††thanks: now at South Dakota School of Mines and Technology††thanks: now at
Carleton University, Ottawa, Ontario, Canada††thanks: now at Imperial College
London, London, England††thanks: now at McGill University, Montreal, Quebec,
Canada††thanks: now at STFC, Rutherford Appleton Laboratory, Harwell Oxford,
England

# A measurement of proton-carbon forward scattering in a proof-of-principle
test of the EMPHATIC spectrometer

M. Pavin  TRIUMF, Vancouver, BC V6T 2A3, Canada  L. Aliaga-Soplin  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Barbi
Department of Physics, University of Regina, SK, S4S 0A2, Canada  L.
Bellantoni  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  S. Bhadra  Department of Physics and Astronomy, York University, Toronto,
Ontario, Canada  B. Ferrazzi  Department of Physics, University of Regina, SK,
S4S 0A2, Canada  L. Fields  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  Department of Physics, University of Notre Dame, Notre
Dame, Indiana 46556, USA  A. Fiorentini  Department of Physics and Astronomy,
York University, Toronto, Ontario, Canada  T. Fukuda  Nagoya University,
Nagoya, Aichi 464-8601, Japan  K. Gameil  TRIUMF, Vancouver, BC V6T 2A3,
Canada  Y. Al Hakim  TRIUMF, Vancouver, BC V6T 2A3, Canada  M. Hartz  TRIUMF,
Vancouver, BC V6T 2A3, Canada  Kavli Institute for the Physics and Mathematics
of the Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan  B. Jamieson  University of
Winnipeg, Winnipeg, MB R3B 2E9, Canada  M. Kiburg  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  N. Kolev  Department of Physics,
University of Regina, SK, S4S 0A2, Canada  H. Kawai  Department of Physics,
Chiba University, Chiba, Chiba 263-8522, Japan  A. Konaka  TRIUMF, Vancouver,
BC V6T 2A3, Canada  P. Lebrun  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  T. Lindner  TRIUMF, Vancouver, BC V6T 2A3, Canada  T.
Mizuno  Department of Physics, Chiba University, Chiba, Chiba 263-8522, Japan
N. Naganawa  Nagoya University, Nagoya, Aichi 464-8601, Japan  J. Paley  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  R. Rivera
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  G.
Santucci  Department of Physics and Astronomy, York University, Toronto,
Ontario, Canada  O. Sato  Nagoya University, Nagoya, Aichi 464-8601, Japan  T.
Sekiguchi  Institute of Particle and Nuclear Study (IPNS), High Energy
Accelerator Research Organization (KEK), Tsukuba, 305-0801, Japan  A. Sikora
University of Winnipeg, Winnipeg, MB R3B 2E9, Canada  G. Slater  TRIUMF,
Vancouver, BC V6T 2A3, Canada  A. Suzuki  Kobe University, Kobe, Hyogo
657-8501, Japan  T. Sugimoto  Kobe University, Kobe, Hyogo 657-8501, Japan  M.
Tabata  Department of Physics, Chiba University, Chiba, Chiba 263-8522, Japan
L. Uplegger  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  T. Vladisavljevic  Kavli Institute for the Physics and Mathematics of the
Universe (WPI), The University of Tokyo Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba, Japan

###### Abstract

The next generation of long-baseline neutrino experiments will be capable of
precision measurements of neutrino oscillation parameters, precision neutrino-
nucleus scattering, and unprecedented sensitivity to physics beyond the
Standard Model. Reduced uncertainties in neutrino fluxes are necessary to
achieve high precision and sensitivity in these future precise neutrino
measurements. New measurements of hadron-nucleus interaction cross sections
are needed to reduce uncertainties of neutrino fluxes. We report measurements
of the differential cross section as a function of scattering angle for
proton-carbon interactions with a single charged particle in the final state
at beam momenta of $20$, $30$, and $120\>$GeV/c. These measurements are the
result of a beam test for EMPHATIC, a hadron-scattering and hadron-production
experiment. The total, elastic and inelastic cross-sections are also extracted
from the data and compared to previous measurements. These results can be used
in current and future long-baseline neutrino experiments, and demonstrate the
feasibility of future measurements by an upgraded EMPHATIC spectrometer.

††preprint: FERMILAB-PUB-21-273-E-ND-SCD

##  I Introduction

Measurements of hadron interactions spanning two orders of magnitude
($1-100\>$GeV/c) of incident particle momenta are of crucial importance for
reducing the neutrino production modeling uncertainty in accelerator-based and
atmospheric neutrino experiments. The neutrino flux uncertainty is the
dominant uncertainty in many neutrino measurements, including neutrino nucleus
cross-section measurements, sterile neutrino searches, and CP violation
measurement in atmospheric neutrinos. Long-baseline neutrino experiments are
entering a precision era with the future Hyper-Kamiokande [1] and DUNE [2]
projects. Uncertainties in the energy dependence of the neutrino flux and
cross section are amongst the most challenging systematic uncertainties in
these neutrino experiments.

Neutrinos are produced by the decays of hadrons produced in proton
interactions in nuclei. Since it is at best extremely difficult and time
consuming to measure the neutrino beam flux as a function of energy, Monte
Carlo simulations based on hadron interactions and decays are used to make
a-priori predictions of the neutrino flux. This approach is limited by the
sparse hadron interaction data often with significant errors, and hadron
interactions are the dominant systematic uncertainty in the neutrino flux
prediction. Interpolation and extrapolation of the hadron interaction cross
section using phenomenological models introduces additional uncertainties.
Measurements of hadron interactions are used to constrain or scale the models
to provide a more precise prediction of the neutrino flux. A good example of
how data are used in neutrino flux simulations can be found in [3].

Many of the hadron interaction data relevent to GeV-energy neutrino flux
predictions were taken in the second half of twentieth century. Although these
data are very valuable, they are insufficient for the precise neutrino flux
predictions due to low precision and lack of error covariances. In more recent
years, experiments like NA61/SHINE [4, 5, 6, 7], HARP [8, 9] or MIPP [10, 11,
12] took valuable data with the direct requests and input from the neutrino
experiments. These data include cross-section and hadron production
measurement for various targets and beam momenta. Even with these data, the
typical neutrino flux uncertainty in the current generation of the
accelerator-based neutrino experiments is between $5\%$ and $15\%$ due to
limited phase space coverage and other sources of systematic uncertainties.

The neutrino flux uncertainty directly affects all measurements done in a
single (near) detector where far-to-near detector cancellation is not
possible. However the reduction of the neutrino flux uncertainty is also
important for neutrino oscillation measurements, in particular measurements of
CP violation in the lepton sector. Constraining the $\nu_{e}/\nu_{\mu}$ ratio
and measuring $\nu_{e}$ cross-section is of utmost importance for reducing the
systematic uncertainty in CP violation measurements in the Hyper-Kamiokande
and DUNE experiments [1, 13]. These cross sections will be measured in the
intermediate water Cherenkov detector (IWCD) in Hyper-Kamiokande and the DUNE
near detector. However, these measurement is limited by the neutrino flux
uncertainty and reduction of the flux uncertainty to levels of $3\%$ are
necessary. Another example is the measurement of CP violation in atmospheric
neutrinos, which is limited by the neutrino flux uncertainty coming from the
sub-$20\>$GeV/c cosmic ray interactions with the atmosphere.

Several missing pieces of data are necessary to reduce the neutrino flux
uncertainty in current and future accelerator-based and atmospheric neutrino
experiments:

  1. 1.

hadron production in sub-$10\>$GeV pion and kaon interactions on carbon,
aluminium, titanium and iron,

  2. 2.

hadron production in sub-$20\>$GeV proton-air interactions (or equivalent
targets),

  3. 3.

measurements of coherent elastic and quasi-elastic interactions of hadrons for
carbon, aluminium, titanium and iron targets between $1\>$GeV/c and
$120\>$GeV/c,

  4. 4.

measurements of strange hadron production in proton-carbon interactions to
validate older measurements.

The detailed explanation of each point is out of scope of this paper and can
be found in [14]. This paper describes a measurement of (3) above which is
possible using data from an early beam test of EMPHATIC (Experiment to Measure
the Production of Hadrons At a Testbeam in Chicagoland). Future EMPHATIC
measurements will address the remaining items in the list.

##  II EMPHATIC experiment

EMPHATIC is designed to study hadron interactions in the $2-120\>$GeV/c range
at the Fermilab Test Beam Facility (FTBF). The physics program of EMPHATIC
covers previously listed requirements for the improvement of the neutrino flux
in the upcoming long-baseline neutrino oscillation experiments [14].

The EMPHATIC design exploits ~$10\>\mu$m spatial resolution of silicon strip
detectors that results in a compact hadron spectrometer. The dipole magnet is
a custom-built Halbach array of NdFeB magnets with a $\int{Bdl}$ of
approximately $0.25\>$Tm. Beam particle identification is done using gas and
aerogel threshold Cherenkov detectors. Identification of secondary particles
is done by time-of-flight measurements in resistive plate chambers (RPCs) and
by measuring the Cherenkov angle in aerogel ring imaging detector (ARICH)
based on the Belle-II design [15]. A lead calorimeter at the downstream end of
the experiment enables separation of electrons, muons and hadrons. The total
length of the spectrometer is approximately $2\>$m.

In this paper, we present the results of an EMPHATIC test-beam measurement
done in January 2018 using only silicon strip detectors to record particle
trajectories. No magnet and no detectors for secondary particle identification
were used in the test-beam setup. The results include differential cross-
section for p+C$\rightarrow$X± at $20$, $30$, and $120\>$GeV/c, where X± is a
single charged particle within 20 mrad, the acceptances of the tracking
detectors used in this measurement. This enables the measurements of forward
scattering (coherent elastic and quasi-elastic interactions). The event
topology with a single forward charged particle includes coherent-elastic
interactions, quasi-elastic interactions and some inelastic interactions.
Coherent elastic interactions are defined as scattering off the whole nucleus.
Both the incident particle and the target nucleus survive in this case. In
quasi-elastic interactions, the target nucleus is fragmented while the
incident hadron survives. And finally, inelastic interactions are those in
which at least one new meson is produced. We have also fitted a simple model
to our data to extract useful quantities such as total and elastic cross-
section. Results are compared to both Monte Carlo predictions and other
measurements.

##  III Experimental setup

The EMPHATIC test-beam measurements were done at the FTBF. The facility
provides a primary $120\>$GeV/c proton beam from the Main Injector, or a
secondary beam with momentum above $2\>$GeV/c.The beam is delivered in $4\>$s
spills every minute. The intensity is tunable from $1\>$kHz to $100\>$kHz and
the typical beam spot area is $2\>$cm2. The momentum resolution of the
secondary beam ($\Delta p/p$) is approximately $2\%$. The FTBF provides a set
of gas threshold Cherenkov detectors for secondary beam particle
identification. Pion identification is possible above $5\>$GeV/c, while kaon
identification is only possible above $18\>$GeV/c. The pressure in the first
Cherenkov detector was tuned to detect positrons, muons and pions in the
secondary beam. The trigger includes signals from the first Cherenkov detector
in the anti-coincidence with two scintillators to remove all particles except
kaons and protons. The pressure in the second gas Cherenkov detector was tuned
to detect kaons, which can be separated from the protons during the data
analysis.

The FTBF also provides a set of silicon strip detectors (SSDs) with effective
area of $3.8\times 3.8\>$cm2 and the strip pitch of $60\>\mu$m. Each detector
has two silicon strip planes for measuring two independent dimensions. For the
EMPHATIC beam test, four detectors were placed upstream of the target and
three detectors were placed downstream of the target. In addition to silicon
strip detectors, the FTBF provides a silicon pixel telescope consisting of
eight pixel planes located between four upstream SSDs and the target. Four of
the planes have sensitive area of $3.24\times 1.62\>$cm2 and the other four
have an area of $1.62\times 2.43\>$cm2. Due to inefficiencies with the pixel
data acquisition and the smaller effective area, data from the pixels are not
used for this measurement. Instead, the pixel telescope is treated as a
passive material in the beamline and data are corrected for energy losses in
this material. The schematic overview of the setup with defined coordinate
system is shown in Fig. 1.

Figure 1: Schematic overview of the experimental setup. The first trigger
scintillator and gas Cherenkov detectors are located several meters upstream,
and are not shown.

The target is made of Toyo Tanso IG-$43$ graphite which is the target material
of choice in the T2K beamline. The same graphite was used for NA61/SHINE
measurements. The target thickness is $2\>$cm which is approximately $5\%$ of
the interaction length. The measured target density is $1.83\pm 0.04\>$g/cm3.

##  IV Simulation and Data analysis

p [GeV/c] | Target | Number of triggers [$10^{6}$]
---|---|---
$20$ | carbon | $0.463$
$20$ | empty | $0.410$
$30$ | carbon | $1.031$
$30$ | empty | $0.197$
$120$ | carbon | $1.013$
$120$ | empty | $1.068$
Table 1: Collected number of triggers

The data collected with graphite and empty targets are summarized in Tab. 1.
The empty target data are used for silicon strip alignment and for estimating
background interactions in the data analysis. The alignment is done by
selecting $10000$ empty target events with a single hit per silicon strip
plane. A simple line fit is used to fit a track in each event. The tracking
plane positions and angles are determined by minimizing the sum of $\chi^{2}$
values for all $10000$ track fits. Any position misalignment is at sub-micron
level and any angular misalignment is below $0.01\>$mrad.

After the alignment, angular resolution is determined for each dataset by
fitting upstream and downstream tracks separately and calculating the angle
between them in x-z and y-z planes. A Gaussian is fit to the angular
distributions and the width divided by $\sqrt{2}$ is taken as the effective
angular resolution. The effective angular resolution includes intrinsic
angular resolution of the detector and smearing effect caused by multiple
scattering in the detector material.

Silicon strip efficiencies are also calculated based on the empty target data.
For a given silicon strip plane, events are selected by requiring a single
cluster per plane in all other planes. A track is fitted for each event and
extrapolated to the selected plane and checked if there is a cluster present
within $\pm 60\>\mu$m. The efficiencies are better than $99\%$. Both, the
angular resolution for different datasets and silicon plane mean efficiencies
are presented in Fig. 2.

(a)

(b)

Figure 2: The effective angular resolution vs. beam momentum (a) and mean
silicon plane efficiencies (b). The angular resolution is shown for both, the
empty and the carbon target data. Multiple scattering in the target makes the
effective angular resolution in the carbon target data worse at low momentum.
The vertical red line in the efficiency plot separates upstream and downstream
planes.

The positions and efficiencies of the silicon strip planes obtained from these
studies as well as beam-profile measurements from data are used as input
parameters in Geant4-based Monte Carlo simulation[16]. Angular distributions
from the data are used to validate the simulation. The simulation includes
silicon strip and pixel planes, target and trigger scintillators. In total,
$10$ million beam protons are simulated for each beam settings with FTFP_BERT
and QGSP_BERT physics lists from Geant4.10.05.p01. The simulation is used to
estimate detector, acceptance and reconstruction inefficiencies and
corresponding corrections are applied to data. Additionally, simulated events
are used for some of the systematic studies described in Sec. VI.

The measurement of the forward differential cross-section without final-state
momentum measurement is based on the assumption that four-momentum transfer
$t$ is approximately equal to $t\approx-p_{\mathrm{b}}^{2}\theta^{2}$ for
small t, where $p_{\mathrm{b}}$ is the incident beam momentum, and $\theta$ is
the scattering angle. This approximation is valid for coherent elastic and
quasi-elastic interactions. However, it cannot be used for the inelastic
scattering. The measurements presented here include proton-carbon differential
cross-section for events with a single charged particle emitted from the
target within $\pm 20\>$mrad with respect to the beam particle. Such
interactions also include inelastic scattering where for example a neutron and
pion are emitted in the forward detection. Therefore, the approximation for
$t$ does not hold for these events. It is possible to remove inelastic events
by applying an undesirable model-dependent correction. Instead we report
$d\sigma/d(p_{\mathrm{b}}^{2}\theta^{2})$:

$\left(\frac{d\sigma}{d(p_{\mathrm{b}}^{2}\theta^{2})}\right)_{i}=\frac{1}{N_{pot}}\frac{N_{i}}{nd\cdot\Delta(p_{\mathrm{b}}^{2}\theta^{2})_{i}},$
(1)

where $N_{pot}$ is the number of protons on target, $N_{i}$ is the corrected
number of events with a single downstream track in a
$p_{\mathrm{b}}^{2}\theta^{2}$ bin $i$, $nd=0.000179\>$mb-1 is the target
number density multiplied by the target length and
$\Delta(p_{\mathrm{b}}^{2}\theta^{2})_{i}$ is $i$-th bin width. A set of cuts
is applied to the data to remove any background interactions.

###  IV.1 Event selection

The event selection is divided into upstream and downstream track selection.
The purpose of the former is to select a pure proton sample and to remove any
interactions upstream from the target. The purpose of the latter is to select
a pure sample of events with a single scattered charged particle downstream of
the target.

Beam particle identification is done by using gas Cherenkov detector available
in FTBF. One detector used in anti-coincidence with the trigger scintillator
is used to remove pions and electrons in the beam. The gas pressure in the
second detector was set above the kaon threshold. Kaons and any electrons and
pions remaining are removed by cutting out the signal in the recorded ADC
distribution as shown in Fig. 3. Protons are part of the pedestal since they
did not produce any Cherenkov light. The average number of photoelectrons
detected from kaons passing through the detector is around $30$. Any non-
proton contamination after the cut is estimated by fitting the kaon signal and
pedestal to be much smaller than $1\%$. The $120\>$GeV/c beam is a pure proton
beam since it comes directly from the Main Injector and Cherenkov detectors
are not necessary in this case.

Figure 3: The ADC count distribution for the PMT in the second gas Cherenkov
detector for $30\>$GeV/c data. Selected events are located between dashed red
lines.

Additional cuts are applied to remove most of the interactions in the upstream
silicon strips and trigger scintillator. Only events with a single upstream
track with a hit cluster in each plane and a sufficiently low $\chi^{2}$ are
selected. Additionally, events with tracks in the tails of the beam divergence
($dx/dz$ and $dy/dz$) distributions are removed since these are mostly coming
from the upstream interactions. The estimated number of the upstream
interactions remaining after the selection is below $0.1\%$. However, these do
not include interactions in the silicon pixel layers that are between the
upstream strip layers and the target. Finally, a cut is applied to the
incoming beam particle so that scattered particles within $\pm 20\>$mrad
always falls within the acceptance of the downstream silicon strip layers.

The purpose of the downstream selection is to identify forward scattered beam
protons and remove hard inelastic interaction in the pixel telescope, target,
and downstream SSDs. Selected events have only one reconstructed track with a
hit cluster in each downstream plane and the $\chi^{2}$ value below $6$. An
additional cut is applied to remove interactions in silicon pixel layers. The
upstream and downstream tracks in an event are extrapolated toward the center
of the target. A cut is applied on the $x$ and $y$ distances between the
tracks. If an interaction happened somewhere outside of the target, the
difference in $x$ and $y$ positions would be larger. The cut on the $x$ and
$y$ distances is defined as:

$|x_{up}-x_{down}|>3\cdot\sigma_{x}+3\cdot\sigma_{\theta_{x}}\cdot|z_{vert}-z_{targ}|$
(2)

where $\sigma_{x}$ is a width of the $x$ distance distribution and
$\sigma_{\theta_{x}}$ is a width of $\theta_{x}$ distribution. A schematic of
the $x$ and $y$ cut is shown in Fig. 4.

Figure 4: A schematic of the $x$ and $y$ cut. If interaction happens in a
pixel plane, $x$ and $y$ distances between upstream and downstream tracks at
target z position will be significantly different than zero.

To illustrate the effect of the $x$ and $y$ cuts, a reconstructed angle vs.
reconstructed vertex position distribution is shown in Fig. 5 before and after
applying the cuts. Several peaks are visible in the distribution. The first
peak from the left corresponds to the last upstream silicon strip plane. The
next four peaks correspond to the eight pixel planes (pixel planes come in
pairs, which are only $5\>$cm apart. The largest peaks shows interactions in
the target. The last peaks correspond to the first downstream silicon strip
plane. After $x$ and $y$ cuts are applied, inelastic interactions outside of
the target are removed in both data and simulation.

(a) Data

(b) Simulation

Figure 5: Reconstructed angle vs. reconstructed vertex $z$ position for
proton-carbon data (a) and FTFP_BERT G4.10.04.p2 Monte Carlo (b) at
$30\>GeV/c$ before (top) and after (bottom) $x$ and $y$ cuts. First peak at
$z=-70\>$cm shows interactions in the last upstream silicon plane. The next
four peaks are in fact four double peaks (clearly visible in simulation) and
they show interactions in eight pixel planes. The large peak at $z=70\>$cm
includes interactions in the target, and the last peak includes interactions
in the first downstream silicon strip detector.

The raw differential cross-section needs to be corrected for various
inefficiencies such as: SSD inefficiencies, reconstruction inefficiencies,
selection inefficiencies and interactions outside of the target. The
efficiency corrections can be grouped into two groups: corrections based on
Monte Carlo simulation and corrections based on the data.

###  IV.2 Monte Carlo correction factors

Monte Carlo efficiency includes silicon strip efficiency, reconstruction
efficiency and selection efficiency. However, it does not include smearing
effects caused by detector resolution. The efficiency factor is defined as:

$\epsilon_{i}=\frac{N_{i,sel,true}}{N_{i,true}},$ (3)

where $i$ is the $p^{2}\theta^{2}$ bin number, $N_{i,sel,true}$ is the number
of selected downstream tracks in the true bin $i$, and $N_{i,true}$ is the
number of true tracks in the bin $i$ before the selection. The efficiency is
calculated only for beam particles hitting the target without any prior
interaction. The correction factor is defined as an inverse efficiency. A
Geant4 based Monte Carlo simulation has been used to calculate the
corrections. The simulation includes the target, silicon strip layers, silicon
pixel layers and the trigger scintillator. Two physics lists are used to
calculate the correction factor: FTFP_BERT and QGSP_BERT from Geant4.10.05.p1.
The Monte Carlo efficiency is presented in Fig. 6. The differences in
efficiency between datasets come from the differences in the fraction of
inelastic events. Selected events with a single forward low momentum charged
proton or pion tend to have lower efficiency. The probability of scattering in
downstream tracking layers and multiple scattering increases for low momentum
particles. Therefore the $\chi^{2}$ of these tracks tends to be higher on
average, resulting in lower efficiency.

(a)

(b)

(c)

Figure 6: Downstream selection efficiency for proton-carbon data at
$20\>$GeV/c (a), $30\>$GeV/c (b), and $120\>$GeV/c (c) for FTFP_BERT and
QGSP_BERT G4.10.05.p1 physics lists.

###  IV.3 Data correction factors

Pixel interactions removed by $\Delta x$ and $\Delta y$ cuts are elastic
interactions with higher four-momentum transfer and inelastic interactions.
Since they happen before the beam hits the target, any interacting beam
particle is lost and needs to be removed from the number of protons on target.
A normalization correction is applied to the number of incoming beam
particles. The correction is estimated from the empty target data:

$N_{POT,cor}=N_{tout,rem}\cdot C\cdot\frac{N_{tin,POT}}{N_{tout,POT}},$ (4)

where $N_{tout,rem}$ is the number of removed pixel interactions in the empty
target data, $C$ is the purity correction based on simulation, and
$\frac{N_{tin,POT}}{N_{tout,POT}}$ is the ratio of number of selected events
after upstream selection in the carbon target and empty target data. The
purity correction is a ratio of the true removed pixel interactions and the
total number of removed events. Empty target data is used for this correction
to avoid any bias from including interactions in the target. The normalization
correction is $2.0\%$, $2.3\%$, and $3.0\%$ for $20$, $30$, $120\>$GeV/c data
respectively.

##  V Systematic uncertainties

Several systematic contributions are considered in the analysis: beam purity,
the number of interactions in upstream detectors (beam loss), target density
and thickness uncertainties, and efficiency variations. As previously
mentioned, kaon contamination in the proton beam after gas Cherenkov cut is
estimated to be negligible. Beam loss is caused by interactions in the pixel
telescope as explained in the previous section. Since the beam loss is between
$2\%$ and $3\%$ and the purity correction is around $95\%$, any systematic
uncertainty is going to be small. The beam loss systematic contribution
includes the statistical uncertainty from the empty target data and purity
variation estimated by using FTFP_BERT and QGSP_BERT physics lists. Values are
below $1\%$ for all three datasets. A normalization uncertainty from the
measured target density and thickness is estimated to be $2\%$ and it is the
dominant contribution at low $p^{2}\theta^{2}$.

The efficiency uncertainty includes contributions from MC statistics, SSD
plane efficiencies, differences in $\chi^{2}$ distributions between data and
MC, differences in angular resolution, and model differences. Silicon
efficiencies in simulation are reduced in all planes by their uncertainties,
and the efficiency is reevaluated. The difference between the nominal and
reevaluated efficiency is taken as a systematic uncertainty.

A similar approach is used for the variation of cut parameters. The $\chi^{2}$
distribution from the data has a longer tail compared to the distribution from
simulation. This is caused by a small number of track clusters with multiple
active strips in data. These clusters are created by a passing charged
particle and emitted delta electron. Delta electrons induce signals in the
neighbouring strips and create a systematic shift in the measured position of
the original particle. Reconstructed tracks with such clusters will have
increased $\chi^{2}$ value. The $\chi^{2}$ value used in MC cut is adjusted so
that the fraction of removed events is the same as the one in the data. The
efficiency is reevaluated after using the new cut and the difference is taken
as a systematic uncertainty.

Similarly, the angular resolution in Monte Carlo simulation can be from $3\%$
to $7\%$ different from the data, depending on the dataset. Angular resolution
parameters in $\Delta x$ and $\Delta y$ cuts are varied within $\pm 7\%$ and
the difference is taken as a systematic uncertainty.

Finally, differences in efficiency estimated with FTFP_BERT and QGSP_BERT are
used as a systematic uncertainty. These differences are caused by the
variation in the number of events with a single low momentum pion in the
forward direction. Low momentum pions ($<5\>$GeV/c) have lower selection
efficiency compared to elastically scattered beam particles. Effective angular
resolution for these pions is worse due to increase in multiple scattering.
Therefore, these pions will be overrepresented in the tails of the angular
distribution or they will have increased $\chi^{2}$ values. The difference
between models is largest for higher $p^{2}\theta^{2}$ values because of
higher fraction of low momentum pions.

Two co-dominant contributions in the efficiency uncertainty are coming from
SSD efficiency variations and angular resolution differences and are between
$1\%$ and $2\%$. The total efficiency uncertainty is between $2\%$ and $3\%$
and it is the dominant systematic uncertainty contribution at higher
$p^{2}\theta^{2}$.

##  VI Differential cross section results

Differential cross-section results are presented in Fig. 7. Comparisons with
FTFP_BERT and QGSP_BERT physics lists are also included. Both physics list
give a similar predictions with significant differences from the data. The
differences vary from $0$ to $40\%$. Total, statistical, and systematic
uncertainties are also presented in Figs. 8-10.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7: The p+C differential cross-section at $20\>$GeV/c (a), $30\>$GeV/c
(c), and $120\>$GeV/c (e), and their corresponding comparisons to the
FTFP_BERT and QGSP_BERT models from Geant 4.10.05.p01 (b), (d), and (f).

(a)

(b)

(c)

Figure 8: The total, statistical and systematic uncertainty for p+C
differential cross-section at $20\>$GeV/c (a) and different contributions to
the systematic uncertainty (b), correlation matrix (c).

(a)

(b)

(c)

Figure 9: The total, statistical and systematic uncertainty for p+C
differential cross-section at $30\>$GeV/c (a) and different contributions to
the systematic uncertainty (b), and correlation matrix (c).

(a)

(b)

(c)

Figure 10: The total, statistical and systematic uncertainty for p+C
differential cross-section at $120\>$GeV/c (a) and different contributions to
the systematic uncertainty (b), and correlation matrix (c).

###  VI.1 Model fits

To compare our results with previous data it is necessary to extract total,
coherent-elastic or inelastic cross-sections. Typically, the total cross-
section can be extracted by doing transmission measurement in which the number
of surviving beam particles is related to the total cross-section:

$N_{S}=N_{0}e^{-nd\sigma_{tot}},$ (5)

where $N_{S}$ is the number of surviving beam particles, $N_{0}$ is the
initial number of beam particles, $nd$ is the target number density multiplied
by the target thickness, and $\sigma_{tot}$ is the total cross-section. An
alternative approach is to measure the differential cross-section and use the
optical theorem to extract the total cross-section. The optical theorem states
that the total-cross section is proportional to the imaginary part of the
scattering amplitude at $t=0\>$GeV2. An advantage of EMPHATIC is in the
ability to do a combined measurement with both techniques, since all
interacting and non-interacting events have been recorded.

Coherent elastic and quasi-elastic proton-carbon interactions are governed by
non-perturbative QCD, and there are no simple QCD predictions for our
measurements. However, we have fitted a simple phenomenological model to the
data to extract desired parameters. Similar models have been used in many
older measurements such as [17] and more recently in proton-proton
interactions in ATLAS experiment [18, 19]. The full model used in the fit is:

$\displaystyle
M(p^{2}\theta^{2};A,B,B_{pN},B_{I},\sigma_{tot},\sigma_{tot,pN},C,\Lambda)=\frac{1}{16\pi}\left(\frac{\sigma_{tot}}{\hbar
c}\right)^{2}(1+\rho^{2})e^{-Bp^{2}\theta^{2}}$ (6a)
$\displaystyle+\frac{1}{16\pi}\mathcal{H}(p^{2}\theta^{2}-\Lambda)\left(\frac{8\pi\alpha
Z_{1}Z_{2}\hbar c}{p^{2}\theta^{2}}\right)^{2}e^{-Bp^{2}\theta^{2}}$ (6b)
$\displaystyle-2\frac{1}{16\pi}\mathcal{H}(p^{2}\theta^{2}-\Lambda)(\rho\cos{\Delta\Phi}+\sin{\Delta\Phi})\frac{\sigma_{tot}}{\hbar
c}\frac{8\pi\alpha Z_{1}Z_{2}\hbar c}{p^{2}\theta^{2}}e^{-Bp^{2}\theta^{2}}$
(6c) $\displaystyle+N(A)\cdot\frac{1}{16\pi}\left(\frac{\sigma_{tot,pN}}{\hbar
c}\right)^{2}e^{-B_{pN}p^{2}\theta^{2}}$ (6d)
$\displaystyle+\frac{1}{16\pi}\left(\frac{C}{\hbar
c}\right)^{2}e^{-B_{I}p^{2}\theta^{2}}$ (6e)
$\displaystyle+\mathcal{H}(10^{-4}[GeV^{2}]-p^{2}\theta^{2})\frac{1}{nd\cdot
10^{-4}[GeV^{2}]}e^{-(\sigma_{tot}+\sigma_{C-el}+\sigma_{C})\cdot n\cdot d}$
(6f)

The model assumes that the nucleon distribution inside carbon nucleus follows
the normal distribution and the coherent-elastic differential cross-section
Eq. 6a is an exponential function of the four-momentum transfer ($t\approx
p^{2}\theta^{2}$). The normalization is determined by the optical theorem and
relates to the total cross-section $\sigma_{tot}$, while the exponential
parameter $B$ is proportional to the sum of squares of proton and nuclear
radii. Often, it is assumed that the coherent nuclear amplitude is purely
imaginary. However, this is not well measured and we assume a small real
amplitude as well. The ratio of the real to imaginary part of the amplitude is
denoted as $\rho$.

The Coulomb differential cross-section (Eq. 6b) is a simple Rutherford formula
with the exponential form factor. It is assumed that the carbon nuclear charge
density follows the nucleon distribution. This assumption follows from the
work by Kopeliovich and Tarasov [20]. The Coulomb scattering is divergent at
$t=0\>$GeV2 and we include a cutoff parameter $\Lambda$ to remove the
divergence.

Possible interference between coherent-elastic and Coulomb scattering is
included in the third line of Eq. 6. Interference is zero if the nuclear
amplitude is purely imaginary. However, we have already assumed that this is
not the case. In addition, the nuclear amplitude gains a modifying phase
$\Delta\Phi$ due to the presence of Coulomb field.

Quasi-elastic interactions are defined as elastic interactions on a single
nucleon. Therefore, quasi-elastic differential cross-section (Eq. 6d) will
have the same $t$ dependence as coherent-elastic differential cross-section,
but only with different parameters. The effective number of nucleons visible
to a beam proton is denoted as $N(A)$

Inelastic contamination (Eq. 6e) in our measurements is mostly coming from
events with a single forward charged particle (mostly pions). We assume that
such background mostly comes from $\Delta$ resonance production. Also, Geant4
simulation suggests that the background is almost flat in $p^{2}\theta^{2}$ or
has a exponential shape with a small slope. Therefore, we assume the same
functional dependence as coherent-elastic and quasi-elastic differential
cross-sections, only with different parameters.

Finally, non-interacting contributions (Eq. 6f) is calculated by using Eq. 5.
Instead of using only the total nuclear proton-carbon cross-section, we have
also integrated Eq. 6b and Eq. 6c to get the total effective cross-section.
The number of surviving particles is normalized to get the same dimension as
the differential cross-section. The Heaviside step function ensures that
surviving beam particles are only placed in in the first true
$p^{2}\theta^{2}$ bin ($0-10^{-4}\>$GeV2).

The full model is first smeared to account for the bin migration. Migration
matrices are generated from the empty target data and the Geant4 simulation of
the multiple scattering in the target (see Fig. 12). The $\chi^{2}$ is
minimized by varying the model parameters. The relative phase $\Delta\Phi$ is
not an independent parameter and it is taken from the calculation by
Kopeliovich and Tarasov [20]. The $\rho$ parameter is set to be a constant
with a value of $-0.13$, taken from [21]. Since $N(A)$ and $\sigma_{tot,pN}$
appear only as a product, they are merged into a single parameter. The fits
are presented in Figs. 13 \- 15. All of the model contributions are also
shown. The $\chi^{2}$/ndf values for all fit configuration are presented in
Fig. 11. Since the inelastic background has the same functional
$p^{2}\theta^{2}$ dependence as the quasi-elastic differential cross-section
and they are similar in size, corresponding fit parameters have large
uncertainties. Therefore, we are not confident in reporting these values
independently.

Figure 11: The $\chi^{2}$/ndf values for all fit configurations.

However, we extracted the elastic slope $B$ and the total cross-section
$\sigma_{tot}$. The total coherent elastic cross-section $\sigma_{el}$ is
calculated by integrating Eq. 6a. Additionally, the total inelastic cross-
section is estimated as $\sigma_{tot}-\sigma_{el}$. To estimate systematic
uncertainties, fits are repeated in different configurations. The $\rho$
parameter is varied between $-0.20$ and $-0.05$ according to [21]. The
migration matrix is recalculated by using the PDG approximation of the
multiple scattering in the target:

$\theta_{0}=\frac{13.6\text{MeV}}{\beta
cp}z\sqrt{\frac{x}{X_{0}}}\left[1+0.038\log\left(\frac{x}{X_{0}}\right)\right]$
(7)

The initial value of $\Lambda$ parameter is varied within its uncertainties
and fixed during the fit. The value of $\Lambda$ is around $2\cdot
10^{-5}\>$GeV2 for all datasets. The values of the extracted parameters and
their uncertainties for different datasets are summarized in Tab. 2.

Table 2: Extracted parameters and their uncertainties $p$ [GeV/c] | Parameter |  $B$ [(GeV)-2] |  $\sigma_{tot}$ [mb] |  $\sigma_{el}$ [mb] |  $\sigma_{inel}$ [mb]
---|---|---|---|---|---
$20$ | Value | $80.9$ | $344.3$ | $74.7$ | $269.3$
| Stat. error | $7.1$ | $12.3$ | $8.4$ | $14.9$
| Syst. error (low) | $-1.6$ | $-10.0$ | $-2.86$ | $-7.1$
| Syst. error (high) | $+2.5$ | $+11.7$ | $+3.0$ | $+10.2$
$30$ | Value | $85.1$ | $362.8$ | $79.1$ | $283.8$
| Stat. error | $4.1$ | $8.2$ | $5.2$ | $9.7$
| Syst. error (low) | $-1.5$ | $-10.0$ | $-3.0$ | $-7.0$
| Syst. error (high) | $+3.1$ | $+12.2$ | $+2.8$ | $+9.6$
$120$ | Value | $79.3$ | $335.9$ | $72.7$ | $263.3$
| Stat. error | $2.9$ | $6.7$ | $3.9$ | $7.8$
| Syst. error (low) | $-3.9$ | $-15.6$ | $-3.2$ | $-9.3$
| Syst. error (high) | $+2.4$ | $+9.1$ | $+2.0$ | $+7.0$

(a)

(b)

(c)

Figure 12: Migration matrices for $20\>$GeV/c data (a), $30\>$GeV/c data (b),
$120\>$GeV/c data (c). Figure 13: The model fit for $20\>$GeV/c data. Figure
14: The model fit for $30\>$GeV/c data. Figure 15: The model fit for
$120\>$GeV/c data.

(a)

(b)

(c)

Figure 16: Comparisons of the total (a), elastic (b), and inelastic cross-
section (c) obtained from the fits with older data. The total cross-section is
compared to the data from Bellettini et al. [17]. The elastic cross-section is
compared to values obtained from Bellettini et al. [17] and Schiz et al. [22].
The inelastic cross-section is compared to the results from Bellettini et al.
[17], NA61/SHINE collaboration [4, 6], Denisov et al. [23], and MIPP
collaboration [24].

A comparison of the cross-section results with the older measurements is
presented in Fig. 16. The statistical and systematic uncertainties of the
extracted cross-sections are similar in size. The main reason for the large
systematic uncertainty is coming from the variation of the $\rho$ parameter.
Unfortunately, our current data and methods do not allow us to extract the
$\rho$ parameter with any precision due to large migration between the first
four upstream bins. To improve this in the future, we will reduce the
migration effect by reducing the material budget. Additionally, removing
inelastic backgrounds by using a momentum measurement will allow us to measure
the quasi-elastic cross-section.

##  VII Summary and future measurements

We have measured forward differential cross-section in proton-carbon at $20$,
$30$, and $120\>$GeV/c with a simple setup consisting of silicon strip
detectors. These results feature a novel technique that uses both transmission
measurement and the optical theorem to extract the cross-section. Future
EMPHATIC runs will have momentum measurements and the particle identification
for secondary particles. Additionally, the material budget will be
significantly reduced (by $40\%$), since the dead material (pixel telescope)
will be removed. With increased statistics and these improvements, we will be
able to greatly reduce our uncertainties on the extracted cross-sections. A
fast DAQ rate will allow us to take many different datasets and create a
cross-section table for the important interactions contributing to the
neutrino flux in different experiments.

##  VIII Acknowledgements

This document was prepared by members of the EMPHATIC Collaboration using the
re- sources of the Fermi National Accelerator Laboratory (Fermilab), a U.S.
Department of Energy, Office of Science, HEP User Facility. Fermilab is
managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-
AC02-07CH11359. Support for participating scientists was provided by the DOE
(USA), the 2017 U.S.-Japan Science and Technology Cooperation Program in High
Energy Physics, and NSERC and NRC, Canada. We thank the Fermilab Test Beam
Facility for its excellent technical support, use of its detectors and beam.

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##  Appendix A Results

Table 3: Measured differential cross-section for $20\>$GeV/c data. $p^{2}\theta^{2}$ range | $d\sigma/d(p^{2}\theta^{2})$ | Stat. error | Stat. error | Syst. error | Syst. error | Tot. error | Tot. error
---|---|---|---|---|---|---|---
[GeV/c] |  [mb$\cdot$(GeV/c)-2] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%]
$0.0000-0.0025$ | $2052289.364$ | $7126.864$ | $0.347$ | $53265.051$ | $2.595$ | $53739.724$ | $2.619$
$0.0025-0.0050$ | $6793.436$ | $412.672$ | $6.075$ | $180.526$ | $2.657$ | $450.430$ | $6.630$
$0.0050-0.0075$ | $4828.061$ | $349.346$ | $7.236$ | $132.106$ | $2.736$ | $373.489$ | $7.736$
$0.0075-0.0100$ | $3857.142$ | $312.856$ | $8.111$ | $105.574$ | $2.737$ | $330.188$ | $8.560$
$0.0100-0.0150$ | $2674.627$ | $184.129$ | $6.884$ | $74.013$ | $2.767$ | $198.447$ | $7.420$
$0.0150-0.0200$ | $2142.355$ | $165.286$ | $7.715$ | $59.941$ | $2.798$ | $175.820$ | $8.207$
$0.0200-0.0250$ | $1732.284$ | $149.091$ | $8.607$ | $49.076$ | $2.833$ | $156.961$ | $9.061$
$0.0250-0.0300$ | $1206.000$ | $124.389$ | $10.314$ | $33.697$ | $2.794$ | $128.873$ | $10.686$
$0.0300-0.0350$ | $888.948$ | $107.017$ | $12.039$ | $25.047$ | $2.818$ | $109.909$ | $12.364$
$0.0350-0.0400$ | $803.549$ | $102.051$ | $12.700$ | $23.286$ | $2.898$ | $104.674$ | $13.026$
$0.0400-0.0450$ | $655.121$ | $92.648$ | $14.142$ | $18.295$ | $2.793$ | $94.437$ | $14.415$
$0.0450-0.0500$ | $328.323$ | $65.665$ | $20.000$ | $9.419$ | $2.869$ | $66.337$ | $20.205$
$0.0500-0.0550$ | $493.315$ | $81.101$ | $16.440$ | $15.138$ | $3.069$ | $82.501$ | $16.724$
$0.0550-0.0600$ | $603.047$ | $89.897$ | $14.907$ | $18.037$ | $2.991$ | $91.689$ | $15.204$
$0.0600-0.0700$ | $403.360$ | $52.513$ | $13.019$ | $11.561$ | $2.866$ | $53.771$ | $13.331$
$0.0700-0.0800$ | $394.693$ | $52.278$ | $13.245$ | $12.9776$ | $3.288$ | $53.865$ | $13.647$
$0.0800-0.0900$ | $377.595$ | $51.867$ | $13.736$ | $12.053$ | $3.192$ | $53.249$ | $14.102$
$0.0900-0.1000$ | $344.685$ | $49.751$ | $14.434$ | $10.870$ | $3.154$ | $50.925$ | $14.774$
$0.1000-0.1100$ | $268.391$ | $44.123$ | $16.440$ | $8.946$ | $3.333$ | $45.021$ | $16.774$
$0.1100-0.1200$ | $315.072$ | $48.048$ | $15.250$ | $10.701$ | $3.396$ | $49.225$ | $15.624$
$0.1200-0.1300$ | $177.247$ | $36.180$ | $20.412$ | $5.573$ | $3.144$ | $36.607$ | $20.653$
$0.1300-0.1400$ | $199.990$ | $39.221$ | $19.612$ | $6.306$ | $3.153$ | $39.725$ | $19.864$
$0.1400-0.1500$ | $258.929$ | $45.074$ | $17.408$ | $8.222$ | $3.175$ | $45.817$ | $17.695$
Table 4: Measured differential cross-section for $30\>$GeV/c data. $p^{2}\theta^{2}$ range | $d\sigma/d(p^{2}\theta^{2})$ | Stat. error | Stat. error | Syst. error | Syst. error | Tot. error | Tot. error
---|---|---|---|---|---|---|---
[GeV/c] |  [mb$\cdot$(GeV/c)-2] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%]
$0.0000-0.0025$ | $2069050.634$ | $3828.485$ | $0.185$ | $53689.117$ | $2.595$ | $53825.446$ | $2.602$
$0.0025-0.0050$ | $8299.600$ | $244.317$ | $2.944$ | $219.998$ | $2.651$ | $328.771$ | $3.961$
$0.0050-0.0075$ | $5170.900$ | $192.708$ | $3.727$ | $137.906$ | $2.667$ | $236.969$ | $4.583$
$0.0075-0.0100$ | $3837.658$ | $166.384$ | $4.336$ | $104.313$ | $2.718$ | $196.379$ | $5.117$
$0.0100-0.0150$ | $2799.597$ | $100.695$ | $3.597$ | $75.476$ | $2.696$ | $125.841$ | $4.495$
$0.0150-0.0200$ | $2044.561$ | $86.092$ | $4.211$ | $55.046$ | $2.692$ | $102.185$ | $4.998$
$0.0200-0.0250$ | $1463.394$ | $73.078$ | $4.994$ | $39.521$ | $2.701$ | $83.080$ | $5.677$
$0.0250-0.0300$ | $1134.254$ | $64.421$ | $5.680$ | $31.196$ | $2.750$ | $71.577$ | $6.311$
$0.0300-0.0350$ | $789.365$ | $53.710$ | $6.804$ | $22.106$ | $2.800$ | $58.081$ | $7.358$
$0.0350-0.0400$ | $660.948$ | $49.402$ | $7.474$ | $18.443$ | $2.790$ | $52.732$ | $7.978$
$0.0400-0.0450$ | $514.906$ | $43.832$ | $8.513$ | $15.346$ | $2.980$ | $46.440$ | $9.019$
$0.0450-0.0500$ | $491.541$ | $42.946$ | $8.737$ | $13.618$ | $2.770$ | $45.053$ | $9.166$
$0.0500-0.0550$ | $378.509$ | $37.851$ | $10.000$ | $10.880$ | $2.875$ | $39.384$ | $10.405$
$0.0550-0.0600$ | $393.893$ | $38.624$ | $9.806$ | $11.484$ | $2.916$ | $40.296$ | $10.230$
$0.0600-0.0700$ | $317.420$ | $24.637$ | $7.762$ | $8.860$ | $2.791$ | $26.181$ | $8.248$
$0.0700-0.0800$ | $289.509$ | $23.638$ | $8.165$ | $8.024$ | $2.772$ | $24.963$ | $8.623$
$0.0800-0.0900$ | $306.383$ | $24.530$ | $8.006$ | $8.860$ | $2.892$ | $26.081$ | $8.513$
$0.0900-0.1000$ | $253.683$ | $22.250$ | $8.771$ | $7.710$ | $3.039$ | $23.547$ | $9.282$
$0.1000-0.1100$ | $256.723$ | $22.603$ | $8.805$ | $8.440$ | $3.2886$ | $24.128$ | $9.398$
$0.1100-0.1200$ | $212.069$ | $20.696$ | $9.759$ | $6.613$ | $3.118$ | $21.727$ | $10.245$
$0.1200-0.1300$ | $201.800$ | $20.180$ | $10.000$ | $6.466$ | $3.204$ | $21.191$ | $10.501$
$0.1300-0.1400$ | $205.943$ | $20.292$ | $9.853$ | $6.225$ | $3.023$ | $21.226$ | $10.307$
$0.1400-0.1500$ | $178.935$ | $19.075$ | $10.660$ | $5.725$ | $3.200$ | $19.915$ | $11.130$
Table 5: Measured differential cross-section for $120\>$GeV/c data. $p^{2}\theta^{2}$ range | $d\sigma/d(p^{2}\theta^{2})$ | Stat. error | Stat. error | Syst. error | Syst. error | Tot. error | Tot. error
---|---|---|---|---|---|---|---
[GeV/c] |  [mb$\cdot$(GeV/c)-2] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%] |  [mb$\cdot$(GeV/c)-2] | [%]
$0.0000-0.0025$ | $2073312.212$ | $2521.099$ | $0.122$ | $53750.653$ | $2.593$ | $53809.744$ | $2.595$
$0.0025-0.0050$ | $10237.337$ | $177.832$ | $1.737$ | $266.174$ | $2.600$ | $320.114$ | $3.127$
$0.0050-0.0075$ | $6173.195$ | $137.968$ | $2.235$ | $160.449$ | $2.599$ | $211.611$ | $3.428$
$0.0075-0.0100$ | $4520.413$ | $118.183$ | $2.614$ | $117.526$ | $2.600$ | $166.672$ | $3.687$
$0.0100-0.0150$ | $2933.287$ | $67.383$ | $2.297$ | $76.317$ | $2.602$ | $101.807$ | $3.471$
$0.0150-0.0200$ | $1897.459$ | $54.169$ | $2.855$ | $49.458$ | $2.607$ | $73.351$ | $3.866$
$0.0200-0.0250$ | $1268.315$ | $44.400$ | $3.501$ | $33.121$ | $2.611$ | $55.393$ | $4.367$
$0.0250-0.0300$ | $945.892$ | $38.424$ | $4.062$ | $24.812$ | $2.623$ | $45.739$ | $4.836$
$0.0300-0.0350$ | $735.341$ | $33.883$ | $4.608$ | $19.339$ | $2.630$ | $39.014$ | $5.306$
$0.0350-0.0400$ | $521.670$ | $28.630$ | $5.488$ | $13.663$ | $2.619$ | $31.723$ | $6.081$
$0.0400-0.0450$ | $490.855$ | $27.789$ | $5.661$ | $12.930$ | $2.634$ | $30.650$ | $6.244$
$0.0450-0.0500$ | $390.669$ | $24.908$ | $6.376$ | $10.461$ | $2.678$ | $27.016$ | $6.915$
$0.0500-0.0550$ | $351.783$ | $23.664$ | $6.727$ | $9.422$ | $2.678$ | $25.470$ | $7.240$
$0.0550-0.0600$ | $334.268$ | $23.233$ | $6.951$ | $9.088$ | $2.719$ | $24.947$ | $7.463$
$0.0600-0.0700$ | $263.960$ | $14.687$ | $5.564$ | $7.130$ | $2.701$ | $16.327$ | $6.185$
$0.0700-0.0800$ | $206.983$ | $13.091$ | $6.325$ | $5.698$ | $2.753$ | $14.277$ | $6.898$
$0.0800-0.090$ | $216.332$ | $13.391$ | $6.190$ | $6.132$ | $2.834$ | $14.728$ | $6.808$
$0.0900-0.1000$ | $196.612$ | $12.853$ | $6.537$ | $5.723$ | $2.911$ | $14.070$ | $7.156$
$0.1000-0.1100$ | $199.731$ | $13.199$ | $6.608$ | $5.827$ | $2.918$ | $14.428$ | $7.224$
$0.1100-0.1200$ | $142.426$ | $11.054$ | $7.762$ | $4.012$ | $2.817$ | $11.760$ | $8.257$
$0.1200-0.1300$ | $158.757$ | $11.800$ | $7.433$ | $4.873$ | $3.070$ | $12.767$ | $8.042$
$0.1300-0.1400$ | $127.473$ | $10.478$ | $8.220$ | $3.985$ | $3.126$ | $11.210$ | $8.794$
$0.1400-0.1500$ | $150.903$ | $11.407$ | $7.559$ | $4.651$ | $3.082$ | $12.319$ | $8.164$


# MeerKAT caught a Mini Mouse: serendipitous detection of a young radio pulsar
escaping its birth site

Motta, S. E.1,2, Turner, J. D.3, Stappers, B.3, Fender, R. P.2, Heywood,
I.2,4,5, Kramer, M.6, Barr, E.D.6
1Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Brera, via E.
Bianchi 46, 23807 Merate (LC), Italy
2University of Oxford, Department of Physics, Astrophysics, Denys Wilkinson
Building, Keble Road, OX1 3RH, Oxford, United Kingdom
3Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
The University of Manchester, Manchester M13 9PL, UK
4Department of Physics and Electronics, Rhodes University, PO Box 94, Makhanda
6140, South Africa
5South African Radio Astronomy Observatory, Cape Town, South Africa.
6 Max-Planck-Institut fur Radioastronomie, Auf dem Hügel 69, D-53121, Bonn,
Germany

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

In MeerKAT observations pointed at a Galactic X-ray binary located on the
Galactic plane we serendipitously discovered a radio nebula with cometary-like
morphology. The feature, which we named ‘the Mini Mouse’ based on its
similarity with the previously discovered ‘Mouse’ nebula, points back towards
the previously unidentified candidate supernova remnant G45.24$+$0.18. We
observed the location of the Mini Mouse with MeerKAT in two different
observations, and we localised with arcsecond precision the 138 ms radio
pulsar PSR J1914+1054g, recently discovered by the FAST telescope, to a
position consistent with the head of the nebula. We confirm a dispersion
measure of about 418 pc cm-3 corresponding to a distance between 7.8 and 8.8
kpc based on models of the electron distribution. Using our accurate
localisation and 2 period measurements spaced 90 days apart we calculate a
period derivative of (2.7 $\pm$ 0.3) $\times$ 10 -14 s s-1. We derive a
characteristic age of approximately 82 kyr and a spin down luminosity of 4
$\times$ 1035 erg s-1, respectively. For a pulsar age comparable with the
characteristic age, we find that the projected velocity of the neutron star is
between 320 and 360 km/s if it was born at the location of the supernova
remnant. The size of the proposed remnant appears small if compared with the
pulsar characteristic age, however the relatively high density of the
environment near the Galactic plane could explain a suppressed expansion rate
and thus a smaller remnant.

###### keywords:

accretion, accretion discs – black hole physics – X-rays: binaries – stars:
jets – Pulsars: individual: PSR J1914+1054g

††pubyear: 2020††pagerange: MeerKAT caught a Mini Mouse: serendipitous
detection of a young radio pulsar escaping its birth site–MeerKAT caught a
Mini Mouse: serendipitous detection of a young radio pulsar escaping its birth
site

##  1 Introduction

Pulsar wind nebulae (PWN) are the result of the interaction between the
relativistic particle winds produced by rotationally-powered pulsars and the
surrounding medium. The rapid rotation of the magnetic field of the neutron
star (NS) powers a relativistic wind, which, via interaction with the ambient
medium, generates a termination shock downstream of which synchrotron
radiation emerges with a spectrum extending from the radio band up to the
$\gamma$-rays (see, e.g., Gaensler & Slane, 2006, for a review). Sometimes a
PWN is surrounded by a shell-like supernova remnant (SNR), legacy of the
explosion that gave birth to the pulsar itself, and in this case the system is
termed ‘composite’ (Matheson & Safi-Harb, 2005).

If a pulsar moves through the interstellar medium (ISM) at a supersonic speed,
a bow shock forms, which redirects and channels the pulsar wind in the
direction opposite to that of the pulsar’s motion. This may result in a
detectable tail which can extend for several parsecs behind the NS (see, e.g.,
Kargaltsev et al., 2015). In such cases, the SNR associated with the formation
of the NS may be located parsecs away from the PWN, although the cometary tail
may either connect to or point in the direction of the supernova shell. Among
the several tens of PWN known, only a small number of objects present such a
cometary morphology, which is indicative of high proper velocities and/or a
dense ISM. High spatial resolution observations, in radio and in the X-ray
band are adding to this group (e.g., Klingler et al., 2018).

Detailed studies of the PWNe and their pulsars can provide crucial information
on these systems, as the PWNe’s appearance, spectrum, and radiative efficiency
depend on the pulsars’ parameters (e.g., spin, spin-down power, surface
magnetic field and its orientation), on the pulsars’ velocity, and on the
properties of the pulsar wind (e.g., flow speed and magnetisation).
Additionally, since PWNe have a well-defined central engine and are often
close enough to be resolvable with high angular resolution observations, they
represent excellent laboratories for studying both relativistic particle winds
and the shocks that result when such outflows collide with the ISM, thus
offering the opportunity to constrain the properties of their environment.

As part of the ThunderKAT Large Survey Program, which is aimed at providing a
long-term view of interesting transients in the radio band, we observed the
field of the black hole binary GRS 1915+105 with the MeerKAT radio telescope
at L-band with a few arcsec angular resolution (Motta et al., 2021). In the
MeerKAT field of the source we identified a feature that closely resembles
‘the Mouse’ (Yusef-Zadeh & Bally, 1987), a radio nebula with axial symmetry,
consisting of a bright ‘head’ and a long ‘tail’, observed in the direction of
the Galactic Centre region, which hosts the young radio pulsar PSR
J1747$-$2958 (Camilo et al., 2002). Based on the resemblance with the Mouse,
we named the newly identified feature in the GRS 1915+105 field ‘the Mini
Mouse’.

This paper is structured as follows; in §2 we describe the imaging and time-
domain data acquisition. In §3 we report the discovery of the Mini Mouse, the
identification of PSR J1914+1054g, recently discovered by FAST, as the
counterpart, and calculate the spin period derivative. Finally, in §4, we
discuss the inferred nature of the Mini Mouse from these measurements.

##  2 Observations and data Analysis

###  2.1 Continuum observations

We observed the field of GRS 1915+105 61 times with MeerKAT as part of the
ThunderKAT Large Survey Project (Fender et al., 2016) between December 2018
and April 2022. We observed at a central frequency of 1.28 GHz across a 0.86
GHz bandwidth (856 – 1712 MHz). The correlator delivered either 4096 or 32768
channels, with a 8-s integration time per visibility point, which were binned
down to 1024 channels for consistency before any further analysis. Between 58
and 64 of the 64 available dishes were used in the observations, with a
maximum baseline of 7.698 km. Of 61 observations, 60 consisted of 15 minutes
of on-source time, book-ended by two 2 min scans of the secondary calibrator
J2011$-$0644, plus a 10 min observation of a primary calibrator (J1939$-$6342)
(Motta et al., 2021). One observation lasted 90 minutes, of which 60 min was
on-source, 20 minutes on the primary calibrator, and 3 minutes on the
secondary calibrator.

Imaging was conducted via a set of Python scripts specifically tailored for
the semi-automatic processing of MeerKAT data
(OxKAT111https://github.com/IanHeywood/oxkat, Heywood 2020). Initial flagging
to remove the first and final 100 channels from the observing band,
autocorrelations, zero amplitude visibilities, and RFI was performed in CASA
(McMullin et al., 2007). Further flagging was performed using the TRICOLOUR
package 222https://github.com/ska-sa/tricolour/, after averaging the data in
time (8 s) and frequency (8 channels) for imaging purposes. We imaged the
field of GRS 1915+105 using WSClean (Offringa et al. 2012) and combining the
visibilities from all our observations after uv-subtracting the variable
emission from GRS 1915+105. Direction independent self-calibration was
performed using CUBICAL (Kenyon et al., 2018) by solving for phase and delay
corrections for every 32 seconds of data.

###  2.2 Search for a pulsar counterpart

The most sensitive pulsar search previously conducted that covered the
position of the Mini Mouse is the ongoing FAST Galactic Plane Pulsar Snapshot
(GPPS) survey (Han et al., 2021), with a 10 $\upsigma$ sensitivity threshold
between 1 and 10 $\upmu$Jy for periods of 10-2 and 10 s. The FAST GPPS survey
recently discovered a faint ($S_{1400}$ = 33 $\upmu$Jy) pulsar, PSR
J1914+1054g (hereafter J1914) with a spin period of 138 ms, and a position
consistent with the head of the Mini Mouse within a 1.5′ uncertainty (Han et
al., 2021).

In order to confirm the association between either J1914 or an undiscovered
pulsar and the Mini Mouse head, we conducted a 2 hr observation (henceforth
referred to as OBS1) as part of the TRAPUM Large Survey project (Stappers &
Kramer, 2016) with a nominal 10 $\upsigma$ sensitivity of 10.6 $\upmu$Jy. We
observed at a central frequency of 1284 MHz and a bandwidth of 856 MHz
(identical to that used in the continuum observations), split into 4096
channels, with a sampling time of 153 $\times$ 10-6 s. We used all 64
available dishes which gives the minimum coherent beam (CB) size. A CB is
formed by coherently summing the digitised signals from each receiver after
correcting for the geometric delay, and accesses a much smaller field of view
than the primary (incoherent) beam does. The on-site Filterbank and
BeamForming User-Supplied Equipment (FBFUSE) computer cluster, developed by
the Max-Planck Institüt für Radioastronomie (Barr, 2017), uses the beamforming
package mosaic333https://github.com/wchenastro/Mosaic by Weiwei Chen to derive
a set of delay polynomials that will synthesise multiple CBs. This enables the
tessellation of hexagonally packed beams across a source (Chen et al., 2021).
For OBS1, 266 beams were arranged in a rectangle overlapping at their 75 per
cent power width, to densely cover the full length and breadth of the nebula.
The beam at the centre of the field of view was placed on the head of the Mini
Mouse at the position of largest continuum flux. An additional 66 beams were
used to tile over the portion of the 1.5′ position error region that was not
covered by the rectangle.

Approximately 45 minutes into the observation, a failure of one of the 8
capture nodes of the Accelerated Pulsar Search User Supplied Equipment
(APSUSE) resulted in ensuing data being corrupted in some beams. The
observation was suspended a short time later. Luckily, the 7 most central
beams positioned on the head of the Mini Mouse were unaffected, yielding 104
minutes of good data. The corresponding filterbanks were processed offline to
search for J1914 directly before any global periodicity search was attempted.

Raw data is recorded on the APSUSE file system in the
SIGPROC444http://sigproc.sourceforge.net/ filterbank format, segmented by beam
and in 5 minute chunks. The initial search for J1914 was conducted first on
the innermost beam as it is located both at the point of maximum sensitivity
(boresight) and at the position of maximum flux of the nebula’s head. The
filtool program, which is part of pulsarX555https://github.com/ypmen/PulsarX
by Yunpeng Men, was used to clean Radio Frequency Interference (RFI) and to
stitch together the continuous data into a single filterbank file. Using
psrchive’s dspsr (Van Straten & Bailes, 2011), the filterbank file was folded
using an ephemeris containing J1914’s period and the DM for the epoch reported
in Han et al. (2021). clfd666https://github.com/v-morello/clfd by Vincent
Morello was then applied to the full resolution folded data to clean any
lingering RFI. Finally, a search over period and DM was performed with pdmp
(Van Straten & Bailes, 2011; Hotan et al., 2004) with a window of 50 $\upmu$s
in period and 20 units of DM. The observation yielded a detection of J1914
with a significance of 19.4 in the beam directly placed on the Mini Mouse
head, with $P$ = 138.867651 ms and a DM of 418.0 $\pm$ 0.3 pc cm-3. As a
result of this detection at the head of the nebula, no full scale periodicity
search of all CBs was attempted. Using the spin period measured by the FAST
telescope about 2 years before777The period measured by FAST was kindly
provided by Prof. JinLin Han via private communication. we estimated a
tentative period derivative of about 3 $\times$ 10-14 s s-1.

In order to obtain a second accurate measurement of the spin period of J1914
with MeerKAT, and to meaningfully constrain the spin derivative, we requested
and obtained a Director’s Discretionary Time (DDT) observation of the Mini
Mouse position (henceforth OBS2, project code DDT-20221028- SM-01). Only 7
beams at 75 per cent overlap were required to cover J1914’s position derived
from OBS1. The optimal tiling pattern selected by mosaic is a central beam
surrounded by a hexagon of 6, a configuration suited for signal-to-noise-based
localisation techniques. The reduction in the number of beams also allowed for
observing at a time resolution of 76$\times$10-6 s. These data were reduced
and searched in the same way as in OBS1. The observing parameters and
resources used for both observations are summarised in Tab. 2.

Table 1: A summary of the observing parameters and resources used for the two MeerKAT observations of J1914. † The value refers to the co-ordinates of the central CB. Parameter | OBS1 | OBS2
---|---|---
UTC Start Time (yyyy-MM-dd-hh:mm:ss) | 2022-08-03-21:03:30 | 2022-11-01-16:54:47
Start MJD | 59794.877431 | 59884.704630
Duration (s) | 6296 | 7186
Number of dishes | 64 | 62
Central frequency (MHz) | 1284 | 1284
Bandwidth (MHz) | 856 | 856
Channels | 4096 | 4096
Sampling time (s) | 156 $\times$ 10-6 | 72 $\times$ 10-6
Right Ascension† (hh:mm:ss) | 19:14:09.46 | 19:14:09.66
Declination† (dd:mm:ss) | +10:54:43.7 | +10:54:42.2

Table 2: Measured and inferred quantities for J1914 derived from OBS2. The
value in brackets denotes the 1 $\upsigma$ uncertainty on the rightmost digit.
Measured quantities
---
Right Ascension, $\alpha$ (J2000) | 19${}^{\text{h}}$14${}^{\text{m}}$09$\aas@@fstack{s}$83${}^{+0.41}_{-0.12}$
Declination, $\delta$ (J2000) | +10°54′35.9$\aas@@fstack{\prime\prime}$${}^{+13.4}_{-2.0}$
Pulse period, $P$ (s) | 0.138867860(17)
Pulse period derivative $\dot{P}$ (s s-1) | 2.7(3) $\times$10-14
Duty cycle (%) | 14
Dispersion measure, DM (pc cm-3) | 418.90(26)
Flux density, $S_{\mathrm{1284}}$ ($\upmu$Jy) | 62.1
Inferred quantities
Distance (NE2001) (kpc), $d_{1}$ | 7.8
Distance (YMW16) (kpc), $d_{2}$ | 8.8
Characteristic age, $\tau_{c}$ (kyr) | 82(11)
Surface dipole magnetic field strength, $B$ (G) | $1.9(1)\times 10^{12}$
Spin-down luminosity, $\dot{E}$ (erg $\mathrm{s}^{-1}$) | $4.0(6)\times 10^{35}$
Radio pseudo-luminosity, L1284 at $d_{1}$ ($m\mathrm{Jy\,kpc^{2}}$) | 3.8
X-ray Luminosity, L${}_{\rm X}(1-10\,\rm{keV})$ at $d_{1}$ (erg s-1) |  $<7\leavevmode\nobreak\ \times$ 1032
Figure 1: A portion of the field centred on GRS 1915+105 as seen by the
MeerKAT radio telescope at 1.28 GHz. The total on-source time is 15.5 hr. The
restored beam for this map is circular and has a radius of 6.6", shown in the
bottom left corner of the image. The Mini Mouse and the SNR associated with
the birth of pulsar J1914 are marked by a rectangle and circle, respectively.
The location of GRS 1915+105 is marked by a cross. Inset: a zoom into the Mini
Mouse. Contours are equally spaced, and span the range 10–200 uJy. The ‘tooth’
at the edge of the nebula is likely a background source.  Figure 2: A plot of
$\dot{P}$ against $P$ for the young pulsar populace, J1914 inclusive. The
canonical radio pulsars emerge towards the lower right of the plot. Pulsars
with confirmed associations with SNRs, PWNe or detections at high energies,
according to the ATNF Catalogue (Manchester et al., 2005) are indicated, as
are the contour lines for $B$, $\tau_{\text{c}}$ and $\dot{E}$. Figure 3:
Second MeerKAT detection of J1914 folded at the best period and dedispersed.
Bottom panel: Frequency against pulse phase across the band with a resolution
of 128 channels. Middle panel: Band-integrated time series for the 2 hr
observation showing the flux for each 2 minute sub-integration. Top panel:
Integrated pulse profile made by stacking the time series into 128 bins.
Evidence for scattering in the ISM can be seen in the asymmetric broadening of
the pulse profile.

Figure 4: The OBS1 (cyan) and OBS2 (yellow) localisation of J1914 from SeeKAT.
The crosses indicate the maximum likelihood position. The bold white cross is
the weighted mean of the two positions. The ellipses (left) are the 75 per
cent power radii of the CBs. The contours (right) are the 1 (bold), 2 and 3
$\upsigma$ levels of the likelihood fit.

##  3 Results

An image of the MeerKAT field is shown in Fig. 1, which also includes a zoom
into the Mini Mouse. The Mini Mouse appears as a long structure extending from
position RA, DEC $19^{\text{h}}14^{\text{m}}09.5^{\text{s}}$, +10°54′42.7″ for
over 5′ in the East-North-East direction, with a flux density varying along
its axis between about 0.08 and 0.2 mJy beam-1 (marked by a rectangle in Fig.
1). Unlike the original Mouse, the Mini Mouse does not have an obviously
extended head at the MeerKAT resolution of 6.6″), and remains unresolved in
the transverse direction for its entire length, albeit brighter in the first
2′ than in the tail. Further observations at higher angular resolution and/or
higher frequency will help to clarify the finer angular scale structure of
this nebula.

Our continuum radio map shows several bright extended structures, including
HII regions and several shell-like non-thermal radio structures, many of which
can be associated with supernova remnants (SNRs). One such structure is
located to the East-North-East of the Mini Mouse, and is a previously
unidentified dim, remarkably circular SNR candidate G45.24$+$0.18 (marked by a
circle in Fig. 1. The geometrical centre of the SNR is located within 30″ from
the extension of the Mini Mouse axis of symmetry, and 12′ away from the head
of the Mini Mouse. The SNR has an apparent radius of 5.7′ and a flux density
of 20 to 40 $\upmu$Jy beam-1.

We detected J1914 in OBS2, this time with a significance of 24.3 $\upsigma$,
as can be seen in Fig. 3. The results of the detection and analysis to be
discussed hereafter are reported in Tab. 2. Using the difference in period,
$\Delta P$, and time, $\Delta t$, between OBS1 and OBS2 we derive for the
first time888FAST published the timing of one single visit to J1914, based on
which a first estimate of the pulsar period was made (Han et al., 2021). The
period derivative could not be estimated based on one single observation.  the
period derivative, $\dot{P}$ = $\Delta P/\Delta t$, of J1914 to be 2.7(3)
$\times$ 10-14 s s-1. Using both the NE2001 (Cordes & Lazio, 2002) and YMW16
(Yao et al., 2017) electron density models, we find the distance for a DM of
418.9 pc cm-3 to be $d_{1}$ $\sim$ 7.8 and d2 $\sim$ 8.8 kpc respectively,
with the usual caveat of large uncertainties associated with this method. This
distance range places J1914 (and thus the Mini Mouse) in the same region of
the Galaxy hosting the black hole binary GRS 1915+105 (8.6${}^{+2.0}_{-1.6}$
kpc, Reid et al. 2014). At the above distance the Mini Mouse has a projected
length between 11.9 and 13.4 pc, and the SNR that we tentatively associated
with the pulsar birth has a radius between 12.8 and 14.4 pc (assuming that the
remnant is spherically symmetrical).

###  3.1 Localisation

Given a flux density of 62.1 $\upmu$Jy and a rms noise of about 50-55
$\upmu$Jy, we do not expect J1914 to be identifiable as a point source in the
image here. However, we are able to localise J1914 to arcsecond accuracy using
SeeKAT,999https://github.com/BezuidenhoutMC/SeeKAT by Mechiel C. Bezuidenhout
the Python implementation of TABLo (Tied Array Beam Localiser, Bezuidenhout et
al. 2023), which is used to localise pulsars discovered by both the TRAPUM and
MeerTRAP101010More TRAnsients and Pulsars with MeerKAT projects (see
Vleeschower et al. 2022; Bezuidenhout et al. 2022 for respective examples).
SeeKAT implements a novel method of maximum-likelihood estimates using the S/N
in each CB and a model of the PSF from mosaic. The PSF changes shape and
orientation as the source moves through the sky (Chen et al., 2021) so we
model it at the observation midpoint. The beams used for the localisation are
shown in the left hand panel of Fig. 4. The S/N in each beam was obtained by
folding the data with dspsr using an ephemeris of the best period and DM for
the observation epoch, before reducing these folded data to a single
subintegration and frequency channel and obtaining the S/N using the psrstat
command. The results from SeeKAT are shown on the right hand panel of Fig. 4.
The position quoted in Tab. 2 is the OBS2 result because the S/N is higher
than OBS1. The weighted mean position of OBS1 and OBS2 is also shown for
discussion purposes.

S/N values in OBS1 disfavour a position within the beam directly on the nebula
head, and instead indicate that it lies on its North-Western edge, towards a
little spur that may or may not be noise. The analysis of OBS2 yields a
bimodal likelihood, seemingly the result of probability leakage towards the
gaps in the CB ring111111mosaic’s default is to pack beams within a circle
region. Unfortunately, the 6-beam hexagon has gaps due to the ellipticity of
the CBs. Care should have been taken when planning OBS2 to make sure the
source was observed closer to the zenith, as more circular CBs would better
enclose the central beam.. There is an island of 1 $\upsigma$ contour overlap
very closely to the weighted mean position, although both still appear in
front of the nebula.

###  3.2 Period derivative significance

As mentioned in §3, we had two MeerKAT epochs that were not phase connected
and we used the period and its uncertainty, and standard error propagation to
calculate $\dot{P}=$ 2.7(3) $\times$ 10-14 s s-1. However, this calculation
assumes that the period errors are the dominant source of uncertainty. In
order to verify such an assumption, we calculated other contributions to the
uncertainty on $\dot{P}$. Firstly, we estimated the error in the pulse arrival
time at the Earth due to an assumed position error. The Römer delay correction
for an erroneous source position changes the apparent spin-period as the Earth
moves in its orbit (see, e.g., Lorimer & Kramer, 2005; Edwards et al., 2006).
In the worst case scenario the period is measured at the closest and furthest
position from the source on the ecliptic sphere. Using the largest 1
$\upsigma$ error on RA and DEC from Tab. 2 of 6.2″ and 13.4″ and assuming
these are approximately equivalent to the uncertainty in ecliptic longitude
and latitude, the maximum change in arrival time is 43.4 ms. This yields an
apparent change in period of 3.8 $\times$ 10-10 s over the 6 months, which
would translate into a negligible additional $\dot{P}$ of 2.4 $\times$ 10-17 s
s-1.

Another small apparent change in $P$ could be caused by the Doppler effect
from the transverse motion of the pulsar as projected on the celestial sphere,
which is known as the Shklovskii effect (Shklovskii, 1970). We estimate that
the upper limit of this effect may induce an apparent $\dot{P}$ of $\sim$ 7
$\times$ 10-20 s s-1, which is much smaller than our uncertainty, and thus can
be ignored.

###  3.3 X-ray serendipitous observations

The position of J1914 was observed serendipitously by the Neil Gerhels Swift
Observatory (Swift) for a total of 8.3 ks, although no source is detected
significantly according to the Swift-XRT LSXPS Upper limit server (Evans et
al., 2023). We derived an upper limit to the 1-10 keV X-ray flux of
approximately 8 $\times$ 10-14 erg cm-2 s-1, assuming a black-body spectrum
with temperature 2 keV and an equivalent column density in the direction of
the source of 1.36 $\times$ 1022 cm-3.

##  4 Discussion

In the MeerKAT observations of the black hole binary GRS 1915+105 we
discovered an unusual collimated linear nebula, which based on the similarity
with the Mouse feature found in the ’80s in the direction of the Galactic
Centre (Yusef-Zadeh & Bally, 1987), we named the Mini Mouse. At a distance of
12′ from the Mini Mouse head, we also identified a circular feature that we
classify as a candidate SNR based on its morphology, the apparent centre of
which is found on the direction indicated by the tail of the Mini Mouse. The
relative positions of the Mini Mouse and of the faint candidate remnant are
strongly reminiscent of three similar nebulae with radio pulsar engines: the
original Mouse (Yusef-Zadeh & Bally, 1987; Camilo et al., 2002), the ‘Frying
Pan’ (Kesteven et al., 1987; Camilo et al., 2009) nebula, and the ‘Cannon
ball’ pulsar PSR J0002+6216 (Schinzel et al., 2019; Kumar et al., 2023). All
three systems have an accompanying SNR, which have been associated with the
birth of the escaping pulsars. Such a resemblance motivated our pulsar search.

Our MeerKAT observations localise J1914 with an accuracy of approximately 10″
to a position fully consistent with the head of the Mini Mouse, hence
supporting a physical association. Thus, we interpret the Mini Mouse nebula as
the bow shock produced by the pulsar escaping at supersonic speed through the
local ISM away from its birth location. Synchrotron radiation emerges from the
pulsar relativistic wind interacting in the nebular magnetic field, similarly
to what was concluded for the case of the aforementioned Mouse, Frying Pan,
and cannon-ball nebulae.

Although the J1914 is localised on the head of the Mini Mouse, its a position
lies on the North-Western edge of it rather than to the center of the head. In
principle we do not expect the pulsar to be in front of the radio emission, as
the bow shock is formed ahead of the wind termination shock at the boundary
where the ram pressure of the ISM equals that of the PWN (Kargaltsev et al.,
2017, e.g.,). However, the ISM likely has pronounced density variability based
on the flux variation along the tail in Fig. 1 so it is possible that the
pulsar is moving into a higher density pocket and the the distance between the
two shocks is shrinking. An alternative explanation could be that there may be
emission on smaller angular scales here that is being missed in the image.
Finally, the discrepancy between the continuum map and the pulsar localization
inferred from the timing could be explained in terms of a systematic
positional offset which may affect MeerKAT images, and is generally of the
order 1-2″ or larger (Mauch et al., 2020, e.g., ). High angular resolution
observations of the Mini Mouse will clarify this issue.

Our position uncertainty has an area of $7.5\leavevmode\nobreak\
\times\leavevmode\nobreak\ 10^{-6}$. The Mini Mouse is directly in the centre
of the first Galactic plane quadrant at $l=45^{\circ}$, $b=0^{\circ}$. The
region bound by $0^{\circ}<l<90^{\circ}$ and $|b|<\leavevmode\nobreak\
2.5^{\circ}$ contains 910 pulsars, giving a rough probability of chance
alignment of 1.5 $\times\leavevmode\nobreak\ 10^{-5}$, and hence we are
confident that the Mini Mouse nebula is the result of J1914 in motion.

The MeerKAT data yielded a period $P$ and period derivative $\dot{P}$ of 138
ms and $2.7(3)\leavevmode\nobreak\ \times\leavevmode\nobreak\
10\leavevmode\nobreak\ ^{-14}$s respectively for J1914, which imply a spin-
down luminosity of -$\dot{E}$ = 4$\pi^{2}\leavevmode\nobreak\
I\leavevmode\nobreak\ \dot{P}/P^{3}$ = $4.0(6)\times 10^{35}$ erg
$\mathrm{s}^{-1}$ (where $I$ = 1045 g cm2 is the neutron star moment of
inertia), a characteristic age $\tau_{c}=P/2\dot{P}=82$ kyr, and surface
magnetic dipole field strength $B$ = 3.2 $\times$ 10${}^{19}(P\dot{P})^{1/2}$
= 2.1 $\times$ 1012 G. These parameters place J1914 near the young and
energetic pulsars in the $P$-$\dot{P}$ diagram (see Fig. 2), characterised by
an average spin-down luminosity $\dot{E}\sim 10^{36}$ erg $\mathrm{s}^{-1}$,
and a characteristic age $\tau_{c}$ ranging from 10 to 100 kyr. Given the
upper limit to the X-ray luminosity of the Mini Mouse, assuming isotropic
emission, we obtain an upper limit to the X-ray luminosity of L${}_{\rm
X}<7\times 10^{32}$erg/s, and thus an upper limit to conversion efficiency of
the spin-down luminosity into X-ray emission of Lx/$\dot{E}<$ 1.5 $\times$
10-3. The non-detection is not surprising as this limit is a factor of about 6
higher than the limit estimated for the ‘Frying Pan pulsar’, which is also
undetected in X-rays Camilo et al. (2009).

If we assume that the pulsar actual age is approximately equal to its
characteristic age (which is not necessarily true, see Gaensler & Frail 2000),
the SNR should be approximately 80 kyr old. At such an age a typical remnant
in a low density ambient medium is expected to have entered the Snowplough
expansion phase, having transitioned from the Sedov-Taylor adiabatic expansion
phase about 50 kyr after detonation (see Jiménez et al., 2019, and references
therein). In the Snowplough phase the radio shell should have a very low
surface brightness $\Sigma$, and large diameter $D$ according to the
$\Sigma-D$ inverse relationship (see, e.g., Vukotić et al., 2019). At our DM-
based distances the SNR shell would have a diameter of 12.8 pc or 14.4 pc,
which is more typical of a remnant in the mid-to-late Sedov-Taylor phase, with
an age of about 20 kyr. Such a discrepancy can be explained if the ISM is
sufficiently dense (Frail et al., 1994), as efficient radiative cooling from
expansion into a high density ambient medium can inhibit the Sedov-Taylor
phase, a plausible scenario given that this remnant is located on the Galactic
plane (see, e.g. Terlevich et al., 1992; Jiménez et al., 2019). We note that
the distance derived from the DM measure might not be accurate, and hence we
could in principle decide to ignore it and instead derive the distance from
the $\Sigma-D$ relation. However, this method has often been treated with
scepticism due to possible intrinsic biases in the correlation, and in
particular due to the fact that (i) the $\Sigma-D$ relation is derived from
independently determined distances, which each have their own uncertainties
(Green, 1991); (ii) SNRs show a diversity of intrinsic properties, for example
the population of SNRs in the LMC that have are roughly all the same distance
from Earth (Green, 1984). Therefore we decided to wait for additional
information on the source to make this attempt.

Again assuming that the pulsar characteristic age of 82 kyr is close to the
pulsar actual age, and that the faint circle of emission is the progenitor
remnant, we can obtain an estimate of the pulsar’s transverse velocity
component, $v_{\perp}$, by considering the distance between the centre of the
SNR and the head of the Mini Mouse. For a pulsar distance of 7.8 or 8.8 kpc
the resulting projected pulsar velocity is between 320 and 360 km/s, which is
well within the kick velocity distribution for young, isolated pulsars,
centred at approximately 300 km/s, with a dispersion of approximately 190 km/s
(Hansen & Phinney, 1997).

If the connection between J1914 and the faint SNR is correct, then we may have
a faint, fast-spinning, distant young pulsar with a high kick velocity, i.e. a
member of an under-sampled population, which could help extrapolating the
local young pulsar velocity distribution to the wider Galactic one (Hansen &
Phinney, 1997). Under the assumption that the magnetic moment of the pulsar
remains constant, the actual age and the characteristic age of a pulsar are
connected by the relation $\tau=\tau_{\text{c}}[1-P_{0}/P)^{n-1}]/(n-1)$,
where $P_{0}$ is the pulsar spin period at birth and $n$ is the breaking index
of rotation (Manchester et al., 1978). Using the standard assumptions of
$P_{0}$ $\ll$ $P$ and $n$ = 3 in the case of magnetic dipole breaking (see,
e.g. Camilo et al., 2002, for the case of the Mouse pulsar) and
$\tau=\tau_{\text{c}}$, the above relation implies that P0 is between 10-20
ms, which is consistent with the expected theoretical values for a newborn
radio pulsar and thus supports our hypothesis of a young and fast spinning
pulsar.

##  5 Summary and conclusions

In the MeerKAT data dedicated to the monitoring of a Galactic X-ray binary, we
found a radio nebula, which we named "the Mini Mouse". Such a feature is
produced by a supersonic pulsar escaping the location of its birth, marked by
the presence of the faint and previously unknown supernova remnant candidate
G45.24$+$0.18 also discovered in the MeerKAT data. Time-domain observations
found the signal from a radio pulsar in correspondence of the tip of the Mini
Mouse, confirming the association of the nebula with a previously poorly
localised faint pulsar discovered by the FAST telescope, J1914+1054g.

The Mini Mouse is the fourth case of a bow shock associated with an escaping
pulsar, for which both the pulsar signal and the SNR associated with its birth
have been observed. Additional high angular resolution observations of the
Mini Mouse will clarify its finer scale structure, and will bring a better
characterisation of the local ISM, while additional high time-resolution
observations of J1914+1054g will significantly improve the timing solution,
thus providing a better constraints on the pulsar properties.

The ThunderKAT discovery of the Mini Mouse and the TRAPUM confirmation of the
association with J1914+1054g constitute an excellent example of immense
potential of the MeerKAT data. Thanks to the detection of structures similar
to the Mouse and Mini Mouse, MeerKAT will help unveiling more young radio
pulsars which will add to the still small population of such objects, which is
predicted to count thousands of members in our Galaxy (e.g. Lorimer et al.,
1993).

## Acknowledgements

The authors thank the anonimous referee that reviewed this work providing
useful suggestions to improve it. SEM acknowledges JinLin Han for providing
the spin period of PSR J1914+1054g from the FAST GPPS, and Lauren Rhode for
comments on an early version of this work. SEM acknowledge financial
contribution from the agreement ASI-INAF n.2017-14-H.0 and from the INAF
mainstream grant. JDT acknowledges funding from the United Kingdom’s Research
and Innovation Science and Technology Facilities Council. All the authors
thank the staff at the South African Radio Astronomy Observatory (SARAO) for
scheduling the MeerKAT observations presented here. TRAPUM observations used
the FBFUSE and APSUSE computing clusters for data acquisition, storage and
analysis. These clusters were funded and installed by the Max-Planck Institüt
für Radioastronomie (MPIfR) and Max-Planck-Gesellschaft. The MeerKAT telescope
is operated by the South African Radio Astronomy Observatory, which is a
facility of the National Research Foundation, an agency of the Department of
Science and Innovation. SAOImage DS9 was used for image analysis and
presentation.

## Data Availability

The un-calibrated MeerKAT visibility data presented in this paper are publicly
available in the archive of the South African Radio Astronomy Observatory at
https://archive.sarao.ac.za. The Continuum MeerKAT observations were taken as
part of the ThunderKAT Large Survey Program, project code SCI-20180516-PW-01.
The project code for the TRAPUM Science Working Group collaborated with is
SCI-20180923-MK-03, and for the DDT observation is DDT-20221028-SM-01. Data
that are not available thorough public archives, and all source code, will be
shared on reasonable request to the corresponding author.

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