Hidden photon measurements using the longbaseline cavity of laser interferometric gravitationalwave detector
Abstract
We suggest a new application for the longbaseline and high powered cavities in a laserinterferometric gravitationalwave (GW) detector to search for WISPs (weakly interacting subeV particles), such as a hidden U(1) gauge boson, called the hiddensector photon. It is based on the principle of a light shining through the wall experiment, adapted to the laser with a wavelength of 1064 or 532 nm. The transition edge sensor (TES) bolometer is assumed as a detector, which the dark rate and efficiency are assumed as and 0.75, respectively. The TES bolometer is sufficiently sensitive to search for the lowmass hiddensector photons. We assume that the reconversion cavity is mounted on the reconversion region of hiddensector photons, which number of reflection and length are assumed as 1000 and 10, 100, and 1000m. We found that the secondpointfive and the second generation GW experiments, such as KAGRA and Advanced LIGO with a regeneration cavity and TES bolometers. The expected lower bounds with these experiments wit the reconverted mirror are set on the coupling constant for hiddensector photon with a mass of eV within 95% confidence level. The third generation detector, Einstein Telescope, will reach at a mass of eV within 95% confidence level. Although the operation and construction of the RC will demand dedicated optical configurations, the cavities used in GW detection are expected to measure the strong potential for finding the hiddensector photons.
Further author information: (Send correspondence to Yuki Inoue)
Yuki Inoue: Email: iyuki@post.kek.jp, Telephone: +81298645200 ex 2711
1 Introduction
The theories of beyond the standardmodels predict an extra U(1) gauge corresponding to the hidden sectors [1, 2, 3, 4, 5]. Lowmass particles residing in the hidden sectors are expected to weakly interact with the visible sectors; hence they are called WISPs (weakly interacting subeV particles). In an experimental search, WISPs should be revealed by weak kinetic mixing between a photon and a hiddensector photon [6]. The probability of a conversion after propagating through distance in a vacuum is given by
(1) 
where , , and are the photon energy, coupling constant, and a mass of the hiddensector photon, respectively. The hiddensector photon reconverts into a photon after propagating through a wall. This scheme is known as the “light shining through a wall (LSW)” experiment [7, 8]. The probability of the photon existing through a wall is given by
(2)  
where and are the lengths of the conversion and reconversion regions, respectively.
Many LSW experiments have been proposed and implemented on a microwave light and laser at [9, 10].
The ALPS experiment obtained a coupling constant of at a mass of eV within confidence level limits [11].
However, the ALPS sensitivity in the lowmass region is limited by the lengths of the conversion and reconversion regions.
Currently, the ALPS experiment is being upgraded to ALPSIIb [9].
This paper investigates whether a longbaseline cavity with a highpowered laser in a laser interferometric gravitationalwave (GW) detector is suitable for the hiddensector photon experiments.
The GW sensitivity is conferred by two stateoftheart longbaseline cavities and a highpowered laser. The laser generates a large number of the hiddensector photons.
Therefore, the combination of lasercavity and high power laser is an excellent source of the hiddensector photons. When a reconversion region with a reconversion cavity (RC) is placed at the backside of an arm in the GW detector, these hiddensector photons might be reconverted to the visible photons. Figure 1 illustrates concept of our proposed experiment based on KAGRA [12, 13]. In this paper, we present the expected sensitivity of the hiddensector photon searching, using several types of the longbaseline cavity.
2 Assumption
The sensitivity to the coupling constant and the mass of the hiddensector photon is evaluated in three GW experiments; Advanced LIGO (AdvLIGO) [14], KAGRA [12, 13], and Einstein Telescope (ET) [15]. AdvLIGO is the secondgeneration GW experiment realized by two interferometers. These are located in Hanford, WA and Livingston, LA, USA, each with 4 km FabryPerot cavities. The optical source of both interferometers is a 532 and 1064 nm Nd:YAG laser. Using a powerrecycling scheme [14], the effective input power is approximately 5.2 kW per cavity. The FabryPerot cavity stores the laser power using highly reflective mirrors. The average number of the laser reflections is 287, providing a stored laser power of 745 kW. The secondpointfive generation GW experiment, KAGRA, employs the mirrors at the 20 K to reduce thermal noise. The cavity length in the experiment is 3 km and the total stored laser power is 410 kW. In ET proposed as the thirdgeneration GW experiment, the telescope detector is split into two interferometers optimized to lowfrequency and highfrequency GWs, called ETDLF and ETDHF, respectively. The cavity length of 10 km and the stored power of 10 MW with the ETDHF are ideally suited for studying the hiddensector photons. The parameters of the GW experiments are listed in Table 1.
Project  ALPSIIb  AdvLIGO  KAGRA  ET 

Wavelength  
Power  30 W  5.2 kW  825 W  500 W 
Finesse  7859  450  1550   
#reflection  5000  287  987   
Stored power  150 kW  745 kW  410 kW  10 MW 
baseline  100 m  4000 m  3000 m  10 km 
The transition edge sensor (TES) bolometer [9] is used as a reconverted photon detector at the end of the reconversion region. When the additional optical power is deposited on the TES detector, the bolometer island heats up, increasing the resistance. We can read a power during the steep resistance change. The TES bolometer detects the small temperature changes as the photons are absorbed and converted to heat. In a realistic configuration, we use fibers as the photons are translated to the TES bolometer. the onephoton detection efficiency with fibers is [9]. The detected number of the regenerated photons on the TES detector is given by
(3) 
where is the number of the photons in the incident beam, and and are the numbers of laser reflections in the RC and the conversion cavity (CC), respectively [7].
The incident beam is obtained by , where is an initial power input to the cavity.
The stored laser power is defined by .
Each the number of refraction correspond to finesse as .
When we these cavities are unused, we have and .
The dark rate of TES is [9].
3 Sensitivity and discussion
To assess the expected sensitivity, we assume that the number of the detected photons is the sum of the expected signal and the background , where is the observation time. From the background, we estimate the number of the detected photons to be significance level. The sensitivity curve as a function of is calculated with significance by the term of . The expected sensitivities of ALPSIIb, AdvLIGO, KAGRA, and ET are plotted in Figure 2. The length of each the reconversion regions is assumed as 1000 m. We find that AdvLIGO is slightly more sensitive than KAGRA. This is because that the stored power of AdvLIGO is larger than that of KAGRA. The most sensitive experiment is ET, by the virtue of its power and longbaseline cavity. Moreover, these sensitivities are expected to exceed that of the ALPSIIb experiment, with of the order of .
We evaluated the effect of the RC on the sensitivity although the installation is very challenging. This is because that we have to align the large mirrors while tuning the phase and the beam shape to resonance. Furthermore, we have to achieve 1000 reflection. We discuss the possibility of RC in the case of KAGRA. In order to realize RC, we should resolve three points:

the alignment,

the large mirror and the antireflection (AR) coating,

the resonant condition.
First, we consider to the possibility of the alignment. The KAGRA places the beam reducing telescope (BRT) behind the endmirror in the arm. When we align the mirror of RC, we use the split beam from the BRT as a reference. This is because that this beam aligns the optical axis of CC. In this way, we realize the alignment of the long baseline resonator. Second, we examine the possibility of the large mirror and the antireflection (AR) coating. The beam spot diameter of KAGRA is less than 60 mm with 1 km points from the start of the reconversion region. Therefore, we need the large mirror with a diameter of 300 mm, which correspond to the beam width with . The LIGO experiment employ the ARcoated fused silica mirrors with a diameter of 340 mm [17]. Therefore, we can make the sufficient large mirrors. Third, we should discuss the resonant condition. We can apply the green lock laser, placed in the ALPSII experiment [9]. The beam in BRT can divide the beam splitter. The split beam is converted the green laser while keeping the phase of beam. The green laser is injected to RC and locking to resonant condition. Therefore, the technology of RC has a sufficient realization.
In the study, the refraction time of RC was assumed as 1000. Adopting this cavity, the sensitivity of KAGRA dramatically improved by a factor of six as shown in Fig. 3. From Eq. (3), the number of reflections is proportional to . The RC length from 10 m to 1000 m improves the sensitivity by three orders of magnitude. On the other hand, the conversion and reconversion length depend on the mass scale. The mass cutoff at these length is proportional to and , respectively. However, in the real case, the mass cutoff is derived by combining the length of both regions.
Figure 4 shows the dark matter predictions and the previous experiments.
The AdvLIGO (reconversion region=1000 m) is overplotted in same figure.
As shown in Fig. 4, the AdvLIGO results are expected to surpass the previous exclusion limits .
In the secondpointfive generation GW experiments, AdvLIGO is expected to achieve a coupling constant at a mass of eV, even without the RC.
By placing the RC in the conversion region, this result should improve to , implying that we can improve the XENON10 limits by over one order of magnitude.
Furthermore, we can close the gap between the XENON10 and CROWS limits.
These results may be constrained by string physics and cold dark matter.
We superimpose the arrowed regions of these predictions in Fig. 4.
The blue and green regions are predicted by the beyond the standardmodel of the string theory [18].
The blue areas correspond to the hidden Higgs mass which is
similar to a hidden photon mass . The green areas correspond to models with a chiral
Higgs particle, in which a mass hierarchy exists .
The orange region delineates the allowed region of the cold dark matter.
This region is constrained by the effective number of neutrinos, which measured by WMAP which constitute the cosmic microwave background [21].
The motivations for these scientific exploits are detailed elsewhere [16, 18].
4 Conclusion
We suggest a new application for interferometers used in the GW experiments.
The TES bolometer is sufficiently sensitive to search for the lowmass hiddensector photons, which are candidates of the hidden Higgs and/or cold dark matter.
Even if we cannot measure significant signals, the sensitivity calculations suggest that we can expand the parameter space of the current measurements.
5 Acknowledgments
We are also thankful to Koji Arai and for this expertise with Advanced LIGO. We are thankful to Yuta Michimura and for this expertise with KAGRA. We are thankful to Aine Kobayashi for the comment to study of science motivation. The authors would like to thank Toshikazu Suzuki and Takayuki Tomaru for commenting on this study. The suggestions of Akiteru Takamori were very helpful in clarifying the paper. We thank Masaya Hasegawa and Shugo Oguri for the critical reading of the manuscript. We extend my appreciation to Masashi Hazumi for their assistance and support. The authors were supported by JSPS KAKENHI Grant Numbers and 25707014.
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