Double Gauge Boson Production in the SM EFT Ian Lewis University of Kansas 1708.soon in progress with Sally Dawson and Julien Baglio August 3, 2017 DPF 2017 Fermilab W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 1 / 30
Goal: Find New BSM Physics LHC very successful so far: Discovered Higgs boson and obtained huge amount of date. However, have only confirmed the SM. O ( 1 TeV ) lower bounds on new physics: W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 2 / 30
“Model Independent” Parameterization In the absence of direct evidence, useful to have a model independent formulation of new physics. Philosophy: We know the SM is there at the EW scale with a very SM-like Higgs boson. Treat SU ( 2 ) × U ( 1 ) Y as a good symmetry. SM effective field theory (EFT): ∞ c n , k n = 1 ∑ ∑ L = L SM + Λ n O n , k k O n , k : SU ( 3 ) × SU ( 2 ) L × U ( 1 ) Y gauge invariant 4 + n dimensional higher order operators. Λ : scale of new physics. Allows for a systematic parameterization of deviations from SM predictions without doing too much damage to lower energy measurements. W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 3 / 30
“Model Independent” Parameterization SM effective field theory (EFT): ∞ c n , k n = 1 ∑ ∑ L = L SM + Λ n O n , k k Typically restrict to flavor universal and baryon number conserving operators: n = 1: neutrino mass Weinberg PRL43 (1979) n = 2: 59 independent operators Buchmüller, Wyler, NPB 268 (1986); Grzadowski, Iskrzynski, Misiak, Rosiek, JHEP1010; Giudice, Grojean, Pomaral, Rattazi JHEP0706; Contino, Ghezzi, Grojean, Muhlleitner, Spira JHEP1307 There are global analyses of SMEFT Corbett, Eboli, Goncalves, Gonzalez-Fraille, Plehn, Rauch JHEP 1508; Butler, Eboli, Gonzalez-Fraille, Gonzalez-Garcia, Plehn, Rauch JHEP 1607; Berthier, Trott JHEP 1505; Falkowski, Riva JHEP 1502; Brivio, Trott arXiv: 1706.08945 [hep-ph]etc. Choices have to be made. Examples of sets of operators: SILH: “Strongly interacting light Higgs” Giudice, Grojean, Pomaral, Rattazzi JHEP 0706 (2007) 045 HISZ Hagiwara, Ishihara, Szalapski, Zeppenfeld PRD48 (1993) 2182 “Warsaw Basis” Grzadkowski, Iskrzynski, Misiak, Rosiek JHEP 1010 (2010) 085 Choice of operators different among bases, but complete bases are equivalent. W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 4 / 30
W + W − production q q W + Z/γ W + q ′ q W − ¯ W − q ¯ Informative to focus on one process. Of particular interest is the electroweak sector. Focus on W + W − production at the LHC. Sensitive to anomalous trilinear gauge boson couplings (ATGCs) Operators effecting ATGCs: µ W b ρ ν W cµ ε abc W a ν O HD = | Φ † D µ Φ | 2 O HWB = Φ † σ a Φ W a µ ν B µ ν = O 3 W ρ Φ † ← → O ( 3 ) � � D µ σ a Φ ℓ L γ µ σ a ℓ L O ll = ( ℓ L γ µ ℓ L )( ℓ L γ µ ℓ L ) = i H ℓ W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 5 / 30
W + W − production Operators effecting ATGCs: µ W b ρ ν W cµ ε abc W a ν O HD = | Φ † D µ Φ | 2 O HWB = Φ † σ a Φ W a µ ν B µ ν = O 3 W ρ Φ † ← → � � O ( 3 ) D µ σ a Φ ℓ L γ µ σ a ℓ L O ll = ( ℓ L γ µ ℓ L )( ℓ L γ µ ℓ L ) = i H ℓ In the EW sector have to choose input parameters: G F , M W , M Z EFT alters relationships between other parameters and input parameters: s 2 W → s 2 W + δ s 2 g Z → g Z + δ g Z v → v ( 1 + δ v ) W , where s W = sin θ W , c W = cos θ W and W = 1 − M 2 g 1 s 2 W √ g Z = G F = M 2 cos θ W 2 v 2 Z W = − v 2 � � � � H ℓ − 1 s W c W δ v + 1 C ( 3 ) δ sin 2 δ v = + C HWB 2 C ℓℓ 2 s W c W 4 C HD Λ 2 c 2 W − s 2 W − v 2 � δ v + 1 � δ g Z = 4 C HD Λ 2 W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 6 / 30
W + W − production Another language, anomalous couplings Hagiwara, Peccei, Zeppenfeld, Hikasa NPB482 (1987) : � � ν V µ ν + λ V µ ν W − µ V ν − W − g 1 V ( W + µ ν W + µ V ν )+ κ V W + µ W − W + ρ µ W − µ ν V νρ δ L = − ig WWV M 2 W V = Z , γ g WWZ = g cos θ w , g WW γ = e Parameterize deviations from SM: γ = 1 + δ g γ g 1 1 + δ g Z g 1 = κ Z = 1 + δκ Z κ γ = 1 + δκ γ Z 1 1 λ Z = 0 and λ γ = 0 in SM. SU ( 2 ) L implies: δκ γ = cos θ 2 δ g γ � � W δ g 1 1 = 0 λ γ = λ Z Z − δκ Z sin θ 2 W Three independent parameters: λ Z , δ g 1 Z , δκ Z W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 7 / 30
Matching ATGCs in two prescriptions Had 5 dimension-6 operators, only three combinations independent. In Warsaw basis: � s W v 2 � 1 C HWB + 1 δ g 1 = 4 C HD + δ v Z Λ 2 c 2 w − s 2 c W w v 2 � � 1 2 s W c W C HWB + 1 δκ Z = 4 C HD + δ v Λ 2 c 2 w − s 2 W v δλ Z = Λ 2 3 M W C 3 W Anomalous coupling language generic enough that any basis can be matched onto it. W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 8 / 30
Experimental results ATGCs actively being searched for in W + W − production by both ATLAS JHEP 1609 and CMS 1703.06095 W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 9 / 30
Missing Terms q q W + Z/γ W + q ′ q W − ¯ W − q ¯ Have not included anomalous quark gauge boson couplings. Highly constrained by LEP. But, SM contains cancellations to unitarize amplitudes: growth with energy cancels. Anomalous quark couplings can spoil cancellation and have growth with energy. This was recently pointed out Zhang PRL118 (2017) 011803 W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 10 / 30
Missing Terms Anomalous quark-gauge boson couplings occur from the operators � � O ( 3 ) Φ † σ a D µ Φ − ( D µ Φ ) † σ a Φ Q Li γ µ σ a Q Lj ¯ = i HQ , i j � � O ( 1 ) Φ † D µ Φ − ( D µ Φ ) † Φ Q Li γ µ Q Lj ¯ = i HQ , i j � � Φ † D µ Φ − ( D µ Φ ) † Φ q Ri γ µ q R j = O Hq , i j i ¯ Parameterize via anomalous couplings: g Z Z µ q γ µ �� � � � � T 3 − sin 2 W Q q + δ g Zq − sin 2 W Q q + δ g Zq = P L + L P R q L R + g � L ) u γ µ P L d + hc . � W + µ ( 1 + δ g W √ 2 SU ( 2 ) invariance implies δ g W L = δ g Zu L − δ g Zd L . W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 11 / 30
Refit Experimental results ATGCs limits from ATLAS JHEP 1609 . In practice want to take differential distributions from experimental collaborations, extract constraints on anomalous couplings. Problem: we do not decay the W + . W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 12 / 30
Refit Experimental results Solution: repurpose ATLAS ATGC 95% C.L. JHEP 1609 . Each 2D plot set 3rd parameter to zero. Can fit ellipsoid. W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 13 / 30
Refit Experimental Results Define χ 2 : ∆χ 2 = y T C − 1 y where y T = ( δ g 1 Z − µ g 1 Z , δκ Z − µ κ Z , λ Z − µ λ Z ) With 3-parameter fit require that ∆χ 2 < 7 . 815. Fit to the 2D plots and find means and covariant matrix: µ g 1 = 0 . 00935 , µ κ Z = 0 . 00518 , µ λ Z = − 0 . 000185 Z 1 . 55 1 . 28 − 0 . 0563 × 10 − 4 = C 1 . 28 1 . 76 − 0 . 0455 − 0 . 0563 − 0 . 0455 0 . 511 W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 14 / 30
Refit Experimental Results 0.04 Correlation Matrix Fit 0.04 Correlation Matrix Fit ATLAS Result: 1603.01702 ATLAS Result: 1603.01702 λ Z = 0 δ g Z = 0 1 0.02 0.02 95 % C.L. Limits 95 % C.L. Limits 1 δ g Z λ Z 0 0 -0.02 -0.02 -0.04 -0.04 -0.04 -0.02 0 0.02 0.04 -0.04 -0.02 0 0.02 0.04 δ�κ Z δ�κ Z 0.04 Correlation Matrix Fit ATLAS Result: 1603.01702 δ�κ Z = 0 0.02 95 % C.L. Limits 1 δ g Z 0 -0.02 -0.04 -0.04 -0.02 0 0.02 0.04 λ Z W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 15 / 30
Refit Experimental Results Assume strongest constraint comes from last bin. Scan over allowed ATGCs and determine allowed � ∞ d σ σ ( p W + 500 GeV dp W + > 500 GeV ) = T T dp W + T Now scan over all parameters and determine allowed regions taking into consideration LEP constraints on anomalous quark couplings Falkowski, Riva JHEP 1502 : δ g Zd ( 2 . 3 ± 1 ) × 10 − 3 = L δ g Zu ( − 2 . 6 ± 1 . 6 ) × 10 − 3 = L δ g Zd ( 16 . 0 ± 5 . 2 ) × 10 − 3 = R δ g Zu ( − 3 . 6 ± 3 . 5 ) × 10 − 3 = R Accept points that fall within allowed region of σ ( p W + > 500 GeV ) . T W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 16 / 30
Refit Blue: Including only ATGCs. Red dots: adding in anomalous quark couplings Inner regions allowed W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 17 / 30
Maximizing Allowed Cross Section Anomalous quark couplings set to zero ATGCs set to zero. 1 / Λ 4 terms dominate in tails and the bounds on anomalous couplings. Falkowski, Gonzalez-Alonso, Greijo, Marzocca, Son JHEP 1702 (2017) 115 Assuming C i � 1, anomalous couplings correspond to Λ � 2 . 8 TeV. W + W − SM EFT Ian Lewis (Kansas) DPF August 3, 2017 18 / 30
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