. µ = M Z / + Inclusive case Esclusive case σ = σ NLO - σ NLO * (σ LO / σ LO ) = = (pb) cuts: p t > 5 GeV η < NLO massless NLO massive LO massless LO massive.5.5 µ/µ (pb) NLO massive qq initiated gg initiated qg initiated Exclusive case µ = M Z / +.5 µ/µ cuts: p t > 5 GeV η <.5 µ/µ (PRD 78 (8) 7)

10 Zb b: b distributions, massive vs massless.5 dσ/db (fb/gev) LO massless LO massive µ r = µ f = M Z + =.7 GeV =. GeV dσ(massive) / dσ(massless).5 LO ratio cuts: p t > 5 GeV η < m _ bb (GeV) m _ bb (GeV).5 dσ/db (fb/gev) NLO massless NLO massive µ r = µ f = M Z + Inclusive case =.6 pb =. pb dσ(massive) / dσ(massless).5 NLO ratio cuts: p t > 5 GeV η < m _ bb (GeV) m _ bb (GeV) (PRD 78 (8) 7)

11 Wb b/zb b, b distributions: testing rescaling LO NLO dσ / db (fb/gev) dσ / db (fb/gev) cuts: p t > 5 GeV - η < - - µ = M w + dσ NLO(Inc) - dσ NLO(Inc) * (dσ LO / dσ LO ) = = dσ NLO(Exc) - dσ NLO(Exc) * (dσ LO / dσ LO ) = = b - (GeV) dσ / db (fb/gev) dσ / db (fb/gev) dσ NLO(Inc) - dσ NLO(Inc) * (dσ LO / dσ LO ) = = µ = M Z + dσ NLO(Exc) - dσ NLO(Exc) * (dσ LO / dσ LO ) = = cuts: p t > 5 GeV η < b - (GeV) Wb b: PRD 7 (6) 7 Zb b: PRD 78 (8) 7 Clear effect in the low b invariant mass region.

12 LHC: scale dependence and theoretical uncertainty at NLO p t > 5 GeV η <.5 p t > 5 GeV η <.5 σ [pb] W + bb µ = M W W + bb NLO Inc NLO Exc LO 5 σ [pb] 5 W - bb 5 W - bb Total qq qg 5.5 µ/µ.5 µ/µ (PRD 8:5, 9) NLO corrections very large, particularly for inclusive production; large NLO scale-dependence (LO: %, NLO inc : 5%, NLO exc : %), induced by the opening of the qg( qg) Wb b + q ( q ) channel; theoretical uncertainty not only given by scale-dependence!

13 5 pt>5 GeV Zbb 8 pt>5 GeV NLO Inc NLO Exc LO 6 σ [pb] 5 µ = M Z + Total gg qq qg.5 µ/µ.5 µ/µ NLO corrections still large, particularly for inclusive production; more moderate NLO scale-dependence (LO: 5%, NLO inc : %, NLO exc : 5%): qg( qg) Zb b + q( q) channel not as dominant.

14 W + b b = = p b > 5 GeV T pb > 5 GeV T s = TeV σ LO (pb) σ NLO,inc (pb) σ NLO,exc (pb) s = TeV σ LO (pb) σ NLO,inc (pb) σ NLO,exc (pb) Zb b p b > 5 GeV T pb > 5 GeV T = = s = TeV σ LO (pb) σ NLO,inc (pb) σ NLO,exc (pb) s = TeV σ LO (pb) +6 σ NLO,inc (pb) σ NLO,exc (pb)

15 LHC: some interesting NLO distributions dσ / dp t [ pb / GeV ] - p t > 5 GeV η >.5 E CM = TeV LO NLO Inc NLO Exc W + bb _ k-factor Leading b-jet p t b,l [ GeV ] b,sl Subleading b-jet p t [ GeV ]

16 dσ / dp t [ pb / GeV ] p t > 5 GeV η >.5 E CM = TeV Zbb _ LO NLO Inc NLO Exc - - k-factor Leading b-jet p t b,l [ GeV ] b,sl Subleading b-jet p t [ GeV ] NLO distributions cannot be rescaled from LO ones via a K-factor; large corrections in particular for Wb b and in the inclusive case.

17 dσ / dp t W + [ pb / GeV ] - - p t > 5 GeV η >.5 W + bb _ LO NLO Inc NLO Exc Z dσ / dp t [ pb / GeV ] - - p t > 5 GeV η >.5 Zbb _ LO NLO Inc NLO Exc E CM = TeV E CM = TeV - k-factor W + p t [ GeV] - k-factor p t Z [ GeV ]

18 Comparison with massless b-quark results... dσ / db - [ pb / GeV ] p t > 5 GeV η >.5 W - bb _ LO NLO Inc NLO Exc LO massless NLO Inc massless NLO Exc massless dσ / dr bb - [ pb / R bb - ] p t > 5 GeV η >.5 E CM = TeV LO NLO Inc NLO Exc LO massless NLO Inc massless NLO Exc massless W - bb _ - E CM = TeV ratios b - [ GeV ] ratios R bb -

19 dσ / db - [ pb / GeV ] p t > 5 GeV η >.5 E CM = TeV Zbb _ LO NLO Inc NLO Exc LO massless NLO Inc massless NLO Exc massless dσ / dr bb - [ pb / R bb - ] 8 6 p t > 5 GeV η >.5 E CM = TeV Zbb _ LO NLO Inc NLO Exc LO massless NLO Inc massless NLO Exc massless ratios b - [ GeV ] ratios R bb -

20 W + b-jet Campbell, Ellis, Febres Cordero, Maltoni, L.R., Wackeroth, Willenbrock (PRD 79:, 9) Consistently combine FNS ( ) and 5FNS ( = ) at NLO in QCD: q b b b b q q + O(α s ) corrections q W W. q q Wb b at tree level and one loop ( ). q q Wb bg at tree level ( ). bq Wbq at tree level and one loop ( = ). bq Wbq g and bg Wbq q at tree level ( = ) 5. gq Wb bq at tree level ( ) avoiding double counting: b g q b q b q q b b(x, µ) = α s π ln µ m b x dy y P qg ( x y) g(y, µ) W indeed: a fully consistent NLO 5FNS calculation (S-ACOT scheme). W

21 improved scale dependence: NLO corrections to gq Wb bq partially included; need to keep for final state b quarks (one b quark has low p T ) four signatures studied: exclusive/inclusive, with single and double-b jets, using p j T > 5 GeV, ηj <.5, cone algorithm with : Wb, W(b b) (exclusive) Wb and Wb + j, W(b b) and W(b b) + j (inclusive) which can be combined to obtain different backgrounds,... both contributions play important complementary roles (Tevatron/LHC, inclusive/exclusive);

22 NLO results at a glance: Exclusive cross sections (pb) Collider Wb W(b b) TeV W + (= W ) 8.+.6[-.5]= [-.]=.7 LHC W +.+8.[.6]= [.7]=. LHC W [.6]= [6.5]=.7 Inclusive cross sections (pb) Collider Wb + X W(b b) + X TeV W + (= W ).77+.[.77]= [.9]=.56 LHC W [68.9]= [5.9]=6. LHC W [.6]= [.6]=.5 first number: Processes + (pure FNS) second number: Processes (pure 5FNS plus qg Wb b + q ) number in square brackets: Process 5 alone (qg Wb b + q )

23 Ongoing and future activity on W/ZQ Q production... Provide input to experimental studies: D, CDF: W + b study (see Febres Cordero s and Thomson s talks), Higgs and single-top working groups; CMS Higgs working group: provide parton level distributions with specific cuts and interface with NLO parton shower Monte Carlo (POWHEG): study Z + b as background to H ZZ inclusive production; study Z + b and Z + b to measure b-pdf. ATLAS study of WH with H b b in boosted regime (Butterworth, Piacquadio, et al.). Z + b-jet using both FNS with and 5FNS NLO calculations: bg Zb at tree level and one loop (with = ); bg Zb + g, bq Zb + q (with = ); q q, gg Zb b at tree level and one loop (with ); q q, gg Zb b + g and gq(g q) Zb b + q( q) (with ). quite different pattern: one loop corrections to q q, gg b bz are now a piece of the NNLO 5FNS calculation, comparable to two-loop corrections to (and double parton emission from) bg Zb (?)

24 Possible to use Z + b to measure b-pdf? reduce the PDF error in H + b production? Resum large final state collinear logs from g b b splitting in Wg Wb b (and Zg Zb b) (with S. Dawson). Need too investigate NLO corrections to qg( qg) Wb b + q ( q )? (now within reach) more in D. Wackeroth s talk tomorrow