Brian Batell University of Pittsburgh

Status of Light Dark Sectors

Annual Theory Meeting, Durham University 18 -20 December 2017

measσ) / meas - Ofit

(O-3 -2 -1 0 1 2 3

)2Z

(M(5)hadα∆

tmbmcmb0Rc0RbAcA

0,bFBA

0,cFBA

)FB

(QlepteffΘ2sin

(SLD)lA(LEP)lA

0,lFBAlep0R

0hadσ

ZΓZM

WΓWMHM 0.0 (-1.4)

-1.2 (-0.3)0.2 (0.2)0.2 (0.0)0.0 (0.3)

-1.6 (-1.7)-1.1(-1.0)-0.8 (-0.7)0.2 (0.4)

-2.0 (-1.7)-0.7 (-0.8)0.9 (1.0)2.5 (2.7)0.0 (0.0)0.6 (0.6)0.0 (0.0)

-1.2 (-1.2)0.0 (0.0)0.0 (0.0)0.4 (0.0)-0.1 (0.0)

measurementHwith M measurementHw/o M

Plot inspired by Eberhardt et al. [arXiv:1209.1101]

G fitter SM

Sep 13

The Standard Model works really well!!

102 104 106 108 1010 1012 1014 1016 1018 1020!0.04

!0.02

0.00

0.02

0.04

0.06

0.08

0.10

RGE scale Μ in GeVHiggsquarticcouplingΛ

3Σ bands inMt % 173.1 & 0.6 GeV !gray"Α3!MZ" % 0.1184 & 0.0007!red"Mh % 125.7 & 0.3 GeV !blue"

Mt % 171.3

Αs!MZ" % 0.1163Αs!MZ" % 0.1205Mt % 174.9

FlavorElectroweak

QCD

HiggsVacuumStability

These problems strongly suggest there is particle physics beyond the Standard Model

Conceptual mysteries & hints:

• Naturalness (Higgs Mass & C.C.)

• Fermion Masses and Flavour Puzzle• Strong CP Problem

• Grand Unification

• Inflation• Quantum Gravity

Empirical facts requiring new dynamics:

• Dark Matter• Neutrino Masses

• Matter-Antimatter Asymmetry of the Universe

Possibilities for new physics:

#1. New heavy states states; masses much larger than the weak scale

Search for anomalous phenomena or rare processes with precision measurements

[See talk by J. Mattias]

Possibilities for new physics:

#2. New light charged states; masses near the weak scale ~ 100 GeV

T

T

g

g

t

t†

Produce states directly at high energy colliders like LHC

Possibilities for new physics:

#3. New light gauge singlet states, masses can be below the weak scale

SM

SM

Singlet

Singlet

L � O(p)SMO(q)

singlet

⇤p+q�4

Generic “Portal”

Probe these states directly using high intensity/precision experiments

��-�� ��-� ��-� ��-� �� ���

��-��

��-�

��-�

��-�

Mass of particle (GeV)

Cou

plin

g to

Sta

ndar

d M

odel

SUSYTechnicolor

WIMPs…

Where is the New Physics?

Dark MatterSterile Neutrinos

Axion, ALPs...

Intensity Frontier

Energy Frontier

g2

M2⇠ GF

• Gauge singlets - not charged under SM gauge symmetries

• Set of new particles with following properties:

• May be very light, well below weak scale ~100 GeV

• They may interact weakly with ordinary matter through a “portal”

StandardModel

Portal Dark Sector

The Dark Sector Paradigm

Z V

X

X

κV �

✏

(µS + �S2)H†H

Neutrino portal

Higgs Portal

Vector Portal✏

2Bµ⌫V

µ⌫

yLHNNL

H

H H

S

Portals

9

Motivations for Dark Sectors

• Dark Matter

• Neutrino Mass

• Strong CP (axion)

• Flavor (flavons)

• SUSY (SUSY breaking, gravitino)

• Electroweak naturalness (Neutral Naturalness, Relaxion, NNaturalness)

• Inflation

10

Historical precedent

• In 1930s, the “Standard Model” was photon, electron, nucleons

• Beta decay: n ! p+ e�

Continuous spectrum!

• Pauli proposes a radical solution - the neutrino!

n ! p+ e� + �

• Perfect example of a dark sector• neutrino is electrically neutral (QED gauge singlet)

• very weakly interacting and light

• interacts with “Standard Model” through “portal” - (p�µn)(e�µ⇥)

Dark Matter

• Disparate range of gravitational evidence

• Search for non-gravitational DM interactions top priority

Thermal Dark Matter Window

[Figure from G. Krnjaic]

�

�

SM

SM

�

�

0001001011

0.0001

0.001

0.01

Dark matter production via thermal freeze-out

• At early times, , both DM annihilation and production (inverse annihilation) are efficient

• As temperature drops, , DM production is kinematically disfavored, and DM begins to annihilate away

• However, Hubble expansion causes DM dilution, making DM annihilation more and more rare

• Eventually, DM will freeze-out, once annihilation rate becomes smaller than the Hubble rate

• Relic abundance of DM controlled by the annihilation cross section

T � m�

T . m�

h�vi

�

�

SM

SM

�

�

0001001011

0.0001

0.001

0.01

Thermal freeze-out

⌦� ⇡ 0.1

✓pb

h�vi

◆

� W,Z

� W,Z

WIMP Miracle

h�vi ⇠ ⇡↵2W

m2�

⇠ 1 pb⇥✓

↵W

(1/30)

◆2 ✓TeV

m�

◆2

WIMP Phenomenology

�

�

SM

SM

�

�

Indirect Detection

Direct Detection

Production at Colliders

[See talk by M. Cirelli]

Lee-Weinberg Bound

L ⇠ GF [���][f � f ]

h�vi ⇠G2

Fm2�

⇡⇡ 1 pb⇥

⇣ m�

5GeV

⌘2

m� & O(GeV)

Light DM interacting through weak interactions generically overproduced

�

Z

f

f�

L � g� Z 0µ ��µ �+ gf Z

0µ f �µ f

h�vi ⇠g2� g2f m

2�

m4Z0

⇠ 1 pb⇥⇣ g�0.5

⌘2 ⇣ gf0.001

⌘2 ⇣ m�

100MeV

⌘2✓1GeV

mZ0

◆4

� f

f�

Z 0

Lee-Weinberg bound is evaded if new light mediators are present

[Boehm, Fayet]

Direct vs. Secluded Annihilation

Two characteristic regimes: L � g� Z 0µ ��µ �+ gf Z

0µ f �µ f

� f

f�

Z 0

Z 0

�

�

Z 0

m� < mZ01. Direct annihilation: m� > mZ02. “Secluded annihilation:

[Pospelov, Ritz, Voloshin]

h�vi ⇠g2� g2f m

2�

m4Z0

⇠ 1 pb⇥⇣ g�0.5

⌘2 ⇣ gf0.001

⌘2 ⇣ m�

100MeV

⌘2✓1GeV

mZ0

◆4h�vi ⇠

g4�8⇡m2

�

Requires sizable portal coupling to deplete DM abundance

Requires only minuscule portal coupling to maintain

kinetic equilibrium

[Boehm, Fayet]

Dark sector models

• We can classify models based on the mediator particle.

��

2Bµ�V

µ�

Neutrino portal

Higgs Portal

Vector Portal

yLHN

(AS + �S2)H†H

• There are a few simple models that use one of the renormalizable “portals”

• Beyond this, we can consider gauging certain anomaly free combinations of the SM symmetries, e.g., , etc. B � L,Lµ � L⌧

• In general we can also consider gauging anomalous symmetries, or consider scalar particles coupled through higher dimension operators (e.g., axion portal)

• Finally, we can straightforwardly couple the dark matter to the mediator

Z V

X

X

κV �

✏

(µS + �S2)H†H

Neutrino portal

Higgs Portal

Vector Portal✏

2Bµ⌫V

µ⌫

yLHNNL

H

H H

S

Portals

20

Vector Portal Dark Matter

StandardModel

�Mediator

Portal

Vµ

✏

2Bµ⌫V

µ⌫ + gDVµ��µ�

Dark photon model

Vµ mV ,m�, ✏, gD• is the dark photon; is the dark matter; Four parameters �

• We can treat the kinetic mixing as an interaction, e.g.,

• Or we can diagonalize the Lagrangian via

• This gives the interaction: L �X

f

Qf ✏ e Vµ f�µf

✏q2

1

q2

eQf ✏ eQf “Milli-dark charge”

[Holdom][Pospelov, Ritz, Voloshin][Arkani-Hamed, Finkbeiner, Slatyer, Weiner]

• Both direct and secluded annihilation are possible; phenomenology is different in each case

CMB as a probe of the dark sector

• The cosmic microwave background provides a sensitive test of DM annihilation around the epoch of recombination

• If the annihilation products include energetic photons, electrons, this will modify ionization history, leaving imprints on the CMB anisotropies

• Current constraints probe thermal dark matter candidates below about 10 GeV

[see, e.g., Slatyer, Padmanabhan, Finkbeiner]

arXiv:1502.01589

A closer look at the CMB bounds

• The CMB bounds depend on the particle physics model and DM cosmology

• In general, the DM annihilation cross section can be written as

h�vi = a+ bv2 + . . .

• DM was highly non-relativistic during the recombination epoch, and therefore the bounds can be evaded if annihilation proceeds in the p-wave

• In the dark photon model, p wave annihilation to the SM occurs if DM is a scalar

V γ, Z

χ

χ†SM

-Vector mediator has J =1-scalars are spin = 0;-Conservation of J requires L = 1

• Asymmetric DM, Split DM (inelastic) also evade CMB bounds

Vector portal (and cousins) often motivated by anomalies

Example: Muon Anomalous Magnetic Moment (~ )

10

10

10

10

m100 MeV10 MeV 500 MeV

Excluded bymuon g-2

|muon g-2|<2σ

Excluded byelectron g-2 vs α

−3

−4

−5

−6

V

κ2

µ

µ

V �

Fayet, Pospelov

3�

✏2

25

[See also talk by C. Davies]

Significant progress has been made in the last decade

0.001 0.01 0.1 1 1010-5

10-4

10-3

10-2

mA' @GeVD

e

Hidden Photon Æ invisible HmA' > 2 mcL

am, 5s

am,±2s favored

ae

10-3 10-2 10-1 1

10-5

10-4

10-3

10-2

mA' [GeV]

ϵ

APEXTest

A1PHENIX

U70

E141

E774

aμ, 5σ

aμ,±2σ favored

ae

BaBar

KLOE

KLOEHADES

Orsay

NA48/2

2008 Today

Figs. from R. Essig

26

mVmV

Z V

X

X

κV �

Dark photon decays

BB, Pospelov, Ritz

1.00.5 2.00.2 5.00.1 10.010 8

10 7

10 6

10 5

10 4

mV GeV

VGeV

1.00.5 2.00.2 5.00.1 10.0

1.00

0.50

0.20

0.10

0.05

0.02

0.01

mV GeV

Br V

e e+ -

µ µ+ -

τ τ + -

hadrons

✏

27

Dark Higgs

How is the dark photon mass generated?

V

V

hD Production and decay of Dark Higgs through

vector portal

+…

BB, Pospelov, Ritz

h′V

V

e−

e+

γ V

h′

V

BB, Pospelov, Ritz;

e+

e−

V

γ

6 leptons

2 leptons + photon

Essig Schuster, Toro;Reece Wang;

Low-energy e+e- colliders

Dark sector searches at B-factories

BELLE, (2015)BaBAR, (2014) 29

mh0 [GeV]mV

Belle II

e+

e−

V

γ

2 leptons + photon

Belle II projections (Fig. from C. Hearty)

mV

Lifetime

10!2 0.1 110!9

10!8

10!7

10!6

10!5

10!4

10!3

10!210!2 0.1 1

10!9

10!8

10!7

10!6

10!5

10!4

10!3

10!2

mA' !GeV"Ε

A' Decay Length cΤ

Prompt !$10 Μm"Displaced !$1 cm"Displaced !&1 cm"Invisible !&100 cm"Invisible !&100 m"

Essig, Harnik, Kaplan, Toro

Z V

X

X

κV �

mV

✏

• Depending on lifetime, one can search for a bump in the invariant mass distribution or a displaced vertex/long-lived particle

�V ⇠ ✏2↵mV ) c⌧V ⇠ 1

✏2↵mV

Electron beam dump/fixed target experimentsBjorken, Essig, Schuster, Toro;Freytsis, Ovanesyan, Thaler;Andreas, Niebuhr, Ringwald;

e� e�e� e�VV

Z

�

e+

e+

• Current/planned experiments(APEX,HPS,MAMI,DarkLight, VEPP-3, MESA, mu3e, SHiP...) will cover a lot of new ground!

• Look for a e+e- resonance or displaced vertex

32 mV

SHiP experiment (Search for Hidden Particles)

• New fixed target facility proposed at CERN

• 400 GeV protons, ~1020 protons-on-target

http://www.cern.ch/ship

• Powerful capability to search for weakly interacting, long-lived particles that decay visibly

33

mV

Dark photons at LHCbIlten, Soreq, Thaler, Williams, Xue

Two proposals:

• Both displaced vertex and resonance searches are possible

34

• Exclusive search:

• Inclusive search

see 1710.02867 for first LHCb limits (1.6/fb)

mV

Beam Dump Search for Light Dark Matter

[BB, Pospelov Ritz]

p ��

Target/Dump DetectorDirt

ProtonBeam

e�, n, p, . . .

[deNiverville, Pospelov Ritz][McKeen, deNiverville, Ritz]

35

[deNiverville, Chen, Pospelov, Ritz] https://github.com/pgdeniverville/BdNMC/releases

• BdNMC: Publicly available proton beam fixed target DM simulation tool developed by Patrick deNiverville (U. Victoria) and collaborators

Production of the DM beam

Detection of DM via scattering

Elastic NC nucleon or electron scattering

Inelastic NC neutral pion - like scattering

Deep Inelastic scattering

Neutral mesons decays

q

q χ

χ†γ V

�

�

V�q

q

Bremsstrahlung + vector meson mixing

Direct production

36

MiniBooNE Dedicated Dark Matter Search

• Dedicated off target / beam dump run mode

• Neutrino flux significantly reduced (~1/30), DM production unaffected

• Ran from Nov. 2013 - Sep. 2014 - collected 1.9E20 POT

37

[arXiv:1702.02688 PRL 118, 221803 (2017)]

MiniBooNE-DM search

38

• Ongoing analysis in electron and inelastic neutral pion channel

• Utilize timing to reject neutrino background

• DM-nucleon channel

[arXiv:1702.02688 PRL 118, 221803 (2017)]

Future dark matter searches at Fermilab

Motivation: expand physics drivers of Short and Long Baseline Neutrino programs with dark sector searches

Figs. from R. Van de Water

• Option 1: Upgrade Booster Neutrino Beam Dump

• Reduce neutrino background by up to 3 orders of magnitude

• Option 2: New beam dump target station

• Run concurrently with neutrino experiments

39

Many other approaches to search for light dark matter!

• New direct detection techniques for light dark matter

• Electron beam dump experiments

• Fixed target missing momentum experiments

� �

V

e� e�

A′

Z

e−

e−

χ

χ

• Low energy colliders (meson factories)

40

Many other new ideas to search for light dark matter!

41

Neutrino Portal Dark Matter

StandardModel

�Mediator

Portal

N

yLHN + �N��+ h.c.

Type I Seesaw

m⌫ ⇠ y2v2

M

yLHN +1

2MN2 + h.c.

⌫/`

hHi

✓gp2W�

µ `†�µN + h.c.+ . . .U

✓ ⇠ yv

M⇠

rm⌫

M⇠ 10�5 ⇥

⇣ m⌫

0.05 eV

⌘1/2✓GeV

M

◆1/2

U

Minkowski; Yanagida; Mohapatra, Senjanovic; Gell-Mann, Ramond, Slansky; Schechter, Valle

Minimal Neutrino Portal DM (Type I seesaw)

• Mediator is a Majorana sterile neutrino

• Dark sector consists of a Majorana fermion and a real scalar� �

N

• Type I Seesaw mechanism generates small masses for light neutrinos

• For masses in the thermal window, neutrino Yukawa coupling is tiny

• Direct annihilation to light neutrinos is inefficient, and direct detection, accelerator tests of this scenario are challenging

• Secluded annihilation is still viable, and indirect detection offers a probe

⌫/`

hHi

�

�

�

N

NSecluded Annihilation

• Annihilation is efficient �� ! NN

• Indirect detection: gamma-rays, antiprotons from DM annihilation, distortion of CMB anisotropies

[BB, Han, Shams Es Haghi]

χχ→���χ = ��� ���

�� = �� ����� = �� ����� = ��� ���

��-� � �� �����-�

�

��

���

�γ [���]

� ��

γ/��

γ[���

]

γ ������� �������

χχ→���χ = ��� ���

�� = �� ����� = �� ����� = ��� ���

� �� �����-�

�

��

��_ [���]

� �_� ���_/�� �

_[���

]� ������� �������

• Can be probed by Fermi, AMS-02, Planck, …

Spectra display mild dependence on sterile

neutrino masses

m� > mN

[BB, Han, Shams Es Haghi]

Ibarra, Lopez-Gehler, Molinaro, Pato Tang, Zhu

Campos, Queiroz, Yaguna, Weniger

Indirect detection constraints

For related studies, see also

Dirac Neutrino Portal

• Mediator is a (pseudo-)Dirac sterile neutrino

• An approximate lepton number symmetry allows for light SM neutrinos even if the Yukawa coupling (and active sterile mixing) is large�`

• Dark sector consists of a Dirac fermion and a complex scalar� �

• Large mixing allows for a sizable DM - SM neutrino coupling

[BB, Han, McKeen, Shams Es Haghi] [Bertoni, Ipek, Nelson, McKeen]

• Important implications for cosmology and phenomenology

Direct annihilation to light SM neutrinos

• DM can be a thermal relic if mixing is large (due approx. lepton number)

m� > mN

• Thermal target in plane:

����� ����� ����� � �� �����-��

��-��

��-��

��-�

��-�

��-�

��-�

m� [GeV]

h�vi ' Y

32⇡m2�

Y

m� � Y

h�vi =

1 pb

• Note that CMB constraints evaded

τ→νμν

τ→ν�π����νμ→ντ

�→����

�→����

� �� ��� ���� ��� �����-�

�����

�����

�����

�� (���)

|�τ��

π→μν �����

�→μν

τμ /����

��� ���������

�→μν��→����

�→�����→μ

����

��-�

��-�

��-�

|��

π→�ν

τμ/����

�����

π → �νπ → μν

�→�ν��→����

�→�����→�

�→�ν

��-�

��-�

��-�

|����

“Invisible” Sterile Neutrino

�

�

⌫4

[Bertoni, Ipek, DM, & Nelson][BB, Han, McKeen, Shams Es Haghi][De Gouvea,Kobach]

• Fermi constant (muon lifetime); PMNS non-unitarity; EW precision; CKM unitarity

• Muon, tau, Meson decays (peak searches); lepton universality tests;

• Invisible Z, Higgs decays; Drell-Yan (W decays)

• Atmospheric oscillations (relevant for )

Phenomenology

mN > m�,m�

⌫⌧

K+

µ+

χ

φ

χ

ν

ν∗

⌫h

K+

µ+

χ

φ

χ

ν

ν∗

130 140 150 160 170 180 190 2001

5

10

50

100

500

1000

pμ (MeV)

dNK→μ+inv.

dpμ

(MeV

-1)

y2�Uμ 4�2=10-3, m4=10 GeV, mϕ=3mχ

mχ=15MeV

mχ=60 MeV

m4=250 MeV�Uμ 4�2=10-8

E949: kaons1012

NA62 will collect ~ 1 order of magnitude more Kaons

Meson decays

On-shell Off-shell

Small scale structure

• Strong DM - neutrino scattering can delay DM kinetic decoupling

• Pressure due to DM-neutrino coupling resists gravitational collapse (analogous to coupled photon-baryon plasma)

• Formation of structures smaller than horizon size at DM kinetic decoupling are suppressed

[Boehm, Fayet, Schaeffer][Boehm, Riazuelo, Hansen, Schaeffer][Boehm, Mathis, Devriendt, Silk][Bertoni, Ipek, McKeen, Nelson][Olivares-Del Campo Boehm, Palomares-Ruiz,Pascoli]

⌫ ⌫

� �

�

M > Mcuto↵

= 108Msolar

✓Td

keV

◆�3

• Smallest structures observed via gravitational lensing have masses of order 108 solar masses

• Late kinetic decoupling leads to a lower bound on mass of gravitationally bound objects

Direct Detection• DM acquires coupling to the Z boson at one loop; • Leads to spin-independent coherent scattering • Probes DM heavier than few GeV

� ��

⌫ ⌫

Z

• Constraints can be weakened if DM split; other probes are complementary

Naturalness of light scalar

� �

N

��m2

� ⇠ y2

16⇡2m2

N

• Naturalness “constraint” is complementary to invisible neutrino constraints

Thermal target

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

|�τ� ���� � ��=�π

|�τ� ���� � �� ����

�����=�� -����=����=�� -���� ����

���� ���� � ��

��-��

��-�

��-�

��-�

�χ=�ϕ/� (���)

� τ=� �� ��

��

χ�

�ϕ�

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

� ���

�→μ+����

|�μ� ���� � ��=�π

|�μ� ���� � �� ����

�����=�� -����=����=�� -���� ����

��-��

��-�

��-�

��-�

� μ=� �� ��

���

χ�

�ϕ�

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

|��� ���� � ��=�π

|��� ���� � �� ����

�����=�� -����=����=�� -���� ����

��-��

��-�

��-�

��-�

� �=� �� �������

χ�

�ϕ�

��=���χ

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

|�τ� ���� � ��=�π

|� ���� � �����

�����=��-�� ��=�π

�����=��

-�� ������

���� ���� � ���χ=�ϕ/� (���)

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

� ���

�→μ+����

|�μ� ���� � ��=�π

|� ����� � �����

�����=��-�� ��=�π

�����=��

-�� ������

⟨σ�⟩<� �

�

���� ����

��� � ⊙

��� � ⊙

|��� ���� � ��=�π

|� �� ����� � �����

�����=��-�� ��=�π

�����=��

-�� ������

��=��� ���

h�vi ' Y

32⇡m2�

• Represent conservative constraints on the thermal hypothesis

• New ideas to probe remaining open parameter space are welcome!

Outlook

• Dark sectors may play a role in addressing a number of outstanding mysteries in particle physics and cosmology

• Thermal dark matter implies coupling between DM and SM; requires new mediators, interactions for masses below ~ GeV

• Vector portal and neutrino portal provide two simple, motivated scenarios, each with its own rich and characteristic phenomenology

• Testing these scenarios requires new, complementary experimental strategies to the ones employed for WIMPs

• The dark sector could be much richer than the scenarios I’ve outlined. We’ve only scratched the surface on this subject!

54