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 → 3 ℓ + 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! 1/13 | 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 q γ 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! 2/13 | J. Baglio Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

W ± Z production at the LHC e � 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: e e g f W R = − ( s W Q f ) / c W , q q W g f L = ( I 3 f − s 2 W Q f ) / ( s W c W ) . W � W and Z produced at the LHC q q 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: A W → ℓ 1 ν A Z → ℓ 2 ℓ 3 A ab → WZ � A ab → WZ → 3 ℓν LO LO LO = , LO,DPA Q 1 Q 2 λ 1 ,λ 2 Q i = q 2 i − M 2 V i + iM V i Γ V i , 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 q γ → WZq ′ → 3 ℓν q ′ 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 4/13 | 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] p s = 13TeV | ATLASfid pp → e + ν e µ + µ − | 10 0 10 1 NLOQCD 10 − 1 10 0 LO [ µ + µ − e + ν e ] NLOQCDEW LO [ µ + µ − e − ¯ ν e ] NLO EW [ µ + µ − e + ν e ] LO 10 -1 NLO EW [ µ + µ − e − ¯ 10 − 2 ν e ] � GeV [fb/GeV] fb � 10 -2 d p T , e ± 10 − 3 d σ 10 -3 10 − 4 10 -4 √ s = 13 TeV, TGC setup 10 − 5 10 -5 40 K NLOQCD 5 30 3 20 1 10 δ [%] qq ′ [ µ + µ − e + ν e ] δ ¯ 30 δ qγ [ µ + µ − e + ν e ] 0 qq ′ [ µ + µ − e − ¯ δ EW [%] δ ¯ ν e ] 10 δ DPA δ DPA δ ¯ δ qγ δ qγ [ µ + µ − e − ¯ qq ′ qq ′ ν e ] ¯ qγ − 10 10 30 − 20 − 30 100 200 300 400 500 600 0 100 200 300 400 500 600 p T, e [GeV] p T , e ± [GeV] Excellent agreement! ⇒ DPA is an efficient tool to get reliable NLO EW results in a fast way 5/13 | 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 � d σ 3 1 ( 1 + cos 2 θ ) + A 0 2 ( 1 − 3 cos 2 θ ) + A 1 sin ( 2 θ ) cos φ σ d cos θ d φ = 16 π 1 2 sin 2 θ cos ( 2 φ ) + A 3 sin θ cos φ + A 4 cos θ + A 2 � + A 5 sin 2 θ sin ( 2 φ ) + A 6 sin ( 2 θ ) sin φ + A 7 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! � A 5 , A 6 , A 7 from imaginary parts of spin-density ρ � expected to be very small 4 linked to L-R asymmetry in Z ∗ → ℓ + ℓ − decay � A Z 3 , A Z 6/13 | J. Baglio Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Coordinate systems x’ z’ P’ 1 p’ p’ p P’ p P’ P’ 1 V 2 2 V z’ x’ Collins−Soper Helicity y’ y’ � Collins-Soper (CS) coordinate system [Collins, Soper, 1977] : z ′ bisector of � 1 and − � P ′ P ′ 2 , points into the hemisphere of � p V (in lab frame) � Helicity (HE) coordinate system [Bern et al, arXiv:1103.5445] : z ′ = � p V , Lab Side-note: ATLAS uses a modified helicity c.s. with z ′ = � p V , WZ − c . m ⇒ Z polarization observables contaminated by missing E T ! 7/13 | J. Baglio Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019

Polarization fractions Notation: e = 3, µ − = 6, θ i = ∠ ( � p ′ z ′ ) in V rest frame, ℓ i ,� c = ( g 2 L − g 2 R ) / ( g 2 L + g 2 R ) d σ � � ≡ 3 + 2 sin 2 θ 3 f W ± ( 1 ∓ cos θ 3 ) 2 f W ± + ( 1 ± cos θ 3 ) 2 f W ± L R 0 σ d cos θ 3 8 d σ ≡ 3 � ( 1 + cos 2 θ 6 + 2 c cos θ 6 ) f Z L + ( 1 + cos 2 θ 6 − 2 c cos θ 6 ) f Z R σ d cos θ 6 8 � + 2 sin 2 θ 6 f Z 0 leading to L = 1 R = 1 0 = 1 f V 4 ( 2 − A V 0 + d V A V 4 ) , f V 4 ( 2 − A V 0 − d V A V 4 ) , f V 2 A V 0 , R = d V d Z = 1 f V L − f V 2 A V 4 , c , d W ± = ∓ 1 � f L + f R + f 0 = 1 � Values of f L , f R depend on reference frame and coordinate system 8/13 | 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: � 1 d cos θ f ( θ ) 1 d σ � f ( θ ) � = d cos θ, σ − 1 � 1 � 2 π d φ f ( θ, φ ) 1 d σ � f ( θ, φ ) � = d cos θ d cos θ d φ. σ − 1 0 Now use DPA angular decomposition + expectations to get fiducial polarization observables as L = − 1 2 + d V � cos θ 6 � + 5 2 < cos 2 θ 6 >, f V A 1 = � 5 sin 2 θ cos φ � , . . . For distributions: σ → d σ/ dp T , V , or d σ/ d η V , ... � 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 A i no longer describe the full differential xs � Fiducial observables nonetheless contain spin information AND are measurable (data already there!) 9/13 | 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 A 0 A 1 A 2 A 3 A 4 1 . 026 ( 2 ) + 5 − 6 − 0 . 286 ( 2 ) + 4 − 3 − 1 . 314 ( 2 ) + 3 − 3 − 0 . 251 ( 2 ) + 2 − 2 − 0 . 447 ( 7 ) + 3 HE LO − 3 HE NLOEW 1 . 028 − 0 . 284 − 1 . 324 − 0 . 252 − 0 . 438 1 . 016 ( 1 ) + 3 − 4 − 0 . 326 ( 2 ) + 2 − 3 − 1 . 413 ( 2 ) + 10 − 12 − 0 . 229 ( 1 ) + 2 − 1 − 0 . 295 ( 7 ) + 11 HE NLOQCD − 11 HE NLOQCDEW 1 . 017 − 0 . 326 − 1 . 420 − 0 . 229 − 0 . 287 Method A 0 A 1 A 2 A 3 A 4 1 . 397 ( 3 ) + 4 − 5 0 . 229 ( 1 ) + 3 − 3 − 0 . 945 ( 1 ) + 2 − 2 0 . 003 ( 2 ) + 0 . 3 − 0 . 613 ( 8 ) + 4 CS LO − 1 − 4 CS NLOEW 1 . 402 0 . 225 − 0 . 952 0 . 008 − 0 . 608 1 . 513 ( 3 ) + 7 − 7 0 . 192 ( 1 ) + 2 − 2 − 0 . 918 ( 3 ) + 2 0 . 061 ( 4 ) + 4 − 0 . 469 ( 6 ) + 10 CS NLOQCD − 2 − 4 − 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 10/13 | 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 A 0 A 1 A 2 A 3 A 4 1 . 035 ( 2 ) + 2 − 2 − 0 . 304 ( 1 ) + 2 − 1 − 0 . 705 ( 1 ) + 0 . 3 0 . 063 ( 1 ) + 0 . 04 − 0 . 017 ( 1 ) + 1 HE LO − 1 − 0 . 1 − 1 HE NLOEW 1 . 039 − 0 . 307 − 0 . 717 0 . 050 − 0 . 020 0 . 985 ( 2 ) + 5 − 6 − 0 . 306 ( 1 ) + 4 − 0 . 734 ( 1 ) + 2 0 . 031 ( 1 ) + 2 0 . 003 ( 1 ) + 1 HE NLOQCD − 3 − 2 − 2 − 1 HE NLOQCDEW 0 . 986 − 0 . 308 − 0 . 742 0 . 023 0 . 001 Method A 0 A 1 A 2 A 3 A 4 1 . 254 ( 2 ) + 2 − 3 0 . 239 ( 2 ) + 2 − 2 − 0 . 488 ( 1 ) + 1 − 1 − 0 . 061 ( 0 . 3 ) + 0 . 03 0 . 035 ( 1 ) + 1 CS LO − 0 . 4 − 1 CS NLOEW 1 . 266 0 . 234 − 0 . 493 − 0 . 053 0 . 023 1 . 267 ( 2 ) + 4 − 4 0 . 221 ( 1 ) + 1 − 1 − 0 . 455 ( 2 ) + 2 − 0 . 021 ( 1 ) + 3 0 . 023 ( 1 ) + 1 CS NLOQCD − 2 − 3 − 1 CS NLOQCDEW 1 . 273 0 . 218 − 0 . 457 − 0 . 016 0 . 016 � PDF and scale errors very small � EW corrections important in A 3 and A 4 , sensitive to c Origin: EW corrections to Z → µ + µ − decay � Results depend on coordinate system 11/13 | J. Baglio Polarization at NLO in WZ production at the LHC Moriond EW Session, 17/3/2019