Quantum Interference in the NMSSM Higgs Sector B. Das, S. Moretti, - PowerPoint PPT Presentation

Quantum Interference in the NMSSM Higgs Sector B. Das, S. Moretti, S. Munir, P. Poulose The 15th Workshop of the LHC Higgs cross section working group Based on 1. Eur.Phys.J. C77 (2017) no.8, 544 2. Phys. Rev. D98 (2018) no.5, 055020 CERN December 12, 2018 Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 1 / 19

Light Higgs: Objectives To analyse the quantum interference effects, both in the CPC and CPV-NMSSM, considering the full propagator matrix for pp → H obs → γγ when Two or more mass states exist near M H obs ∼ 125 GeV Mass difference is comparable to decay widths Quantum interference effects become sizable, invalidating the narrow width approximation (NWA) To investigate how such mutually interfering states can be distinguished from a single resonance at the LHC. Our analyses go beyond the state of the art, as current penomenological analyses normally neglect off-diagonal effects. Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 2 / 19

Light Higgs: Di-photon Production through Gluon Fusion in the NWA The amplitude-square for gg → H i → γγ � 2 M D i σ M ∗ | M | 2 = � � M P i λ M ∗ � � � D H i (ˆ s ) P i λ D i σ λ,σ = ± 1 i =1 , 5 λ, σ : gluon, photon helicities, D H i (ˆ s ): propagator matrix Larger splitting between the Higgs boson masses = ⇒ NWA in the i − th Higgs boson propagator 2 � � 1 π s ) | 2 = � � s − m 2 | D i (ˆ → δ (ˆ H i ) � � s − m 2 � ˆ H i + im H i Γ H i � m H i Γ H i � � The total cross-section for pp → H i → γγ in the NWA: m 2   � 1 Hi 1  g ( x 1 ) g ( s / x 1 ) � 2 � � 2 �  � � � � � σ ( pp → H i → γγ ) = dx 1 � M P i λ � M D i σ m 2 1024 sm 3 Hi H i Γ H i x 1 i =1 − 5 λ = ± σ = ± s g ( x ) are the pdfs for the two gluons. Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 3 / 19

Light Higgs: Di-photon Production through Gluon Fusion: Beyond the NWA √ Beyond the NWA: two (or more) Higgses are almost mass degenerate at a given ˆ s : − 1 i I m ˆ i I m ˆ i I m ˆ i I m ˆ  m 11 Π 12 (ˆ s ) Π 13 (ˆ s ) Π 14 (ˆ s ) Π 15 (ˆ s )  i I m ˆ i I m ˆ i I m ˆ i I m ˆ Π 21 (ˆ s ) m 22 Π 23 (ˆ s ) Π 24 (ˆ s ) Π 25 (ˆ s )   i I m ˆ i I m ˆ m 33 + i I m ˆ i I m ˆ i I m ˆ   D H (ˆ s ) = ˆ s Π 31 (ˆ s ) Π 32 (ˆ s ) Π 33 (ˆ s ) Π 34 (ˆ s ) Π 35 (ˆ s )     i I m ˆ i I m ˆ i I m ˆ i I m ˆ Π 41 (ˆ s ) Π 42 (ˆ s ) Π 43 (ˆ s ) m 44 Π 45 (ˆ s )   i I m ˆ i I m ˆ i I m ˆ i I m ˆ Π 51 (ˆ s ) Π 52 (ˆ s ) Π 53 (ˆ s ) Π 54 (ˆ s ) m 55 s − m 2 H i + i I m ˆ I m ˆ m ii ≡ ˆ Π ii (ˆ s ), Π ij (ˆ s ): the absorptive parts of the Higgs self-energies i − th Higgs state can undergo resonant transition to the j − th state, invalidating the NWA. g γ H i H j f, � All f, W ± , H ± q, � q g γ The total cross section beyond the NWA: � 1 � 1 dx 1 g ( x 1 ) g ( τ/ x 1 ) 2 � 2 � � � � � � � � � 2 � � σ ( pp → H i → H j → γγ ) = d τ � M Pi λ � D ij (ˆ s ) � M Dj σ � � � � s 3 � � x 1 1024 π ˆ 0 τ i , j =1 − 5 λ = ± σ = ± √ s ( τ = ˆ s The differential cross section wrt ˆ s ) √ � 1 d σ 2 ˆ g ( x 1 ) g (ˆ s / sx 1 ) s dx 1 2 � � � � � � 2 � � 2 � � � � � √ = � M P i λ � D ij (ˆ s ) � M D j σ � � s 3 s x 1 1024 π ˆ � d s ˆ τ i , j =1 − 5 λ = ± σ = ± Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 4 / 19

Light Higgs: Numerical Setup, Scan and Constraints Model parameters: Dimensionful parameters are in GeV M 0 ≡ M Q 1 , 2 , 3 = M U 1 , 2 , 3 = M D 1 , 2 , 3 = M L 1 , 2 , 3 = M E 1 , 2 , 3 : 800 − 2000 , 2 ≡ 2 M 1 = M 2 = 1 3 M 3 : 100 − 500 , f ≡ A ˜ t = A ˜ b = A ˜ τ : − 3000 − 0 , tan β : 2 − 8 , M 1 A ˜ λ : 0 . 58 − 0 . 70 , κ : 0 . 3 − 0 . 6 , µ eff : 100 − 200 , A λ : 200 − 1000 , A κ : − 300 − 0 , φ 0 = φ 1 2 = φ A ˜ f = φ λ = φ A λ = φ A κ : 0 [Phys.Rev. D 86, 071702 (2012), Adv. High Energy Phys. 2015, 509847 (2015)] Two separate scans: φ κ = 0 o (CPC-NMSSM) φ κ = 3 o (CPV-NMSSM) Mass-degeneracy condition: m H 2 − m H 1 < 2 GeV (LHC mass resolution) [Phys.Rev.Lett. 114, 191803 (2015)] We assume 123 < M h 1 < 127 GeV ( ± 2 GeV uncertainty from unknown higher order corrections) Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 5 / 19

Light Higgs: Cross section for pp → H obs ( H 1 , H 2 ) → γγ We have studied the distribution of differential cross sections with respect √ s for pp → H obs ( H 1 , H 2 ) → γγ at the LHC with √ s = 14 TeV to ˆ considering the following three cases: Case 1: Two independent Breit-Wigner (BW) resonances. Case 2: With tree-level interference between H 1 and H 2 . Case 3: With full propagator matrix. Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 6 / 19

Light Higgs: Cross sections for pp → H obs ( H 1 , H 2 ) → γγ (CPC-NMSSM, φ κ = 0 o ) BP φ κ M 0 M 1 / 2 A 0 tan β λ κ A λ A κ µ eff (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) 0 ◦ 1 1380.9 458.51 − 2946 . 2 4.39 0.6970 0.4594 423.23 − 5 . 271 113.60 2 1598.3 471.51 − 2875 . 0 4.34 0.6907 0.4823 402.53 − 17 . 117 110.86 3 1498.2 379.87 − 2822 . 4 3.91 0.6969 0.4538 385.05 − 16 . 566 117.92 Input values for the three selected CPC-NMSSM Benchmark Points (BPs) 12 Case 1: 50.36 fb Case 1: 53.10 fb Case 1: 53.58 fb 7.5 BP1 ( ϕ κ = 0 °) BP2 ( ϕ κ = 0 °) Case 2: 52.41 fb 15 BP3 ( ϕ κ = 0 °) Case 2: 58.36 fb Case 2: 57.54 fb Bin size: 2 MeV Case 3: 59.78 fb Bin size: 2 MeV Bin size: 2 MeV Case 3: 73.33 fb 9 Case 3: 69.23 fb  ( fb )  ( fb ) 6  ( fb ) 12 s s s 4.5 9 . Δ 6 . Δ . Δ ^ s ^ s d σ ^ s d σ d σ 3 6 d d d 3 1.5 3 0 0 0 125.2 125.3 125.4 125.5 124.8 124.9 125.0 125.1 126.0 126.1 126.2 126.3  ( GeV )  ( GeV )  ( GeV ) s √ s s Distributions of differential cross sections with respect to ˆ s for the three BPs corresponding to Case 1 (Red curve), Case 2 (Green curve) and Case 3 (Blue curve) σ γγ BP m H 1 m H 2 ∆ m H Γ H 1 Γ H 2 (fb) pp (GeV) (GeV) (MeV) (MeV) (MeV) Case 1 Case 2 Case 3 1 125.3688 125.3782 9.4 10.7 9.7 50.36 52.41 59.78 2 124.9498 124.9562 6.4 10.1 9.1 53.58 57.54 69.23 3 126.1641 126.1667 2.6 10.1 9.3 53.10 58.36 73.33 The masses, total decay widths and the integrated cross sections for the three cases Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 7 / 19

Light Higgs: Cross sections for pp → H obs ( H 1 , H 2 ) → γγ (CPV-NMSSM, φ κ = 3 o ) BP φ κ M 0 M 1 / 2 A 0 tan β λ κ A λ A κ µ eff (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) 3 ◦ 4 1366.6 426.35 − 2694 . 3 3.92 0.6878 0.4657 361.11 − 13 . 780 112.79 5 1476.6 363.81 − 2969 . 1 4.67 0.6725 0.4304 485.87 − 35 . 335 120.41 6 1427.1 249.93 − 2918 . 1 4.53 0.6852 0.3360 610.69 − 26 . 038 147.10 Input values for the four selected CPV-NMSSM ( φ κ = 3 o ) BPs 18 Case 1: 48.11 fb 7 Case 1: 44.68 fb Case 1: 56.90 fb 7.5 BP4 ( ϕ κ = 3 °) BP6 ( ϕ κ = 3 °) Case 2: 50.06 fb Case 2: 59.53 fb Case 2: 43.96 fb 15 BP5 ( ϕ κ = 3 °) 6 Bin size: 2 MeV Bin size: 2 MeV Case 3: 43.54 fb Case 3: 56.16 fb Case 3: 71.28 fb Bin size: 2 MeV  ( fb ) 6  ( fb )  ( fb ) 5 12 s s s 4 4.5 . Δ 9 . Δ . Δ 3 ^ s ^ s ^ s d σ d σ 3 d σ 6 d d d 2 1.5 3 1 0 0 0 125.2 125.3 125.4 125.5 125.6 125.5 125.6 125.7 125.8 124.5 124.6 124.7 124.8  ( GeV )  ( GeV ) s  ( GeV ) √ s s Distributions of differential cross sections with respect to ˆ s for the four BPs corresponding to Case 1 (Red curve), Case 2 (Green curve) and Case 3 (Blue curve) σ γγ BP m H 1 m H 2 ∆ m H Γ H 1 Γ H 2 (fb) pp (GeV) (GeV) (MeV) (MeV) (MeV) Case 1 Case 2 Case 3 4 125.3960 125.4052 9.2 9.6 9.5 48.11 50.06 56.16 5 124.6742 124.6757 1.5 9.1 8.4 56.90 59.53 71.28 6 125.6285 125.6393 10.8 11.1 5.9 44.68 43.96 43.54 The masses, total decay widths and the integrated cross sections for the three cases Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 8 / 19

Light Higgs: Shape analysis of the Emerging Profiles 7.5 Case 1 Case 1: 46.56 fb 18 BP10 ( ϕ κ = 10 °) Case 3 Case 2: 49.55 fb 6 Bin size: 2 MeV Case 3: 50.62 fb 15  ( fb )  ( fb ) 4.5 12 s s . Δ . Δ 9 ^ s 3 ^ s d σ d σ 6 BP10 d d Bin size: 1 GeV 1.5 3 Resolution: 1 GeV ∫ Ldt = 300 fb - 1 0 0 125.0 125.1 125.2 125.3 124 125 126  ( GeV )  ( GeV ) s s Case 1 Case 1 60 BP10 60 BP10 Case 3 Case 3 Bin size: 300 MeV Bin size: 300 MeV  ( fb ) Resolution: 300 MeV  ( fb ) Resolution: 300 MeV 45 45 ∫ Ldt = 300 fb - 1 ∫ Ldt = 1000 fb - 1 s s . Δ . Δ 30 30 ^ s ^ s d σ d σ d d 15 15 0 0 124 125 126 124 125 126  ( GeV )  ( GeV ) s s BP φ κ M 0 M 1 / 2 A 0 tan β λ κ A λ A κ µ eff (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) 10 1378.0 173.35 − 2291 . 7 3.99 0.6877 0.4483 564.66 − 266 . 73 172.87 σ γγ BP m H 1 m H 2 ∆ m H Γ H 1 Γ H 2 (fb) pp (GeV) (GeV) (MeV) (MeV) (MeV) Case 1 Case 2 Case 3 10 125.1874 125.1924 5.0 10.3 2.9 46.56 49.55 50.62 Biswaranjan Das (IITG) HXSWG2018 December 12, 2018 9 / 19