Andrea Caputo, Alex Millar, Ciaran O’Hare, Edoardo Vitagliano arXiv:2105.04565

Hidden Photon Limits: A Cookbook

Alex Millar

Hidden/Dark photons

• New U(1) gauge boson with tiny kinetic mixing with the visible photon • Can be non-thermally produced as a good dark matter candidate • Very similar behaviour to axions

2

Alex Millar

Hidden Photons vs ALPs

• Key difference: HP has a polarisation!

• May be randomised or fixed depending on the production mechanism (or somewhere in-between)

• Structure formation may change this, but no detailed studies

3

Alex Millar

Haloscopes for HP DM

• In principle, any axion haloscope using axion-photon mixing is sensitive to HPs

• For an example, take a cavity haloscope

4C. BOUTAN/PACIFIC NORTHWEST NATIONAL LABORATORY; ADAPTED BY APS/ALAN STONEBRAKER

Alex Millar

Haloscopes for HP DM

• Two key differences

• HP does not need a B-field

• The polarisation direction of the HP matters

• (Usually) easy to convert between the two sensitivities

5C. BOUTAN/PACIFIC NORTHWEST NATIONAL LABORATORY; ADAPTED BY APS/ALAN STONEBRAKER

Alex Millar

Reinterpreting axion experiments

• Actually need to be very careful: many experiments use B-field vetos which people have neglected before now

• Polarisations can give a highly non-trivial time varying signal

• Timing and directional data rarely given

6

Alex Millar

Current HP Experiments

• Currently HP experiments make lots of different assumptions

• Some assume fixed, some random: few provide enough information in the results to properly calculate a limit for fixed polarisations

7

Alex Millar

What should an experiment assume?

• Totally randomised is the most optimistic (just factors of 1/3 or 2/3 for )

• Totally constant polarisation is the trickiest scenario

• Simplest analysis (arXiv:1201.5902) gives factors of 0.0025 or 0.0975

• Both time varying and constant signals should be considered

• How do we make our worse case scenario match the best case scenario?

cos2 θ

8

Alex Millar

HP Polarisations

• How do you deal with a fixed polarisation?

• Experiments are sensitive to an axis or a plane

9

Axial experiment(Zenith-pointing)

Planar experiment(North-facing)

Possible DP Polarisations

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Alex Millar

HP Polarisations

• Earth rotates!

• Long measurements sample a cone (or analogue)

• Short measurements sample a single random direction (very bad)

10

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Geocentric coordinates Detector-centric coordinates

Polarisation with respect to an axis

Polarisation with respect

to plane

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North-facingWest-facing

Zenith-facing

Alex Millar

Day long measurements

• To get a sense, one can take the simplest case: measurements lasting n-days exactly

• Experiments sensitive to an axis sweep out a cone (sensitive to a plane is simply the compliment)

11

Optimal (~35°) Unideal (~0°) Worst (90°)

Alex Millar

Day long measurements

• Need find the distribution of angles over some measurement

• Depends strongly on alignment and location (basically, there is a perfect angle with the pole around 35°)

12

Alex Millar

Improvement with long measurements

• Up to an order of magnitude improvement on limits for long measurements

13

Alex Millar

What about for short measurements? • Most experiments do single, short measurements

• Can be made better!

• Split each measurement into parts, and space those parts over the course of a day

• Best results: three if sensitive to an axis, two if sensitive to a plane

14

Alex Millar 15

• Order of magnitude improvement on coupling just from three measurements!

• Does not increase overall data taking time

• Also have to be careful of rescans

• Always rescan with the same alignment

What about for short measurements?

Alex Millar

Current HP Limits

• Rescaled for fixed polarisation (conservative case)

• *Dark E-field assumes time varying signal so may not apply to randomly polarised HP 16

10°6 10°5

Dark photon mass, mX [eV]

10°16

10°15

10°14

10°13

10°12

10°11

10°10

10°9

Kin

etic

mix

ing,

c

Frequency [GHz]10°1 100

Dark photons as dark matterDark photons as dark matter

WISPDMXWISPDMX

Dark E-fieldADMX-1

ADMX-2 ADMX-3

AD

MX

-Sidecar

AD

MX

-Sidecar

CA

PP-1

CA

PP-2

CA

PP-3

HA

YST

AC

-1

HA

YST

AC

-2

SQuAD

SHUKET

rDM = 0.45 GeV cm°3

Alex Millar

Future experiments

• Many more axion and HP experiments coming soon

• We should optimise scanning strategies to ensure robust limits regardless of DP scenario

• Need dedicated HP analyses!

17

10°1510°

1410°

1310°

1210°

1110°

1010°

910°

810°

710°

610°

510°

410°

310°

210°

1100

101102

103104

105

Dark photon mass, mX [eV]

10°18

10°17

10°16

10°15

10°14

10°13

10°12

10°11

10°10

10°9

10°8

10°7

10°6

10°5

10°4

10°3

Kin

etic

mix

ing,

cStandard projection

Optimised projection

Hz kHz MHz GHz THz eV keV

Dark photondark matter

g ! X

Stellarbounds

DM-Radio

DarkE-field

ALPHAMADMAX

LAMPOST

SuperCDMS

LZ

Alex Millar

Conclusions

• Most important message: axion experiments should do dedicated analysis, not just leave them for people to try to reinterpret them

• Polarisation can be very non-trivial: detailed timing and directional data is needed

• Can improve limits be an order of magnitude

• Effects of structure formation should be simulated

18

10°1510°

1410°

1310°

1210°

1110°

1010°

910°

810°

710°

610°

510°

410°

310°

210°

1100

101102

103104

105

Dark photon mass, mX [eV]

10°1810°1710°1610°1510°1410°1310°1210°1110°1010°910°810°710°610°510°410°310°210°1

100

Kin

etic

mix

ing,

c

AD

MX CA

PPH

AY

STA

C

QU

AX

LSW-AD

MX

LSW-UW

A

LSW-SPring-8LSW-SPring-8ALPSALPS

CROW

S

CROW

S CAST

CAST

SHIPSSHIPS

Plimpton-Lawton

Plimpton-Lawton

AFMAFM

Cavendish-Coulomb

Cavendish-Coulomb

Spectroscopy

SpectroscopyTEXONOTEXONO

XENON

DAMIC

SENSEISuperCDMS

FUNK

Tokyo-3

Toky

o-2

Tokyo-1

SHU

KET

Dar

kE-

field

WISPDMX

SQuA

D

DMPathfinder

Solar HB RGSolar HB RG

JupiterJupiter EarthEarth CrabCrabnebulanebula

IGMIGM

Leo TLeo T

Gas clouds

Gas clouds

Neutron stars

Neutron stars

Darkphoton

DM

Hz kHz MHz GHz THz eV keV

DPDM HeIIReionisation(Caputo et al.)

DPDM(Witte et al.)

DPDM(Arias et al.)

COBE/FIRASg ! X

DPDM heatingDPDM heating

Black holesuperradiance

Alex Millar

Experiment Locations

19

Alex Millar

HP Polarisation

• Need find the distribution of angles over some measurement

• Depends strongly on alignment and location (basically, there is a perfect angle with the pole around 35°)

20