Novel measurements of anomalous triple gauge couplings for the LHC - PowerPoint PPT Presentation

Novel measurements of anomalous triple gauge couplings for the LHC Elena Venturini SISSA and INFN Trieste 23 May 2018 PLANCK2018 1707.08060 with A.Azatov, J.Elias-Miro, Y.Reyimuaji In progress with G.Panico, F.Riva, A.Wulzer, A.Azatov, D.Barducci Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

LHC Exploration Search for new resonances → High energy Precision tests of SM → High luminosity Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

EFT EFT: Parametrization at E < Λ of NP with M ≥ Λ ( E ∼ EW scale, Λ ∼ BSM scale) Integration out of heavy fields (Assuming lepton number conservation): ∞ c n L BSM → L SM EFT = L SM + � � Λ n − 4 O n i i n =6 i Observables: c i c ∗ ( c i σ 6 xSM + h . c . ) σ EFT = σ SM + � � Λ 4 σ 6 x 6 j i + + ij Λ 2 i i , j � 1 ( c i σ 8 xSM + h . c . ) � � i + + O Λ 4 Λ 4 i Λ 2 σ SM ∼ E 2 σ 6 xSM Λ 4 σ SM ∼ E 4 σ 6 x 6 ij i Naively Λ 2 Λ 4 Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Focus: D=6-SM interference Energy region with EFT validity and BSM sensitivity E 2 Λ 2 ≫ 0 ∧ E 2 Λ 2 ≫ E 4 Λ 4 Focus : D=6 - SM interference Naively LARGER for ENERGIES E ≪ Λ (EFT validity) Possible enlargement of the E-region with D=6 TRUNCATION validity Information about the SIGN of the Wilson coefficients Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

aTGC NP Sensitivity of Diboson (VV) production → Focus on a(nomalous)TGCs �� � L SM W + ,µν W − µ + W − ,µν W + W 3 ν + W 3 ,µν W + µ W − W 3 � TGC = ig , µ = c θ Z µ + s θ A µ µ ν ∆ L TGC (CP-even): ig ( W + ,µν W − µ + W − ,µν W + µ )( δ g 1 , z c θ Z ν + δ g 1 ,γ s θ A ν )+ 1 + ig ( δκ z c θ Z µν + δκ γ s θ A µν ) W + µ W − ν + + λ z c θ ig µ + λ γ s θ ig W + ,µν W − νρ Z ρ W + ,µν W − νρ A ρ 2 µ m 2 m 2 W W U(1) γ invariance ⇒ δ g 1 ,γ = 0 LEP-II BOUNDS λ z ∈ [ − 0 . 059; 0 . 017] δ g 1 , z ∈ [ − 0 . 054; 0 . 021] δκ z ∈ [ − 0 . 074; 0 . 051] Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

aTGC NP Sensitivity of Diboson (VV) production → Focus on a(nomalous)TGCs �� � L SM W + ,µν W − µ + W − ,µν W + W 3 ν + W 3 ,µν W + µ W − W 3 � TGC = ig , µ = c θ Z µ + s θ A µ µ ν ∆ L TGC | D = 6 (CP-even) [For example SILH basis]: ig ( D µ H ) † ˆ W µν D ν H = O HW ig ′ ( D µ H ) † B µν D ν H = O HB → EW-SSB 1 → ig ( W + ,µν W − µ + W − ,µν W + µ )( δ g 1 , z c θ Z ν + δ g 1 ,γ s θ A ν )+ + ig ( δκ z c θ Z µν + δκ γ s θ A µν ) W + µ W − ν s 2 U(1) γ invariance ⇒ δ g 1 ,γ = 0, D=6 EFT: δκ z = δ g 1 , z − θ δκ γ θ c 2 δ g 1 , z = m 2 δκ Z = m 2 � c HW − tan 2 θ c HB � Z W Λ 2 c HW , Λ 2 Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

aTGC NP Sensitivity of Diboson (VV) production → Focus on a(nomalous)TGC �� � L SM W + ,µν W − µ + W − ,µν W + W 3 ν + W 3 ,µν W + µ W − W 3 � TGC = ig , µ = c θ Z µ + s θ A µ µ ν ∆ L TGC | D = 6 (CP-even) [For example SILH basis]: λ z ig 3 ! ǫ abc W a ,µν W b g νρ W c ,ρ W + ,µν W − νρ W 3 ,ρ = O 3 W → New TGC : 2 µ µ m 2 W λ Z = m 2 W D=6 EFT : λ z = λ γ Λ 2 c 3 W 3 aTGC : δ g 1 , z , δκ γ , λ z LEP-I bounds ⇒ 3 independent parameters in VV production: 3 aTGCs Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Energy behavior of helicity amplitudes Using Goldstone Equivalence formalism H ⊃ V L ( V = W , Z ) tr W µν W µν ⊃ ∂ V T V T V T , ( D µ H ) † D µ H ⊃ ∂ V L V T V L + vV T V T V L SM : Leading energy scaling of SM helicity amplitudes ∼ v q → V T W + T , V L W + ∼ E 0 , q → V T W + L / V L W + � � � � M q ¯ M q ¯ L T E D=6 EFT O HB = ig ′ ( D µ H ) † B µν D ν H ⊃ ∂ W L ∂ Z T ∂ W L + vW T ∂ Z T ∂ W L + v 2 W T ∂ Z T W T + . . . O HW = ig ( D µ H ) † ˆ W µν D ν H ⊃ ∂ V L ∂ V T ∂ V L + vV T ∂ V T ∂ V L + v 2 V T ∂ V T V T + . . . O 3 W = g 3! ǫ abc W a ,µν W b νρ W c ,ρ ⊃ ∂ V T ∂ V T ∂ V T + . . . µ Leading energy scaling of helicity amplitudes with D=6 operators: ∼ E 2 / Λ 2 c HB + E 2 / Λ 2 c HW ∼ E 2 / m 2 q → W − L W + W δ g 1 , Z + E 2 / m 2 � � M q ¯ W δκ Z L ∼ E 2 / Λ 2 c HW = E 2 / m 2 q → Z L W + � � M q ¯ Z δ g 1 , Z L ∼ E 2 / Λ 2 c 3 W = E 2 / m 2 q → V T W + � � M q ¯ W λ Z T Naively expected E 2 enhancement with respect to SM Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference and interference suppression λ Z from WW δ g 1, Z from WW δ g 1, Z from WZ δκ Z from WW, x (- 5 ) δκ Z from WZ σ int / σ SM 6 · 10 - 6 4 · 10 - 6 2 · 10 - 6 0 600 800 1000 1200 m VV [ GeV ] SM × O HW ∼ E 2 in q ¯ δ g 1 , z : q → V L V L SM × O HB ∼ E 2 in q ¯ δκ z : q → W L W L ∼ E 0 in q ¯ q → W L , T Z T ( Interference suppression ) λ Z : SM × O 3W : more information needed SM : q ¯ q → V T ± V T ∓ (Helicity selection rule; Azatov, Contino, Machado, Riva [arXiv:1607.05236]) ˙ q → V T ± V T ± ( O 3 W ∝ w β α w γ β γ ˙ β w α α ˙ O 3W : q ¯ + ¯ w α ¯ w β ¯ w γ ) ⇒ γ ˙ ˙ ˙ ⇒ SM × O 3 W ∼ E 0 ∼ m 2 V → Interference suppression Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Goal Goal: Overcome suppression of SM × O 3 W interference q → V T V T ) ∼ g 4 1 + c 3 W m 2 E 4 � � Λ 2 + c 2 SM V σ ( q ¯ 3 W E 2 Λ 4 Relaxation of the condition for dimension 6 truncation validity c 3 W m 2 E 4 c 8 E 4 E 8 � � � � Λ 2 , c 2 Λ 4 , c 2 V max > max → 3 W 8 Λ 4 Λ 8 c 3 W E 2 E 4 c 8 E 4 E 8 � � � � Λ 2 , c 2 Λ 4 , c 2 → max > max 3 W 8 Λ 4 Λ 8 Sensitivity to the sign of c 3W Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference resurrection: 1 st method Not 2 → 2 BUT 2 → 2 → 4 Not helicity selection rule BUT NOT INTERFERENCE: non trivial distribution in the azimuthal angles of final fermions Duncan,Kane,Repko 85 p l l + W Z θ l - ν φ Z φ W p Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference resurrection: 1 st method BSM TT × SM TT interference q → W T + Z i and Z → l + l − , i = ± (Neglecting V T V L ∼ v 2 → 3 : q ¯ E in SM) δ ( s − m 2 ⊃ π Z ) � ∗ � M SM M BSM l + M ∗ M Z T − → l − ¯ q ¯ q → W T + Z T − q ¯ q → W T + Z T + Z T + → l − ¯ l + 2 s Γ Z m Z q → W + l − ¯ ∝ E 2 → d σ int ( q ¯ l + ) Λ 2 cos(2 φ Z ) Naively expected energy growth d φ Z φ Z : Azimuthal angle of LH (or RH) lepton from Z w.r.t. � p z Modulated and non zero interference; zero after integration ( 2 → 2 ) BUT In Z → l + l − the helicity of l − (or l + ) is not fixed and observed Z for l − (or l + ) with fixed charge → φ c Observable: φ c Z = φ Z ∨ φ c Z = φ Z + π Ambiguity, BUT cos(2 φ Z ) modulation is not affected Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference resurrection: 1 st method BSM TT × SM TT interference q → W i Z j and W → ν l Z → l + l − , i , j = ± q ¯ ∝ E 2 d σ int ( q ¯ q → WZ → 4 ψ ) Λ 2 (cos(2 φ Z ) + cos(2 φ W )) d φ Z d φ W Modulated non zero ∼ E 2 interference even integrating over φ Z or φ W BUT Ambiguity also on φ W In W → ν l � p ν is not observed p ν and φ W reconstruction → φ rec W = φ W ∨ φ rec W = π − φ W 1 � Ambiguity, BUT cos(2 φ W ) modulation is not affected BSM TT × SM LL interference ∝ E 2 d σ int ( q ¯ q → WZ → 4 ψ ) Λ 2 cos( φ Z + φ W ) d φ Z d φ W Hard to be observed due to φ Z helicity-charge (or φ W ) ambiguity cos( φ Z + φ W ) ∼ g 2 L cos( φ c Z + φ W ) + g 2 R cos( φ c Z + π + φ W ) = = ( g 2 L − g 2 R ) cos( φ c Z + φ W ) ∼ 0 [ g L ∼ − 0 . 28 , g R ∼ − 0 . 22] 1 Panico, Riva, Wulzer [arXiv: 1708.07823] Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference resurrection: 1 st method σ int / σ SM · 10 3 60 3.0 4 2 4 200 1st reg. 2.5 40 2nd&3rd reg. 4th reg. 2.0 100 20 σ int / σ SM · 10 3 ϕ W 3 1 3 1.5 0 0 1.0 - 20 - 100 0.5 4 2 4 - 40 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 500 1000 1500 m WZ [ GeV ] ϕ Z Left: Differential interference cross section over SM one as a function the azimuthal angles φ W and φ Z (In [0 , π ]) for the events with W − Z invariant mass m WZ ∈ [700 , 800] GeV . Right: same quantity as a function of the m WZ binned in 2 bins of φ Z and 2 bins of φ W (cos(2 φ ) ≥ 0 , < 0). Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC

Interference resurrection: : 2 nd method Not 2 → 2 LO BUT NLO Virtual gluon exchange effects with α S 4 π suppression: Focus on 2 → 3 with real gluon emission Dixon, Shadmi 94 V T ± V T ± BSM g ∓ V T ± V T ± g ± , ∓ SM: q ¯ q → V ± V ∓ = ⇒ q ¯ q → V ± V ± g ∓ : qualitative change Total helicity ± 1 allowed both in SM and in O 3 W amplitudes Interference in q¯ q → VVj is not forbidden by helicity selection rules Elena Venturini Novel measurements of anomalous triple gauge couplings for the LHC