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Kazuhiro Yamamoto

Institute for Cosmic Ray Research (ICRR)the University of Tokyo

KAGRA face to face meeting 　　　University of Toyama, Toyama, Japan

3 August 2013

Effect of MOMENTUM deposited by EXOTIC particles on interferometeric

gravitational wave detectors

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0. Abstract

Gravitational wave detectors can detect everything.

Can they detect exotic particles ?

Exotic particle : It is not found in experiment although theorist predicts.

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Contents1.Introduction2.Momentum deposition3.KAGRA4.Improvement5.Exotic particle search 6.Summary

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1. Introduction

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Gravitational wave detector (interferometer and resonator)

: Ultra high sensitive sensor Many noise sources : Quantum noise, Thermal noise, Seismic motion, Noise from laser source, Circuit noise, Electric and Magnetic fields, ....

Cosmic rays ?Resonator

First paper : B.L. Baron and R. Hofstadter (Nobel prize 1961),

Physical Review Letters 23 (1969) 184.Interferometer

First paper : A. Giazotto, Phys. Lett. A 128 (1988) 241.

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1. Introduction Not noise, but signal ! Exotic particle search

Exotic particle search using resonator

G. Liu and B. Barish, Physical Review Letters 61 (1988) 271.P. Astone et al., Physical Review D 47 (1993) 4770.

How about interferometer ? (calculation)

K. Yamamoto et al., Physical Review D 78 (2008) 022004.

Interferometer is inferior to resonator as particle detector.(a)Signal to Noise ratio (S/N) is smaller than that of resonator.(b)Cross section is also smaller.

1. Introduction

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Nevertheless, interferometer as exotic particle detector is considered.

Q. How do cosmic ray (or exotic) particles generate noise (or signal) in gravitational wave detector ?

A. Energy deposition of particles makes elastic vibration of resonator or mirror of interferometer.

Process of cosmic-ray excitation (Energy deposition)

(i) Passage of cosmic ray particle in mirror or resonator

(ii) Energy deposition

(iii) Temperature gradient

(iv) Thermal stress

(v) Elastic vibration of mirror or resonator

Mirror or resonator

Cosmic rayparticle

Process of cosmic-ray excitation (Energy deposition)

(i) Passage of cosmic ray particle in mirror or resonator

(ii) Energy deposition

(iii) Temperature gradient

(iv) Thermal stress

(v) Elastic vibration of mirror or resonator

Mirror or resonator

Process of cosmic-ray excitation (Energy deposition)

(i) Passage of cosmic ray particle in mirror or resonator

(ii) Energy deposition

(iii) Temperature gradient

(iv) Thermal stress

(v) Elastic vibration of mirror or resonator Hot

Mirror or resonator

Process of cosmic-ray excitation (Energy deposition)

(i) Passage of cosmic ray particle in mirror or resonator

(ii) Energy deposition

(iii) Temperature gradient

(iv) Thermal stress

(v) Elastic vibration of mirror or resonator

Mirror or resonator

Process of cosmic-ray excitation (Energy deposition)

(i) Passage of cosmic ray particle in mirror or resonator

(ii) Energy deposition

(iii) Temperature gradient

(iv) Thermal stress

(v) Elastic vibration of mirror or resonator

Mirror or resonator

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If we take only energy deposition into account, interferometer is inferior as particle detector. K. Yamamoto et al., Physical Review D 78 (2008) 022004.

According to A. Giazotto, Phys. Lett. A 128 (1988) 241,energy deposition implies momentum deposition.When particles give a suspended mirror in interferometer momentum, pendulum motion can be excited.

Nobody considered the effect of momentum deposition by exotic particle on interferoemter.

1. Introduction

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2. Momentum deposition In the case of cosmic ray ...pendulum motion excited by momentum deposition is smaller than the elasctic motion of mirror by energy deposition.

Energy deposition Thermal stress : Decay time is about 1000 sec. Step response

Momentum deposition Momentum transfer in a moment Impulse response

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2. Momentum deposition Speed of cosmic ray particles is almost same as that of light !

If exotic particles moves more slowly ?

Momentum deposition (speed is the same as that of light (c))

Energy depositionMomentum deposition (slower, speed is v)

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2. Momentum deposition If speed of exotic particle is the same as that of light ... momentum (p) is proportional to energy (E).

If exotic particles run slowly ... energy is almost constant (mc2) even if momentum changes drastically.

Thus, dp/dE is larger when v is smaller than c.

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2. Momentum deposition How much is c/v typically ?

If exotic particles are trapped in gravitational potential of Earth, averaged speed is about 10 km/sec (Virial theorem).

Thus, c/v is about 3*104.

Note : dE/dl (enery deposition per unit length) depends on energy. l is the length of particle track in a mirror.

KAGRA (or 2nd generation) interferometer as exotic particle detector

We must find the pendulum motion by exotic particles. Matched filter is useful.Signal to Noise ratio (S/N) is as follows.

This is similar to S/N of resonators.

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3. KAGRA

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Improvement of interferometer as exotic particle detector

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Displacement (not strain) noise must be small.Long baseline is not necessary.

Lighter mirror is better.

Since we must observe excited pendulum motion,noise below 100 Hz must be smaller.(a) Seismic noise must be small.(b) Pendulum will be cooled to reduce thermal noise.(c) Light power will be small to reduce radiation pressure noise.

4. Improvement

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Improvement of interferometer as exotic particle detector

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How about CLIO ?

Signal to Noise ratio (S/N) of CLIO is only half of that of KAGRA !

Note : Limit sensitivity at cryogenic temperature is assumed.

4. Improvement

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Improvement of interferometer as exotic particle detector

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For example ...Mirror : 100 times smaller than KAGRA mirror Size is on the order of 1 mm (mass is 30 mg).Baseline : table topLaser power : 0.25 W No Fabry-Perot cavity (shot noise : 10-16 m/rtHz)Tempearture of mirror : 20 KExcellent seimic vibration system : smaller than 10-16 m/rtHz above 10 HzSignal to Noise ratio is 10 times larger than that of KAGRA and resonators.

4. Improvement

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Mass of target particle

5. Exotic particle search

If particle is too light, it must stop in a mirror.

Lower limit of mass of target particle KAGRA : 4.5 *109 GeV Table top interfetomer : 1.8*106 GeV

Proton : 1 GeV, Top quark : 170 GeV, Higgs (like) particle : 125 GeV

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5. Exotic particle search Lower limit of mass of target particle KAGRA : 4.5 *109 GeV Table top interfetomer : 1.8*106 GeV

What kinds of exotic particles are targeted ? Magnetic monopole C. Bernard et al., Nuclear Physics B 242(1984)93.

Nuclearite E. Witten, Physical Review D 30(1984)272. A. De Ru´jula and S. L. Glashow, Nature 312(1984)734.

Mirror dust particle R. Foot and S. Mitra, Physical Review D 68(2003)071901(R).

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5. Exotic particle search How often can we observe ? Lower limit of mass of target particle KAGRA : >4.5 *109 GeV Table top interfetomer : >1.8*106 GeV

Average (or critical) density of Universe 5*103 eV/cm3

If Universe is dominated by exotic particle, we can observe an exotic particle every two months (KAGRA) or every eight months (Table top interferometer) in the best case.

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6. SummaryMomentum deposition of exotic particle can excite mirror pendulum motion.

When this particle moves more slowly than light, the exctitation could be large.

Signal to Noise ratio of KAGRA as exotic particle detector is comparable with that of resonators.

Signal to Noise ration of Table top interferometer with tens mg mirrors is 10 times larger than that of KAGRA.

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6. SummaryOnly extremely heavy particles (larger than 106 GeV) can be target.

We observe an exotic particle every a few or several months in the best case if Universe is dominated by these exotic particles.

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If you are interested with this topic,here are details in Japanese !

http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=1112

It was written in 2008 ...

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Thank you for your attention !

Improvement of interferometer as exotic particle detector

4. Improvement