Lomonosov (Moscow State) University

19-25 August 2021

Moscow Russia

CPV in e+e-H at 1 TeV ILC

N ATA Š A V U K A Š I N O V I Ć , T. A G AT O N V I Ć - J O V I N E T A L .
V I N C A I N S T I T U T E O F N U C L E A R S C I E N C E S , U N I V E R S I T Y O F B E LG R A D E ,FA C U LT Y O F S C I E N C E , U N I V E R S I T Y O F K R A G U J E VA C

20th Lomonosov conference on Elementary Particle Physics

Outline• Introduction• SM-like Higgs boson as a CPV mixture of CP even and odd states• Ways to probe HVV vertices (V = Z, W) in Higgs production and decays• Higgs production in ZZ-fusion, 𝜙 distributions• ILC & ILD• Method of the CP measurement• Preselection• MVA selection• Reconstructed CPV observable for signal and background• Summary

20th Lomonosov conference on Elementary Particle Physics, August 2021

2Introduction• Experimentally observed size of the CP violation (CPV) is insufficient to explain the baryon
asymmetry of the Universe  search for new sources of the CPV beyond the SM is necessary• Higgs boson is the only fundamental scalar discovered, related to quite a few unknowns (massstabilization – hierarchy problem, contribution to the energy density of the Universe, connection
to the dark matter and gravity, etc.)• It is conceivable that new sources of CPV may be introduced in an extended Higgs sector.
• ILC precision to measure the CPV mixing angle (𝜓𝐶𝑃) between the Higgs scalar andpseudoscalar states seems to be the most promising in the fermionic 𝐻 → 𝜏𝜏 decay at 250 GeV(Table 1, JHEP 2020, 139 (2020)) – see D. Jeans talk
• Other possibilities (i.e. HVV vertices) are worth exploiting as well as the other center-of-massenergies offered by the ILC staged physics programme• Here we report on the status of the on-going CPV analysis in the eeH production at 1 TeV ILC

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ILC & ILD• The International Linear Collider (ILC) is a high-luminosity linear 𝑒-𝑒+ collider with center-of-massenergy range of 250 -500 GeV (extendable to 1 TeV) aimed for precision studies in the Higgs sector
operating as a Higgs factory, detecting new physics phenomena in a direct or indirect way. It is
designed to achieve a luminosity of 1.35 · 1034 cm-2s-1 and provide an integrated
luminosity of 400 fb-1 in the first four years of running (2 ab-1 in a little over a decade).
• The electron beam will be polarized to 80 %, and the baseline plan includes an undulator-based
positron source which will deliver 30 % positron polarization• The well-defined collision energy at the ILC, highly polarized beams and low background levels,will enable these precision measurements•••••

Excellent track momentum resolution: 𝛿(1/p) = 2 × 10-5 GeV-1
Very powerful vertex detectors: 𝛿(SV) < 4 μ𝑚
Jet energy resolution: 𝜎E, jet < 3.5 % over 100 GeVLepton (electron and muon) identification efficiency: above 99 %Good hermeticity down to cos(𝜃) ≈ 0.984
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SM-like Higgs boson as a CPV mixture ofCP even and odd states• SM-like Higgs boson could be a mixture of scalar (𝐻) and pseudoscalar state (𝐴):ℎ = 𝐻 cos  + 𝐴 sin • Correlation between spin orientations of VV carries informationon the Higgs CP state• Numerous Higgs production processes at linear machines can be
exploited (hZ, WW-fusion, ZZ-fusion) at various c.m. energies• Both Higgs production and decays can be studied

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Ways to probe HVV vertices (V=Z, W)
in Higgs production and decays• hVV vertex (CPV at a loop level):• hff vertex (CPV at a tree level):• Suppressed effect in VV-fusion w.r.t. (i.e.) Higgs to  decay, but relatively highstatistics available ( ~27000 inclusively produced Higgs bosons in ZZ-fusion in 1 ab-1
at 1 TeV ILC, however approximately half in the central tracker)

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Ways to probe HVV vertices (V=Z, W)
in Higgs production and decays• Information on spin orientations of 𝑉𝑉 states is contained in theangle 𝜙 between production (decay) planes

Higgs production in ZZ-fusion• Angle between planes is the angle between unit vectors
orthogonal to those planes:𝑛1 =𝑞𝑒 − × 𝑞𝑒 −𝑖𝑓

𝑞𝑒 − × 𝑞𝑒 −𝑖𝑓and 𝑛2 =𝑞𝑒 + × 𝑞𝑒 +𝑖𝑓

𝑞𝑒 + × 𝑞𝑒 +𝑖𝒏𝟐(1)𝑓• There is more than one way (convention) to define n1 and n2
from 3 vectors forming the planes (1st plane: initial electron,final electron, Ze-; 2nd plane: initial positron, final positron, Ze+)• Orientation of n1 and n2 could be in the same hemisphere (anglebetween n1 and n2 smaller than 180 deg.) or in the opposite(angle between n1 and n2 larger than 180 deg.)

20th Lomonosov conference on Elementary Particle Physics, August 2021

𝒏𝟏x7

• Since vectors n1 and n2 have the same direction, the angle
between planes can be retrieved through the arccos
function as:

Higgs production in ZZ-fusion𝒏𝟐• 𝜙 = 𝑎 arccos( ±𝑛1 ∙ 𝑛2 )• Sign ± retain natural domain of arccos function (witch has afeature of returning angles from I and II quadrants also forangles larger than 180 deg.)• a defines how the second (positron) plane is rotated w.r.t.
the first (electron) plane; If it falls backwards (as illustrated)
a=-1, otherwise a=1. Direction of Z in the e- plane regulates
the notion of direction (fwd. or back.) by the right hand rule
• a=𝑞𝑍𝑒− ∙ 𝑛1 × 𝑛2x𝒏𝟏

𝑞𝑍𝑒− ∙ 𝑛1 × 𝑛2

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Examples of 𝜙 distributions• We are correctly reproducing  distributions at the generator
level both for h𝑉𝑉 production and decay vertices (𝑉 = 𝑍, 𝑊)• All distributions are obtained for 𝜓CP = 0eehhWW*

20th Lomonosov conference on Elementary Particle Physics, August 2021

S. Bolognesi et al.,On the spin and parity of a single produced resonance at the LHC,
arXiv:1208.4018 [hep-ph] for Higgs to ZZ* and WW* decays

9Method of the  CP measurement• Consider 𝐻𝑏𝑏 and 𝐻 𝑊𝑊  4 jets decays• 1. Cover most of the Higgs width (~ 80 %)Inclusive eeH channel 1 ab-1 @ 1 TeV ILC• 2. Avoid high cross-section 𝑒 + 𝑒 − → 𝑒 + 𝑒 − 𝛾 backgroundpresent in inclusive reconstruction• Isolate 2 leptons (e+ 𝑒 − )• Reconstruct 𝜙• Suppress background with MVA• Describe 𝜙 of the signal and background with PDFs
• Reconstruct 𝜙 of the signal from pseudo-data (𝑆 + 𝐵)
• Fit 𝜓𝐶𝑃 from the 𝜙 distribution• Repeat pseudo experiments• Combine channels

20th Lomonosov conference on Elementary Particle Physics, August 2021

s / 1 ab-1 pol (-0.8,+0.3)• 3. Combine results• Select ZZ-fusion (signal is mixed with 𝐻𝑍) using m (e+ 𝑒 − )Total #entries: 2718

1401201008060

Cut on 200 GeV402000100200300

400500600700800Mee [GeV]

Dilepton mass distribution

109001000

Higgs production in ZZ-fusion• WHIZARD v1.95, 500GeV/0.5 ab-1, 1 TeV/ 1 ab-1 , 1.4 TeV/1 ab-1, unpolarized• t-channel process, electrons (spectators) are scattered forward - not full statistics available in the tracker• Due to this fact 1 TeV is the optimal energy for this study (already at i.e. 1. 4 TeV the number of events with bothelectron is the tracker is 1/5 of the available statistics) . At 500 GeV i.e. x-section for ZZ fusion is relatively small(7.2 fb) and number of events in the tracker is order of magnitude smaller than at 1 TeV• Around 7103 eeh events with both e+ and e- in the tracker in 1 ab-1 at 1 TeV ILC with (-0.8, +0.3) polarized beams

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Preselection• ILC samples at 1 TeV, assuming ℒ = 1 ab-1, generated with LR
polarization (-1, 1) are normalized to polarization (-0.8, +0.3):
1 − 𝑃𝑒 −1 + 𝑃𝑒+1 − −0.8
𝑊pol =∙=222∙

1 + 0.3= 0.5852• Preselection: find 2 isolated electrons (𝑒 + 𝑒 − )• Goal: find electrons spectators from ZZ-fusion and reduce high crosssection backgrounds• Requirements:• Track energy: 𝐸track > 100 GeV – spectators are energetic (3.3% loss)• Impact parameter: 𝑑0 < 0.1, 𝑧0 < 1.0• Ratio of deposition: 𝑅cal > 0.95

• Optimize cone vs. track energy

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2Isolation curve: 𝐸cone< 40 𝐸track GeV − 20 GeV 220th Lomonosov conference on Elementary Particle Physics, August 2021

13Signal and background preselection efficiencies
1 TeV/1 ab−1/pol(−80%, +30%)

Sample𝜎 [fb]

Input

OutputEfficiency [%]Signal:𝑒 + 𝑒 − → 𝑒 + 𝑒 − 𝐻(𝐻 → 𝑏𝑏)

15.1

𝑁𝑡𝑟𝑢𝑒 = 1121*
norm
𝑁signal= 3600𝑁𝑡𝑟𝑢𝑒 = 875*
norm
𝑁sig/iso= 280078 %Background samples:𝑒 − 𝑒 + → 𝑒 − 𝑒 + 𝑞𝑞**2577.3𝑛𝑜𝑟𝑚
𝑁𝑒𝑣= 226160𝑒 − 𝑒 + → 𝑒ν𝑞𝑞***8963.3𝑛𝑜𝑟𝑚
𝑁𝑒𝑣= 1730000

𝑒 − 𝑒 + → 𝑞 𝑞 ∗∗9375.3

𝑛𝑜𝑟𝑚
𝑁𝑒𝑣
= 877528

𝑛𝑜𝑟𝑚
𝑁𝑒𝑣=40.0046 ‰𝛾𝛾 → 𝑞 𝑞𝑞 𝑞

126.0𝑛𝑜𝑟𝑚
𝑁𝑒𝑣=73835

𝑁𝑡𝑟𝑢𝑒 = 282
𝑛𝑜𝑟𝑚
𝑁𝑒𝑣= 930

1.26 %

𝛾𝛾 → 𝑒 − 𝑒 + 𝑞𝑞

3.1𝑛𝑜𝑟𝑚
𝑁𝑒𝑣=1817

𝑛𝑜𝑟𝑚
𝑁𝑒𝑣=50.25 %* Small current sample size, ** q=b, ***q=b,c20th Lomonosov conference on Elementary Particle Physics, August 2021

𝑁𝑡𝑟𝑢𝑒 = 1447
𝑛𝑜𝑟𝑚
𝑁𝑒𝑣= 5470
𝑁𝑡𝑟𝑢𝑒 = 428
𝑛𝑜𝑟𝑚
𝑁𝑒𝑣= 346

2.42 %
0.02 %

B:S=2.5:1
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Reconstructed CPV observable for signal and background20th Lomonosov conference on Elementary Particle Physics, August 2021

15MVA selection• MVA is trained with 14 sensitive variables: 𝑝𝑒 − , 𝑝𝑒 + , 𝐸𝑒 − , 𝐸𝑒 + , 𝑝𝑇 𝑒 − 𝑒 − , 𝑝 𝑇 𝑒 + 𝑒 + , 𝑝𝑇 𝑞1 , 𝑝𝑇 𝑞2 , 𝐸𝑞1 ,𝐸𝑞2 ,𝑚𝐻 , 𝐸𝐻 , 𝑝𝑇 𝐻 , 𝑝𝑇𝑚𝑖𝑠𝑠• Three the most sensitive observables are: 𝑚𝐻 ,𝐸𝑒 − and 𝐸𝑒 +• Best significance ~ 42 for BDT > 0.013 (training)• BDT efficiency ~ 70%, B:S= 1:2.6• Approximately ¼ of the available signal statistics analyzed

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After MVA• MVA reverses backround to signal ratio to 1: 2.6• Shapes maintained, yet large signal fluctuations• Additional signal samples will be added
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Summary• Only few results of the CPV Higgs mixing angle measurements are available from the future projects.
Primarily in the (more sensitive) Higgs fermionic decays and at lower center-of-mass energies• 1 TeV ILC offers optimal statistics (cross-section – pseudorapidity interplay) to probe CPV also in theHVV vertices• Sensitive angle ϕ between Higgs production planes is reconstructed in ZZ-fusion with the expectedbehavior for CP=0. Polarized data samples are fully simulated with 1 ab-1 (0.2 ab-1) of integrated
luminosity for background (signal). Result will be further improved since only ¼ of available signal
statistics is used
• Background ϕ distribution is CPV insensitive and it is effectively suppressed with the staged event
selection• Further improvements are on the way (additional MVA observables, combination of results fromsamples with different polarization schemes).
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BACKUP

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Higgs decays: 𝐻→𝑊𝑊* and 𝐻→𝑍𝑍*• Unit vectors orthogonal to decay planes (one possible

H → WW ∗definition):𝑛1 =𝑞𝑓 𝑉 × 𝑞𝑓(𝑉)𝑞𝑓 𝑉 × 𝑞𝑓(𝑉)and 𝑛2 =𝒏𝟐𝑞𝑓(𝑉∗ ) × 𝑞𝑓(𝑉∗ )𝑞𝑓 𝑉∗ × 𝑞𝑓(𝑉∗ )• n1 and n2 are now in ‘the opposite’ directions, to preserve
correct arcos output (in the range 0-180 deg.) define  as:*𝜙 = 𝑎 arccos(− 𝑛1 ∙ 𝑛2 )• where 𝑎 defines how the second (off-shell boson 𝑉 ∗ ) plane isrotated w.r.t. the first (on-shell boson) plane; If it falls
backwards (as illustrated) 𝑎 = −1 , otherwise 𝑎 = 1 .
Direction of the on-shell boson (𝑉) regulates the notion ofdirection (fwd. or back.)• 𝑎=𝒏𝟏𝑞𝑉 ∙ 𝑛1 × 𝑛2
𝑞𝑉 ∙ 𝑛1 × 𝑛2

• It is essential to distinguish between fermion andantifermion (jet-charge)
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20• Examples of possible definitions of n1 and n2 in ZZ-fusion:
1. 𝜙1 = arccos +𝑛1 ∙ 𝑛2

where 𝑛1 =𝑞𝑒 − × 𝑞𝑒 −𝑖𝑞𝑒 − × 𝑞𝑒 −𝑖2. 𝜙2 = arccos −𝑛1 ∙ 𝑛2

where 𝑛1 =3. 𝜙3 = arccos( +𝑛1 ∙ 𝑛2 ) where 𝑛1 =𝑓and𝑛2 =𝑓𝑞𝑒 + × 𝑞𝑒 +𝑖𝑓

𝑞𝑒 + × 𝑞𝑒 +𝑖𝑞𝑍 𝑒− × 𝑞𝑒−
𝑖𝑞𝑍 𝑒− × 𝑞𝑒−
𝑖𝑞𝑍 𝑒− × 𝑞𝑒−
𝑖𝑞𝑍 𝑒− × 𝑞𝑒−

and𝑛2 =

𝑓𝑞𝑍 𝑒− × 𝑞𝑒 +𝑓𝑞𝑍 𝑒− × 𝑞𝑒 +𝑓and𝑖𝑛2 =𝑞𝑍 𝑒+ × 𝑞𝑒 +𝑓𝑞𝑍 𝑒+ × 𝑞𝑒 +𝑓• No matter how we define a unit vector orthogonal to a production (decay) plane,
consistently defined 𝜙 leads to the same results (in production and decay).

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