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 WH associated production, August 2007

Higgs Mass (GeV) 105 110 115 120 125 130 135 140 145 150 ) (pb) b b → B(H × WH) → p (p σ

• 1

10 1 10

b b ν l → WH

: D

• 1

Neural Net, 1.7 fb

• bserved ( ___ ) and exp. (- - -) limit

Preliminary

, PRL)

• 1

’05 (174 pb D , PRL)

• 1

CDF ’06 (320 pb

• 1

CDF: Neural Net, 1.7 fb

• bserved ( ___ ) and exp. (- - -) limit

Preliminary

Standard Model

→ Results for ZH associated production, August 2007

)

2

(GeV/c

H

m 105 110 115 120 125 130 135 140 145 ) (pb) b b → BR(H × ZH) → p (p σ Limit 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

• 1

DØ Preliminary, L=1.1 fb b ll b → ZH

SM Cross Section

Observed Limit Expected Limit

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 → D0 evidence of single-top, March 2007

• 5

5 10 15 DØ Run II 0.9 fb-1

σ(pp

_ → tb+tqb) [pb]

• 5

5 10 15

Decision trees Matrix elements Bayesian NNs * = preliminary Combination*

• Z. Sullivan, PRD 70, 114012 (2004), mt = 175 GeV
• N. Kidonakis, PRD 74, 114012 (2006), mt = 175 GeV

4.9 +1.4

• 1.4

pb 4.6 +1.8

• 1.5

pb 5.0 +1.9

• 1.9

pb 4.8 +1.3

• 1.3

pb

The Calculation

Wb¯ b/Zb¯ b production

• NLO

calculation, with mb = 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: pT

b,¯ b > mb

and (pb + p¯

b)2 > 4m2 b.

− → Error on the differential cross section from mb = 0 approximation expected to be small (∼ 10% from LO estimates) but relevant, difficult to quantify due to non trivial contribution of mb coming from phase space and matrix elements.

Calculation with full mb effects

LO Feynman diagrams:

q q′ W b b q q′ W b b

q¯ q′ → Wb¯ 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

Including O(αs) corrections

ˆ σNLO

ij

(x1, x2, µ) = α2

s(µ)

• f LO

ij (x1, x2) + αs(µ)

4π f NLO

ij

(x1, x2, µ)

• ≡

ˆ σLO

ij (x1, x2, µ) + δˆ

σNLO

ij

(x1, x2, µ) , δˆ σNLO

ij

= ˆ σvirt

ij

+ ˆ σreal

ij

.

• Virtual Corrections: consist of one-loop diagrams interfered with 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)

Virtual corrections: calculating ˆ σvirt

ij ˆ σvirt

ij

=

• d (PS3)
• |Avirt(ij → W/Z b¯

b)|2

where:

• |Avirt(ij → W/Z b¯

b)|2 =

• D

A0A†

D + A† 0AD

• =
• D
• 2Re
• A0A†

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. − → IR divergencies will cancel with ˆ σreal

ij .

Virtual corrections: calculating ˆ σvirt

ij

• The Wb¯

b Diagrams

− → Counting: 2 diagrams at LO - ∼30 at NLO - 2 pentagons

Virtual corrections: calculating ˆ σvirt

ij The gg → Zb¯ b Diagrams

− → Counting: 8 diagrams at LO - ∼100 at NLO - 12 pentagons

Real corrections: calculating ˆ σreal

ij ˆ σreal

ij

=

• d (PS4)
• |Areal(ij → W/Z b¯

b + k)|2 − → 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, δs and δc to isolate soft and collinear divergent regions, where IR singularities are extracted analytically. − → Same soft/collinear structure as Ht¯ t/Hb¯ b, tested against one-cutoff PSS and dipole subtraction method. − → Physical quantities are independent of δs and δc, for small enough values of these parameters.

Real corrections: calculating ˆ σreal

ij Independence of the total cross section of δs and δc cuts

• 30
• 20
• 10

10 20 30 40 σtotal (pb) Total (all channels) NLO Inclusive Soft+Coll+Virt+Tree Hard non-coll 1e-05 0.0001 0.001 0.01 δs 3.28 3.32 3.36 3.4 2 -> 4 2 -> 3 cuts: pt > 15 GeV |η| < 2 R = 0.7 δc = 10

• 5

µr = µf = MZ + 2mb

δs run for the Zb¯ b total cross section δc run for the Wb¯ b total cross section − → In the following we will fix δs = 10−3 and δc = 10−5

Numerical Results, Tevatron

General Setup

− → For the Wqq′ vertex we take the following CKM matrix elements: Vud = Vcs = 0.975 and Vus = Vcd = 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 αs and CTEQ6L1, while for NLO results 2-loop evolution of αs and CTEQ6M. − → Mass Values: we use for the weak bosons MZ = 91.1876 GeV and MW = 81.410 GeV, a fixed bottom-quark mass mb = 4.62 GeV and fixed top-quark mass mt = 170.9 GeV (entering through virtual corrections).

b-jet identification

− → We use the kT 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 mb = 0). − → b-jet kinematical cuts: → Transverse momentum of the b-jets: pt > pt, min (15 GeV) for both b and b jets. → Pseudorapidity: |η| < ηmax (2) for both b and b jets.

Summary of LO and NLO total cross sections

massive and massless calculation, setting µr = µf = MV + 2mb (V = W, Z).

Cross Section, Wb¯ b mb = 0 (pb) [ratio] mb = 0 (pb) [ratio] σLO 2.20[-] 2.38[-] σNLO inclusive 3.20[1.45] 3.45[1.45] σNLO exclusive 2.64[1.2] 2.84[1.2] Cross Section, Zb¯ b mb = 0 (pb) [ratio] mb = 0 (pb) [ratio] σLO 2.21[-] 2.37[-] σNLO inclusive 3.34[1.51] 3.64[1.54] σNLO exclusive 2.75[1.24] 3.01[1.27]

Scale dependence and theoretical uncertainty

0.5 1 2 4 µf/µ0 1 2 3 4 5 σtotal (pb) LO NLO inclusive NLO exclusive cuts: pt > 15 GeV |η| < 2 R = 0.7 µ0 = Mw/2 + mb 0.5 1 2 4 µf /µ0 1 2 3 4 5 σtotal (pb) LO NLO inclusive NLO exclusive

cuts: pt > 15 GeV |η| < 2 R = 0.7 µ0 = MZ/2 + mb

Wb¯ b: PRD 74 (2006) 034007 Zb¯ b: PRELIMINARY

− → Bands obtained by varying both µR and µF between µ0/2 and 4µ0 (with µ0 = mb + MV /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

0.5 1 2 4 µ/µ0 1.5 2 2.5 3 3.5 4 4.5 5 σtotal (pb) NLO massless NLO massive LO massless LO massive 0.5 1 2 4 µ/µ0 1 2 3 4 5 σtotal (pb) NLO massive qq initiated gg initiated qg initiated

cuts: pt > 15 GeV |η| < 2 R = 0.7 µ0 = MZ/2 + mb Inclusive case _

0.5 1 2 4 µ/µ0 1.5 2 2.5 3 3.5 4 4.5 σtotal (pb) NLO massless NLO massive LO massless LO massive 0.5 1 2 4 µ/µ0 1 2 3 4 σtotal (pb) NLO massive qq initiated gg initiated qg initiated

cuts: pt > 15 GeV |η| < 2 R = 0.7 µ0 = MZ/2 + mb Exclusive case 0.5 1 2 4 µ/µ0

• 0.1
• 0.05

0.05 ∆σ (pb) Inclusive case Esclusive case cuts: pt > 15 GeV |η| < 2 R = 0.7 σ

NLO - σ NLO * (σ LO / σ LO )

µ0 = MZ/2 + mb

mb mb mb= 0 mb= 0

∆ σ =

PRELIMINARY

Zb¯ b: mb¯

b distributions, LO vs NLO

100 200 300 400 mbb (GeV) 0.01 0.1 1 10 100 dσ/dmbb (fb/GeV) LO massive NLO massive 100 200 300 400 mbb (GeV) 0.6 0.8 1 1.2 1.4 1.6 dσ(NLO) / dσ(LO) NLO / LO

cuts: pt > 15 GeV |η| < 2 R = 0.7 µr = µf = MZ + 2mb

Inclusive case

_ _ _

σtotal = 3.34 pb σtotal = 2.21 pb

100 200 300 400 mbb (GeV) 0.01 0.1 1 10 dσ/dmbb (fb/GeV) LO massive NLO massive 100 200 300 400 mbb (GeV) 0.4 0.8 1.2 1.6 dσ(NLO) / dσ(LO) NLO / LO σtotal = 2.21 pb

µr = µf = MZ + 2mb

Exclusive case

cuts: pt > 15 GeV |η| < 2 R = 0.7

σtotal = 2.75 pb

_ _ _

PRELIMINARY

Zb¯ b: mb¯

b distributions, massive vs massless

30 60 90 120 150 180 mbb (GeV) 1 10 dσ/dmbb (fb/GeV) LO massless LO massive 30 60 90 120 150 180 mbb (GeV) 0.5 1 1.5 dσ(massive) / dσ(massless) LO ratio

cuts: pt > 15 GeV |η| < 2 R = 0.7 µr = µf = MZ + 2mb

σtotal = 2.21 GeV σtotal = 2.37 GeV

_ _ _

30 60 90 120 150 180 mbb (GeV) 1 10 100 dσ/dmbb (fb/GeV) NLO massless NLO massive 30 60 90 120 150 180 mbb (GeV) 0.5 1 1.5 dσ(massive) / dσ(massless) NLO ratio

cuts: pt > 15 GeV |η| < 2 R = 0.7 µr = µf = MZ + 2mb

Inclusive case σtotal = 3.34 pb σtotal = 3.64 pb

_ _ _

PRELIMINARY

Wb¯ b/Zb¯ b, mb¯

b distributions: testing rescaling

• 2
• 1

1 2 ∆ dσ / dmbb (fb/GeV) dσ

NLO(Inc) - dσ NLO(Inc) * (dσ LO / dσ LO )

50 100 150 200 mbb (GeV)

• 2
• 1

1 2 ∆ dσ / dmbb (fb/GeV) dσ

NLO(Exc) - dσ NLO(Exc) * (dσ LO / dσ LO )

cuts: pt > 15 GeV |η| < 2 R = 0.7 µ = Mw + 2 mb

mb mb= 0 mb mb= 0 mb mb= 0 mb mb= 0

• 2
• 1

1 2 ∆ dσ / dmbb (fb/GeV) dσ

NLO(Inc) - dσ NLO(Inc) * (dσ LO / dσ LO )

30 60 90 120 150 180 mbb (GeV)

• 2
• 1

1 2 ∆ dσ / dmbb (fb/GeV) dσ

NLO(Exc) - dσ NLO(Exc) * (dσ LO / dσ LO )

cuts: pt > 15 GeV |η| < 2 R = 0.7 µ = MZ + 2 mb

mb mb= 0 mb mb= 0 mb mb= 0 mb mb= 0

• Wb¯

b: PRD 74 (2006) 034007 Zb¯ b: PRELIMINARY

Not accurate in the low mb¯

b invariant mass region.

Summary

• We have calculated the NLO QCD corrections to Wb¯

b/Zb¯ b production at hadron colliders including full bottom-quark mass effects.

• We observe considerable reduction of the theoretical uncertainty in the total

cross section with respect to the LO calculation. Specifically the 40% LO uncertainty is reduced to 20% for inclusive NLO production and to 10% for exclusive NLO production for both Wb¯ b and Zb¯ b.

• Mass effects reduce by 8% to 10% the total cross section, affecting in

particular the low invariant mass region of the b¯ b pair.

• Our results are of relevance to the search for a SM-like Higgs particle in the

V H (V = W, Z) associated production channel and to the measurement of single-top production, both processes of great interest to the high energy community.

Outlook

• We will keep studying the phenomenological impact of our calculation.
• We are currently studying the impact of our calculation on searches for

single-top production, where we also consider final states with less than two b-quarks (with J. Campbell, F. Maltoni, S. Willenbrock).

• We will implement our calculation for the LHC case. Since at the LHC gluon

initiated processes are enhanced, we expect some fundamental differences to appear.

• Our calculation can be naturally extended to other important processes like

Zt¯ t, γt¯ t and γb¯ b production.