Comments on Interference Effects on Di- Higgs Boson Production - PowerPoint PPT Presentation

Comments on Interference Effects on Di- Higgs Boson Production Double Higgs Production at Colliders Workshop @ Fermilab Marcela Carena Fermilab and UChicago Fermilab, Spetember 7, 2018

Interference Effects in Di-Higgs Production: gg à S à HH Models with additional singlets open a door for strong first order phase transitions Singlet extension of the SM can serve as a benchmark, challenging to test at colliders • Consider case of Spontaneous Z 2 breaking • Find that interference effect can enhance di-Higgs production up to 40%, improving LHC reach Parameters in the potential can be traded by V ( s, φ ) = − µ 2 φ † φ − 1 s s 2 + λ ( φ † φ ) 2 + λ s 4 s 4 + λ s φ x 2 s 2 φ † φ , 2 µ 2 m H =125 GeV, v=246 GeV spontaneous symmetry breaking defines μ 2 and μ 2S m S , tan β (=v s /v), sin θ , in terms of the original quartic couplings & the vevs Besides singlet-doublet mixing governed by sin θ , di-Higgs final states are characterized by two trilinear coupling: L ⊃ λ HHH H 3 + λ SHH SH 2 . m 2 tan β cos 3 θ − sin 3 θ H � � λ HHH = − , 2 tan β v x x x 2 tan β v sin 2 θ (tan β cos θ + sin θ )(1 + m 2 m 2 H S λ SHH = − ) . 2 m 2 H

̂ ̂ Interference Effects in Di-Higgs Production: gg à S à hh Models with additional singlets open a door for a strong first order phase transition Singlet extension of the SM can serve as a benchmark, challenging to test at colliders + # = ! %%&#→(( = ) " ! " + − - . + 0 Γ- x 3 = ! %%→(( = ) □ (slowing varying function of ̂ ! □ + ) 3 = ! %%→( ∗ →(( = ) " 5 (slowing varying function of ̂ ! " + ) x x M.C. Z. Liu and M. Riembau. ‘18

̂ ̂ ̂ ̂ ̂ ̂ Di-Higgs Production and Interference effects " ! "#$ = & "#$ "() * +# ,) = c "#$ P / ! 01$ = & 01$ (slowing varying function of ̂ / ) 2 = ! "#$ 2 + ! 01$ 2 + 256 ! "#$ ! 01$ ! 2 = ! "#$ + ! 01$ ∗ ∗ ∗ = 8. :. +8;< + 256 & "#$ & 01$ => ? @ A + 2BC & "#$ & 01$ DE[?(@ A)] R int B.W. Re. Int . / − C 2 ) /( ̂ => ? @ A = / − C 2 2 + Γ 2 C 2 • Background real • Re. Int.– from the real part of the propagator: −L ̂ / ΓC at parton level no contribution to the rate DE[?(@ A)] = / − C 2 2 + Γ 2 C 2 è shift the mass peak. [When convoluting with PDF, may generate residual contribution to signal rate]

̂ ̂ ̂ ̂ ̂ ̂ Di-Higgs Production and Interference effects " ! "#$ = & "#$ "() * +# ,) = c "#$ P / ! 01$ = & 01$ (slowing varying function of ̂ / ) 2 = ! "#$ 2 + ! 01$ 2 + 256 ! "#$ ! 01$ ! 2 = ! "#$ + ! 01$ ∗ ∗ ∗ = 8. :. +8;< + 256 & "#$ & 01$ => ? @ A + 2BC & "#$ & 01$ DE[?(@ A)] I int Im. Int.–from the imaginary part of propagator / − C 2 ) /( ̂ => ? @ A = / − C 2 2 + Γ 2 C 2 I in ∗ ∗ BC & "#$ & 01$ = c MNO |c QRO |sin(V "#$ − V 01$ ) −L ̂ / ΓC DE[?(@ A)] = / − C 2 2 + Γ 2 C 2 When phase V "#$ − V 01$ (strong phase) is none-zero, there is a new interference effect that cannot be neglected

Imaginary parts contributing to the Interference effects Triangle loop function x Phase of the loop function √ √ τ = s / 2m f ˆ Once above the threshold, SM Higgs imaginary piece increases real & slowly varying and real piece decreases. Background real Real Interference from the real part of the propagator and real part of loop function (shifts the mass peak; no contribution to the signal rate besides residual effect of PDF’s) Im. Interference from the imaginary part of propagator with imaginary part of loop function (rare case, changes signal rate)

Strong phase in the loop functions The solid, dotted, and dashed curves correspond to scattering angles of 0, 0.5 and 1, respectively Relative strong phase (yellow curve) allows for a non-vanishing interference effect between the singlet resonance diagram and the SM box diagram.

Interference Line shape Logarithmic to see other components; Dashed represent destructive interference; Dark blue, unique on-shell constructive interference

Interference Line shape Logarithmic to see other components; Dashed represent destructive interference; Dark blue, unique on-shell constructive interference

Relevance of the on-shell interference Relative size of the on-shell interference effect w.r.t. the resonant BW signal, averaged over scattering angle [-0.5,0.5] For different parameters, it could be up to 40% below 1 TeV or increase even further for heavier singlet masses. Interference effect could play an important role in the pheno and further determination of model parameters if the heavy scalar is discovered.

Relevance of the on-shell interference Based on the pp à HH à bb γγ , analysis [arXiv:1502.00539] we perform a differential analysis of the lineshapes: M.C. Z. Liu and M. Riembau. ‘18 • Black/red lines, w/wo interference effect; • Purple shaded region, 1 st Order Phase Transition (FOPT) through an EFT analysis • Correct inclusion of the interference effect extends the sensitivity in FOPT region

�� �� �� � �� � �� �� � � � � ��� ��� ��� � � ��� ��� ��� Di-Higgs Production as a signal of Enhanced Yukawa couplings Bauer, MC, Carmona (1801.00363) Correlation between enhanced Higgs-fermion couplings and di-Higgs production in 2HDM w/ flavour symmetry (2HDFM) n uij ¯ ✓ � † 1 � † n dij ¯ ✓ � 1 � 2 ◆ ◆ Q i ˜ L I Y 3 y u Q i � 1 u j + y d 2 � 1 d j ij ij Λ 2 Λ 2 ✓ � † 1 � † n ` ij ¯ �� Br( H → hh ) �� ◆ L i ˜ + y ` 2 10 � 1 ` j + h.c. , (8) ij Λ 2 7 �� 5 �� 90 90% 3 10 �� �� 80 2 80% 7 70 70% 2 m f i ⌘ m f i � � ⇣ 5 g ' f Li f Ri =  ' g ' f i ( ↵ , � ) + n f i f ' ( ↵ , � ) = v , 50 50% 3 f i v � � 30 30% 20 � 20% � g Hhh = (18) 10 10% � c � − ↵ � ⇥� 1 � f h ( α , β ) s � − ↵ �� 3 M 2 A � 2 m 2 h � M 2 � � M 2 ⇤ H A - ��� ��� ��� v ��� ��� ��� ⇥� �� � ⇥ ⇤ � � � � v − FIG. 1: The color coding shows the dependence of g hhh = � 3 f h ( α , β ) c 2 ⇥ � − ↵ ( m 2 h � M 2 A ) + m 2 ⇤ h s � − ↵ Br( H ! hh ) on c � − ↵ and t � for M H = M H ± = 550 v GeV, M A = 450 GeV. The dashed contours correspond to constant | κ h f | for n f = 1.

Di-Higgs Production as a signal of Enhanced Yukawa couplings Bauer, MC, Carmona (1801.00363) Correlation between enhanced Higgs-fermion couplings and di-Higgs production in 2HDM w/ flavour symmetry Visible in resonant & non-resonant, dedicated LHC searches FIG. 2: Left: Cross section for Higgs pair production in units of the SM prediction as a function of κ h f for c � − ↵ = − 0 . 45 ( − 0 . 4) and M H = M H ± = 550 GeV, M A = 450 GeV in blue (green) at √ s = 13 TeV. Right: Invariant mass distribution for the di ff erent contributions to the signal with c � − ↵ = − 0 . 45 and κ h f = 5 (blue), κ h f = 4 (green) f = 3 (red) at √ s = 13 TeV, respectively. Solid (dot-dashed) lines correspond to the NLO (LO) calculation for and κ h the sum of the resonant and non-resonant production, while dotted (dashed) lines correspond to the pure resonant (non-resonant) contributions. 13

Outlook The 125 GeV Higgs p recision measurements call for a significant degree of alignment, with important implications for additional Higgs bosons searches Phase shift between SM and new physics can have important implications • Enhance LHC sensitivity to simple models with a strong first order phase transition Also relevant for • 2HDFMs with enhanced light quark Higgs couplings • Novel on-shell info on Higgs total width • Performing scalar resonant searches above the top threshold