EFT analysis of the off-shell Higgs data Aleksandr Azatov CERN - PowerPoint PPT Presentation

EFT analysis of the off-shell Higgs data Aleksandr Azatov CERN HXSWG meeting 24 Oct. 2014 work with C.Grojean,A.Paul, E.Salvioni arXiv:1406.6338

Recent Constraints on the Higgs width Recently both CMS and ATLAS collaborations presented the studies of the off-shell Higgs production by studying gg → h → ZZ → 4 l , 2 l 2 ν processes (CMS-PAS-HIG-14-000, CMS-HIG-14-002, ATLAS-CONF-2014-042) One can interpret these measurements to constrain the total width of the Higgs boson ( Caola,Melnikov )

Off-Shell Higgs production on-shell cross secyion g 2 prod. g 2 decay σ ∼ Γ off-shell cross section: σ ∼ g 2 prod. g 2 decay S + g prod. g decay I + B Assuming the on-shell cross section is exactly as in the SM � Γ Γ σ Off − shell ∼ S + I + B Γ SM Γ SM Γ < 5 . 4 × Γ SM

Flat direction in the Higgs couplings space What kind of flat direction in the Higgs coupling space are we exploring ? to keep the on-shell rate the same � � g 2 gg → h g 2 g 2 gg → h g 2 h → ZZ h → ZZ = Γ Γ SM To keep SM like yields in the other channels we need as well � g i � g i = g j g j SM The flat direction is along g i = g SM µ, Γ = Γ SM µ 4 i i ∝ µ 2 thus we need an invisible decay width However Γvisible ∝ g 2 Γinvisible = Γ SM ( µ 4 − µ 2 ) The same flat direction is constrained also by the invisible Higgs decay searches Γ � 3Γ SM

What else can we learn from the off-shell Higgs production measurements? If there is a mass gap between the new physics states and the SM ones we can parametrize its effects by the higher dimensional operators. Generically the effects of the higher dimensional operators are becoming larger at higher energies ⇒ the far off-shell region is becoming very important.

Operators effecting the Higgs decay Let us look at the modifications of the hZZ vertex (see also 1403.4951,1410.5440 ) m 2 v hZ µ Z µ + c 1 v hZ µν Z µν + c 2 v hZ µ ∂ ν Z µν + c � Z v � hZ µ Z µ c 0 c 0 is constrained strongly by the on-shell Higgs measurements. v hZ µν Z µν + c 2 v hZ µ ∂ ν Z µν contribute only to the The terms c 1 transverse polarizations of the Z boson so the overall growth of the cross section with energy is SM like. c � The contribution v � hZ µ Z µ growth as ∼ s relative to the SM. 68% : c � ∈ [ − 0 . 7 , − 0 . 17] ∪ [0 . 42 , 0 . 84] ,

Operators effecting the Higgs decay Electroweak precision measurements and on-shell Higgs measurements favour the assumption that the Higgs boson is part of the electoweak doublet. hZZ interactions can be modified by the following dimension 6 operators ( D µ H ) † σ a D ν HW µν, a , ( D µ H ) † D ν HB µν , H † HB µν B µν , � � � � H † σ a ← → H † ← → ( D µ W µν ) a , ( D µ B µν ) D ν H D ν H ⇒ hZ µν Z µν , h ∂ µ Z ν Z µν ⇒ weak constraints on the Wilson coefficients. � � 2 H † ← → ⇒ hZ µ Z µ are strongly constrained by the ( ∂ µ ( H † H )) 2 , D µ H on shell measurements � hZ µ Z µ appears only at dim 8 level ( D µ H ) 2 � ( H † H ) which leads to the Λ 4 irrelevant constraints on the scale Λ.

Operators effecting the Higgs production At dimension-6 level there are two operators modifying the Higgs production in gluon fusion (see also 1406.1757 ) L dim-6 = c y y t | H | 2 c g g 2 Q L � ¯ 48 π 2 v 2 | H | 2 G µν G µν Ht R + h . c . + s v 2 g 2 L = − c t m t 48 π 2 c g h v ¯ v G µν G µν , tth + c t = 1 − Re ( c y ) s Current measurements have a strong degeneracy ATLAS � CMS 68 � ,95 � along c t + c g = 1 line. 2.0 1.5 1.0 0.5 � SM c g 0.0 The degeneracy becomes even stronger if the � 0.5 operators are generated by the top-like states. � 1.0 g 2 v G µν G µν + e 2 − c t m t v ¯ 48 π 2 c g h 18 π 2 c g h v γ µν γ µν tth + � 1.5 s � 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 c t

gg → h → ZZ matrix element behavior on shell σ ∼ | c t + c g | 2 Z off shell Z g g c t Z Z M gg → ZZ = M bcg + c t M c t + c g M c g g g Z g ∼ log 2 ˆ s M ++00 ∼ M ++00 M ++00 , ∼ ˆ s c g bcg c t c g m 2 t Z g In the SM there in order to preserve unitarity there is a cancellation between the triangle diagram which is logarithmically divergent and the box diagrams. New physics contribution grows with ˆ s - high energy bins become very important.

First bounds from CMS-PAS-HIG-14-002 10 5 c g 0 � 5 � 10 � 10 � 5 0 5 10 c t imposing the condition 0.15 c t + c g = 1 we find 0.10 P 68% : c t ∈ [ − 4 , − 1 . 5] ∪ [2 . 9 , 6 . 1] 0.05 95% : c t ∈ [ − 4 . 7 , 0 . 5] ∪ [1 , 6 . 7] 0.00 � 15 � 10 � 5 0 5 10 15 c t

Validity of the EFT analysis Effective couplings c t , c g can appear as a result of the dimension six operator. y t | H | 2 c g g 2 L dim-6 = c y Q L � ¯ 48 π 2 v 2 | H | 2 G µν G µν s Ht R + h . c . + v 2 Our analysis is valid only in the range Square of the dimension 6 operators where the effects of the dimension-8 act effectively as the dimension-8 operators can be ignored operators. So we can keep O ( c 2 g ) in 16 π 2 v 4 G µν G µν ( D λ H ) † D λ H c 8 g 2 O 8 = the analysis only if s � c g , c y √ c 8 ≪ c 2 s � ˆ v g , y c 8

High Luminosity 3 ab − 1 14 TeV LHC prospects 2.0 We simulate the signal and the 1.5 background with the MCFM 6.8 code, 1.0 and bin the events in six categories √ 0.5 c g ˆ s = (250 , 400 , 600 , 800 , 1100 , 1500) 0.0 GeV � 0.5 K- factors: we assume the same � 1.0 K-factor for the signal and the � 1.5 � 1.0 � 0.5 0.0 0.5 1.0 1.5 2.0 interfering background and calculate c t them using the ggHiggs code. 1.2 nonlinear analysis 1.0 68% c t ∈ [0 . 74 , 1 . 28] 0.8 linear analysis 68% c t ∈ [0 . 36 , 1 . 66] P 0.6 keeping √ s < 600GeV 0.4 68% c t ∈ [0 . 1 , 1 . 25] 0.2 0.0 � 1 0 1 2 3 c t

Recent progress in gg → h → ZZ (1410.5806) Looking at angular distributions can suppress the q ¯ q → ZZ background and improve the sensitivity on the coupling measurements the direct t ¯ th provides stronger constraints on the top Yukawa couplings

Summary On-shell Higg couplings measurements so far did not observe any significant deviations from the SM. Off-shell Higgs production is very sensitive to the higher dimensional operators in production/decay. Studies of the off-shell Higgs production can be used as an additional independent constraint on the top Yukawa coupling.

Models with ( c t , c g ) degeneracy Simple addition of one vector-like fermion L = − y ¯ Q L t R H − M ∗ ¯ TT − Y ∗ ¯ Q L T R H � yv � Y ∗ v c g ( m H ) ≈ ∂ log Detm m = ⇒ = 1 0 ∂ log v M ∗ Higgs coupling to the gluons is exactly the same as in the SM, however Higgs couplings to the top quarks is modified � � T 1 − Y 2 ∗ v 2 Q L Q L y t ∼ y SM t M 2 ∗ g 2 L = − c t m t 48 π 2 c g h v ¯ v G µν G µν tth + s c t = 1 − Y 2 ∗ v 2 c g = Y 2 ∗ v 2 M 2 M 2 ∗ ∗ Similar effect occurs in the composite Higgs models

Bounds on top partners 8 0.5 L = − y ¯ Q L t R H − M ∗ ¯ TT − Y ∗ ¯ Q L T R H 6 0.4 0.3 Y � 4 c g = c y ∼ Y 2 ∗ v 2 ∗ , M 2 0.1 2 c 8 ∼ Y 2 ∗ v 4 M 4 ∗ 0 1000 1500 2000 analysis ignoring the dimension eight M T � GeV � operator is valid up to the energies √ Figure: 95% exclusion in Y ∗ /top partner s � M ∗ ˆ mass plane.

Recent progress Higgs plus jet: Schlaffer, Spannowsky,Takeuchi,Weiler,Wymant arxiv: 1405.4295, h → ττ, WW ∗ c t ∈ [0 . 71 , 1 . 24] at 95% Higgs plus two jets: Buschmann, Englert , Goncalves ,Plehn Spannowsky arXiv:1405.7651 h → ττ, WW ∗ c t ∈ [0 . 7 , 1 . 3] at 95%