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Doojin Kim

KEK Theory Meeting on Particle Physics Phenomenology

December 6th, 2018

PRL119 (2017) 161801, PLB780 (2018) 543, PRD98 (2018) 075027, JHEP1808 (2018) 155, more in progress,

in collaboration with H. Alhazmi, W. Bonivento, A. Chatterjee, A. De Roeck, K. Dienes, G. Giudice,

K. Kong, P. Machado, Z. Moghaddam, J.-C. Park, S. Shin, B. Thomas, L. Whitehead, J. Yu

Doojin Kim, University of Arizona 3rd KIAS-NCTS-KEK Workshop

Contents

I. Physics Motivation

II. Signatures and Search

III. Phenomenology: Experimental Sensitivities

IV. Conclusions

Doojin Kim, University of Arizona 3rd KIAS-NCTS-KEK Workshop-1-

Current Status of Conventional Dark Matter Searches

No observation of dark matter signatures via non-gravitational interactions (many

searches/interpretations designed/performed under WIMP/minimal dark-sector

scenarios) merely excluding more parameter space in dark matter models

[Cushman, Calbiati and McKinsey (2013); Baudis (2014)] [CMS mono-photon search (2014)]


Conventional Approach

Traditional approaches for DM searches:

Weak-scale mass

Weakly-coupled

Minimal dark sector

Elastic scattering

Non-relativistic


Modified approaches for DM searches:

Other mass scale: e.g., PeV, sub-GeV,

MeV, keV, meV, …

Weaker coupling to the SM: e.g.,

vector portal (dark photon), scalar

portal, axion portal, …

“Flavorful” dark sector: e.g., more

dark matter species, unstable heavier

dark sector states, …

Inelastic scattering (i.e., up-scatter to

an “excited” state)

Relativistic

-2-

Conventional vs. Nonconventional Approach

Traditional approaches for DM searches:

Weak-scale mass

Weakly-coupled

Minimal dark sector

Elastic scattering

Non-relativistic


Two-component Boosted DM Scenario

𝜒0

𝜒0

𝜒1

𝜒1

SM

SM

A possible relativistic source: BDM scenario (cosmic frontier), stability of the two DM species ensured by separate symmetries, e.g., 𝑍2 ⊗ 𝑍2

′ , 𝑈 1 ⊗ 𝑈 1 ′, etc.



𝜒0

𝜒0

𝜒1

𝜒1

SM

SM


′ , 𝑈 1 ⊗ 𝑈 1 ′, etc.

𝑌0 𝑌1

Freeze-out first

Dominant relic

“Assisted” freeze-out mechanism[Belanger, Park (2011)]



𝜒0

𝜒0

𝜒1

𝜒1

SM

SM


′ , 𝑈 1 ⊗ 𝑈 1 ′, etc.

𝑌0 𝑌1

Freeze-out first

Dominant relic

“Assisted” freeze-out mechanism[Belanger, Park (2011)]

Freeze-out later

𝑌1Negligible, non-relativistic relic


“Relativistic” Dark Matter Search

Heavier relic 𝜒0: hard to detect it due to tiny/negligible coupling to SM

Lighter relic 𝜒1: hard to detect it due to small amount

𝜒0

𝜒0

𝜒1

𝜒1

SM

SM


“Relativistic” Dark Matter Search

𝜒0

𝜒0

𝜒1

𝜒1

𝜒1

(Galactic Center at CURRENT universe) (Laboratory)

becomes boosted, hence relativistic!(𝛾1 = 𝑚0/𝑚1)

[Agashe, Cui, Necib, Thaler (2014)]

Heavier relic 𝜒0: hard to detect it due to tiny/negligible coupling to SM

Lighter relic 𝜒1: hard to detect it due to small amount

𝜒0

𝜒0

𝜒1

𝜒1

SM

SM


Boosted DM Detection

Flux of boosted 𝜒1 near the earth

Setting 𝜎𝑣 𝜒0𝜒0→𝜒1𝜒1 to be ~10−26 cm3s−1 and assuming Navarro-Frenk-White DM halo profile, a

standard profile, one finds

ℱ𝜒1 ∝ (interaction strength) × (𝜒0 number)2

~0.8 × 10−7cm−2s−1𝜎𝑣 𝜒0𝜒0→𝜒1𝜒110−26cm3s−1

20 GeV

𝑚0

2

from DM number density

ℱ𝜒1~10−7cm−2s−1 for 𝒪(20 GeV) mass of 𝜒0


Boosted DM Detection

Flux of boosted 𝜒1 near the earth

Setting 𝜎𝑣 𝜒0𝜒0→𝜒1𝜒1 to be ~10−26 cm3s−1 and assuming Navarro-Frenk-White DM halo profile, a

standard profile, one finds

ℱ𝜒1 ∝ (interaction strength) × (𝜒0 number)2

~0.8 × 10−7cm−2s−1𝜎𝑣 𝜒0𝜒0→𝜒1𝜒110−26cm3s−1

20 GeV

𝑚0

2

from DM number density

ℱ𝜒1~10−7cm−2s−1

Too small for small-volume detectors (e.g., conventional

WIMP detectors) large-volume (neutrino) detectors

motivated

Super-/Hyper-Kamiokande (SK/HK): active

volume of 22.4 kt/560 kt

SK

SKY

for 𝒪(20 GeV) mass of 𝜒0

HK


SK Official Results for Elastic Boosted Dark Matter Search

[SK Collaboration, arXiv:1711.05278]m0 (GeV)

m1=200 MeV, mX=20 MeV, g’=0.5 m0 (GeV)


Contents




IV. Conclusions


Benchmark Model: Building Blocks

Vector portal (e.g., dark photon scenario)

Fermionic DM

𝜒2: a heavier (unstable) dark-sector state

Flavor-conserving interaction elastic scattering

Flavor-changing interaction inelastic scattering

ℒint ∋ −𝜖

2𝐹𝜇𝜈𝑋

𝜇𝜈 + 𝑔11 𝜒1𝛾𝜇𝜒1𝑋𝜇 + 𝑔12 𝜒2𝛾

𝜇𝜒1𝑋𝜇 + h. c.+(others)

𝑋

𝜒1𝜒1𝑔11

𝑋

𝑒−

𝑒+

𝜖

𝑋

𝜒2𝜒1𝑔12

-7-


Benchmark Model: Building Blocks

Vector portal (e.g., dark photon scenario)

Fermionic DM

𝜒2: a heavier (unstable) dark-sector state

Flavor-conserving interaction elastic scattering

Flavor-changing interaction inelastic scattering

ℒint ∋ −𝜖

2𝐹𝜇𝜈𝑋

𝜇𝜈 + 𝑔11 𝜒1𝛾𝜇𝜒1𝑋𝜇 + 𝑔12 𝜒2𝛾

𝜇𝜒1𝑋𝜇 + h. c.+(others)

𝑋

𝜒1𝜒1𝑔11

𝑋

𝑒−

𝑒+

𝜖

𝑋

𝜒2𝜒1𝑔12

-7-

Today’s focus


Inelastic Boosted Dark Matter (iBDM) Signatures

-8-



𝑒−/𝑝

𝜒2

𝑋∗ 𝜖

𝑔12

-8-



𝑒−/𝑝

𝑒−

𝑒+

𝜒2

𝑋∗𝑋(∗)

𝜖𝜖

𝑔12 𝑔12

-8-



𝑒−/𝑝

𝑒−

𝑒+

𝜒2

𝑋∗𝑋(∗)

𝜖𝜖

𝑔12 𝑔12

𝑝- or 𝑒-scattering (primary) Decay (secondary)

-8-

(cf. DM vs. iDM in Paddy’s talkBDM vs. iBDM)



𝑒−/𝑝

𝑒−

𝑒+

𝜒2

𝑋∗𝑋(∗)

𝜖𝜖

𝑔12 𝑔12

𝑝- or 𝑒-scattering (primary) Decay (secondary)

Everything happens inside a detector fiducial volume.

The secondary interaction point may be displaced due to either long-lived

𝜒2 – when it decays via an off-shell 𝑋 (i.e., 𝑚2 < 𝑚1 + 𝑚𝑋) – or

on-shell 𝑋 – when kinetic mixing parameter is sufficiently small.

If 𝛿𝑚 = 𝑚2 − 𝑚1 is large enough, other final states (e.g., 𝜇+𝜇−, 𝜋+𝜋−, etc) are available.

-8-

(cf. DM vs. iDM in Paddy’s talkBDM vs. iBDM)


𝒑-Scattering vs. DIS

𝜒2

𝑋∗

𝜖

𝑝

If a momentum transfer is too large, a proton may break apart.

What is large? A Super-K simulation study [Fechner et al, PRD

(2009)] showed about 50 % events accompany (at least) a pion

or a secondary particle for 𝑝𝑝 ≈ 2 GeV.

We categorize any event with 𝑝𝑝 < 2 GeV as the 𝑝-scattering

(i.e., simplified step-function-like transition). 𝑝

-on

ly e

ven

ts f

ract

ion

𝑝𝑝

1

0.5

2 GeV

-9-


𝒑-Scattering vs. DIS: “Semi”-Numerical Study

-10-

We study 𝜎𝜒1𝑝cut/𝜎DIS where 1.07 GeV < 𝑝𝑝 < 2 GeV (Cherenkov detector) is applied to 𝜎𝜒1𝑝 while no cuts

are imposed to 𝜎DIS.



-10-



𝑚𝑋

[GeV

]

𝑚1 [GeV]

𝜎𝜒1𝑝cut/𝜎DIS, 𝐸1 = 50 GeV

/𝜎DIS, 𝐸1 = 50 GeV

DIS more important? Maybe, not (too much penalty on the p-scattering, not a fair game!



-10-



𝑚𝑋

[GeV

]

𝑚𝑋

[GeV

]

𝑚1 [GeV] 𝑚1 [GeV]

𝜎𝜒1𝑝cut/𝜎DIS, 𝐸1 = 50 GeV 𝑁DIS/year/kt, 𝐸1 = 50 GeV,𝑚2 = 1.5𝑚1

/𝜎DIS, 𝐸1 = 50 GeV

𝑔12 = 1, 𝜖 = 10−4

DIS more important? Maybe, not (too much penalty on the p-scattering, not a fair game!)

The expected number of DIS events is indeed small (even before applying cuts).


Background Consideration

Atm.-𝜈 may induce multi-track events (which could be backgrounds)

The dominant source

𝝂𝒆-induced C.C. events

Other subdominant sources

N.C. events: smaller cross section

𝜈𝜏-induced: too small flux, hence negligible

𝜈𝜇-induced C.C.: leaving an energetic (primary) muon (which can be tagged easily)

𝜈𝑒±

𝑝/𝑛

𝑒±

𝑊𝜋±

𝜋±𝑒±

𝜈

𝑒±

𝜈𝜈𝜈

e.g. 𝜋± → 𝜇±𝜈 → 𝑒±𝜈𝜈𝜈, 𝜋± → 𝑒±𝜈


Expected Number of ν-induced Background Events

𝜈𝑒-flux [SK Collaboration, 1502.03916] 𝜈𝑒-cross section [Formaggio, Zeller, 1305.7513]

RES RES


Expected Number of ν-induced Background Events

𝜈𝑒-flux [SK Collaboration, 1502.03916] 𝜈𝑒-cross section [Formaggio, Zeller, 1305.7513]

Most DIS events result in messy final states, not mimicking signal events, while a majority of

resonance events may create a few mesons in the final state [Formaggio, Zeller, 1305.7513].

12 events/kt/yr are potentially relevant, i.e., 4600 events/yr for 380 kt (a full fiducial

mass of HK)

RES RES


SK Study on Multi-track Events

[SK Collaboration (2012)]

Energy of hardest e-like track


SK Study on Multi-track Events

[SK Collaboration (2012)]

Energy of hardest e-like track

Assuming that all 4600 events belong to the category of 1.33-2.5 GeV, ~1000 events/yr and ~100 events/yr involve

two and three tracks.

Decent level of particle identification at HK Cherenkov detectors can suppress such events further (e.g.,

identifying decaying particles such as pions).

Decent vertex resolution (28 cm for 𝐸 = 0.5 GeV) allows for “displaced” signal events: typical displaced vertex

> 50 cm in much of well-motivated parameter space.

Zer0 background search is achievable! (dedicated study in progress)


Contents




IV. Conclusions


Reminder for the Signal of Interest

Remember that dark photon is a “player” in the benchmark model, allowing us to study

phenomenology of dark photon!

𝑒−

𝑒−

𝑒+

𝜒2

𝑋𝑋

Scattering (primary) Decay (secondary)

𝜖𝜖

𝑔12 𝑔12


Event Selection

Selection criteria based on detector performance of Super-/Hyper-K

𝑝th,𝑒 > 0.1 GeV

𝑝th,𝑝 > 1.07 GeV and 𝑝𝑝 < 2 GeV

Δ𝜃𝑝/𝑒−𝑖 = 3° for 𝑝𝑝/𝑒 < 1.33 GeV, Δ𝜃𝑝/𝑒−𝑖 = 1.2

° for 𝑝𝑝/𝑒 > 1.33 GeV (𝑖 = the other

particles)

Both primary and secondary interaction points should appear inside the detector.


Exploring Dark Photon Parameter Space

Case study 1: mass spectra of 𝑚𝑋 > 2𝑚1, 𝜒1𝑇 → 𝜒2𝑇, 𝜒2 → 𝑋∗ → 𝜒1𝑒

−𝑒+ (𝑇 = 𝑒− or 𝑝)

1-year data collection, a fiducial mass of 380kt, 𝑔12 = 1, and a zero background assumption are taken.

HK can probe the uncovered parameter region by up to an order of magnitude in the 𝜖 axis.

No sensitivity is available in the p-scattering channel with 𝐸1 = 0.5 GeV due to threshold (𝑝th,𝑝 = 1.07 GeV vs.

𝑝th,𝑒 = 0.1 GeV).

p-scattering begins to have signal sensitivity with larger 𝐸1, but explores not much due to threshold and angular

resolution (𝜃𝑝/𝑒 = 3° for 𝑝 > 0.1 GeV). A clever search strategy is needed?!


Exploring Dark Photon Parameter Space: Modified Selection

Case study 1: mass spectra of 𝑚𝑋 > 2𝑚1, 𝜒1𝑇 → 𝜒2𝑇, 𝜒2 → 𝑋∗ → 𝜒1𝑒

−𝑒+ (𝑇 = 𝑒− or 𝑝)

We require “displaced” (more than 45 cm) events only, reducing 𝑝th,𝑒 to 10 MeV (for which the vertex resolution is

45 cm).

The case in the left-hand side does not benefit much, as a majority of events are not substantially displaced.

The modified selection scheme allows the proton channel (in the right-hand side) to access some unexplored

parameter space.

The combination between the original and the modified selection schemes would improve the signal sensitivity.


Exploring Dark Photon Parameter Space

Case study 2: mass spectra of 𝑚𝑋 < 2𝑚1, 𝜒1𝑇 → 𝜒2𝑇, 𝜒2 → 𝑋(∗) → 𝜒1𝑒

−𝑒+ (𝑇 = 𝑒− or 𝑝)

1-year data collection, a fiducial mass of 380kt, 𝑔12 = 1, and a zero background assumption are taken.

HK can probe the unexplored parameter space in the 𝜖 axis.

A transition happens at 𝛿𝑚 = 𝑚𝑋 where 𝜒2 decays to an 𝑒−𝑒+ pair through on-shell 𝑋 ↔ off-shell 𝑋.

p-scattering begins to have signal sensitivity with larger 𝐸1, but explores not much due to threshold (𝑝th,𝑝 = 1.07

GeV vs. 𝑝th,𝑒 = 0.1 GeV) and angular resolution (𝜃𝑝/𝑒 = 3° for 𝐸 > 0.1 GeV). A clever search strategy is

needed?!


Exploring Dark Photon Parameter Space: Modified Selection

Case study 2: mass spectra of 𝑚𝑋 < 2𝑚1, 𝜒1𝑇 → 𝜒2𝑇, 𝜒2 → 𝑋(∗) → 𝜒1𝑒

−𝑒+ (𝑇 = 𝑒− or 𝑝)

We require “displaced” (more than 45 cm) events only, reducing 𝑝th,𝑒 to 10 MeV (for which the vertex resolution is

45 cm).

The case in the left-hand side does benefit a little, as some fraction of events are substantially displaced but some

final state particles deposit a small amount of energy.

The modified selection scheme does not help the proton channel access some unexplored parameter space.

The combination between the original and the modified selection schemes would improve the signal sensitivity.


Model-independent Sensitivity

Any model-independent sensitivity just like 𝜎 vs. 𝑚DM in conventional WIMP searches?

Experimental sensitivity with e.g., 90% C.L.

𝜎𝜖: scattering cross section between 𝜒1 and (target) electron

ℱ: flux of incoming boosted 𝜒1 (possibly BDM production mechanism-dependent)

𝐴: acceptance

𝑡exp: exposure time

𝑁𝑒: total # of target electrons

𝑁90: 90% C.L. for a given background assumption

Controllable

Determined by distance between the primary (ER) and the secondary vertices, cuts, energy threshold,

etc. Depending on analyses, some factors can be absorbed into 𝜎𝜖.

𝑁sig = 𝜎𝜖ℱ𝐴𝑡exp𝑁𝑒 > 𝑁90


Example Model-independent Sensitivity

𝑁90 for a zero-BG assumption

Evaluated under the assumption

of cumulatively isotropic 𝜒1 flux

ℓlab different event-by-event, so taking

ℓlabmax for more conservative limit

𝜎𝜖ℱ >2.3

𝐴( ℓlab)𝑡exp𝑁𝑒


Interpretations

★

★

♦

♦


Conclusions and Outlook

The boosted (light) dark matter search is promising and provides a new direction to

study dark matter phenomenology.

Theoretical/experimental studies have been actively conducted and in progress.

These ideas can be tested in Hyper-Kamiokande experiment.

To get around detector acceptance issues, hence maximize the signal sensitivity in HK, it is

highly desired to design clever search strategies.

𝑣𝐷𝑀Scattering

Non-relativistic(𝑣𝐷𝑀 ≪ 𝑐)

Relativistic(𝑣𝐷𝑀~𝑐)

elastic Direct detection Boosted DM (eBDM)

inelastic inelastic DM (iDM) inelastic BDM (𝒊BDM)

thank you !

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