Two Higgs bosons around 125 GeV in the CPV-NMSSM at the LHC Biswaranjan Das IIT Guwahati Higgs Couplings 2016 SLAC, USA With S. Moretti, S. Munir & P. Poulose (Draft in preparation) November 10, 2016 Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 1 / 21
Outline Introduction: Beyond the MSSM The Higgs sector of the CPV-NMSSM Two Higgs bosons around 125 GeV Diphoton production through gluon fusion: NWA and beyond Summary Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 2 / 21
Introduction: Beyond the MSSM The LHC (ATLAS and CMS) data indicate that the properties of the observed Higgs boson are mostly compatible with the Standard Model (SM), although details from di ff erent production and decay modes are needed to understand. Calls for detailed phenomenological studies on the extended Higgs sector of di ff erent beyond Standard Model (BSM) scenarios. Supersymmetric (SUSY) extensions are most popular BSM candidates, resulting a comparatively richer Higgs sector with various features distinct from the SM. The Minimal Supersymmetric Standard Model (MSSM) is the simplest SUSY extention of the SM. MSSM super potential is not conformal invariant. E c + µ ˆ U c − y d ˆ D c − y e ˆ W MSSM = y u ˆ Q ˆ H u ˆ Q ˆ H d ˆ L ˆ H d ˆ H u ˆ H d . (1) Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 3 / 21
Introduction: Beyond the MSSM µ -problem of MSSM: Di ffi culty to generate µ parameter which is naturally of order the EW scale. M 2 H d − M 2 H u tan 2 β µ 2 = − m 2 Z 2 + (2) tan 2 β − 1 For 125 GeV Higgs boson at the LHC, MSSM requires large values of A t . � � M 2 � � �� h = 3 m 4 X 2 X 2 ∆ m 2 t SUSY t t + 1 − (3) ln m 2 M 2 12 M 2 4 π 2 v 2 t SUSY SUSY The LHC Run 2 data severely constrain the parameter space of the MSSM, by excluding tan β above 7.6 for m A = 200 GeV in ττ final state. (ATLAS Col., arXiv:1608.00890) Some unique phenomenological possibilities in the NMSSM, precluded or excluded in the MSSM: Any one of the two lightest Higgs bosons could be the observed one, or both may lie around 125 GeV. Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 4 / 21
CPV-NMSSM Higgs sector NMSSM contains an extra Higgs singlet ˆ S in addition to the two MSSM Higgs doublets. NMSSM superpotential: H d + κ MSSM + λ ˆ S ˆ H u ˆ S 3 ˆ W NMSSM = W Yukawa (4) 3 Solve µ -problem: µ e ff = λ v s (At EWSB scale) 5 new parameters: λ , κ , A λ , A κ , v s 5 neutral Higgs bosons and 5 neutralinos. Enhanced tree-level mass of the SM-like Higgs with reduced fine tuning � � �� 2 Z cos 2 2 β + λ 2 v 2 sin 2 2 β − λ 2 v 2 κ + A λ m 2 H SM ≃ m 2 λ − sin 2 β . κ 2 2 s (5) Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 5 / 21
CPV-NMSSM Higgs sector CP violation could be a necessary condition for EW baryogenesis. CP violation can be invoked at the tree-level of the NMSSM Higgs sector, unlike the NMSSM. λ = | λ | e i φ λ , κ = | κ | e i φ κ . Two Higgs doublets � � � � 1 H + 2 ( v d + H dR + iH dI ) √ , H u = e i φ u d H d = 1 2 ( v u + H uR + iH uI ) H − √ d S = e i φ s and a singlet ( v s + S R + iS I ) (6) √ 2 Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 6 / 21
CPV-NMSSM Higgs sector The tree-level Higgs mass matrix can be given as ⎛ ⎞ M 2 M 2 S SP ⎜ ⎟ M 2 ⎜ ⎟ 0 = ⎠ , (7) ⎝ � � T M 2 M 2 SP P in the basis H T ≡ ( H dR , H uR , S R , H dI , H uI , S I ). M 2 S / M 2 P : Represents mixing between the CP-even/CP-odd states and of the Higgs fields. M 2 SP : Represents mixing between CP-even and CP-odd states. Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 7 / 21
CPV-NMSSM Higgs sector Physical Higgs mass eigenstates from the interaction states: The massless Goldstone boson field G is separated out through a rotation by R G ( H dR , H uR , S R , H I , S I , G ) T = R G ( H dR , H uR , S R , H dI , H uI , S I ) T , (8) and then using another rotation by R H ( H 1 , H 2 , H 3 , H 4 , H 5 , G ) T = R H ( H dR , H uR , S R , H I , S I , G ) T , (9) where the diagonalised squared mass matrix � R G � T � � � R H � T � � m 2 H 1 , m 2 H 2 , m 2 H 3 , m 2 H 4 , m 2 R G M 2 = R H diag H 5 , 0 . 0 (10) H 1 , H 2 , H 3 , H 4 , H 5 : Five physical neutral Higgs bosons in the CPV-NMSSM. In ascending order of their masses: m H 1 ≤ m H 2 ≤ m H 3 ≤ m H 4 ≤ m H 5 . Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 8 / 21
Two Higgs bosons around 125 GeV CPV phases can modify the Higgs mass and decay widths. Thus non-zero CPV phases are strongly constrained by the LHC measurements. Mass-degenerate scenarios were not considered. [S. Moretti, et al., Phys. Rev. D 89, 015022 (2014)] CPV scenarios where the observed Higgs resonance, can actually be explained by two mass-degenerate neutral Higgs states, give improved fit to the LHC data, compared to (a) the CPC-NMSSM. (b) Scenarios with a single Higgs boson ∼ 125 GeV. [S. Moretti, S. Munir., Adv. High Energy Phys. 2015, 509847 (2015)]. Objective: To study the e ff ect of CPV phases on the cross-section of the process gg → H i → H j → γγ , i , j = 1 , .., 5, for scenarios with two mass-degenerate Higgs bosons ∼ 125 GeV in the CPV-NMSSM, with possibilities of mixing in the Higgs propagator. Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 9 / 21
Diphoton production through gluon fusion: NWA and beyond The squared amplitude for gg → H i → γγ , i = 1 , 2 , .., 5 � | M | 2 = s ) | 2 M D σ M ∗ M P λ M ∗ P λ | D H (ˆ D σ , (11) λ , σ = ± λ , σ = ± 1: the gluon and photon helicities, D H (ˆ s ): Higgs propagator. The amplitudes for the production and decay [J. Lee et al., Comput.Phys.Commun. 156 (2004) 283317] � � α s m 2 � � H i S g i ( m H i ) + i λ P g M P λ = M P i λ = i ( m H i ) , (12) 4 π v i =1 − 5 i =1 − 5 � � � � α em m 2 S γ H ( m H ) + i σ P γ H M D σ = M D i σ = H ( m H ) . (13) 4 π v i =1 − 5 i =1 − 5 Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 10 / 21
Diphoton production through gluon fusion: NWA and beyond For the scalar and pseudoscalar form factors we refer [J. Baglio et al., arXiv:1312.4788 [hep-ph]]. The full propagator matrix [J. Ellis et al., Phys.Rev. D70 (2004) 075010] − 1 m 11 + i I m ˆ i I m ˆ i I m ˆ i I m ˆ i I m ˆ ⎛ Π 11 (ˆ s ) Π 12 (ˆ s ) Π 13 (ˆ s ) Π 14 (ˆ s ) Π 15 (ˆ s ) ⎞ i I m ˆ m 22 + i I m ˆ i I m ˆ i I m ˆ i I m ˆ Π 21 (ˆ s ) Π 22 (ˆ s ) 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 m 44 + i I m ˆ i I m ˆ ⎟ Π 41 (ˆ s ) Π 42 (ˆ s ) Π 43 (ˆ s ) Π 44 (ˆ s ) Π 45 (ˆ s ) ⎝ ⎠ i I m ˆ i I m ˆ i I m ˆ i I m ˆ m 55 + i I m ˆ Π 51 (ˆ s ) Π 52 (ˆ s ) Π 53 (ˆ s ) Π 54 (ˆ s ) Π 55 (ˆ s ) (14) H i , and I m ˆ s − m 2 with m ii ≡ ˆ Π ij (ˆ s ): the absorptive parts of the Higgs self-energies, for i , j = 1 − 5. CPV phases turned on = ⇒ Non-zero o ff -diagonal terms Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 11 / 21
Diphoton production through gluon fusion: NWA and beyond Larger splitting between the Higgs boson masses than the sizes of I m ˆ Π ij (ˆ s ), = ⇒ NWA in the i th Higgs boson propagator � � 2 � � 1 π � � s ) | 2 = s − m 2 | D ii (ˆ δ (ˆ H i ) . (15) � � → s − m 2 � � ˆ H i + im H i Γ H i m H i Γ H i [E. Fuchs et al., Eur. Phys. J. C75 (2015) 254] The partonic cross section [J. Ellis et al., Phys.Rev. D70 (2004) 075010] ⎛ ⎞ 1 π 2 × 2 � � � � � ⎝ � s − m 2 � ⎠ . σ ( gg → H i → γγ ) = ˆ � M Pi λ δ (ˆ Hi ) × � M Di σ (16) � � � � � � 1024 π ˆ s m Hi Γ Hi i =1 − 5 λ = ± σ = ± The total cross-section for the process pp → H i → γγ in the NWA m 2 � 1 ⎛ ⎞ Hi 1 ⎠ g ( x 1 ) g ( / x 1 ) 2 � 2 � � � � � ⎝ � s σ ( pp → H i → γγ ) = m 2 . (17) dx 1 � M Pi λ � � � � M Di σ � Hi 1024 sm 3 � � Hi Γ Hi x 1 i =1 − 5 λ = ± σ = ± s Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 12 / 21
Diphoton production through gluon fusion: NWA and beyond Beyond the NWA: I m ˆ Π ij (ˆ s ) become comparable to the Higgs mass di ff erence. i − th Higgs state can undergo resonant transition to the j − th state, invalidating the NWA g γ H i H j f, � f, W ± , H ± q, � q All g γ Figure : Leading order (LO) Feynman diagram for gg → H i → H i → γγ . The total cross section � 1 � 1 dx 1 g ( x 1 ) g ( τ / x 1 ) 2 � 2 � � � � � � 2 � � � � � σ ( pp → H → γγ ) = d τ � � M Pi λ � � D ij (ˆ s ) � M Dj σ � � . (18) s 3 � � x 1 1024 π ˆ 0 τ i , j =1 − 5 λ = ± σ = ± g ( x 1 ) and g ( τ / x 1 ) are the pdfs of the two gluons. Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 13 / 21
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