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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

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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

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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

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Introduction: Beyond the MSSM

The LHC (ATLAS and CMS) data indicate that the properties of the

  • bserved Higgs boson are mostly compatible with the Standard Model

(SM), although details from different production and decay modes are needed to understand. Calls for detailed phenomenological studies on the extended Higgs sector of different 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. WMSSM = yu ˆ Q ˆ Hu ˆ Uc − yd ˆ Q ˆ Hd ˆ Dc − yeˆ Lˆ Hd ˆ E c + µˆ Hu ˆ Hd. (1)

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 3 / 21

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Introduction: Beyond the MSSM

µ-problem of MSSM: Difficulty to generate µ parameter which is naturally of order the EW scale. µ2 = −m2

Z

2 + M2

Hd − M2 Hutan2β

tan2β − 1 (2) For 125 GeV Higgs boson at the LHC, MSSM requires large values of At. ∆m2

h = 3m4 t

4π2v2

  • ln

M2

SUSY

m2

t

  • +

X 2

t

M2

SUSY

  • 1 −

X 2

t

12M2

SUSY

  • (3)

The LHC Run 2 data severely constrain the parameter space of the MSSM, by excluding tanβ above 7.6 for mA = 200 GeV in ττ final

  • state. (ATLAS Col., arXiv:1608.00890)

Some unique phenomenological possibilities in the NMSSM, precluded

  • r 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

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CPV-NMSSM Higgs sector

NMSSM contains an extra Higgs singlet ˆ S in addition to the two MSSM Higgs doublets. NMSSM superpotential: WNMSSM = W Yukawa

MSSM + λˆ

S ˆ Hu ˆ Hd + κ 3 ˆ S3 (4) Solve µ-problem: µeff = λvs (At EWSB scale) 5 new parameters: λ, κ, Aλ, Aκ, vs 5 neutral Higgs bosons and 5 neutralinos. Enhanced tree-level mass of the SM-like Higgs with reduced fine tuning m2

HSM ≃ m2 Zcos22β + λ2v2sin22β − λ2v2

κ2

  • λ − sin2β
  • κ + Aλ

2s 2 . (5)

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 5 / 21

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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 | eiφλ , κ =| κ | eiφκ. Two Higgs doublets Hd =

  • 1

√ 2(vd + HdR + iHdI)

H−

d

  • , Hu = eiφu
  • H+

d 1 √ 2(vu + HuR + iHuI)

  • and a singlet

S = eiφs √ 2 (vs + SR + iSI) (6)

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 6 / 21

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CPV-NMSSM Higgs sector

The tree-level Higgs mass matrix can be given as M2

0 =

⎛ ⎜ ⎜ ⎝ M2

S

M2

SP

  • M2

SP

T M2

P

⎞ ⎟ ⎟ ⎠ , (7) in the basis HT ≡ (HdR, HuR, SR, HdI, HuI, SI). M2

S/M2 P: Represents mixing between the CP-even/CP-odd states

and of the Higgs fields. M2

SP: Represents mixing between CP-even and CP-odd states.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 7 / 21

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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 RG (HdR, HuR, SR, HI, SI, G)T = RG (HdR, HuR, SR, HdI, HuI, SI)T , (8) and then using another rotation by RH (H1, H2, H3, H4, H5, G)T = RH (HdR, HuR, SR, HI, SI, G)T , (9) where the diagonalised squared mass matrix diag

  • m2

H1, m2 H2, m2 H3, m2 H4, m2 H5, 0

  • = RH
  • RGM2
  • RGT

RHT . (10) H1, H2, H3, H4, H5: Five physical neutral Higgs bosons in the CPV-NMSSM. In ascending order of their masses: mH1 ≤ mH2 ≤ mH3 ≤ mH4 ≤ mH5.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 8 / 21

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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 effect of CPV phases on the cross-section of the process gg → Hi → Hj → 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

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Diphoton production through gluon fusion: NWA and beyond

The squared amplitude for gg → Hi → γγ, i = 1, 2, .., 5 | M |2 =

  • λ,σ=±

MPλM∗

Pλ |DH(ˆ

s)|2 MDσM∗

Dσ ,

(11) λ, σ = ±1: the gluon and photon helicities, DH(ˆ s): Higgs propagator. The amplitudes for the production and decay [J. Lee et al., Comput.Phys.Commun. 156 (2004) 283317] MPλ =

  • i=1−5

MPiλ =

  • i=1−5

αsm2

Hi

4πv

  • Sg

i (mHi) + iλPg i (mHi)

  • , (12)

MDσ =

  • i=1−5

MDiσ =

  • i=1−5

αemm2

H

4πv

  • Sγ

H(mH) + iσPγ H(mH)

  • . (13)

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 10 / 21

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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]

DH(ˆ s) = ˆ s ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ m11 + iImˆ Π11(ˆ s) iImˆ Π12(ˆ s) iImˆ Π13(ˆ s) iImˆ Π14(ˆ s) iImˆ Π15(ˆ s) iImˆ Π21(ˆ s) m22 + iImˆ Π22(ˆ s) iImˆ Π23(ˆ s) iImˆ Π24(ˆ s) iImˆ Π25(ˆ s) iImˆ Π31(ˆ s) iImˆ Π32(ˆ s) m33 + iImˆ Π33(ˆ s) iImˆ Π34(ˆ s) iImˆ Π35(ˆ s) iImˆ Π41(ˆ s) iImˆ Π42(ˆ s) iImˆ Π43(ˆ s) m44 + iImˆ Π44(ˆ s) iImˆ Π45(ˆ s) iImˆ Π51(ˆ s) iImˆ Π52(ˆ s) iImˆ Π53(ˆ s) iImˆ Π54(ˆ s) m55 + iImˆ Π55(ˆ s) ⎞ ⎟ ⎟ ⎟ ⎟ ⎠

−1

, (14)

with mii ≡ ˆ s − m2

Hi, and Imˆ

Πij(ˆ s): the absorptive parts of the Higgs self-energies, for i, j = 1 − 5. CPV phases turned on = ⇒ Non-zero off-diagonal terms

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 11 / 21

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Diphoton production through gluon fusion: NWA and beyond

Larger splitting between the Higgs boson masses than the sizes of Imˆ Πij(ˆ s), = ⇒ NWA in the ith Higgs boson propagator |Dii(ˆ s)|2 =

  • 1

ˆ s − m2

Hi + imHiΓHi

  • 2

→ π mHiΓHi δ(ˆ s − m2

Hi).

(15) [E. Fuchs et al., Eur. Phys. J. C75 (2015) 254] The partonic cross section [J. Ellis et al., Phys.Rev. D70 (2004) 075010]

ˆ σ(gg → Hi → γγ) = 1 1024πˆ s

  • i=1−5

⎛ ⎝

λ=±

  • MPi λ
  • 2 ×

π mHi ΓHi δ(ˆ s − m2

Hi ) ×

  • σ=±
  • MDi σ
  • 2

⎞ ⎠ . (16)

The total cross-section for the process pp → Hi → γγ in the NWA

σ(pp → Hi → γγ) = 1

m2 Hi s

dx1 1 1024sm3

Hi ΓHi

  • i=1−5

⎛ ⎝

λ=±

  • MPi λ
  • 2

σ=±

  • MDi σ
  • 2

⎞ ⎠ g(x1)g(

m2 Hi s

/x1) x1 . (17) Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 12 / 21

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Diphoton production through gluon fusion: NWA and beyond

Beyond the NWA: Imˆ Πij(ˆ s) become comparable to the Higgs mass

  • difference. i−th Higgs state can undergo resonant transition to the

j−th state, invalidating the NWA

Hi Hj q, q f, f, W ±, H± γ γ g g All

Figure : Leading order (LO) Feynman diagram for gg → Hi → Hi → γγ.

The total cross section

σ(pp → H → γγ) = 1 dτ 1

τ

dx1 x1 g(x1)g(τ/x1) 1024πˆ s3

  • i,j=1−5

λ=±

  • MPi λ
  • 2

Dij (ˆ s)

  • 2

σ=±

  • MDj σ
  • 2

. (18)

g(x1) and g(τ/x1) are the pdfs of the two gluons.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 13 / 21

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Diphoton production through gluon fusion: NWA and beyond

The differential cross section wrt τ dσ dτ = 1

τ

dx1 x1 g(x1)g(τ/x1) 1024πˆ s3

  • i,j=1−5
  • λ=±

|MPiλ|2 |Dij(ˆ s)|2

σ=±

  • MDjσ
  • 2

, (19) and then substituting τ = ˆ

s s gives

dσ d √ ˆ s = 1

τ

2 √ ˆ s s dx1 x1 g(x1)g(ˆ s/sx1) 1024πˆ s3

  • i,j=1−5
  • λ=±

|MPiλ|2 |Dij(ˆ s)|2

σ=±

  • MDjσ
  • 2

. (20)

Packages used: (a)The above cross sections are calculated by a locally developed fortran program, (b)NMSSMCALC to compute Higgs mass spectrum, decay widths and branching ratios (BRs), (c)LAPACK for propagator matrix inversion, (d)VEGAS for two dimensional numerical integration.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 14 / 21

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Diphoton production through gluon fusion: NWA and beyond

Model parameters: Following supergravity-inspired universality conditions are used on the model parameters M0 ≡ MQ1,2,3 = MU1,2,3 = MD1,2,3 = ML1,2,3 = ME1,2,3, M 1

2 ≡ 2M1 = M2 = 1

3M3, Af ≡ At = Ab = Aτ. (21) Thus the set of CPV-NMSSM model parameters in our analysis: M0, |M 1

2 |, |Af |, tanβ, |λ|, |κ|, µeff, |Aλ|, |Aκ|, φ 1 2 , φf , φ′

λ, φ′ κ.

Mass-degeneracy condition: mH2 − mH1 < 2 GeV (LHC mass resolution). [G. Aad et al. Phys. Rev. Lett. 114, 191803 (2015)]

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 15 / 21

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Diphoton production through gluon fusion: NWA and beyond

CPV-NMSSM Parameter set: φκ = 3o, 10o, 30o. All other phases are set to zero. [J. F. Gunion, et al., Phys. Rev. D 86, 071702 (2012),

  • S. Moretti, S. Munir., Adv. High Energy Phys. 2015, 509847 (2015)]

NMSSM parameter Scanned range M0(GeV) 200-2000 M 1

2 (GeV)

100-1000 Af (GeV)

  • 3000-0

tanβ 1-8 λ 0.4-0.7 κ 0.3-0.6 µeff (GeV) 100-300 Aλ(GeV)

  • 1000-1000

Aκ(GeV)

  • 1000-1000

Table : Ranges of the scanned CPV-NMSSM parameters, with fixed φκ.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 16 / 21

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Diphoton production through gluon fusion: NWA and beyond: Differential cross sections wrt √ ˆ s vs. √ ˆ s

0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 124.2 124.25 124.3 124.35 124.4 124.45 124.5 124.55 124.6 τ(dσtot/dτ) [pb] √ sˆ [GeV] Bin size = 2 MeV Diagonal propagator (no inteference) = 3.32 fb Diagonal propagator (with inteference) = 3.53 fb Full propagator = 3.78 fb CPVNMSSM BP6 σ.BR = 2.88 fb (for H1) σ.BR = 2.11 fb (for H2) mH1 = 124.42 GeV mH2 = 124.43 GeV ΓH1 = 4.55 MeV ΓH2 = 8.01 MeV 5e-05 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 125.1 125.15 125.2 125.25 125.3 125.35 125.4 125.45 125.5 τ(dσtot/dτ) [pb] √ sˆ [GeV] Bin size = 2 MeV Diagonal propagator (no inteference) = 1.17 fb Diagonal propagator (with inteference) = 1.19 fb Full propagator = 1.20 fb CPVNMSSM BP7 σ.BR = 0.33 fb (for H1) σ.BR = 1.04 fb (for H2) mH1 = 125.308 GeV mH2 = 125.312 GeV ΓH1 = 5.63 MeV ΓH2 = 3.92 MeV 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 124.2 124.25 124.3 124.35 124.4 124.45 124.5 124.55 124.6 τ(dσtot/dτ) [pb] √ sˆ [GeV] Bin size = 2 MeV Diagonal propagator (no inteference) = 17.61 fb Diagonal propagator (with inteference) = 18.04 fb Full propagator = 18.53 fb CPVNMSSM BP8 σ.BR = 6.6× 10-3 fb (for H1) σ.BR = 15.47 fb (for H2) mH1 = 124.406 GeV mH2 = 124.413 GeV ΓH1 = 4.47 MeV ΓH2 = 8.96 MeV 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 124.3 124.35 124.4 124.45 124.5 124.55 124.6 124.65 124.7 τ(dσtot/dτ) [pb] √ sˆ [GeV] Bin size = 2 MeV Diagonal propagator (no inteference) = 2.70 fb Diagonal propagator (with inteference) = 3.03 fb Full propagator = 2.97 fb CPVNMSSM BP9 σ.BR = 0.13 fb (for H1) σ.BR = 2.39 fb (for H2) mH1 = 124.48 GeV mH2 = 124.49 GeV ΓH1 = 6.89 MeV ΓH2 = 1.69 MeV

Figure :

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 17 / 21

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Diphoton production through gluon fusion: NWA and beyond: Differential cross sections wrt √ ˆ s vs. √ ˆ s

0.0005 0.001 0.0015 0.002 0.0025 0.003 124 124.05 124.1 124.15 124.2 124.25 124.3 124.35 124.4 τ(dσtot/dτ) [pb] √ sˆ [GeV] Bin size = 2 MeV Diagonal propagator (no inteference) = 16.90 fb Diagonal propagator (with inteference) = 17.14 fb Full propagator = 16.64 fb CPVNMSSM BP10 σ.BR = 1.04× 10-2 fb (for H1) σ.BR = 14.96 fb (for H2) mH1 = 124.16 GeV mH2 = 124.17 GeV ΓH1 = 0.91 MeV ΓH2 = 9.12 MeV

BP M0 M1/2 A0 tanβ λ Aλ Aκ µeff 6 1121.3 462.13

  • 1849.5

3.10 0.6624 196.51

  • 73.12

101.25 7 1224.8 209.70

  • 2624.0

4.35 0.6869 480.86

  • 286.99

145.43 8 1329.5 206.00

  • 2854.8

5.43 0.6743 640.54

  • 288.23

144.02 9 1166.5 158.97

  • 2940.7

2.48 0.6761 306.89

  • 456.92

193.89 10 1044.7 124.67

  • 1835.1

2.46 0.6602 441.92

  • 633.05

265.67 Table : All dimensionful parameters are in GeV.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 18 / 21

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Summary

The NMSSM Higgs sector contains interesting scenarios which are precluded or excluded in the MSSM. Particularly, we focus on the scenarios where the experimentally visible peak can actually be explained by two nearly mass-degenerate neutral Higgs boson states. Its important to consider the full propagator when the mass difference between the two Higgs bosons is comparable to their widths. The combined CMS result in the WW and ZZ decay modes, for the Higgs boson off-shell production in ggF and VBF processes, at 7 and 8 TeV, puts the observed and expected upper limits of 13 and 26 MeV, respectively on the total Higgs decay widths at 95% CL [CMS Col., arXiv:1605.02329]. This combined result on the Higgs total decay widths serves as a stringent constraint on the choices of our benchmark points.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 19 / 21

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Summary

Some points corresponding to these scenarios give an overall slightly improved fit to the data, more so for non-zero values of the CPV phase, compared to the scenarios containing a single Higgs boson near 125 GeV, invalidating the NWA.

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 20 / 21

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Thank You

Biswaranjan Das (IITG) Higgs Couplings 2016 November 10, 2016 21 / 21