# No CC-NSI explanation of the Gallium anomaly

C. Giunti<EMAIL_ADDRESS>Istituto Nazionale di Fisica Nucleare
(INFN), Sezione di Torino, Via P. Giuria 1, I–10125 Torino, Italy  C.A. Ternes
<EMAIL_ADDRESS>Istituto Nazionale di Fisica Nucleare (INFN), Sezione di
Torino, Via P. Giuria 1, I–10125 Torino, Italy

###### Abstract

We show that the Gallium anomaly can not be explained by CC-NSI.

In the first version of this article, we have argued that the Gallium anomaly
can be resolved with charged current neutrino nonstandard interactions (CC-
NSI). Unfortunately, it was not taken into account that in the Gallium
experiments (GALLEX, SAGE, and BEST) the neutrino flux was determined from the
activity of the source, which was obtained from the measurement of the heat
emitted by the source. Therefore, if CC-NSI were present in the production of
the neutrinos, they would be already included in the calculation of the
neutrino flux. Likewise, the cross-section of the detection process
$\nu_{e}+{}^{71}\text{Ga}\to e^{-}+{}^{71}\text{Ge}$ is calculated from the
measured lifetime of ${}^{71}\text{Ge}$, which determines the contribution of
the transition to the ground state of ${}^{71}\text{Ge}$ (see, e.g., Eqs. (3)
and (5) of Ref. Semenov (2020)). The contributions of the transitions to the
excited states are calculated trough the relative Gamow-Teller strength, as
shown, e.g., in Eq. (6) of Ref. Kostensalo  _et al._ (2019). Hence, if CC-NSI
were present in the detection process, they would contribute also to the
lifetime of ${}^{71}\text{Ge}$ and they would have already been included in
the cross section of the detection process. It can be concluded that if CC-NSI
exist, they are included in the standard estimation of the deficit observed in
the Gallium experiments.

In this case, the neutrinos produced and detected in the Gallium experiments
are described by the same _normalized_ state

$|\nu_{s}\rangle=|\nu_{d}\rangle=|\nu\rangle=\dfrac{1}{N}\left(|\nu_{e}\rangle+\sum_{\beta=e,\mu,\tau}\epsilon_{\beta}|\nu_{\beta}\rangle\right),$
(1)

where

$N=\left(1+2\text{Re}[\epsilon_{e}]+\sum_{\beta=e,\mu,\tau}|\epsilon_{\beta}|^{2}\right)^{1/2},$
(2)

such that

$\langle\nu|\nu\rangle=1.$ (3)

Therefore, the effective zero-distance survival probability for the short
baselines of the Gallium experiments, where there are no oscillations due to
the standard solar and atmospheric squared-mass differences, is equal to
unity:

$P_{ee}^{\text{SBL}}=|\langle\nu_{d}|\nu_{s}\rangle|^{2}=|\langle\nu|\nu\rangle|^{2}=1.$
(4)

We conclude that the Gallium anomaly cannot be explained by CC-NSI.

###### Acknowledgements.

We thank Mariam Tórtola and David Vanegas Forero for discussions on this
topic.

## References

  * Semenov (2020) S. V. Semenov, Phys. Atom. Nucl. 83, 1549 (2020).
  * Kostensalo  _et al._ (2019) J. Kostensalo, J. Suhonen, C. Giunti, and P. C. Srivastava, Phys. Lett. B 795, 542 (2019), arXiv:1906.10980 [nucl-th] .


2023

[1]Leonid Petrov

[1], NASA Goddard Space Flight Center, 8800, Greenbelt, 20771, MD, USA

2], University of Texas at Austin, 10,000 Burnet Rd, Austin, 78758, TX, USA

# Precise VLBI/GNSS ties with micro-VLBI

<EMAIL_ADDRESS>Johnathan York<EMAIL_ADDRESS>Joe Skeens
<EMAIL_ADDRESS>Richard Ji-Cathriner<EMAIL_ADDRESS>David
Munton<EMAIL_ADDRESS>Kyle Herrity<EMAIL_ADDRESS>*  [

###### Abstract

We present here a concept of measuring local ties between collocated GNSS and
VLBI stations using the microwave technique that effectively transforms a GNSS
receiver to an element of a VLBI network. This is achieved by modifying the
signal chain that allows to transfer voltage of the GNSS antenna to a
digitizer via a coaxial cable. We discuss the application of this technique to
local tie measurement. We have performed observations with a GNSS antenna and
FD-VLBA radiotelescope and detected a strong interferometric signal from both
radiogalaxies and GNSS satellites.

###### keywords:

VLBI, GNSS, local ties

##  1 Introduction

Space geodetic observation with Very Long Baseline Interferometry (VLBI),
Global Navigation Satellite System (GNSS), Satellite Laser Ranging (SLR), or
Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS)
involves a measurement of travel time of electromagnetic radiation between an
emitter and a receiver and/or rates of its change. The position of a ground
space geodesy instrument is referred to its own unique reference point. In a
similar way, the position of a space-borne emitter or receiver is referred to
its own reference point.

Space geodesy techniques have their strengths and weaknesses. VLBI provides a
reference to inertial space, SLR provides a reference to the Earth’s center of
mass, DORIS provides wide spatial coverage, and GNSS is able to sense site
deformations with a fine time resolution. It was recognized over 20 years ago
that a combination of all space geodesy techniques has the potential to
provide the most accurate results by mitigating the weaknesses of each
individual technique (see for example, r:alt02, ). Combination implies that
observations necessarily must have something common that ties them together.
Ties can be direct in the form of a position vector between either a space-
borne or a ground-based reference point that is precisely known, or indirect,
for instance in the form of Earth rotation parameters that affects all ground
stations.

A number of sites have instruments of more than one technique at distances of
30–500 meters. Direct measurement of their positions with respect to each
other can establish direct ties. Survey techniques measure angles and
distances between markers. These measurements can reach accuracy of 1–3 mm.
However, the ties should provide the positions of technique reference points.
Reference points of microwave techniques, such as VLBI and GNSS, cannot be
directly pin-pointed by markers. An offset of a reference point with respect
to a marker is inferred. In the case of GNSS ground stations, an offset
between a marker on the instrument and its phase center can be calibrated, for
instance, in an anechoic chamber. In the case of VLBI radiotelescopes, markers
are put on the antenna, and the position of a geometric reference point on a
fixed axis that is a projection of a moving axis is derived from processing a
cloud of points measured with a total station at different antenna azimuths
and elevations. Then an assertion is made that the geometric reference point
coincides with the reference point estimated in VLBI data analysis. The
validity of that assertion cannot be evaluated.

The positions of microwave reference points provided by data analysis of both
the GNSS and VLBI techniques may have biases with respect to the geometric
reference points. As long as these biases are permanent and do not depend on
any other variable parameters, they can remain unnoticed. For a number of
applications, for instance for a study of motions caused by plate tectonics or
for mean sea level determination, permanent biases are irrelevant. r:sarti11
showed that antenna gravity deformation caused a 7 mm offset of the microwave
reference point of VLBI station medicina, whose position was determined from
analysis of VLBI group delay with respect to a geometric refrence point
determined from a local survey. Mismodeling antenna gravity deformation will
not affect the least square fit and may not be noticed, but biases in local
tie measurements comparable or exceeding the internal accuracy of GNSS and
VLBI techniques make them close to useless.

The fundamental problem of tie measurements with local surveys is that the
optical technique used by a survey instrument, such as a total station, cannot
measure the phase center of a microwave technique. While the accuracy of
measurements of a vector between markers can be evaluated from a scatter of
residuals, the accuracy of a vector between a marker to a phase center is
poorly known. That makes tie vectors determined with local surveys unreliable.
A typical discrepancy between VLBI positions determined from analysis of group
delays and GNSS positions reduced to the VLBI reference point via tie vectors
determined with local surveys is 5–20 mm (r:ray05, ). Lack of realistic
uncertainties of tie vectors does not allow us to interpret these
discrepancies because we do not know whether they are due to systematic errors
of space geodetic techniques or due to error in tie vectors. That motivated us
to seek for alternative measurements of tie vectors.

##  2 A microwave technique for VLBI/GNSS tie measurements

We are leveraging the High Rate Tracking Receiver (HRTR) to serve as both an
advanced software-defined GNSS receiving system and a general purpose L-band
receiver (r:hrtr12, ; r:yor14, ). It directly digitizes voltage from the
receiver in a range of 1 to 2 GHz at a rate of 2 gigasamples per second. To
access a larger extent of the signal in the 1–2 GHz range, we modified a
commercial GNSS antenna. Specifically, we removed the internal amplifier and
narrowband bandpass filters that are provided, and we have replaced them with
an alternate amplification and filtering stage of our own design. The
aggregate RF system including modified components has a passband of
approximately [1.10, 1.65] GHz. The antenna elements are not altered in this
modification.

The HRTR performs digital downconversion of the input samples and produces up
to nine independently chosen frequency bands 40.912 MHz wide. The HRTR also
allows us to configure the bit depth of the received signal. We utilized
complex encoding for our work, using one bit for the in-phase and one bit for
the quadrature voltage. Datastreams with the baseband signal from each band
are recorded to a general purpose RAID of magnetic harddrives.

In additional to recording voltage from the receiver, HRTR simultaneously
computes conventional GNSS observables on civil GNSS signals in real time and
provides an output convertible to RINEX format. We can recompute conventional
GNSS observables by processing digital records of the baseband signal if
needed.

We noticed that the HRTR has a striking similarity to a radiotelescope that is
an element of a VLBI network. Like a radiotelescope, the HRTR digitizes
voltage from the antenna and records the data with time stamps from a precise
clock. HRTR data are processed after the experiment in a similar way as VLBI.
Extending this analogy further, we came to the idea of using a HRTR itself as
an element of a VLBI network. A GNSS antenna with an effective diameter of
$\sim\\!0.08$ meter surrounded by 0.38 m wide choke ring is roughly four
orders of magnitude less sensitive than a 12–30 meter radiotelescope, it
operates at a lower frequency, and at a first glance does not look
competitive. However, the use of a GNSS antenna as an element of a VLBI
network is very promising for local tie measurement. Observations at short
baselines 30–3000 meters are almost insensitive to the atmospheric path delay.
r:hase99 ; r:var21  demonstrated that baseline length repeatability at a sub-
millimeter level has been achieved from processing of phase delays at short
baselines. We should stress that the baseline vector between two antennas
evaluated from VLBI observations is between the microwave reference points of
the radiotelescopes. Therefore, by processing GNSS/radiotelescope data, we can
eliminate the weakest link in the measurement chain of a tie vector with the
use of conventional local surveys: the offset between a marker and a microwave
reference point.

Figure 1: Measurement concept of VLBI/GNSS ties with a microwave technique.

The measurement concept is presented in Figure 1. The voltage of the emission
received by the GNSS antenna in a range of 1.0 to 2.0 GHz is transferred via a
coaxial cable to an analog-to-digital converter and recorded. The digital
records are re-sampled and re-coded to VDIF format that is commonly accepted
in radio astronomy. Emission received by a VLBI antenna is processed the same
way, but with different hardware. The output of both the GNSS and VLBI
antennas is recorded in the same format. Further processing is performed
exactly the same way as processing of any other VLBI data: the data are
correlated, the fringe fitting procedure finds group delays and phase delay
rates that maximize the fringe amplitude coherently averaged over time and
frequency, and finally group and phase delays are used for determination of
the baseline vector using least squares. Therefore, we expect that a position
vector of a GNSS antenna/radiotelescope baseline will be determined with the
same sub-millimeter accuracy as position vectors of other short baselines.

##  3 Early results

Implementation of VLBI with a GNSS antenna requires overcoming a number of
difficulties (J. Skeens et al. (2023), paper in preparation). It is essential
that the HRTR does not perform any analog signal transformation. It simply
digitizes signal as is, performs digital filtering into several bands, and
writes the digital signal. This early digitization approach shifts the burden
of signal processing to programming. This facilitates the tuning of the
processing pipeline since digital records can be re-processed as many times as
needed.

We performed three 3 hr long observing sessions in 2022 between two
transportable HRTRs and a 25 m radiotelescope fd-vlba. That radiotelescope is
a part of the Very Long Baseline Array dedicated for VLBI and has been
operating since 1991. It is equipped with an H-maser clock. The antenna has a
number of very sensitive receivers, including the one that operates at L-band.
We put the first HRTR within 90 m of the fd-vlba. That HRTR was stabilized by
a Rubidium clock. We put the second HRTR within 9000 m of fd-vlba near the
NASA VLBI station macgo12m. This HRTR was stabilized by the H maser clock used
by macgo12m. Since macgo12m does not have the technical capability to observe
below 2 GHz, we performed observations at only the two HRTRs and fd-vlba.

The observing schedule included observations of seven of the brightest
radiogalaxies and a number of GNSS satellites. We have detected all but one
radiogalaxy at the short baseline with fd-vlba and some sources at the 9 km
long baseline. As expected, no detection was found between the two HRTR
stations. Figure 2 shows fringe phases and normalized fringe amplitudes of
radiogalaxy Cyg-A located at a distance of $7.2\cdot 10^{21}$ m. This goes
well beyond (fourteen orders of magnitude!!) the intended use of the GNSS
equipment. The interferometric fringes of radiogalaxies were stable over time,
and integration could be extended up to 20 minutes without a noticeable
degradation of fringe amplitude.

Figure 2: Fringe phase (upper) and normalized fringe amplitude of Cyg-A at a
90 m long baseline hrtr/fd-vlba. Signal to noise ratio (SNR) 387 was achieved
for 60 seconds of integration time. Left plot shows fringe phase and amplitude
versus frequency and right plot shows fringe phase and amplitude versus time.

Figure 3 shows fringe plots of a GPS satellite over 10 s integration time. The
GPS signal was treated as a random noise in the model of our VLBI data
analysis. The fringe amplitude has a peak at the carrier frequency of 1575.42
MHz, emission near 1 MHz of the peak due to the C/A signal, and a broad
emission due the binary offset carrier modulation of the M-code that has a
detectable power within $\pm 15$ MHz of the carrier. This allows us to compute
group delay over the total bandwidth of $\sim\\!30$ MHz with a precision of
60–90 ps over 10 s. This should be sufficient for resolving phase delay
ambiguities with spacings of 635 ps. Interferometric responses have been
detected at the 9 km long baselines as well. At this stage of the project we
did not yet attempt to perform geodetic analysis.

Figure 3: Fringe phase (upper) and normalized fringe amplitude of a GPS
satellite at a 90 m long baseline hrtr/fd-vlba. SNR 138 was achieved for 10
seconds of integration time. Left plot shows fringe phase and amplitude versus
frequency and right plot shows fringe phase and amplitude versus time.

##  4 Discussion

A vector tie can be determined from both observations of natural sources, such
as radiogalaxies, and from observations of navigational satellites. The
broadband GPS signal due to the modulation of the M-code has flux density
around -200 dBW/m2/Hz (r:tho19, ), i.e. $\sim\\!1$ MJy, while there are only
10 natural radio sources brighter that 0.02 MJy at 1.5 GHz, i.e. a factor of
50 fainter. The scarcity of very strong radiogalaxies makes preparation of a
VLBI schedule optimized for geodesy difficult.

Detection of a radio source requires observations with a sensitive VLBI
antenna. fd-vlba is dedicated for astronomy and its L-band receiver has a
system equivalent flux density (SEFD) of 289 Jy. Compare with SEFD 2500 Jy at
the 2–3 GHz band at 12 m geodetic VLBI antennas. Since sensitivity of an
interferometer is proportional to the square root of the product of SEFD of
individual antennas, VLBI observations of a GPS satellite between a HRTR and a
radiotelescope requires $50^{2}=2500$ times less sensitive radiotelescope than
observations of radiogalaxies. Figures 2–3 seem to contradict that statement.
It turned out fd-vlba receiver worked in a saturated regime when observing a
megajansky source, and fringe amplitude was strongly underestimated. Applying
an additional attenuation is required to mitigate the problem. But in general,
it is much easier to reduce the sensitivity than to increase it.

The primary observable that will be used for determination of the tie vector
will be phase delay. Phase delay ambiguities can be resolved if group delay
can be determined with an accuracy 1/4 of the phase ambiguity spacing or
better and short-term systematic differences between phase and group delays
have a scatter not exceeding that number. Since precision of group delay is
reciprocal to the bandwidth of a detected signal, observations of navigational
satellites with a relatively broad spectrum, such as GPS and Galileo, is
preferable.

Determination of a tie vector between a HRTR and a geodetic VLBI antenna is
interesting, but not exactly what is needed. We need to determine a tie vector
between a VLBI antenna and a permanent GNSS antenna. There are two possible
solutions. First, one can make HRTR a permanent GNSS site. It is expected that
in 2023–2024, permanent HRTRs will be installed within a hundred meters of
each of the ten VLBA antennas. Second, one can install a HRTR on a temporary
monument and determine a tie vector HRTR/radiotelescope using VLBI and a tie
vector between the HRTR and the existing GNSS antenna by processing GNSS
signals from both antennas using double differences. Processing differential
GNSS data at baselines of $\sim\\!\\!100$ m long provides a millimeter level
accuracy owing to cancellation of the atmospheric contribution. Then combining
the VLBI/HRTR and HRTR/GNSS tie vectors, we get a VLBI/GNSS tie.

Radiotelescopes used for radio astronomy often have receivers in 1.2–1.8 GHz
ranges, although very few instruments have the ability to simultaneously
record within a band of 1.15–1.65 GHz that covers navigation signals L1, L2,
and L5. Radiotelescopes dedicated for geodesy usually cannot receive emission
below 2 GHz because of strong high-pass filters installed to mitigate the
impact of radio interference. Some new generation broad-band VLBI Geodetic
Observing System (VGOS) radiotelescopes have a low cutoff frequency as high as
3.0 GHz because broadband receivers are much more susceptible to radio
interference. A solution is to equip existing geodetic radio telescopes with
auxiliary receivers operating in the 1–2 GHz range dedicated to VLBI
observations of navigational satellites. Since the GNSS signal is so strong,
such receivers do not require cooling. The navigational receiver can be
installed alongside the main receiver, and the signal can be directed to it
either with a deployable mirror or with a dichroic plate.

##  5 Summary

We propose a novel concept of GNSS/VLBI tie measurements based on a microwave
technique. We essentially transform a GNSS antenna into an element of the VLBI
network. This method allows us to estimate the tie vector between the VLBI and
GNSS reference points directly using the microwave technique without the need
to determine the position offsets of the microwave reference points with
respect to markers accessible to local surveys.

We expect that the application of this method will have a profound impact
because we expect this method will be bias-free. As a result, vector tie
repeatability can be used as a measure of the accuracy of tie vector
determination. Knowing errors of tie vectors will enable us to close the
budget of the differences of the VLBI reference points reduced to the GNSS
reference points and make an inference about whether these differences are
statistically significant or not.

We ran three 3 hour long observing sessions between the fd-vlba radiotelescope
and a high rate GNSS receiver co-located within 90 m. We have detected fringes
from both natural extragalactic radio sources and GPS satellites with the SNR
well above 100. Thus, we have demonstrated that technical problems related to
GNSS/radiotelescope VLBI can be solved. Future work will be focused on the
determination of vector ties using this technique.

## References

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