Polarization at NLO in WZ production at the LHC 54th Rencontres de - - PowerPoint PPT Presentation

Institut für Theoretische Physik

Polarization at NLO in WZ production at the LHC

54th Rencontres de Moriond EW Session, La Thuile

[in collaboration with LE Duc Ninh, arXiv:1810.11034 (to appear in JHEP)]

17 March 2019, Julien Baglio

Motivation

pp → WZ → 3ℓ + ν important process at the LHC:

triple-gauge coupling studies, new physics searches

High statistics precision! Search for hints of new physics: polarization observables

can be important

Good understanding of theoretical AND experimental errors

needed ⇒ higher-order predictions!

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Status of pp → WZ + X

Next-to-leading order (NLO) QCD: [Ohnemus 1991]; [Frixione, Nason, Ridolfi 1992] NLO electroweak (EW) on-shell: [Bierweiler, Kasprzik, Kühn 2013]; [J.B., Ninh, Weber 2013

(with qγ induced)]

Next-to-next-to-leading order QCD: including off-shell effects

[Grazzini, Kallweit, Rathlev, Wiesemann 1604.08576, 1703.09065]

Full NLO EW off-shell: [Biedermann, Denner and Hofer 1708.06938]

Focus of the talk: polarization observables calculated at NLO QCD (with VBFNLO) + NLO EW in the double-pole approximation (DPA) Latest experimental results: ATLAS paper arXiv:1902.05759 with measurements of gauge boson polarization!

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

W ±Z production at the LHC

e

q q q q e e W W W

Intial beams: Unpolarized Only left-handed quarks interact

with W (max. asymmetry)

Z interacts with both left- and

right-handed quarks, but with different coupling strength: gf

R = −(sWQf)/cW,

gf

L = (I3 f − s2 WQf)/(sWcW).

W and Z produced at the LHC are polarized!

3/13 |

• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Double-pole approximation (DPA)

DPA amplitude at LO: Aab→WZ→3ℓν

LO,DPA

=

• λ1,λ2

Aab→WZ

LO

AW→ℓ1ν

LO

AZ→ℓ2ℓ3

LO

Q1Q2 , Qi = q2

i − M2 Vi + iMViΓVi,

i = 1, 2. For NLO EW in the DPA:

Virtual + Real corrections to production part included ✧ Virtual + Real corrections to decays included ✧ Quark-photon induced qγ → WZq′ → 3ℓνq′ included ✧ Non-factorizable contribution not included ✪ Off-shell effects not included ✪

EW corrections to production and decay parts separated In this presentation: LO and NLO QCD exact, NLO EW calculated in the DPA

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

NLO EW: DPA vs. full calculation

Full NLO EW from [Biedermann, Denner, Hofer arXiv:1708.06938]

10-5 10-4 10-3 10-2 10-1 100 101

[fb/GeV]

pp→e+νeµ+µ− |

ps = 13TeV | ATLASfid

NLOQCD NLOQCDEW LO

1 3 5

KNLOQCD

100 200 300 400 500 600

pT, e[GeV]

30 10 10 30

δEW[%]

δ¯

qq′

δqγ δ DPA

¯ qq′

δ DPA

qγ

600 500 400 300 200 100 40 30 20 10 −10 −20 −30

δqγ[µ+µ−e−¯ νe] δ¯

qq′[µ+µ−e−¯

νe] δqγ[µ+µ−e+νe] δ¯

qq′[µ+µ−e+νe]

pT,e± [GeV] δ[%] 100 10−1 10−2 10−3 10−4 10−5

NLO EW [µ+µ−e−¯ νe] NLO EW [µ+µ−e+νe] LO [µ+µ−e−¯ νe] LO [µ+µ−e+νe]

√s = 13 TeV, TGC setup

dσ dpT,e±

• fb

GeV

• Excellent agreement! ⇒ DPA is an efficient tool to get

reliable NLO EW results in a fast way

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Angular coefficients

See [Gounaris et al 1993; Aguilar-Saavedra, Bernabeu, arXiv:1508.04592; Aguilar-Saavedra et al, arXiv:1701.03115]

Parameterize the differential cross section in the DPA with

dσ σd cos θdφ = 3 16π

• (1 + cos2 θ) + A0

1 2(1 − 3 cos2 θ) + A1 sin(2θ) cos φ + A2 1 2 sin2 θ cos(2φ) + A3 sin θ cos φ + A4 cos θ + A5 sin2 θ sin(2φ) + A6 sin(2θ) sin φ + A7 sin θ sin φ

• In the DPA, link to the spin-density matrix ρ of the W and Z, all

spin information there ⇒ 8 (pseudo-)observables!

A5, A6, A7 from imaginary parts of spin-density ρ

expected to be very small

AZ

3 , AZ 4 linked to L-R asymmetry in Z ∗ → ℓ+ℓ− decay

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Coordinate systems

x’ z’ z’ x’ Collins−Soper Helicity y’ y’ P’

1

P’

2

P’

1

P’

2

p

V

p

V

p’ p’

Collins-Soper (CS) coordinate system [Collins, Soper, 1977]: z′ bisector

• f

P′

1 and −

P′

2, points into the hemisphere of

pV (in lab frame)

Helicity (HE) coordinate system [Bern et al, arXiv:1103.5445]: z′ =

pV,Lab Side-note: ATLAS uses a modified helicity c.s. with z′ = pV,WZ−c.m ⇒ Z polarization observables contaminated by missing ET!

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Polarization fractions

Notation: e = 3, µ− = 6, θi = ∠( p′

ℓi,

z′) in V rest frame, c = (g2

L − g2 R)/(g2 L + g2 R)

dσ σd cos θ3 ≡ 3 8

• (1 ∓ cos θ3)2f W ±

L

+ (1 ± cos θ3)2f W ±

R

+ 2 sin2 θ3f W ±

• dσ

σd cos θ6 ≡ 3 8

• (1 + cos2 θ6 + 2c cos θ6)f Z

L + (1 + cos2 θ6 − 2c cos θ6)f Z R

+ 2 sin2 θ6f Z

• leading to

f V

L = 1

4(2 − AV

0 + dVAV 4 ), f V R = 1

4(2 − AV

0 − dVAV 4 ), f V 0 = 1

2AV

0 ,

f V

L − f V R = dV

2 AV

4 ,

dZ = 1 c, dW ± = ∓1

fL + fR + f0 = 1 Values of fL, fR depend on reference frame and coordinate

system

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Fiducial polarization observables

Relate polarization coefficients to simple observables

Expectations: f(θ) = 1

−1

d cos θf(θ)1 σ dσ d cos θ, f(θ, φ) = 1

−1

d cos θ 2π dφf(θ, φ)1 σ dσ d cos θdφ. Now use DPA angular decomposition + expectations to get fiducial polarization observables as f V

L = −1

2 + dVcos θ6 + 5 2 < cos2 θ6 >, A1 = 5 sin 2θ cos φ, . . . For distributions: σ → dσ/dpT,V, or dσ/dηV, ...

Differential xs with arbitrary cuts, full ME [see also Stirling, Vryonidou, arXiv:1204.6427] In the DPA limit: equivalent to the inclusive polarization observables

In the fiducial case, the 8 Ai no longer describe the full differential xs

Fiducial observables nonetheless contain spin information AND are

measurable (data already there!)

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

W angular coefficients (e+)

13 TeV results with ATLAS fiducial cuts:

Method A0 A1 A2 A3 A4 HE LO 1.026(2)+5

−6 −0.286(2)+4 −3 −1.314(2)+3 −3 −0.251(2)+2 −2 −0.447(7)+3 −3

HE NLOEW 1.028 −0.284 −1.324 −0.252 −0.438 HE NLOQCD 1.016(1)+3

−4 −0.326(2)+2 −3 −1.413(2)+10 −12 −0.229(1)+2 −1 −0.295(7)+11 −11

HE NLOQCDEW 1.017 −0.326 −1.420 −0.229 −0.287 Method A0 A1 A2 A3 A4 CS LO 1.397(3)+4

−5 0.229(1)+3 −3 −0.945(1)+2 −2 0.003(2)+0.3 −1

−0.613(8)+4

−4

CS NLOEW 1.402 0.225 −0.952 0.008 −0.608 CS NLOQCD 1.513(3)+7

−7 0.192(1)+2 −2 −0.918(3)+2 −2

0.061(4)+4

−4

−0.469(6)+10

−10

CS NLOQCDEW 1.518 0.189 −0.921 0.065 −0.463

PDF and scale errors very small EW corrections negligible Results depend on coordinate system

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Z angular coefficients (µ−)

13 TeV results with ATLAS fiducial cuts:

Method A0 A1 A2 A3 A4 HE LO 1.035(2)+2

−2 −0.304(1)+2 −1 −0.705(1)+0.3 −1

0.063(1)+0.04

−0.1

−0.017(1)+1

−1

HE NLOEW 1.039 −0.307 −0.717 0.050 −0.020 HE NLOQCD 0.985(2)+5

−6 −0.306(1)+4 −3

−0.734(1)+2

−2

0.031(1)+2

−2

0.003(1)+1

−1

HE NLOQCDEW 0.986 −0.308 −0.742 0.023 0.001 Method A0 A1 A2 A3 A4 CS LO 1.254(2)+2

−3 0.239(2)+2 −2 −0.488(1)+1 −1 −0.061(0.3)+0.03 −0.4

0.035(1)+1

−1

CS NLOEW 1.266 0.234 −0.493 −0.053 0.023 CS NLOQCD 1.267(2)+4

−4 0.221(1)+1 −1 −0.455(2)+2 −2

−0.021(1)+3

−3

0.023(1)+1

−1

CS NLOQCDEW 1.273 0.218 −0.457 −0.016 0.016

PDF and scale errors very small EW corrections important in A3 and A4, sensitive to c

Origin: EW corrections to Z → µ+µ− decay

Results depend on coordinate system

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Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Example of distributions

Bands show PDF+scale (linear sum) errors

0.0 0.2 0.4 0.6 0.8 1.0

Polarization fraction

pp→e+νeµ+µ− |

ps = 13TeV | ATLASfid | Helicity

L, NLOQCD 0, NLOQCD R, NLOQCD L, NLOQCDEW 0, NLOQCDEW R, NLOQCDEW L, LO 0, LO R, LO

0.6 1.0 1.4

KNLOQCDEW

100 200 300 400 500

pT, W[GeV]

0.9 1.1

KNLOEW

0.0 0.2 0.4 0.6 0.8 1.0

Polarization fraction

pp→e+νeµ+µ− |

ps = 13TeV | ATLASfid | Collins-Soper

L, NLOQCD 0, NLOQCD R, NLOQCD L, NLOQCDEW 0, NLOQCDEW R, NLOQCDEW L, LO 0, LO R, LO

0.6 1.0 1.4 1.8

KNLOQCDEW

100 200 300 400 500

pT, W[GeV]

0.85 0.95 1.05 1.15

KNLOEW

Very different behavior between HE and CS c.s.! Helicity c.s.: NLO corrections and in particular EW corrections sizeable f0 decreases in HE c.s., not in CS c.s. ⇒ HE closer to inclusive behavior

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Summary

Results for fiducial polarization observables (fractions, angular

coefficients, distributions) obtained at full NLO QCD and at NLO EW in DPA for pp → WZ → 3ℓ + ν

Helicity coordinate system more suitable than that of

Collins-Soper: no negative fractions, decrease of f0 at large pT

EW corrections can be important especially for AZ

3,4, due to

radiative decay

Fiducial polarization observable easily defined, gives

information on gauge boson spin, measurable with accumated data ⇒ Experiments can perform this measurement!

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Backup slides

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Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Spin density matrix

Massive gauge boson (spin = 1): 3 polarization states ρ ≡ |ψ >< ψ|, (1) < A > =< ψ|A|ψ >= Tr(Aρ), (2) |ψ > =

3

• λ=1

cλ|λ >, (3) ρ =

3

• λ,λ′=1

cλc∗

λ′

• ρλλ′

|λ >< λ′| (4) ρ is Hermitian: ρ∗

λλ′ = ρλ′λ

Normalization Tr(ρ) = 1 ρ described by 8 real parameters!

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• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Angular coefficients and ρ

Relations between the angular coefficients and the spin-density matrix: A0 = 2ρ00, A1 = 1 √ 2 (ρ+0 − ρ−0 + ρ0+ − ρ0−), A2 = 2(ρ+− + ρ−+), A3 = √ 2b(ρ+0 + ρ−0 + ρ0+ + ρ0−), A4 = 2b(ρ++ − ρ−−), A5 = 1 i (ρ−+ − ρ+−), A6 = − 1 i √ 2 (ρ+0 + ρ−0 − ρ0+ − ρ0−), A7 = √ 2b i (ρ0+ − ρ0− − ρ+0 + ρ−0), (5) where b = 1 for the W ± bosons and b = −c for the Z boson, with c = g2

L − g2 R

g2

L + g2 R

= 1 − 4s2

W

1 − 4s2

W + 8s4 W

≈ 0.21, s2

W = 1 − M2 W

M2

Z

. (6) The above simple relations between Ai and the ρij were proven at LO. In full calculation, there are also other contributions (e.g. γ∗ → ℓ−ℓ+), interference and radiation effects. The above simple relations hence cannot be true, because they include

• nly the spin information of the W or the Z.

A5, A6, A7 come from the imaginary parts of ρij expected to be very small. AZ

3 , AZ 4 depend also on c, originated from the L-R asymmetry in the Z ∗ → ℓ+ℓ− decay. 13/13 |

• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Definition of the fiducial cuts

ATLAS cuts: A charged lepton is combined with a final-state photon if their momenta satisfies the condition of ∆R(l, γ) ≡

• (∆η)2 + (∆φ)2 < 0.1. The dressed lepton’s

momentum is the sum of the initial two momenta. After this recombination step, we use the dressed lepton’s momentum for kinematical cuts and distributions pT,e > 20 GeV, pleading

T,µ

> 20 GeV, psub-leading

T,µ

> 10 GeV, |ηl| < 2.5, 60 < mµ+µ− < 120 GeV CMS cuts: A charged lepton is combined with a final-state photon if their momenta satisfies the condition of ∆R(l, γ) ≡

• (∆η)2 + (∆φ)2 < 0.1. The dressed lepton’s

momentum is the sum of the initial two momenta. After this recombination step, we use the dressed lepton’s momentum for kinematical cuts and distributions pT,e > 20 GeV, pT,µ > 15 GeV, |ηl| < 2.5, |mµ+µ− − MZ| < 10 GeV, ∆R(µ+, µ−) > 0.2, ∆R(e+, µ∓) > 0.3, mT,W =

• 2pT,νpT,e[1 − cos ∆φ(e, ν)] > 30 GeV

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Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

CMS pZ

T distributions

0.0 0.2 0.4 0.6 0.8 1.0

Polarization fraction

pp→e+νeµ+µ− |

ps = 13TeV | CMSfid | Collins-Soper

L, NLOQCD 0, NLOQCD R, NLOQCD L, NLOQCDEW 0, NLOQCDEW R, NLOQCDEW L, LO 0, LO R, LO

0.8 1.2

KNLOQCDEW

100 200 300 400 500

pT, Z[GeV]

0.95 1.05

KNLOEW

0.0 0.2 0.4 0.6 0.8 1.0

Polarization fraction

pp→e+νeµ+µ− |

ps = 13TeV | CMSfid | Helicity

L, NLOQCD 0, NLOQCD R, NLOQCD L, NLOQCDEW 0, NLOQCDEW R, NLOQCDEW L, LO 0, LO R, LO

0.5 1.5 2.5

KNLOQCDEW

100 200 300 400 500

pT, Z[GeV]

0.90 1.00 1.10 1.20

KNLOEW 13/13 |

• J. Baglio

Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019