Searches for hidden-sector particles with BABAR
Bertrand Echenard
Caltechon behalf of the BABAR collaboration

20th Lomonosov conference – virtual Moscow

Hidden sectors in a nutshell
What are hidden (dark) sectors

mediators• Theoretically motivated: many BSM scenarios (e.g. EWSB) andstring theory include dark sectors• Could have rich structure - SM structure is non-trivial after all• Realized that MeV-GeV hidden sector have very desirable
properties: light dark matter candidate, explanation of CP
anomaly (axion), neutrino mass (heavy neutral lepton), …

A’,S,H,a• New particle(s) that don’t couple directly to the SM, but
indirect interactions couple the two sectors via new mediators see next slide

Dark Fermions ?
Dark Forces
Dark
Higgs

• Dark matter could reside in the hidden sector, or mediate the
SM-HS interactions

Dark Matter

Motivates broad exploration of light dark sector – not just limited to dark matter
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The portals

Dim=4

New gauge boson A’ (dark photon) mixing
with SM photon/Z via kinetic mixing ε

Dim=4ScalarH2 (µφ + λφ2)

New dark scalar φ mixing with SM Higgs

FermionyHNL

New heavy neutral lepton mixing with lefthanded SM doublets and the Higgs boson

Dim=5

Vectorε BµνA’µν

Dim=4

There are a few indirect interactions allowed by Standard Model symmetries between thehidden sector and the SM – the “portals”. The lowest dimensional portals include:Axion~ + c2FF~ + c3∂µjµ) a
1/fa(c1tr(GG)

γ

A’

φ

H

N

ν

γ

a

New axion / axion-like particle coupling togauge and fermion fields

γ

And many variations with slightly different couplings(note: small variations can have big phenomenological impacts)
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Dark sectors at B-factories
B-factories offer a clean environment to study dark sectors• Well defined initial e+e- state• Hermetic detector coverage (almost 4π)• Good missing energy reconstruction• Clean displaced vertex identification in ∼1mm < cτ < 10-100cm with cτ > O(1m)being missing energy• Inclusive trigger for multi-track (N>3) hadronic events, dedicated triggers forlow-multiplicity searches

Can probe a wide variety of signatures in
the MeV-GeV range, complementing othertechniques and experimental approaches

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Wide program at BABAR
Extensive “dark sector” program conducted at BABAR over the last decade
Search for dark photon

e+e- → γ A' , A' → e+e-, µ+µe+e- → γ A' , A' → invisible

Search for “muonic dark force”
e+e- → µ+µ- Z' , Z' → µ+µ-

Search for dark bosons
e+e- → γ A' → W' W''

Search for dark Higgs boson
e+e- → h' A' , h' → A' A'

Search for self-interacting DM

e+e- → YD → A’A’A’ → 3X+X- (X=l,π)Search for axion
B→ Ka, a → γγ

Search for B-Mesogenesis

B → Baryon + DM (+mesons)

Exploratory search for dark hadrons
e+e- → πD + X,

πD → e+e-, µ+µ-

Search for leptophilic dark scalare+e- → τ+τ- h' , h' → µ+µ-

Related searches

Search for long-lived particles
Search for low-mass Higgs boson
Search for six-quark dark matter

Published
Preliminary

References in supplementary slides

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The BABAR experiment
BABAR collected ∼500 fb-1 around the ϒ(4S), ϒ(3S) and ϒ(2S) resonances between 1999 - 2008
The BABAR detector

ECM ∼10.5 GeV (at Y(4S))

Collaboration is still active more than 10 years after data taking ended !

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DARK BOSONDARK PHOTON & MUONIC DARK FORCEDark photon searches
Dark photon (A’) search in

Dark photon (A’) search in

Limits on kinetic mixing parameter

Limits on kinetic mixing parametere+e- → γA’(→ e+e-, µ+µ-)

e+e- → γA’(→ invisible)

2017

2014
PRL 113 (2014) 201801
PRL viewpoint

2021

2102.12143

PRL 119 (2017) 131804
PRL highlights

Worldwide program to further
probe these possibilities
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Visible dark photon decays

Ilten et al., JHEP 06 (2018) 004

Alternative dark photon couplings
Extensions of these portals can be constructedby gauging accidental symmetries of the SM or
individual flavor numbers, e.g.
• vector coupling to B−L current• a leptophobic B boson coupling directly tobaryon number• vector mediating protophobic force• Vector coupling to Li-Lj i,j=e,µ,τ

Constraints can be significantly weakened
depending on the model → need multiple
measurement to cover all bases

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Muonic dark force
Muonic dark force: a new force coupling only to the second and third generation of
leptons with a corresponding gauge boson Z’
Such a force could explain various anomalies observed in the muon sector (“g-2”discrepancy, proton radius puzzle), and account for dark matter as sterile neutrinos byincreasing their cosmological abundance via new interactions with SM neutrinos
Current constraints on Z’

Some constraints from neutrino physics havealready been derived, but they only indirectly probe
the existence of Z’ (with large systematics)
BABAR can directly search for a muonic dark force atcolliders via Z’-strahlung :PRD 89 (2014) 113004

e+e- → µ+µ- Z’, Z’ → µ+µ-

e+e- → µ+µ- Z’, Z’ → νν

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Muonic dark force
Search for Z’ in e+e- → µ+µ- Z’, Z’ → µ+µ-

Search for invisible and LFV Z’ decays at
Belle II with 276 pb-1 of data
PRL 124 (2020) 141801

Limits (90% CL) on Z’ coupling

PRD 94 (2016) 011102

First direct measurement, improves uponprevious bounds
Further exclude region favored by the g-2
anomaly

Full Belle II dataset should be able tosignificantly improve
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DARK SCALARDARK HIGGS BOSON & LEPTOPHILIC SCALAR

Dark Higgs boson
Search for dark Higgs boson h’• Dark photon mass is generated via the Higgs
mechanism, adding dark Higgs boson(s) to thedark sector content

αD = gD2 / 4π
gD is the dark sector gauge coupling• Can be produced via Higgsstrahlung process

Dark Higgs decay topology

e+e- → A'* → h' A‘

mh < mA’• Process is only suppressed by ε2 and sensitive tothe dark sector coupling constant αD = gD2 / 4π.

mh > 2mA’

mA’ = 2 GeV

Invisible
decays• Decay topology depends on the dark Higgs anddark photon masses: either invisible (KLOE) or
visible (h’ → A’ A’ at BABAR, Belle)

PromptdecaysMh (GeV)
B. Batell et al., PRD 79 (2009) 115008
R. Essig et al., PRD 80 (2009) 015003

Search for prompt h’ decays at BABAR:
e+e- → A'* → h' A’, h’ → A’ A’, A’ → l+l-,π+πBertrand Echenard-

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Dark Higgs boson

Belle Collaboration, PRL 114 (2015) 211801
BABAR Collaboration, PRL 108 (2012) 211801

No significant signal observed, set limits on the product αDε2

Limits on kinetic mixing ε2 slightly better than direct production for αD = 1/137
On-going search for invisible dark Higgs decays at Belle II
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Leptophilic dark scalar
Search for a leptophilic dark scalar φL in e+e- → τ+τ- φL, φL → l+l- (l=e,µ)More generally, a new light gauge singlet could directly mix with the Higgs boson via thescalar portal.
A new leptophilic scalar interacting mainly with leptons rather than quarks could escapethe current constraints and explain the g-2 anomaly (1606.04943, 1605.04612) and the
KOTO excess (2001.06522)
Mass proportional coupling imply that this scalar is produced preferentially via its coupling
to the tau, and decays mainly to the most massive lepton-pair kinematically accessible
Analysis strategy••••

Final dimuon mass distribution

Consider all 1-prong decays of the tau
Train BDT to increase signal purity
Optimize analysis for each final state andprompt or long-lived φL
Extract signal as a function of dark scalarmass with fits over sliding intervals

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Leptophilic dark scalar
Search for a leptophilic dark scalar φL in e+e- → τ+τ- φL, φL → l+l- (l=e,µ)PRL 125 (2020) 181801(prompt)

Significant improvement over previous bounds
The g-2 region is excluded for almost all masses
below the ditau threshold!
Belle II should be able to further improve
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AXIONAXION-LIKE PARTICLE IN B DECAYSAxion like particle (ALP)
What are axion like particles• Pseudo-Goldstone bosons ubiquitous in BSM physics, coupling predominantly to pairof bosons with non-renormalizable coupling constant suppressed by some heavy scale• Low-mass ALP can mediate dark sector – standard model interactions• Most searches at low energies focus on photon or gluon couplings as effects from
W± coupling are suppressed by GF2
Search for ALP in B → Ka, a → γγ decays• FCNC are extremely suppressed in the SM, so they are aperfect testbed to search for ALP emission by W± boson• Search for ALP in B → Ka decays, exploiting b → s transition• Consider a model in which the axion couples only directly to
W± bosons (photon coupling via triangle diagram)• Axion lifetime becomes important at low masses andcouplings (τ ∼ 1/ma3gaW2) → long-lived axion
E. Izaguirre et al., PRL 118 (2017) 111802
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Axion like particle (ALP)
Search for diphoton decay of an axion (a) in B → Ka, a → γγ
Analysis strategy••••

Combine well-identified K with two photons to form B candidate
Apply kinematic fit to improve axion mass resolution
Train 2 BDTs to separate signal from e+e- → qq (q=u,d,s,c) and e+e- → BB backgounds
Extract signal as a function of axion mass with fits of a mass peak over smooth background
Final mγγ mass distribution

Peaking background at π0,η,η’ masses,
2.6σ excess consistent with B → K ηc, ηc → γγ

Signal yields and local significances

No significant signal is observed
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Axion like particle (ALP)
Extract 90% CL limit on the production cross-section and the a-W coupling parameter gaW
Prompt decays
90% CL upper limits on coupling gaW

Displaced decays

Improvement up to two orders of magnitude
over a large mass range
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SELF-INTERACTING DARK MATTER
Minimal dark sector modelSelf-interacting dark matter
Search for darkonium• Dark sector with a dark (anti-)fermion coupling to the dark photon• For sufficiently large values of the dark fermion-dark photon coupling constant αD, adark fermion – anti-fermion pair could form a bound state → darkonium• The two lowest energy bound states are denoted ηD (JPC = 0++) and YD (JPC = 1--), in
analogy with SM• Can be produced via e+e- → A’ ηD, ηD → A’ A’ and e+e- → γYD, YD → A’ A’ A’

Search for YD in e+e- → γYD, YD → A’ A’ A’, A’ → X+X- (X=e,µ,π)• Dark photon subsequently into pairs of leptons or hadrons• Dark photon lifetime can be large for small values of the
kinetic mixing ε and mass → prompt and displaced vertex
analyses

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Self-interacting dark matter
Search for YD in e+e- → γYD, YD → A’ A’ A’, A’ → X+X- (X=e,µ,π)Analysis strategy
•
•
•
•
•

Final states consist of three pairs of leptons or pions, with two or more electrons / muons
Three dark photons have similar masses
Recoil mass against YD compatible with the photon hypothesis
Do not require presence of ISR photon in the calorimeter, but it must be compatible with signal
hypothesis if emitted inside the calorimeter acceptance
Scan the YD – A’ mass plane to extract signal – estimate background with neighboring mA’ bins
Final YD candidate sample (prompt)

Number of events in signal window (prompt)

BABAR prel.

BABAR prel.

Prompt and displaced vertex analyses compatible with null hypothesis
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Self-interacting dark matter
Extract 90% CL limit on the kinetic mixing parameter ε for different αD values
Constraints on ε for αD = 0.5mYD = 7 GeV

mYD = 9 GeVεεBABAR prel.

Constraints on εmA’ (GeV)
Constraints on εαD = 0.5

mA’ (GeV)
2106.08529, submitted to PRL

Improve constraints on kinetic mixing forlarge values of dark sector coupling
constant and large YD masses

ε

BABAR prel.

BABAR prel.

mA’ (GeV)
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EPILOGUELOOKING FORWARD & CONCLUSION

More to comeOn-going searches for dark sector / dark matter at BABAR
Dark matter and baryogenesis: Search for signature of a
new mechanism of baryogenesis and dark matterproduction in which both the dark matter relic abundance
and the baryon asymmetry arise from neutral B meson
oscillations and decays

PRD 99 (2019) 035031

PRD 91 (2015) 053006

Heavy neutral lepton: Search for a heavy neutral lepton inτ → πππν decays. The heavy neutral lepton distorts the
distribution of the invariant mass and energy of the πππsystemThere is always something new to search for….

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More generally
There is a worldwide effort to search for feebly interacting particles, and BABAR
is only one of the many experiments involved in these searches

1901.09966

Two recent references (among others)
Physics Beyond Colliders at CERN, arxiv: 1901.09966
FIPs 2020 report, arxiv:2102.12143
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Summary
Hidden sectors have emerged as an intriguing possibility to explain dark
matter, and more generally to search for light new physics
Low-energy, high-intensity colliders offer an ideal environment tocomprehensively probe hidden sectors
BABAR has conducted an extensive program to search for hidden sector
signatures, and set stringent limits on their existence
There is a worldwide effort to explore hidden sectors, and BABAR is one of
the many experiments involved in these searches
There are still amazing possibilities at the GeV-scale, and dedicatedprograms are underway to explore them.

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ADDITIONAL MATERIAL

Useful references
Search for dark photon

Search for a Dark Photon in e+e- Collisions at BaBar, Phys. Rev. Lett. 113, 201801 (2014)
Search for Invisible Decays of a Dark Photon Produced in e+e- Collisions at BaBar, Phys. Rev. Lett. 119, 131804 (2017)

Search for muonic dark force

Search for a muonic dark force at BABAR, Phys. Rev. D 94, 011102 (2016)

Search for dark bosons

Search for a Narrow Resonance in e+e- to Four Lepton Final States, arXiv:0908.2821

Search for dark Higgs boson

Search for Low-Mass Dark-Sector Higgs Bosons, Phys. Rev. Lett. 108, 211801 (2012)

Search for leptophilic dark scalar

Search for a Dark Leptophilic Scalar in e+e- Collisions, Phys. Rev. Lett. 125, 181801 (2020)

Search for six-quark dark matter

Search for a Stable Six-Quark State at BABAR, Phys. Rev. Lett. 122, 072002 (2019)

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Visible dark photon decays
Dilepton mass distributions

A dark photon can be produced in
e+e- → γ A’, A’ → e+e-, µ+µe+
e-

e+

γ
εe

A’

l+
l-

BABAR

γ

e-

l+

e +e -l-m(e+e-) (GeV)

Search for a narrow resonance over large
QED background:•

2 tracks + 1 photon•

Constrained fit (beam energy + vertex)•

Particle identification (e/mu)•

Kinematic cuts to improve purity•

Quality cuts on tracks and photons

BABARµ+µmred (GeV)

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Visible dark photon decays
Signal significanceA dark photon can be produced ine+e-e+e- → γ A’, A’ → e+e-, µ+µe+
e-

e+

γ
εe

A’

l+
l-

BABAR

γ

e-

l+
l-

Search for a narrow resonance over large
QED background:µ+µBABAR•

2 tracks + 1 photon•

Constrained fit (beam energy + vertex)•

Particle identification (e/mu)•

Kinematic cuts to improve purity•

Quality cuts on tracks and photons

BABAR

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Invisible dark photon decays
At e+e- colliders, we can search for e+e- → γ A' , A' → invisible by tagging the recoil
photon in “single photon” events
BABAR collected ∼53 fb-1 of data with dedicated single photon triggers during its last yearof data taking
Analysis overview• Missing energy and momentum is best signature• Hermeticity is key, but need to allow somemachine background• Search strategy: select single-photon final state,then look for a bump in missing mass mX (or Eγ)• Main backgrounds: e+e- → γγ and e+e- → γ e+ewith particles outside detector acceptance• Selection variable categories: photon quality,#tracks, extra Ecalorimeter, missing mass/energy
and muon detector information
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Muonic dark force
Search for Z’ in e+e- → µ+µ- Z’, Z’ → µ+µ- events
Analysis overview• Analysis based on data collected at Y(4S), Y(3S) and Y(2S)• Four tracks and no extra neutral energy (Eextra < 200 MeV)
• Particle identification: 2 same-sign tracks identified as muon
• Four-muon invariant mass within 500 MeV of nominal CM-energy• Veto events with a dimuon candidate within 10 MeV of the ϒ(1S) mass for theϒ(2S) and ϒ(3S) dataset to reject ϒ(2S,3S) → ππ ϒ(1S), ϒ(1S) ’ µµ
• Kinematic fit imposing beam-energy constraint is finally performed, but noconstraints on the χ2 are applied
We perform a blind analysis, the selections criteria are optimized on a small subset (5%) of
the data, which is subsequently discarded
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Muonic dark force
We extract the signal separately for the data at the Y(4S), Y(3S) and Y(2S) by performing aseries of fits to the reduced dimuon mass for each sample
For each mass hypothesis, we fit over a fixed range of 0-0.3 GeV (mR < 0.2 GeV) or awindow corresponding to 50 signal resolution (mR > 0.2 GeV). A region of ± 30 MeV around
the J/ψ is excluded
Most significant fit mR = 0.79 GeV

Fit mR = 0.05 GeV
Y(4S)

Y(4S)

BABAR

BABAR

Local /global significance: 4.3σ /1.6σ

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Sterile neutrino dark matter
Dark matter model of sterile neutrino N (SM gauge singlet). After EWSB, Standard Model
neutrinos get a (small) mass and the SM & sterile neutrino mix

Sterile neutrino live and die by this mixing

𝐹𝐹𝛼𝛼𝛼𝛼 𝐻𝐻
sin𝜃𝜃𝛼𝛼𝛼𝛼 =𝑀𝑀𝑁𝑁Dodelson Widrow 1993

Can the mixing angle be large enough to produce enough sterile neutrinos to account for
dark matter and small enough to suppress decays?
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Sterile neutrino dark matter
Constraints from astrophysics (monochromatic x-ray linefrom N’ γν decays and small scale structures) imply thatthe mixing angle is too small to produce the observed relicdensity
BUT, a new neutral interaction coupling to leptons andneutrinos could boost the sterile N production without
increasing the decay

Horiuchi et al. 2013

New dark force coupling to 2nd / 3rd generation of leptons(Lµ-Lτ, anomaly free). The corresponding gauge boson Z’
must be light – O(GeV) or less – to avoid constraints frommagnetic dipole measurements and provide the correct
rate enhancement
Z’ decays to muons, taus and neutrinos when kinematicallyaccessible

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Dark Higgs boson
Wrong-sign combinations

Search for dark Higgs boson h’

BABAR

Analysis overview• Search for events with three dark
photons of similar mass, consistent with
e+e- → A’ A’ A’ hypothesis• Six candidates are selected from the full
BABAR dataset, no event with 6 leptons• Estimate background from- wrong-sign combinations, e.g.
e+e- → (e+e+) (e-e-) (µ+µ-)- sidebands from final sample
Distribution consistent withpure background hypothesis
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Leptophilic dark scalar
Validate efficiency with control samples and derive corresponding corrections
Dielectron
Sample of Ks → π+π- in τ decays
obtained with a similar selection
procedure

Dimuon
BDT response for data with recoilpT > 2 GeV to suppress non-modelled
components

Data globally well reproduced by MC predictions, corrections between 2-7%
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Leptophilic dark scalar
Final mass spectra for each final state and lifetime
Dielectron (prompt)

Dimuon (prompt)

Dielectron (displaced)

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Leptophilic dark scalar
Extract signal as a function of dark scalar mass with fits over sliding intervals(background MC independent)
Fit 966 mass hypotheses, step size taken as signal
resolution (1-50 MeV depending on mφ)dielectron

Fit includes signal, peaking and continuum
background components:

BABAR

mee (GeV)

dimuon• Signal modeled from signal MC and interpolated
between simulated mass points• Continuum background modelled by second or thirdorder polynomials• Peaking background (π0, J/ψ, ψ(2S)) modelled frombkg MC

Signal efficiency validated by data/MC comparison of sideband regions. Derive correction
factors (2-7%) applied to MC

BABAR

mµµ (GeV)

Signal efficiency varies between 0.2-26%
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Axion like particle (ALP)
Extract signal as a function of axion mass with fits over sliding intervals(prompt decays, background MC independent)
Fit 476 mass hypotheses, step size taken as
signal resolution (8-14 MeV)
Fit includes signal, peaking and continuum
background components:• Signal modeled from signal MC and interpolated
between simulated mass points• Continuum background modelled by first or
second order polynomials• Peaking background modelled from bkg MC

Signal MC resolution validated by data/MC
comparisons of B → Kπ0 and B → Kη , found to
be consistent within 3%
Signal efficiency varies between 2%-33%

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