Revisiting the di-Higgs production processes at the FCC-hh · Revisiting the di-Higgs production...
Transcript of Revisiting the di-Higgs production processes at the FCC-hh · Revisiting the di-Higgs production...
Revisiting the di-Higgs production processes at the
FCC-hh
Shankha Banerjee
IPPP, Durham University
January 16, 2020
Based onEur. Phys. J. C (2018) 78: 322 (with C. Englert, M. Mangano, M. Selvaggi and M. Spannowsky)
Phys.Rev. D100 (2019) 073012 (with F. Krauss and M. Spannowsky)
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 1 / 51
Plan of my talk
Motivation
Status of the di-Higgs searches
Di-Higgs in the EFT
Non resonant di-Higgs production at the HL-LHC
Di-Higgs + jet at FCC-hh
tthh at FCC-hh
Summary and Outlook
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 2 / 51
Motivation
Di-Higgs provides means to directly probe Higgs self coupling
Indirect probe: Through radiative corrections of single Higgs productions
[Goertz et. al.; 2013, McCullough; 2013, Degrassi et. al.; 2016]
Challenging task : small di-Higgs cross-section in SM (39.56+7.32%−8.38% fb at
NNLO + NNLL at 14 TeV with the exact top-quark mass dependence at
NLO [deFlorian et. al.; 2013, Borowka et. al.; 2016]) ← partial cancellation
of triangle and box diagram contributions
LHC or 100 TeV colliders : self-coupling measurement at 10-50% precision
possible → size of dataset, beam energy, control over systematics
Assuming SM couplings, HL-LHC prediction: −0.8 < λλSM
< 7.7 at 95% C.L.
[ATL-PHYS-PUB-2017-001]
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 3 / 51
Motivation
Enhancement of σhh → s-channel heavy di-Higgs resonance [xSM models
etc.] [Muhlleitner et. al.; 2015; Ramsey-Musolf et. al.; 2016 etc.], new
coloured particles in loops [Kribs et. al.; 2012, Nakamura et. al.; 2017] or
HD operators [Nishiwaki et. al.; 2013] → kinematics altered → requires
different experimental search strategies
Till date → major focus on BSM di-Higgs sector → enhancement in
production
New physics can affect Higgs decays → exotic Higgs decays now actively
studied [Curtin et. al.; 2015]
Worthwhile to consider exotic decays for di-Higgs → present bounds on
variety of Higgs decays : BR very weak (10-50%) [SB, Batell, Spannowsky;
2016]
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 4 / 51
Di-Higgs production cross-sections as functions of√s
Di-Higgs cross-sections [Baglio et. al.; 2015]
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 5 / 51
Status of the di-Higgs searches
Channel CMS (NR) CMS (R) ATLAS (NR) ATLAS (R)
(×SM) [fb, (GeV)] (×SM) [fb, (GeV)]
bbbb 75 1500-45 13 2000-2
(260-1200) (260-3000)
bbγγ 24 240-290 22 1100-120
(250-900) (275-400)
bbτ+τ− 30 3110-70 12.7 1780-100
(250-900) (260-1000)
γγWW∗ 200 40000-6100
(γγ`νjj) (260-500)
bb`ν`ν 79 20500-800 300 6000-170
(300-900) (500-3000)
WW∗WW∗ 160 9300-2800
(260-500)
Table: Non-resonant (NR) and resonant (R) double Higgs production. Numbers in
brackets show the range of the heavy scalar mass.
NR: Non-resonant, R: Resonant
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 6 / 51
SMEFT motivation
Many reasons to go beyond the SM, viz. gauge hierarchy, neutrino mass, dark
matter, baryon asymmetry etc.
Plethora of BSM theories to address these issues
Two phenomenological approaches:
Model dependent: study the signatures of each model individually
Model independent: low energy effective theory formalism – analogous to
Fermi’s theory of beta decay
The SM here is a low energy effective theory valid below a cut-off scale Λ
A bigger theory (either weakly or strongly coupled) is assumed to supersede the SM
above the scale Λ
At the perturbative level, all heavy (> Λ) DOF are decoupled from the low energy
theory (Appelquist-Carazzone theorem)
Appearance of HD operators in the effective Lagrangian valid below Λ
L = Ld=4SM +
∑d≥5
∑i
fiΛd−4
Odi
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 7 / 51
Relevant operators
Dimension 6 operators which modify the Higgs self-interactions
OΦ,1 = (DµΦ†)ΦΦ†(DµΦ) OΦ,2 =1
2∂µ(Φ†Φ)∂µ(Φ†Φ)
OΦ,3 =1
3(Φ†Φ)3 OΦ,4 = (DµΦ†)(DµΦ)Φ†Φ OGG = G a
µνGa,µνΦ†Φ
OΦ,2/3 only modify Higgs self-couplings but OΦ,1/4 also modify HVV
couplings and V masses
OΦ,1 contributes to mZ and not to mW → Violates Custodial symmetry →Strongly constrained by T -parameter → Neglected for collider studies
Redundancy amongst operators upon using EOMs → OΦ,2, OΦ,3 and OΦ,4
are not independent
Including SM Yukawa, the operator OΦ,f = (Φ†Φ)LΦfR + h.c., where
L = (f uL , fdL )T becomes relevant
One can remove OΦ,4 using EOMs → Left with (OΦ,2,OΦ,3,OΦ,f ,OGG )
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 8 / 51
Non-linear EFT realisation
Many popular BSM extensions which give rise to modification of Higgs
interactions
Composite Higgs models assume that the Higgs is a pNGB of a strongly
coupled UV completion
The electroweak chiral Lagrangian best describes the low-energy effects of astrongly-coupled embedding of the SM
Lewχ ⊃ − V (h) +g2s
48π2G aµνG
µνa
(kg
h
v+
1
2k2g
h2
v2+ · · ·
)
−v√
2(uiL d i
L)Σ
[1 + c
h
v+ c2
h2
v2+ · · ·
](yuij u
jR
ydij d
jR
)+ h.c.,
with
V (h) =1
2m2
hh2 + d3
m2h
2vh3 + d4
m2h
8v2h4 + · · · .
Here the SU(2)× U(1) symmetry is non-linearly realised Σ(x) = e iσaφa(x)/v
with the Goldstone bosons φa (a=1,2,3) and the Pauli matrices σa
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 9 / 51
Non-linear EFT realisation
5 vertices are of imminent importance, viz., kg , k2g , c , c2, d3 in the top-Higgs
sector
kg and c → can be constrained from gluon-fusion, VBF, tth production
k2g , c2 and d3 → can be constrained at LO from double-Higgs processes
To over-constrain the parameter space of Lewχ it is necessary to access as
many di-Higgs processes as possible, viz., pp → hh, hhj , hhjj , tthh
tthh is the only process with appreciable cross-section that has the ability to
constrain c2 at tree-level
Here however, we will discuss in terms of the following simplified Lagrangian
Lsimp = LSM + (1− κλ)λSMh3 + κtthh(tLtRh2 + h.c.)−
1
8κgghhG
aµνG
µνa h2,
where λSM = λv =m2
h2v
and κλ = λBSM/λSM
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 10 / 51
Bases translations
[Giudice, Grojean, Pomarol, Rattazzi; 2007, Feruglio; 1993]
Coupling Non-linear EFT Simplified Lagrangian SILH
hhh d3 κλ 1 + (c6 − cτ/4− 3cH/2)ξ
tthh c2 −√
2v
ytκtthh −(cH + 3cy + cτ/4)ξ/2
gghh k2g −12π2v2
g2s
κgghh 3cg( y2
t
g2ρ
)ξ
Table: Relationship between the hhh, tthh and gghh vertices in three different bases,
where ξ ≡ (v/f )2.
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 11 / 51
Non resonant di-Higgs production at the HL-LHC
[A. Adhikary, SB, R. K. Barman, B. Bhattacherjee, S. Niyogi; 2017]
We choose channels based on the rate and cleanliness
Focus on final states with leptons and/or photons
Focus on 11 channels, viz.
bbγγ
bbτ+τ− → bb``+ /ET , bb`τh + /ET , bbτhτh + /ET
bbWW ∗ → bb``+ /ET , bb`jj + /ET
WW ∗γγ → ``γγ + /ET , `jjγγ + /ET
WW ∗WW ∗ → `±`±jjjj + /ET , ```jj + /ET , ````+ /ET
4τ, WW ∗τ+τ−, ZZ∗τ+τ−, 4γ, ZZ∗γγ, 4Z may be important at 100 TeV
colliders
Follow CMS and ATLAS analyses (when available) and optimise upon them
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 12 / 51
Non resonant di-Higgs production at the HL-LHC: bbγγ
S/B = 0.19 and S/√
B = 1.76σ CMS (ATLAS) projection: 1.6σ (1.05σ)
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 13 / 51
Non resonant di-Higgs production at the HL-LHC: bbWW ∗
Leptonic: S/B = 0.01 and S/√
B = 0.62; CMS projection: S/B = 0.009 and S/√
B = 0.59
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 14 / 51
Non resonant di-Higgs production at the HL-LHC:
Summary
[A. Adhikary, SB, R. K. Barman, B. Bhattacherjee, S. Niyogi; 2017]
Bleak prospects for discovering SM non-resonant di-Higgs channel at
HL-LHC with 3 ab−1 data
bbγγ is the cleanest (S/B ∼ 0.19) but suffers from small rate
Combined significance ∼ 3σ from the aforementioned channels
Purely leptonic case for bbWW ∗ shows promise but needs better handle over
backgrounds → data driven backgrounds
Both semi-leptonic and leptonic channels for γγWW ∗ show excellent S/B
(0.11 and 0.4 respectively) → need larger luminosity (considering CMS and
ATLAS datasets separately to form 6 ab−1) or higher energy colliders
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 15 / 51
Di-Higgs + jet at FCC-hh
[SB, C. Englert, M. Mangano, M. Selvaggi, M. Spannowsky; 2018]
Observing the Higgs self-coupling at the HL-LHC seem difficult at the
moment
Di-Higgs cross-section increases by 39 times going from 14 TeV → 100 TeV
Extra jet emission becomes significantly less suppressed: 77 times
enhancement from 14 TeV → 100 TeV collider → extra handle
Recoiling a collimated Higgs pair against a jet exhibits more sensitivity
(decorrelates pT ,h and mhh) to λhhh as compared to pp → hh → statistically
limited at the LHC
Study hhj → bbτ+τ−j → bbτh(τ`)τ`j and hhj → bbbbj
Use substructure technique: BDRS [Butterworth, et. al.; 2008] with mass
drop and filtering
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 16 / 51
Di-Higgs + jet at FCC-hh (jbbτ+τ−)
R = 1.5, pjT> 110 GeV, τ -tag efficiency 70%, b-tag efficiency 70%, b-mistag rate 2%; Combined τhτh and τhτ`
Backgrounds: EW (example: HZ/γ∗+ jet), QCD+EW (Example: bbZ/γ∗+ jet), tt+ jet
TEvis.1τ
φ∆0 0.5 1 1.5 2 2.5 3
Cro
ss-s
ecti
on
[fb
]
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45 SMλSMλ2
SMλ0.5EWQCD+EW
jtt
TEvis.2τ
φ∆0 0.5 1 1.5 2 2.5 3
Cro
ss-s
ecti
on
[fb
]
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45SMλ
SMλ2SMλ0.5
EWQCD+EW
jtt
bbR∆0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Cro
ss-s
ecti
on
[fb
]
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16 SMλSMλ2
SMλ0.5EWQCD+EW
jtt
[GeV]filteredhM
0 20 40 60 80 100 120 140 160 180 200
Cro
ss-s
ecti
on
[fb
]
0
0.05
0.1
0.15
0.2
0.25
0.3SMλ
SMλ2SMλ0.5
EWQCD+EW
jtt
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 17 / 51
Di-Higgs + jet at FCC-hh (jbbτ+τ−)
[GeV]T2M0 100 200 300 400 500 600
Cro
ss-s
ecti
on
[fb
]
0
0.05
0.1
0.15
0.2
0.25SMλ
SMλ2SMλ0.5
EWQCD+EW
jtt
[GeV]ττh,collinearM
0 50 100 150 200 250 300
Cro
ss-s
ecti
on
[fb
]
0
0.1
0.2
0.3
0.4
0.5SMλ
SMλ2SMλ0.5
EWQCD+EW
jtt
[GeV]filteredT,h
p0 100 200 300 400 500 600 700 800 900 1000
Cro
ss-s
ecti
on
[fb
]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09 SMλSMλ2
SMλ0.5EWQCD+EW
jtt
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 18 / 51
Di-Higgs + jet at FCC-hh (jbbτ+τ−)
observable reconstructed object
pT
2 hardest filtered subjets
2 visible τ objects (τ` or τh)
hardest non b, τ -tagged jet
reconstructed Higgs from filtered jets
reconstructed Higgs from visible τ final states
pT ratios2 hardest filtered jets
2 visible τ final state objects
mT2 described before
∆R
two hardest filtered subjets
two visible τ objects (τ`τ` or τ`τh)
b-tagged jets and lepton or τhb-tagged jets and jet j1lepton or τh with jet j1
Mcolττ collinear approximation of h → ττ mass
Mfilt filtered j1 and j2 (and j3 if present)
Mvis.hh filtered jets and leptons (or lepton and τh)
�ET reduce sub-leading backgrounds
∆φbetween visible τ final state objects and �ETbetween filtered jets system and `` (or ` τh) systems
Njets number of anti-kT jets with R = 0.4
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 19 / 51
Di-Higgs + jet at FCC-hh (jbbτ+τ−)
[SB, C. Englert, M. Mangano, M. Selvaggi, M. Spannowsky; 2018]
signal [fb] QCD+QED [fb] QED [fb] ttj [fb] tot. background [fb] S/B S/√
B, 30/ab
κλ = 0.5 0.428
0.95 0.27 2.31 3.53
0.121 39.44
κλ = 1 0.363 0.103 33.44
κλ = 2 0.264 0.075 24.31
0.76 < κλ < 1.28 3/ab
0.92 < κλ < 1.08 30/ab
at 68% confidence level using the CLs method.
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 20 / 51
Comparison with optimised cut-and-count analysis
cutcross section after cut [fb]
κλ = 1 κλ = 0.5 κλ = 2 QCD+EW EW ttj
preselection 0.86 1.09 0.56 11.73 2.20 4090.29
mT2 > 120 GeV 0.65 0.78 0.45 4.65 1.10 300.68
∆Φ(τvis,2, /ET ) < 1.5 0.62 0.74 0.43 4.43 1.05 196.36
100 GeV < Mτ,τ < 150 GeV 0.48 0.57 0.33 0.96 0.26 28.05
∆Φ(τvis,1, /ET ) < 1.5 0.47 0.56 0.32 0.92 0.25 21.75
∆R(b1τvis,1) > 0.8 0.47 0.56 0.32 0.92 0.25 20.28
pT (Hτvis,1τvis,2) > 60.0 GeV 0.45 0.53 0.31 0.88 0.24 19.02
∆R(b1τvis,2) > 0.8 0.44 0.52 0.31 0.87 0.24 18.91
100 GeV < Minv,filt < 150 GeV 0.32 0.38 0.22 0.43 0.06 5.78
∆R(b1b2) > 0.8 0.32 0.38 0.22 0.43 0.06 5.46
∆R(τvis,1τvis,2) > 0.8 0.31 0.37 0.22 0.42 0.06 5.15
0.36 0.44 0.26 0.95 0.27 2.31
BDT performance [fb]
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 21 / 51
Di-Higgs + jet at FCC-hh (jbbbb)
Major background: pure QCD: g → bb (soft and collinear splittings →Resulting fat jets (R = 0.8) are one-pronged.
Signal: H → bb; clear two prongs
Requre: τ2,1 < 0.35 and 100 GeV < mSD < 130 GeV
signal QCD QCD+EW EW tot. background S/B × 103 S/√
B, 30/ab
κλ = 0.5 0.094
4.3 0.1 0.003 4.4
20.8 7.67
κλ = 1 0.085 19.1 6.61
κλ = 2 0.071 16.2 5.85
[GeV](1)jm
0 50 100 150 200
No
rmal
ised
0
0.05
0.1SMλ
QCDQCD+EWKEWK
)(1) (j2,1τ0 0.2 0.4 0.6 0.8 1
No
rmal
ised
0
0.01
0.02
0.03
0.04SMλ
QCDQCD+EWKEWK
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 22 / 51
Constraining κλ and κtthh from tthh at 100 TeV
Feynman diagrams showing the impact of the three effective vertices, viz.,
hhh, tthh and gghh
g
g t
t
h
h
g
g t
t
h
h
g
g
h
t
h
t
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 23 / 51
Constraining κλ and κtthh from tthh at FCC-hh
σ/σSM with respect to κλ, κtthh, κgghh
First row shows σ/σSM at 100 TeV and at 14 TeV [Frederix et. al.; 2014]
-4 -2 2 4 κλ
1.0
1.5
2.0
2.5
3.0
σ
σSM
-4 -2 2 4 κλ
1.0
1.5
2.0
2.5
σ
σSM
-0.003 -0.002 -0.001 0.001 0.002 0.003κtthh [GeV-1]
2
4
6
8
10
12
σ
σSM
-6.×10-7 -4.×10-7 -2.×10-7 2.×10-7 4.×10-7 6.×10-7κgghh [GeV
-2]1.0
1.5
2.0
2.5
3.0
σ
σSM
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 24 / 51
Constraining κλ and κtthh from tthh at FCC-hh
Unlike many di-Higgs processes, in tthh cross-section increases with λ > λSM
For κλ, growth of cross-section for λ < 0 has different features at 14 TeV
and 100 TeV machines
In linear EFT scenarios, the coupling modifying ggh and gghh are correlated
→ In non-linear EFT they are uncorrelated
We vary κλ and κtthh to obtain bounds on these couplings
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 25 / 51
Constraining κλ and κtthh from tthh at FCC-hh
[SB, F. Krauss, M. Spannowsky; 2019]
For κλ = 1, σ100 TeVtthh /σ14 TeV
tthh ∼ 75
14 TeV study yields ∼ 13 signal events and κλ . 2.5 at 95% CL [Englert et.
al.; 2014]
For the 100 TeV analysis, we consider final state with 6 b-tagged jets, 1
isolated lepton, at least 2 light jets and /ET
Several backgrounds at play, viz., QCD processes: ttbbbb, tthbb, ttZbb and
EW processes tthZ , ttZZ
Fake backgrounds: ttbb+ jets, tth+ jets, ttZ+ jets, W±bbbb+ jet,
W±cccc+ jets, W±bb+ jets, ttcccc , misidentifying c or light jets as
b-tagged jets
We assume b-tagging efficiency of 80%, 10% (1%) mistagging efficiency for
c-jets (light jets)
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 26 / 51
tthh Scale choices
Process category µ2F µ2
R
ttHH, ttZZ , ttHZ 14
H2T + 2m2
t + {2m2H , 2m2
Z ,m2H + m2
Z}14
H2T + 2m2
tttHbb, ttZbb 1
4H2T + m2
H,Z + 2m2t
14
H2T + 2m2
t
tt + b’s, c’s or light jets 14
H2T + 2m2
t14
H2T + 2m2
tW + b’s, c’s or light jets 1
4H2T + m2
W14
H2T
Table: Renormalisation and factorisation scales used for the various processes
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 27 / 51
Constraining κλ and κtthh from tthh at FCC-hh
For the ttZ/h+ jets, we consider a merged sample, where additional jets
ensue from QCD radiation including the g → bb splitting
We ensure that the additional jets do not contain > 1 B-mesons by requiring
that the B-hadron closest to the jet axis satisfies xB = |~pB ||~pj | ×
~pB ·~pj|~pB ||~pj | > 0.7
Reflects b-quark fragmentation → Allows to suppress ”doubly-tagged” b-jets
We first reconstruct the two Higgs bosons by minimising the following χ2
χ2HH =
(mbi ,bj −mh)2
∆2h
+(mbk ,bl −mh)2
∆2h
,
i 6= j 6= k 6= l run over all the 6 b-tagged jets, mh = 120 GeV taking into
account invisible decays of B-mesons and ∆h = 20 GeV
We then require require |mbi ,bj −mh| < ∆h and |mbk ,bl −mh| < ∆h
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 28 / 51
Constraining κλ and κtthh from tthh at FCC-hh
Then we take the 2 remaining b-jets and minimise the following χ2
χ2th =
(mbi ,jk ,jl −mt)2
∆2t
,
k 6= l and ∆t = 40 GeV We then require |mbi ,jk ,jl −mt | < ∆t
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
60 80 100 120 140 160 180
(
1/σdσ/d
m
)
/
3
.
0
G
e
V
mh [GeV℄
mh distribution
mh1
mh2
0
0.05
0.1
0.15
0.2
0.25
0 100 200 300 400 500 600 700
(
1/σdσ/d
m
)
/
1
4
.
0
G
e
V
mh [GeV℄
mvist distribution
mthad
mvis
tlep
Finally we require mvistlep < mt
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 29 / 51
Constraining κλ and κtthh from tthh at FCC-hh
[SB, F. Krauss, M. Spannowsky; 2019]
At the design luminosity of 30 ab−1, we expect ∼ 260 signal events for
κλ = 1 and ∼ 1900 background events, with S/B ∼ 0.14 and statistical
significance of S/√B ∼ 5.9
Upon taking κtthh = 0, one obtains (using the CLs method) at 68% CL with5% (10%) systematic uncertainty
−3.20 < κλ < 2.60 (−3.43 < κλ < 2.92) 3/ab
−2.89 < κλ < 2.15 (−3.27 < κλ < 2.70) 30/ab
Upon taking κλ = 1, one obtains (using the CLs method) at 68% CL with5% (10%) systematic uncertainty
−0.59 TeV−1 < κtthh < 0.95 TeV−1 (−0.71 TeV−1 < κtthh < 1.07 TeV−1) 3/ab
−0.43 TeV−1 < κtthh < 0.78 TeV−1 (−0.63 TeV−1 < κtthh < 0.99 TeV−1) 30/ab
Ultimate goal is to perform a global fit using the pp → hh, pp → hhj ,
pp → hhjj and pp → tthh with all these couplings to find correlated boundsShankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 30 / 51
Resonant di-Higgs at HL-LHC and FCC-hh
Bounds on σ(pp → H → hh) at HL-LHC (left) from various channels and at FCC-hh
(right) from bbbb
[A. Adhikary, SB, R. K. Barman and B. Bhattacherjee; 2018, D. Barducci, K. Mimasu, J.
M. No, C. Vernieri and J. Zurita; 2019]
[GeV]Hm200 300 400 500 600 700 800 900 1000
hh)
(fb
)→
H
→(p
p σ
12
1020
100200
10002000
1000020000 γγbb
bbbbττbb
WWbbγγWW
95% C.L Upper Limit (5% Systematic)
Right plot: isocontours of sensitivity on κ2 × BR (κ2 × BR is defined by
σ(pp → H1 → H2H2 → bbbb
)= σH1
× κ2 × BR and σH1is production of SM-like Higgs
with mass mH1)
FCC-hh can set stringent limit on κ× BR → factor ∼ 40 improvement with respect to
HL-LHCShankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 31 / 51
Summary and Outlook
Search for Higgs pair production is an important enterprise to understand the
Higgs cubic coupling
Non-resonant di-Higgs searches at the HL-LHC yields a significance of ∼ 3σ
100 TeV collider studies show promise for di-Higgs + jet → κλ can be
constrained to ∼ 8%
Possible to disentangle κtthh and κλ by combining pp → hh, pp → hhj and
pp → hhjj with pp → tthh. Also other final states in pp → tthh.
Possible to constrain λhhhh from one loop EW correction to tthh at FCC-hh
[SB, J. Lindert; ongoing]
Systematic uncertainties need to be understood better in the future in order
to make strong claims about these channels
A global analysis with several di-Higgs channels will ultimately shed light on
the couplings of the scalar sector and with the scalar and the top-quarks
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 32 / 51
Backup slides
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 33 / 51
Non resonant di-Higgs production at the HL-LHC: bbγγ
[A. Adhikary, SB, R. K. Barman, B. Bhattacherjee, S. Niyogi; 2017]Cleanest channel in spite of the low rate
Major backgrounds: QCD-QED bbγγ, hbb, tth, Zh
Dominant fakes: ccγγ, jjγγ, bbjγ, ccjγ, bbjj
Selection cuts
Nj < 6
0.4 < ∆Rγγ < 2.0, 0.4 < ∆Rbb < 2.0, ∆Rγb > 0.4
100 GeV < mbb < 150 GeV
122 GeV < mγγ < 128 GeV
pT,bb > 80 GeV, pT,γγ > 80 GeV
Event rates with 3000 fb−1 of integrated luminosity
Cut flow Signal SM Backgrounds S√B
hh → 2b2γ hbb tth Zh bbγγ∗ Fake 1 Fake 2
Order NNLO NNLO (5FS) + NLO NNLO (QCD) + LO LO LO
NLO (4FS) NLO EW
2b + 2γ 31.63 21.20 324.91 39.32 25890.31 1141.18 393.79 0.19
lepton veto 31.63 21.20 255.66 39.32 25889.94 1141.18 393.79 0.19
Nj < 6 31.04 21 192.05 39.23 25352.78 1064.64 167.32 0.19
∆R cuts 22.19 7.75 38.71 23.48 4715.21 130.10 28.81 0.31
mbb 12.71 1.53 13.80 1.09 862.37 22.11 6.88 0.42
mγγ 12.36 1.5 13.16 1.06 26.54 22.11 6.88 1.46
pT,bb ,pT,γγ 12.32 1.48 13.03 1.06 26.54 21.82 6.88 1.46
significance: S/B = 0.17 and S/√
B = 1.46
With additional /ET < 50 GeV, S/B = 0.19 and S/√
B = 1.51
Changing to: 90 GeV < mbb < 130 GeV: S/B = 0.19 and S/√
B = 1.64
bbγγ∗ = bbγγ + ccγγ + jjγγ, Fake1 = bbjγ + ccjγ, Fake2 = bbjj
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 34 / 51
Multivariate technique employed to further optimise search
Boosted decision tree (BDT) algorithms chosen
Overtaining checked using the Kolmogorov-Smirnov test
Variables chosen (according to the best discriminatory power):
mbb, pT ,γγ , ∆Rγγ , pT ,bb, ∆Rb1γ1 , pT ,γ1 , ∆Rbb,
pT ,γ2 , ∆Rb2γ1 , ∆Rb2γ2 , pT ,b1 , ∆Rb1γ2 , pT ,b2 , /ET
S/B = 0.19 and S/√B = 1.76σ CMS (ATLAS) projection: 1.6σ (1.05σ)
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 35 / 51
Non resonant di-Higgs production at the HL-LHC: bbWW ∗
Two scenarios considered: leptonic: bb``+ /ET and semi-leptonic: bb`jj + /ET
Major backgrounds: tt: leptonic and semi-leptonic, Wbb+ jets:
semi-leptonic, ``bb: leptonic and semi-leptonic
Subdominant backgrounds: bbh, tth, ttV , Vh, Vbb, VVV : leptonic and
semi-leptonic
Variables for bb``+ /ET
pT ,`1/2, /ET , m``, mbb, ∆R``, ∆Rbb, pT ,bb, pT ,``, ∆φbb ``,
Variables for bb`jj + /ET
pT ,`, /ET , mjj , mbb, ∆Rjj , ∆Rbb, pT ,bb, pT ,`jj , ∆φbb `jj , ∆R` jj ,
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 36 / 51
Limits on κλ from hh→ bbγγ: Various hypotheses
[A. Adhikary, SB, R. K. Barman, B. Bhattacherjee, S. Niyogi; 2017]
Our results corroborate with ATLAS’ HL-LHC predictions
−0.86 < κλ < 7.96 CBA for κλ = 1 optimisation; SM null hypothesis
−0.63 < κλ < 8.07 BDT analysis for κλ = 1 optimisation; SM null hypothesis
−0.81 < κλ < 6.06 BDT analysis for κλ = 5 optimisation; SM null hypothesis
−1.24 < κλ < 6.49 BDT analysis for κλ = 5 optimisation; κ = 5 null hypothesis.
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 37 / 51
Non resonant di-Higgs production at the HL-LHC: bbτ+τ−
Major backgrounds: tt (hadronic, semi-leptonic and leptonic), ``bb, hbb, Zh,
ttX , bbjj
Variables for τhτh, τhτ` and τ`τ`:
pT ,bb, mbb, ∆Rbb, Mτhτh , mT2, ∆φτh1/ET, mvis
hh , pvisT ,hh, ∆Rvis
hh
pT ,bb, mbb, ∆Rbb, Mτhτl , mT2, ∆φτh/ET, ∆φτ`/ET
, mvishh , ∆Rvis
hh
pT ,bb, mbb, ∆Rbb, Mτlτl , mT2, ∆φτ`1/ET, ∆φτ`2
/ET, mvis
hh
τhτh: S/B = 0.013, S/√B = 0.74; τhτ`: S/
√B = 0.49; τ`τ`: S/
√B = 0.08
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 38 / 51
Non resonant di-Higgs production at the HL-LHC: bbτ+τ−
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 39 / 51
Non resonant di-Higgs production at the HL-LHC: bbWW ∗
Semi-leptonic: S/B = 1.2 × 10−4 and S/√
B = 0.13
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 40 / 51
Non resonant di-Higgs production at the HL-LHC: γγWW ∗
We study fully leptonic: `+`−γγ + /ET and semi-leptonic: `jjγγ + /ET states
Fully hadronic case entails an enormous background
Backgrounds: tth, Zh + jets, ``γγ + jets (leptonic) and
Wh + jets, `νγγ + jets (in addition for semi-leptonic case)
In addition demand b-jet veto to control the tth backgrounds
Variables for `+`−γγ + /ET
pT ,`(1,2), /ET , m``, mγγ , ∆Rγγ(``), pT ,``, pT ,γγ , ∆φ`` γγ
Variables for `jjγγ + /ET
pT ,`1 , /ET , mγγ , ∆Rγγ , pT ,γγ , pT ,`j , ∆φ`j γγ , ∆R`j , mT
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 41 / 51
Non resonant di-Higgs production at the HL-LHC: γγWW ∗
Leptonic: S/B = 0.40; Less than 1 signal event; Higher luminosity/energy
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 42 / 51
Non resonant di-Higgs production at the HL-LHC: γγWW ∗
Semi-leptonic: S/B = 0.11; Less than 5 signal events; Higher luminosity/energy: Perfect channel at 100 TeV colliders
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 43 / 51
Non resonant di-Higgs production at the HL-LHC: 4W
We consider `±`± + 4j + /ET (SS2`), 3`+ 2j + /ET (3`) and 4`+ /ET (4`)
Lose cleanliness (rate) upon including more jets (leptons)
Major backgrounds for SS2`: WZ , tt, W±W±, Vh, ttX , VVV , 4`
For SS2`, demand two same-sign leptons with pT > 25 GeV and at least two
jets with pT > 30 GeV
Major backgrounds for 3`: Same as before save for W±W±
For 3`, pT ,`1/2/3> 25, 20, 15 GeV and |mZ −m``| > 20 GeV
Variables for SS2`
m`±`± , ∆R`i jk , mjj
Variables for 3`
m`i`j , ∆R`i`j , m```, meff, /ET , pT ,`i , njet
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 44 / 51
Non resonant di-Higgs production at the HL-LHC: 4W
SS2`: S/B = 1 × 10−3, S/√
B = 0.11
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 45 / 51
Non resonant di-Higgs production at the HL-LHC: 4W
3`: S/B = 3 × 10−3, S/√
B = 0.20
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 46 / 51
Machinery in a nutshell
Di-Higgs samples and backgrounds generated at LO with MG5 aMC@NLO
Signal samples decayed using Pythia-6
NN23LO parton distribution function employed
Default factorisation and renormalisation scales used
Shower + hadronisation using Pythia-6
Delphes-3.4.1 used for detector simulation
Jets: anti-kT algorithm, pT > 20 GeV, R = 0.4 (FastJet)
Total energy around e, µ, γ required to be < 12%, 25%, 12% within ∆R = 0.5
b-tag efficiency: 70%, j → b: 1%, c → b: 30%
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 47 / 51
mT2
Dominant tt background can be greatly tackled with this variable
Designed for the case where a pair of equal mass particles (A and A′) decay :
A→ B + C , A′ → B ′ + C ′
B and B ′ are visible particles and C and C ′ are not observed
mT2 gives the maximal possible mass of parent particle A; provides greatest
lower bound on mA = mA′
mT2(mB ,mB′ ,bT ,bT ′ ,pTΣ,mC ,mC ′) ≡ mincT +cT ′=pΣ
T
{max(mT ,mT ′)}
m2T (bT , cT ,mb,mc) ≡ m2
b + m2c + 2(ebec − bT · cT ), with e2 = m2 + p2
T
Bounded above by top mass but unbounded below for the di-Higgs process
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 48 / 51
BDRS
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 49 / 51
N-Subjettines: Backup
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 50 / 51
tthh cross-sections: Backup
Channel Cross-section [pb]
tthh (κλ = 1) 0.016
tthh (κλ = 2) 0.022
tthh (κλ = 0) 0.014
tthh (κλ = −1) 0.013
tthh (κλ = −2) 0.015
tthh (κtthh = −0.003) 0.175
tthh (κtthh = 0.003) 0.132
ttbbbb 0.174
ttcccc 0.174
ttbb+jets 46.30
tthbb 0.076
tth+jets 12.825
tthZ 0.045
ttZZ 0.057
ttZbb 0.165
ttZ+jets 25.663
W±bbbb+ jet 0.036
W±cccc+ jet 0.092
Table: Table shows the generation level cross-sections for the signal and background processes. We require the Higgs bosons to decay to a pair of
b/c quarks, the Z -bosons to all quarks. Furthermore, we require the W±-bosons to decay leptonically. These branching ratios are included in these
cross-sections. For the signals, κλ , is the ratio of the Higgs self-coupling to the SM value and κtthh is the coupling of the four point tthh interaction.
The processes with b/c quarks in the final state in the matrix element level have a further requirement of mbb/cc/bc > 50 GeV, pT (b/c) > 25 GeV,
D-parameter > 0.4, |y| < 4.0.
Shankha Banerjee (IPPP, Durham University) 3rd FCC Physics and Experiments Workshop 51 / 51