NLO QCD corrections to Wb b/Zb b production at hadron colliders - PowerPoint PPT Presentation

NLO QCD corrections to Wb ¯ b/Zb ¯ b production at hadron colliders Laura Reina RADCOR 07, Florence, October 2007 • Motivations: Wb ¯ b/Zb ¯ b main background to → WH/ZH associated production; → single-top production. • Wb ¯ b/Zb ¯ b NLO QCD calculation, b massive. • Numerical results: inclusive/exclusive cross-sections (Tevatron). • Summary and outlook. In collaboration with F. Febres Cordero and D. Wackeroth

Motivations

Associated production of SM Higgs with weak vector bosons → NNLO QCD corrections have been calculated − for the signal [O.Brien, A.Djouadi and R.Harlander, 2004] → O ( α ) EW corrections have been calculated for − the signal [M.L.Ciccolini, S.Dittmaier and M.Kramer, 2003] → Results for ZH associated → Results for WH associated production, August 2007 production, August 2007 2 ) (pb) Observed Limit ) (pb) WH l b b → ν ZH ll b b → 1.8 Expected Limit b -1 b D 0 ’05 (174 pb , PRL) b 10 → 1.6 b BR(H → -1 CDF ’06 (320 pb , PRL) 1.4 B(H × ZH) Preliminary 1.2 -1 CDF: Neural Net, 1.7 fb → × observed ( ___ ) and exp. (- - -) limit p WH) 1 (p 1 -1 DØ Preliminary, L=1.1 fb Preliminary σ -1 Limit D 0 : Neural Net, 1.7 fb 0.8 observed ( ___ ) and exp. (- - -) limit → 0.6 p (p 0.4 σ -1 10 0.2 SM Cross Section Standard Model 0 105 110 115 120 125 130 135 140 145 105 110 115 120 125 130 135 140 145 150 2 m (GeV/c ) H Higgs Mass (GeV)

SM Single-Top production → NLO QCD corrections have been thoroughly − studied [T.Stelzer, Z.Sullivan and S.Willenbrock, 1998; B.W.Harris, E.Laenen, L.Phaf, Z.Sullivan and S.Weinzierl, 2002; . . . ] → NLO EW corrections have been calculated for − the (SM and MSSM) signal [M.Beccaria, G.Macorini, F.M.Renard and C.Verzegnassi, 2006] → CDF data sample, October 2006 → D 0 evidence of single-top, March 2007 DØ Run II 0.9 fb -1 * = preliminary 4.9 +1.4 Decision trees pb -1.4 4.6 +1.8 pb Matrix elements -1.5 5.0 +1.9 pb Bayesian NNs -1.9 4.8 +1.3 Combination* pb -1.3 N. Kidonakis, PRD 74, 114012 (2006), m t = 175 GeV Z. Sullivan, PRD 70, 114012 (2004), m t = 175 GeV -5 -5 0 0 5 5 10 10 15 15 _ → tb+tqb) [pb] σ (pp

The Calculation

Wb ¯ b/Zb ¯ b production • NLO calculation, with m b = 0 approximation avail- able in MCFM [J.Campbell and R.K.Ellis] [R.K.Ellis and S.Veseli, 1998] → Kinematical cuts were imposed in the massless approximation in order to − simulate mass effects: b ) 2 > 4 m 2 p T b > m b and ( p b + p ¯ b . b, ¯ − → Error on the differential cross section from m b = 0 approximation expected to be small ( ∼ 10% from LO estimates) but relevant, difficult to quantify due to non trivial contribution of m b coming from phase space and matrix elements.

Calculation with full m b effects LO Feynman diagrams: Subprocesses at LO: b q W q q ′ → Wb ¯ → Wb ¯ b − b : q ¯ b b → Zb ¯ q → Zb ¯ − b : q ¯ b and W q ′ q ′ b Zb ¯ b : gg → Zb ¯ b q ′ → Wb ¯ q ¯ b q → Zb ¯ q ¯ b gg → Zb ¯ b

Including O ( α s ) corrections � ij ( x 1 , x 2 ) + α s ( µ ) � σ NLO α 2 f LO f NLO ˆ ( x 1 , x 2 , µ ) = s ( µ ) ( x 1 , x 2 , µ ) ij ij 4 π σ LO σ NLO ≡ ˆ ij ( x 1 , x 2 , µ ) + δ ˆ ( x 1 , x 2 , µ ) , ij σ NLO σ virt σ real δ ˆ = ˆ + ˆ . ij ij ij • Virtual Corrections: consist of one-loop diagrams interfered with LO amplitude q ′ → Wb ¯ – Wb ¯ b : one subprocess, q ¯ b – Zb ¯ q → Zb ¯ b and gg → Zb ¯ b : two subprocesses, q ¯ b • Real Corrections: consist of tree level diagrams with one extra parton q ′ → Wbb + g and q (¯ – Wb ¯ q ) g → Wb ¯ b + q ′ (¯ q ′ ) b + k : two subprocess, q ¯ – Zb ¯ q → Zb ¯ b + g , gg → Zb ¯ b + k : three subprocesses, q ¯ b + g and q ) g → Zb ¯ q (¯ b + q (¯ q )

σ virt Virtual corrections: calculating ˆ ij � |A virt ( ij → W/Z b ¯ � σ virt b ) | 2 ˆ = d ( PS 3 ) ij where: b ) | 2 = � � � � � � |A virt ( ij → W/Z b ¯ � � � A 0 A † D + A † A 0 A † 0 A D = 2 R e . D D D → Use dimensional regularization to regularize UV and IR divergencies. − − → UV divergencies are canceled by a suitable set of counterterms. → Calculate each diagram as linear combination of Dirac structures with − coefficients that depend on both tensor and scalar integrals. → Tensor integrals reduced analytically to scalar integrals and organized to − avoid spurious divergences due to appearance of inverse power of Gram Determinant. σ real → IR divergencies will cancel with ˆ ij . −

σ virt Virtual corrections: calculating ˆ - The Wb ¯ b Diagrams ij − → Counting: 2 diagrams at LO - ∼ 30 at NLO - 2 pentagons

σ virt Virtual corrections: calculating ˆ ij The gg → Zb ¯ b Diagrams − → Counting: 8 diagrams at LO - ∼ 100 at NLO - 12 pentagons

σ real Real corrections: calculating ˆ ij � |A real ( ij → W/Z b ¯ � σ real b + k ) | 2 ˆ = d ( PS 4 ) ij − → IR divergencies associated with the integration over the PS of the extra parton, can be extracted using the so called Phase Space Slicing (PSS) method with two cutoffs . − → PSS with two cutoffs uses two unphysical parameters, δ s and δ c to isolate soft and collinear divergent regions, where IR singularities are extracted analytically. t/Hb ¯ → Same soft/collinear structure as Ht ¯ − b , tested against one-cutoff PSS and dipole subtraction method. − → Physical quantities are independent of δ s and δ c , for small enough values of these parameters.

σ real Real corrections: calculating ˆ ij Independence of the total cross section of δ s and δ c cuts Total (all channels) NLO Inclusive 40 Soft+Coll+Virt+Tree Hard non-coll 30 -5 20 δ c = 10 2 -> 4 µ r = µ f = M Z + 2m b σ total (pb) 10 0 cuts: p t > 15 GeV -10 |η| < 2 R = 0.7 -20 2 -> 3 -30 3.4 3.36 3.32 3.28 1e-05 0.0001 0.001 0.01 δ s δ s run for the Zb ¯ δ c run for the Wb ¯ b total cross section b total cross section → In the following we will fix δ s = 10 − 3 and δ c = 10 − 5 −

Numerical Results, Tevatron

General Setup → For the Wqq ′ vertex we take the following CKM matrix elements: − V ud = V cs = 0 . 975 and V us = V cd = 0 . 222, while we neglect contribution of the third generation (suppressed by corresponding PDFs or CKM matrix elements). − → PDF: for LO results we use 1-loop evolution of α s and CTEQ6L1, while for NLO results 2-loop evolution of α s and CTEQ6M. − → Mass Values: we use for the weak bosons M Z = 91 . 1876 GeV and M W = 81 . 410 GeV, a fixed bottom-quark mass m b = 4 . 62 GeV and fixed top-quark mass m t = 170 . 9 GeV (entering through virtual corrections).

b -jet identification − → We use the k T jet algorithm with R = 0 . 7 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 m b = 0). − → b -jet kinematical cuts: → Transverse momentum of the b -jets: p t > p t, min (15 GeV) for both b and b jets. → Pseudorapidity: | η | < η max (2) for both b and b jets.

Summary of LO and NLO total cross sections massive and massless calculation, setting µ r = µ f = M V + 2 m b ( V = W, Z ). Cross Section, Wb ¯ b m b � = 0 (pb) [ratio] m b = 0 (pb) [ratio] σ LO 2.20[-] 2.38[-] σ NLO inclusive 3.20[1.45] 3.45[1.45] σ NLO exclusive 2.64[1.2] 2.84[1.2] Cross Section, Zb ¯ b m b � = 0 (pb) [ratio] m b = 0 (pb) [ratio] σ LO 2.21[-] 2.37[-] σ NLO inclusive 3.34[1.51] 3.64[1.54] σ NLO exclusive 2.75[1.24] 3.01[1.27]

Scale dependence and theoretical uncertainty 5 5 LO LO NLO inclusive NLO inclusive NLO exclusive NLO exclusive 4 4 σ total (pb) σ total (pb) 3 3 2 2 cuts: p t > 15 GeV cuts: p t > 15 GeV |η| < 2 | η | < 2 µ 0 = M w /2 + m b µ 0 = M Z /2 + m b 1 R = 0.7 R = 0.7 1 0.5 1 2 4 0.5 1 2 4 µ f / µ 0 µ f / µ 0 Wb ¯ Zb ¯ b : PRD 74 (2006) 034007 b : PRELIMINARY → Bands obtained by varying both µ R and µ F between µ 0 / 2 and 4 µ 0 (with − µ 0 = m b + M V / 2 ( V = W, Z )). • LO uncertainty ∼ 40%. • Inclusive NLO uncertainty ∼ 20%. • Exclusive NLO uncertainty ∼ 10%.

Zb ¯ b , scale dependence: LO vs NLO and massless vs massive NLO massless NLO massive 5 5 _ NLO massive qq initiated LO massless 4.5 gg initiated 4 LO massive qg initiated 4 0.05 σ total (pb) σ total (pb) 3 3.5 Inclusive case Esclusive case 3 µ 0 = M Z /2 + m b 2 Inclusive case cuts: p t > 15 GeV 2.5 0 1 NLO - σ NLO * ( σ LO / σ LO ) | η | < 2 ∆ σ = σ m b m b = 0 m b m b = 0 2 µ 0 = M Z /2 + m b R = 0.7 0 1.5 ∆σ (pb) 1 2 4 1 2 4 -0.05 0.5 0.5 µ / µ 0 µ / µ 0 4.5 NLO massless NLO massive cuts: p t > 15 GeV 4 NLO massive qq initiated -0.1 4 |η| < 2 LO massless gg initiated LO massive qg initiated R = 0.7 3 3.5 σ total (pb) σ total (pb) 0.5 1 2 4 3 2 µ / µ 0 2.5 Exclusive case cuts: p t > 15 GeV 1 2 | η | < 2 µ 0 = M Z /2 + m b R = 0.7 0 1.5 0.5 1 2 4 0.5 1 2 4 µ / µ 0 µ / µ 0 PRELIMINARY