# New level of precision in study of neutron beta-decay.
Theoretical basics and experimental backgrounds

V.V. Vasiliev 111e-mail<EMAIL_ADDRESS>NRC ”Kurchatov Institute” - ITEP
25, B. Cheremushkinskaya, Moscow, Russian Federation

###### Abstract

The article provides a theoretical substantiation for a significant increase
in the level of accuracy in determining the neutron lifetime using an
alternative concept of neutron beta decay. Neutrons are distributed among
different subsets depending on the sign of the scalar product of the neutron
spin vector and the momentum of the electron emitted during decay. Therefore,
the neutron lifetime can be determined separately for each of the subsets as
the inverse frequency of its decay, which is to be averaged over the number of
neutrons in this subset. The total neutron lifetime on the total set of
neutrons is calculated by averaging the partial (basic) lifetimes, considering
their weights. The weights of the basic lifetimes are calculated by two
weighing methods, leading, respectively, to the so-called lifetime of
”nonpolarized” neutrons, the weighted average lifetime of neutrons and the
central lifetime, i.e. the arithmetic mean for the basic lifetimes of
neutrons. The dependence between different average neutron lifetimes through
the integral asymmetry parameter calculated by using known experimental data
leads to simple analytical expressions. The numerical estimate of the weighted
average neutron lifetime gives a value that is in good agreement with the
results of the well-known experiments, which proves the validity of the
proposed concept of neutron beta decay. This article includes necessary
conditions for a new experiment to bring the neutron lifetime determination to
a new level of accuracy.

###### keywords:

neutron, decay, electron , asymmetry, set theory

††journal: Chinese Journal of Physics

## Introduction

One of the mysteries of modern physics is the inexplicably wide variety of
experimental data on the measurement of the neutron lifetime. The case is that
the measured values [1] fill two intervals: 875 - 900 s and 900 - 937 s. Such
a variety of values obtained on neutron beams from different reactors in
different countries by teams of qualified researchers requires careful
analysis and explanation.

An essential feature of the experiments of the last thirty years is a refusal
to use registration of electrons when measuring the neutron lifetime in beta
decay. The main emphasis was then placed on recoil protons in decay, and then
experiments using storage of ultracold neutrons before beta decay in traps of
various types took the lead. A possible reason for such a transition was an
explicit or implicit desire to save the experiment from the uncertainty that
the electron-spin asymmetry of neutron decay could introduce into the
determination of the lifetime when registering electrons. In the experiments,
proton traps were used, in which recoil protons from neutron decay were
accumulated before being thrown onto the detector and then traps of ultracold
neutrons where exactly the number of neutrons was recorded depending on the
storage time became main instruments. These methods of accumulation led to a
certain way of forming an average value for the neutron lifetime, integrating
in different ways all the details of the beta decay, in particular the
asymmetry of electron emission. In this work, the goal is to return the study
of the neutron beta decay to the registration of decay electrons in order to
reveal all the details of the process and, due to these details, significantly
increase the accuracy of determining the lifetime and, possibly, find an
explanation for the above range of values.

The problem is that in order to improve the accuracy of the neutron lifetime,
both from the point of view on its physical essence as well as in measuring it
in experiments, it is necessary to adapt the basic known relations, describing
the asymmetry of electrons emitted by neutrons, to the experimental realities.

Improving accuracy becomes achievable due to the introduction of more accurate
ideas about the neutron beta-decay with the involvement of the basic
representations of the set theory and the theory of probability. It is
important to mention that the possible application of new methods for
recording the electron counting rates will make it possible to prevent
distortion or artificial simplification of the decay pattern at the stage of
measurements. Based on the literature data, numerical estimates prove the
validity of introduced refinements.

##  1 Theory of two-channel neutron decay. Consequences for the neutron
lifetime

The generally accepted description of the probability of a neutron beta decay
is the Jackson-Treiman-Wilde formula (1957). In a simplified form it is
usually represented by the dependence of the probability $W$ on the angle
$\theta_{e}$ between the direction of electron emission and the direction of
the neutron spin [2]:

$dW(E_{e},\Theta_{e})=dE_{e}\cdot d\Theta_{e}\cdot
W_{0}\left(1+A\cdot\frac{v_{e}}{c}\cdot\cos\theta_{e}\right)\mbox{,}$ $None$

where $E_{e}$ is the electron kinetic energy, $A$ is the correlation
coefficient of the electron emission with the direction of the neutron spin,
$\theta_{e}$ is an electron emission angle relative to the direction of the
neutron spin, $\Theta_{e}$ is a solid angle of electron emission,
$\frac{v_{e}}{c}$ is the speed of the electron relative to the light speed,
and $W_{0}$ is a constant. The value of the coefficient $A$ is known from many
experiments. Below we used two values of $A$: the value from 2010 year
$A_{2010}=-0.1173\pm 0.0013$ [3] and the value from 2020 year
$A_{2020}=-0.11958\pm 0.00012$ [4].

For each neutron, formula (1) ascribes the possibility of decay with an
arbitrary direction of the electron momentum relative to the neutron spin. The
probability of neutron decay with an electron escaping against the direction
of the neutron spin is higher than with the electron momentum in the direction
of the spin. Thus, formula (1) shows that the number of neutrons, which decay
with electrons against the direction of the spin, is more than the number of
those that decay with the emission of electrons in the direction of the
neutron spin. This means that as a result of the decay of neutrons, two
different final states are formed, differing in the sign of the scalar product
$\left(\vec{s}_{n}\cdot\vec{p}_{e}\right)$, where the vector $\vec{s}_{n}$ is
the spin of the neutron and the vector $\vec{p}_{e}$ is the momentum of the
electron. Hence, it is legitimate to consider the beta decay of a neutron as a
two-channel process. It is exactly this interpretation of beta decay that is
discussed in this work.

Depending on the final state during decay, we distinguish two types of
neutrons. Neutrons of the first type - the so-called $L\mbox{–neutrons}$ \-
are able to emit electrons at the moment of decay against the direction of
their own spin. In contrast to them, neutrons of the second type,
$R\mbox{–neutrons}$, are able to emit electrons in the direction of their own
spin in time of decay.

Obviously, these two types of neutrons have different properties just at the
moment of their decay, which makes it possible to distinguish two implicit
subsets corresponding to two types of neutrons in the total set of neutrons.
Then, any set of neutrons $T$ with the number of neutrons $N_{T}$ can be
considered as the sum of two subsets of neutrons: the subset of
$L\mbox{–neutrons}$ with the number of neutrons $N_{L}$ and the subset of
$R\mbox{–neutrons}$ with the number of neutrons $N_{R}$, moreover
$N_{T}=N_{L}+N_{R}$. The value of the ratio $\frac{\bar{v}_{e}}{c}$ , where
$\bar{v}_{e}$ -is the electron velocity averaged over the electron spectrum,
is assumed to be equal for decays in both subsets. Let us point out that the
ratio $\frac{\bar{v}_{e}}{c}$\- is the eigenvalue of the helicity of
electrons, i.e. $\frac{\bar{v}_{e}}{c}$ \- is the value of the average
projection of the electron spin on the electron momentum. Another difference
from the concept of a generalized particle, which is the base for formula (1),
is the separate determination of the decay constants on the indicated subsets
of neutrons. On the subset of $L\mbox{–neutrons}$ with the number of neutrons
$N_{L}$, the decay constant is defined as the reduced counting rate on this
particular set:

$\lambda_{nL}=\frac{1}{N_{L}}\cdot\frac{dN_{L}}{dt}\mbox{.}$ $None$

Similarly, on the subset of $R\mbox{–neutrons}$ with the number of neutrons
$N_{R}$, the decay constant is

$\lambda_{nR}=\frac{1}{N_{R}}\cdot\frac{dN_{R}}{dt}\mbox{.}$ $None$

The total decay constant $\lambda_{nT}$ is defined here on the total set $T$
as the count rate reduced to the total number of neutrons of this set:

$\lambda_{nT}=\frac{1}{N_{T}}\cdot\frac{dN_{T}}{dt}\mbox{.}$ $None$

Then, after differentiating the sum $N_{T}=N_{L}+N_{R}$ , the following
relation holds:

$\lambda_{nT}=\lambda_{nL}\cdot\frac{N_{L}}{N_{L}+N_{R}}+\lambda_{nR}\cdot\frac{N_{R}}{N_{L}+N_{R}}\mbox{.}$
$None$

Comparison (3.1) with the full width rule [5], [6], which for the total decay
constant in parallel decay in the conventional form is written as the sum of
partial constants:

$\lambda_{nT}=\sum_{i}\lambda’_{i}\mbox{,}$ $None$

where $i$ \- is the channel number, shows the following. Partial constants in
case (3.2) are determined with loss of generality, since

$\lambda’_{i}=\frac{1}{N_{T}}\cdot\frac{dN_{i}}{dt}\mbox{,}$

so they contain different quantities in the denominator and under the sign of
the derivative, while in the record of the full constant on the right side of
(2.3) there is the same quantity, both in the numerator and in the
denominator, i.e. the total number of particles $\sum_{i}^{k}N_{i}$. Thus, it
was shown in (3.1) that the terms in the sum (3.2) contain hidden parameters
which will be revealed if the partial constants are determined correctly in
accordance with the definition of the reduced decay frequency, i.e.

$\lambda_{i}=\frac{1}{N_{i}}\cdot\frac{dN_{i}}{dt}\mbox{.}$

These hidden parameters are weights like those used in the record (3.1), and
after correction the sum (3.2) looks like this

$\lambda_{nT}=\sum_{i=1}^{k}\lambda_{i}\cdot\frac{N_{i}}{\sum_{i=1}^{k}N_{i}}=\sum_{i=1}^{k}\lambda_{i}\cdot\omega_{i}\mbox{,}$

where the weight $\omega_{i}$ for the $i\mbox{-th}$ channel is

$\omega_{i}=\frac{N_{i}}{\sum_{i=1}^{k}N_{i}}\mbox{.}$

A weight is a probability of any particle to belong to the subset of particles
that have the property of decay into a given channel with a rate reduced to
the number of particles belonging only to this subset. It should be noted once
again that in the definitions (2.1) and (2.2) and in the above correction of
the full width rule under the sign of the derivative and in the denominator is
the same value - the number of neutrons with the ability to decay into the
given channel.

The definition of the partial (basic) decay constant as the reduced decay rate
of particles with ability to decay into the given channel is a new refinement
of the decay constant concept for the case of parallel channels.

Since (3.1) is the formula for the weighted average, the notation
$\lambda_{nW}\equiv\lambda_{nT}$ will be used below. Then (3.1) takes the form

$\lambda_{nW}=\lambda_{nL}\cdot\omega_{L}+\lambda_{nR}\cdot\omega_{R}\mbox{.}$
$None$

A decay channel weight is the ratio of a partial constant for a given channel
to the sum of partial constants for all channels [5], [6]. Then, in the
notation (3.1), one can use the relations

$\frac{N_{L}}{N_{L}+N_{R}}=\frac{\lambda_{nL}}{\lambda_{nL}+\lambda_{nR}}$

and

$\frac{N_{R}}{N_{L}+N_{R}}=\frac{\lambda_{nR}}{\lambda_{nL}+\lambda{nR}}\mbox{.}$

According to this definition the weighted average neutron decay constant (4)
takes the form:

$\lambda_{nW}=\frac{\lambda^{2}_{nL}}{\lambda_{nL}+\lambda_{nR}}+\frac{\lambda^{2}_{nR}}{\lambda_{nL}+\lambda_{nR}}\mbox{.}$

It is convenient to represent decay constants (2.1) and (2.2), using formula
(1), through the quantities

$\lambda_{n0}=\frac{\lambda_{nL}+\lambda_{nR}}{2}$

and

$\Delta=|A|\cdot\frac{\bar{v}_{e}}{c}\mbox{,}$

which, taking into account the average angles of electron emission for
$L\mbox{-neutrons}$ and $R\mbox{-neutrons}$, gives

$\lambda_{nL}=\lambda_{n0}\cdot(1+\Delta)$

and

$\lambda_{nR}=\lambda_{n0}\cdot(1-\Delta)\mbox{.}$

The lifetime $\tau_{n0}$ is

$\tau_{n0}=\frac{1}{\lambda_{n0}}$

and will be conventionally called as the lifetime of ”nonpolarized” neutrons.
Partial (basic) lifetimes for subsets of $L\mbox{-neutrons}$ and
$R\mbox{-neutrons}$ are defined in the usual way $\tau_{S}=1/\lambda_{S}$,
where $S=nL,nR$. The lifetimes of $L\mbox{-neutrons}$ and $R\mbox{-neutrons}$
take the form

$\tau_{nL}=\tau_{nCentre}\cdot(1-\Delta)\mbox{,}$ $None$
$\tau_{nR}=\tau_{nCentre}\cdot(1+\Delta)\mbox{,}$ $None$

where $\tau_{nCentre}=\tau_{n0}/(1-\Delta^{2})$. For consistency, it is
convenient to express $\tau_{n0}$ through $\tau_{nCentre},\Delta$:

$\tau_{n0}=\tau_{nCentre}\cdot\left(1-\Delta^{2}\right)\mbox{.}$ $None$

The lifetime of ”nonpolarized” neutrons is also expressed as a weighted
average of the basic lifetimes $\tau_{nL}$ and $\tau_{nR}$ like (4) by the
formula

$\tau_{n0}=\tau_{nL}\cdot\omega_{L}+\tau_{nR}\cdot\omega_{R}\mbox{,}$ $None$

where the weights indicated in (7) and introduced earlier in (4) get the form

$\omega_{L}=\frac{\tau_{nR}}{\tau_{nL}+\tau_{nR}}=\frac{1}{2}+\frac{\Delta}{2}\mbox{,}$
$None$
$\omega_{R}=\frac{\tau_{nL}}{\tau_{nL}+\tau_{nR}}=\frac{1}{2}-\frac{\Delta}{2}\mbox{.}$
$None$

At the same time, the weighted average neutron lifetime is defined as
$\tau_{nW}=~{}1/\lambda_{nW}$ and is expressed through the values
$\tau_{nCentre},\Delta$ by the formula:

$\tau_{nW}=\tau_{nCentre}\cdot\left(1-\frac{2\cdot\Delta^{2}}{1+\Delta^{2}}\right)\mbox{.}$
$None$

For the weighted average neutron lifetime, the following expression is also
valid:

$\tau_{nW}=\tau_{nL}\cdot W_{nL}+\tau_{nR}\cdot W_{nR}\mbox{,}$ $None$

where the $\tau\mbox{-weight}$ of the $L\mbox{-channel}$ and the
$\tau\mbox{-weight}$ of the $R\mbox{-channel}$ have the following dependence
on $\Delta$:

$W_{nL}=\left(\frac{1}{2}+\frac{\Delta}{1+\Delta^{2}}\right)\mbox{,}$ $None$
$W_{nR}=\left(\frac{1}{2}-\frac{\Delta}{1+\Delta^{2}}\right)\mbox{.}$ $None$

So the weights (8.1), (8.2) for the lifetime of nonpolarized neutrons and the
weights (11.1), (11.2) for the average weighted lifetime differ due to the
definitions of the quantities $\lambda_{n0}$ and $\lambda_{nW}$. Expressions
(5.1), (5.2) show the symmetry of the decay pattern around the centre - the
point $\tau_{nCentre}$ on the axis of the trial lifetime. Then a functional
describing the decay depending on the trial lifetime must be symmetric about
the centre. If the functional is symmetric and, at the same time, has a
minimum to the left of the centre of symmetry at the point of the weighted
average neutron lifetime (9), then, by virtue of symmetry, it will also have a
reflected minimum to the right of the centre at the point $\tau_{nW}^{M}$.
This so-called mirror neutron lifetime $\tau_{nW}^{M}$ is expressed by the
formula:

$\tau_{nW}^{M}=\tau_{nCentre}\left(1+\frac{2\cdot\Delta^{2}}{1+\Delta^{2}}\right)\mbox{.}$
$None$

The reasons similar to the above introduction of lifetime of ”nonpolarized”
neutrons lead to the hypothesis of the existence of one more parameter in the
totality of the temporal characteristics of neutrons - the mirror lifetime for
”nonpolarized” neutrons
$\tau_{n0}^{M}=~{}\tau_{nCentre}\cdot\left(1+\Delta^{2}\right)$. This gives
rise to the criteria for constructing the error functional required to
describe the experimental data depending on the trial lifetime $\tau$:

1\. Symmetry about the central point $\tau_{nCentre}$.

2\. The minima at points $\tau_{nW}$ and $\tau_{nW}^{M}$ are symmetrical about
the centre.

3\. Correspondence of the error functional to the number of degrees of
freedom.

Thus, the parameters describing the beta decay of neutrons, by means of simple
calculations, are reduced to the elementary concepts of set theory and
probability theory [7]. Therefore, the total decay constant in parallel decay
is the weighted average value of the basic lifetimes in the set of channels.
The detailed description of neutron decay as a parallel decay in the proposed
alternative model leads to new physical quantities that can be estimated
numerically on the base of literature data.

In addition, it will be shown below that in the selection of one of the
channels in parallel decay and with a precise study of the counting rates of
decay products in this channel [8], it is possible to measure the basic
lifetime defined on the separate subset of particles.

##  2 Estimation of the split effect in neutron decay

Thus, the effect of the splitting of the lifetime (5.1), (5.2) is associated
with the asymmetry parameter $\Delta=|A|\cdot\frac{\bar{v}_{e}}{c}$. In this
case, this parameter is the relative shift of the basic lifetimes. The second
factor in this formula, the average velocity of electrons in units of the
speed of light, is determined from the spectrum of electrons from neutron
decay, which measured in [9], where the spectrum of electrons was shown as
symmetric in energy and, therefore, the maximum of the symmetric spectrum is
located at the average value $\bar{T}_{e}$ of the electron kinetic energy,
$\bar{T}_{e}=391\,\mbox{keV}$. Using the formula,

$\left(\frac{\bar{v}_{e}}{c}\right)=\sqrt{\left(\frac{\bar{T}_{e}}{\bar{T}_{e}+m_{e}\cdot
c^{2}}\right)\cdot\left(2-\frac{\bar{T}_{e}}{\bar{T}_{e}+m_{e}\cdot
c^{2}}\right)}$

where $m_{e}\cdot c^{2}=511\,\mbox{keV}$, we obtain the estimate equals to
$\left(\frac{\bar{v}_{e}}{c}\right)=0.824$. For the electron-spin correlation
coefficient A, two values, mentioned above $A_{2010}$ and $A_{2020}$ are used.
With the value $A_{2010}=-0.1173$, the square of the relative time shift is
very close in size to ratio $1/107$, since $\Delta^{2}\approx 1/107.04$. With
the value $A_{2020}=-0.11958$, the square of the relative temporal shift is
almost equal to the ratio $1/103$. For further calculations, the designation
$\Delta^{2}=1/\eta$ is convenient. In the arguments $\tau_{nCentre},\eta$,
formulas (9), (12) get simpler forms:

$\tau_{nW}\cdot\left(\eta+1\right)=\tau_{nCentre}\cdot\left(\eta-1\right)\mbox{,}$
$None$
$\tau_{nW}^{M}\cdot\left(\eta+1\right)=\tau_{nCentre}\cdot\left(\eta+3\right)\mbox{.}$
$None$

Considering the role of the parameter $\eta$ for the specified relationship
between the neutron lifetimes, we will call it here as a split-parameter,
i.e., the parameter characterizing the effect of splitting the neutron
lifetime - the split effect. For the primary estimates of the above totality
of neutron lifetimes, two values of the split-parameter are used: $\eta=103$
and $\eta=107$. Based on the values of the parameters
$\tau_{nCentre}\mbox{,}\eta$, we can determine the basic lifetimes
$\tau_{nL}\mbox{,}\tau_{nR}$ from the system of equations

$\left\\{\begin{array}[]{rcl}\tau_{nL}+\tau_{nR}=2\cdot\tau_{nCentre}\mbox{,}\\\
\tau_{nL}/\tau_{nR}=(\sqrt{\eta}-1)/(\sqrt{\eta}+1)\mbox{.}\end{array}\right.$
$None$

The numerical value for the central lifetime is given in the paper [10], which
is unique in the sense that only there the experimental data on the electron
counting rates are described by the error functional depending on the trial
neutron lifetime. That article shows that this dependence is symmetric for the
neutron decay and the center of symmetry coincides with the value $900.00\pm
0.15\,\mbox{s}$. Considering the calculations of the previous section, we take
this value here as an estimate of the central neutron lifetime
$\tau_{nCentre}$.

Based on this result for the central lifetime and taking into account the two
values of the split-parameter, the numerical estimates for values (6), (9),
and (12) are as follows.

Estimates of neutron lifetimes
---
Split-parameter, $\eta$ | 107 | 103
Lifetime of “nonpolarized” neutrons, s | 891.59 | 891.26
Weighted average neutron lifetime, s | 883.33 | 882.69
Neutron mirror lifetime, s | 916.67 | 917.31

Thus, when deriving the total decay constant from primary principles based on
the elementary set theory and the probability theory [7], a situation of
contradiction with the concept of a generalized particle and the resulting
full width rule arises. Considering here the neutron beta decay as a two-
channel process is also a definite violation of the established traditions.
However, two different final states in neutron beta decay are adopted by
default after the theoretical discovery of electron-spin asymmetry in 1957 and
received multiple experimental confirmations up to now. To prove the
legitimacy of using the simple formulas obtained here when dividing the total
set of neutrons into the two disjoint subsets, it is necessary to show that
there is a fundamental possibility to determine experimentally the lifetimes
on these different subsets. The next section is devoted to this problem.

##  3 Determination of lifetime for a subset of neutrons

The purpose of this section is to prove the fundamental possibility of
determining the lifetime on a selected subset of neutrons from the counting
rates of electrons.

Now we consider any facility or device as a neutron source, from an isotope
neutron source to a reactor or an accelerator with a neutron-producing target.
Let us install a vacuum chamber in a magnetic field with neutrons passing
through. An electron detector monitors the chamber. Electrons, which are the
decay product of neutrons passing through this chamber or some area of the
chamber, go to the electron detector along the magnetic field.

Let $N$ of neutrons is in the chamber volume in the time interval $dt$.
Neutrons passing through or being in a given area decay exponentially and
their number changes as

$N(t)=N_{0}\cdot exp(-\lambda\cdot t)\mbox{,}$ $None$

where $N_{0}$ is the initial number of neutrons at $t=0$. The quantity
$\lambda$ is the decay constant and the reciprocal of the lifetime $\tau$,
i.e. $\lambda=1/\tau$. In differential form, law (16) has the following
expression,

$\frac{dN}{dt}=-\lambda\cdot N\mbox{.}$ $None$

Where on the left is the rate of neutron loss in the monitored area: the minus
sign on the right reflects the process of neutron loss. However, since the
decay of one neutron is the production of one electron, the rate of electron
production $\frac{dN_{e}}{dt}$ in this region is equal in magnitude to the
rate of neutron loss and will be written with the plus sign on the right side
as follows:

$\left|\frac{dN}{dt}\right|=+\lambda\cdot N\mbox{.}$ $None$

In this case, electrons generated in the monitored area are collected on an
electron detector with a certain efficiency, which we denote as
$\varepsilon_{1}$, and are registered by the detector with an efficiency of
$\varepsilon_{2}$. Let us describe the transport and registration of electrons
by the detector, multiplying the left and right sides of (18) by the total
efficiency $\varepsilon=\varepsilon_{1}\cdot\varepsilon_{2}$:

$\varepsilon\cdot\left|\frac{dN}{dt}\right|=\lambda\cdot\left(\varepsilon\cdot
N\right)\mbox{.}$ $None$

As a result, in equality (19), the electron-counting rate by the detector is
on the left, and there is the product of the decay constant times by the value
in parentheses on the right. The value in parentheses equals to the number of
neutrons that the detector ”sees”, i.e., it receives signals from them in the
form of registered electrons. It means there is the rule for detectors -”You
only get from what you can see”. Let us repeat (19) in a simpler form,
introducing the designation for the electron-counting rate $R_{D}$ and the
number $N_{D}$ of neutrons, visible by the detector:

$R_{D}=\lambda\cdot N_{D}\mbox{.}$ $None$

Based on equation (20), we set the problem to determine the decay constant by
measuring only the electron counting rates and completely rejecting any
measurements of the number of neutrons in the right-hand side of (20), i.e.
excluding measuring the number of neutrons, ”visible” by the electron
detector. To solve this problem, let us add a condition of varying the number
of neutrons to ensure changes in the electron-counting rate in the wide range,
the upper limit of which is several times higher than the lower limit. For the
case of variations, equation (20) transforms into a system of equations.
Omitting the index $D$ to simplify the notation and adding the error
$\sigma_{i}$ in measuring the count rates in all series at each step and at
all steps of variations this system receives the following form:

$\left\\{\begin{array}[]{rcl}R_{1}\pm\sigma_{1}&\approx&\lambda\cdot
N_{1}\mbox{,}\\\ R_{2}\pm\sigma_{2}&\approx&\lambda\cdot N_{2}\mbox{,}\\\
\ldots&\approx&\ldots\mbox{,}\\\ R_{k}\pm\sigma_{k}&\approx&\lambda\cdot
N_{k}\mbox{.}\end{array}\right.$ $None$

The initial number of neutrons changes in steps, therefore, the neutron
numbers in the field of view of the detector also change in steps, passing in
the process of variations successively $k$ values of $N_{i}$. In this case,
only the electron-counting rates are measured and recorded in a continuous
mode. At each stage of the number of neutrons, a sufficient number of
independent series of measurements are carried out at low counting rates,
i.e., counting small numbers of pulses in long reading intervals. The result
of each independent series is a pair of numbers: the average count rate and
the error in the each series. To ensure the accuracy of the count rate values,
a high-frequency timer based on a stable frequency generator measures the
readout time intervals. Let us write a system of equations (21) for the set of
$k$ neutron numbers, representing the numbers as members of an arithmetic
progression $N_{i}=~{}\frac{1}{\mu}\cdot~{}m_{i}$. Here $\frac{1}{\mu}$ is the
difference of the arithmetic progression or the step of a scale of neutron
numbers, a decimal number; the integer number $m_{i}$ is the $i\mbox{-th}$
number of the scale division corresponding to the neutron number. We get the
system of decay equations:

$\tau\cdot\left(R_{i}\pm\sigma_{i}\right)\approx\frac{1}{\mu}\cdot
m_{i}\mbox{.}$ $None$

The step size of the scale $1/\mu$ uniquely determines the set of integers
$m_{i}$ \- the numbers of the scale divisions corresponding to the array of
pairs of numbers for the given value $\tau$. Here $i=1,2,\ldots k$ , $k$\- is
the full number of measurements, including all repeated measurements of the
count rate at each step of the neutron number. The task is reduced to the
choice of the optimal scale factor $\mu$. It is necessary to choose such a
step of the neutron number scale $1/\mu$ , which forms the optimal arithmetic
progression, the selection of whose members provides the best description of
the array of pairs $R_{i},\sigma_{i},i=1,2,\ldots k$. To estimate the sequence
(scale) of neutron numbers, realized in a variation experiment, a scale
adjustment operator has been constructed, which has the following form:

$\aleph_{i}=round\left[\frac{round\left[\mu\cdot\tau\cdot
R_{i},0\right]}{\mu},p\right]\mbox{.}$ $None$

The operator $round[C,p]$ is used to return the value of $C$, rounded to the
$p\mbox{-th}$ decimal place. For example, $round[2.178,2]=2.18$;
$round[2.1859,3]=2.186$; $round[2.19,0]=2$. The structure of the operator (23)
exactly corresponds to the equation (22). Operator (23) forms a scale with a
step of $1/\mu$. Using the trial lifetime $\tau$ and the scale factor $\mu$,
the number of divisions corresponding to the count rate $R_{i}$ is calculated
by the internal operator $round[\mu\cdot\tau\cdot R_{i},0]$ by rounding to the
nearest integer. In this case, the estimate $\aleph_{i}$ for the neutron
numbers $N_{i}$ is made with a fixed approximation accuracy $p$, which fact is
important to confirm the convergence depending on the accuracy at the solution
point. The following error functional $F_{\mu,p}(\tau)$ is constructed for the
required range of $\tau$ for different $p$:

$F_{\mu,p}(\tau)=\sum_{i=1}^{k}\frac{\left(R_{i}-\frac{1}{\tau}\cdot\aleph_{i}(p,\mu,\tau)\right)^{2}}{\sigma_{i}^{2}}\mbox{.}$
$None$

The functional (24) is investigated for different $\mu$-factors, and the
solution is an optimal value of the $\mu$-factor, which ensures the reduction
of the functional at the minimum to unity, together with the coordinate of the
minimum on the axis of the trial lifetime.

Thus, the system of equations (22) is solved by the least squares method with
one parameter, which is the difference of the arithmetic progression optimal
for minimizing the error functional (24), which describes the experimental
data array using the adjustment operator (23) for the decay scale tuning.

The method was first proposed in [11] and is applicable to any radioactive
decay. Under the condition of the presence of a single channel or selection of
one decay channel and with dense filling of a sufficiently wide range of
counting rates of decay products (in this case, electrons), the integer
approximation of neutron numbers is sufficient for solving, i.e., for $\mu=1$
or for any $\mu$ and $p=0$. The only solution in this case coincides with the
minimum of the parabolic dependence of the functional on the trial lifetime.
Then, to determine the error of the solution, it is sufficient to determine
the value of the $\mu\mbox{-factor}$ at which the minimum of the functional
will be fixed on a level close to $\chi^{2}=1$ for any accuracy of the
solution. In this case, the error is determined by the half-width of the
parabola at a level determined by the number of measurements.

However, as shown above, in the neutron case, the decay picture is more
complex. Difference in the decay of $L\mbox{-neutrons}$ and
$R\mbox{-neutrons}$ leads to the need to separate the electron counting rate
from $L\mbox{-neutrons}$ in the form of an equation

$R_{L}\pm\sigma_{L}=\lambda_{L}\cdot N_{L}\mbox{,}$ $None$

and the electron counting rate from $R\mbox{-neutrons}$ in the form

$R_{R}\pm\sigma_{R}=\lambda_{R}\cdot N_{R}\mbox{.}$ $None$

The sum of the counting rates (25.1) and (25.2) is expressed in terms of the
total number of neutrons with a coefficient in the form of a weighted average
decay constant $\lambda_{W}$:

$R_{L}+R_{R}=\lambda_{W}\cdot\left(N_{L}+N_{R}\right)\mbox{.}$ $None$

With an adequate method of averaging primary counts in the distribution of
measured count rates, it is possible to save information on the decays of
$L\mbox{-neutrons}$ (25.1) and $R\mbox{-neutrons}$ (25.2). As result of
summation and averaging, the average value of the neutron lifetime described
by the weighted average decay constant (26) is inevitably present.

Therefore, the weighted average decay constant describes the change in the
total number of neutrons in decay. Calculation of the dependence of functional
(24) on the trial lifetime for different values of the scale step, considering
the above guidelines, solves the problem of minimizing the functional, finding
the center of its symmetry, and determining the value of the weighted average
neutron lifetime.

In the case of using a polarized neutron beam, the scale adjustment method can
be applied separately when registering electrons emitted against the direction
of neutron polarization (25.1) and registering electrons emitted in the
direction of neutron polarization (25.2). In this case, a strict spatial
separation of the decays of $L\mbox{-neutrons}$ and $R\mbox{-neutrons}$ is
realized, which makes it possible to determine their lifetimes separately by
the above method. The control experiment is reduced to rearrangement of
detectors or to spin-flip of the initial polarized beam by $180^{\circ}$ and
repetition of measurements. To vary the initial number of neutrons in the case
of a neutron beam, experiments can use the known optical methods that provide
necessary changes of the neutron flux with the required fixation. In the case
of a ”white” neutron beam or the use of non-reactor sources, the method is
also applicable if the method for measuring the electron-counting rate meets
the requirements for sensitivity to a difference of decay frequencies and
provides a differential measurement of decay frequencies in the realized
range.

The values of the $\mu$ -factor in the case of the neutron decay are
determined by the estimate of the split-parameter from the previous section.

##  4 Discussion of the results

Now then, considering the neutron beta decay as an example of two-channel
decay on the basis of set theory and probability theory, describes the
asymmetry of beta decay in the concept of two disjoint subsets of neutrons and
leads to the two basic lifetimes of neutrons.

The integral asymmetry coefficient $\Delta$ plays the role of a relative shift
of the basic lifetimes and allows to calculate the weights of two neutron
decay channels. The total neutron lifetime is calculated as a weighted average
of the indicated basic lifetimes. In addition to the weighted average, an
important role is played by the arithmetic average of the basic lifetimes, the
difference of which from the weighted average value is evidence of the
existence of a lifetime split effect in the neutron beta decay.

The value of the weighted average lifetime is in a good agreement with the
results of the experiment of NIST (USA) $\tau_{n}=887.7\pm 1.2(stat)\pm
1.9(syst)\,\mbox{s}$ [12] and the experiment of PNPI (Russian Federation)
$\tau_{n}=881.5\pm 0.9\quad\mbox{s}$ [13].

Let us explain here the combination of the words “in a good agreement”. The
doubled total error of the result [12] is 4.5 seconds. The doubled error of
the result [13] is 1.8 seconds. The lower confidence interval (at
$2\sigma\mbox{-level}$) of the first result coincides with the upper limit of
the second result within 0.1 second. The result for $A_{2010}$ lies precisely
at this intersection of the boundaries of the confidence intervals, i.e., it
is separated from both results by exactly two errors of each of them. The
result from $A_{2020}$ is less only by 0.7 s. By the way, this coincidence is
a proof of good mutual agreement between the indicated results.

Thus, the concept of two-channel neutron decay put forward in this work based
on set theory and a more accurate determination of the main decay parameters
is confirmed by independent experiments. With an adequate definition of the
neutron decay constants as characteristics of two sets of neutrons with
different final states the application of the weighted average value, what is
usual for the theory of probability, works successfully for the total neutron
lifetime.

It is possible to extrapolate this approach to other multichannel processes in
order to refine the values of important nuclear physics constants.

According to the proposed concept, new physical quantities are introduced to
describe the beta decay of a neutron - the basic lifetimes of neutrons - the
lifetime of $L\mbox{-neutrons}$ emitting an electron during decay against the
direction of the neutron spin and the lifetime of $R\mbox{-neutrons}$ emitting
an electron in the direction of the neutron spin during decay.

It is shown that the basic lifetimes of neutron can be conveniently expressed
in terms of the central neutron lifetime and the split parameter
$\eta=1/\Delta^{2}$, $\eta=107$ or $\eta=103$, The lifetime of
$L\mbox{-neutrons}$ in these parameters is

$\tau_{nL}=\tau_{nCentre}\cdot\left(1-\frac{1}{\sqrt{\eta}}\right)\mbox{.}$

The lifetime of $R\mbox{-neutrons}$ in these parameters is

$\tau_{nR}=\tau_{nCentre}\cdot\left(1+\frac{1}{\sqrt{\eta}}\right)\mbox{.}$

The total neutron lifetime is calculated here as the weighted average of the
basic lifetimes $\tau_{nL}$ and $\tau_{nR}$, taken with the following weights

$W_{nL}=\left(\frac{1}{2}+\frac{\sqrt{\eta}}{\eta+1}\right)$

and

$W_{nR}=\left(\frac{1}{2}-\frac{\sqrt{\eta}}{\eta+1}\right)\mbox{,}$

respectively. The values of the basic lifetimes of the neutron are also
determined by solving the system of equations (15) and equal to the following
values in dependence of $\eta$\- value.

Estimates of basic neutron lifetimes
---
Split-parameter, $\eta$ | 107 | 103
Lifetime of L-neutrons, s | 812.99 | 811.32
Lifetime of R-neutrons, s | 987.01 | 988.68

A completely new physical quantity is the mirror neutron lifetime
$\tau_{nW}^{M}$. An indication of the existence of this physical constant is
given here for the first time. However, an experimental result close to this
value is known for a long time as equal to $918\pm 14\,\mbox{s}$ from the
research [14], where the neutron decay electron count was used. This result is
traditionally placed in the PDG summary tables for the neutron lifetime in the
lower part, which is not included in calculating the average value. The
author, however, believes that this experimental result is physically
justified.

The above estimate, obtained because of symmetry considerations about the
central lifetime, can also be expressed by the following formula:

$\tau_{nW}^{M}=\tau_{nL}\cdot W_{nR}+\tau_{nR}\cdot W_{nL}\mbox{.}$

Nevertheless, the main result for comparison is the weighted average neutron
lifetime, the estimate of which, as indicated above, is in full agreement with
the known experimental data.

It is impossible not to mention one more coincidence from the above triad of
averages. In this work, for the first time, the problem of determining the so-
called lifetime of ”nonpolarized” neutrons is formulated, which is the inverse
of the arithmetic mean of the decay constants of $L\mbox{-neutrons}$ and
$R\mbox{-neutrons}$. This result coincides with the value of the neutron
lifetime obtained by P.E. Spivak [17] in 1988: $\tau_{n}=891\pm 9\,\mbox{s}$.
The value of the neutron lifetime error in that work coincides with the
difference between the arithmetic mean neutron lifetime and the lifetime of
the ”nonpolarized” neutron. Moreover, this error interval at the lower limit
coincides with the value of the weighted average neutron lifetime. Hence, the
error corresponds to the structure of average values for the neutron lifetime,
i.e., the error is physically substantiated, and the result of [17] generally
also confirms the validity of the estimates obtained in the present paper.

Discussing the two different lifetime results of the experiment of NIST, USA
$\tau_{n}=887.7\pm 1.2(stat)\pm 1.9(syst)\,\mbox{s}$ [12] and the experiment
of PNPI, Russian Federation $\tau_{n}=881.5\pm 0.9\quad\mbox{s}$ [13] the
author must give PDG2020 average value $879.4\pm 0.6\,\mbox{ s}$ to compare
with. It disagreed at some level with the mentioned results. The reasons for
this difference are quite explainable. The UCN-storage experiments always give
lifetimes less than the true neutron lifetime. With increasing accuracy, these
experiments give the lower approximation to the true lifetime, since
containing side channels of neutron leakage. To prove the lack of side
channels of leakage, you can only know the true lifetime with much higher
accuracy. For example when neutrons are stored in magnetic traps, a bias in
the estimate of the lifetime is inevitable due to the unaccounted systematic
error, which is characteristic of the ”bowl”-type magnetic traps. This error
is associated with the depolarization of ultracold neutrons at the nodes of an
inhomogeneous magnetic field that keeps neutrons of only a certain
polarization in the trap [15]. Depolarization occurs when a neutron passes
through the field nodes, i.e. zero magnetic field, with a spin flip relative
to the field. Spin-flip at the field nodes leads to the loss of neutrons i.e.
reduces the storage time of neutrons in the trap. This effect is difficult to
measure or calculate especially if it is only a few seconds versus the neutron
lifetime of about 900 seconds. Mathematically, the presence of nodes in
a”bowl”-type system consisting of a bottom and walls is very easy to prove,
which was done in [16]. A detailed discussion of this source of a systematic
error is beyond the scope of this work.

The results show that the neutron beta decay during the registration of decay
products looks a little more difficult. However, the detailing of experimental
study of this process by adequate methods leads to the level of accuracy of
the order of hundredth seconds. This level of accuracy will solve many
contradictions and explain all the accumulated information about the beta
decay of neutrons.

##  5 Conclusion

It is shown that the neutron beta decay is a unique example of two-channel
process. A new element was the use of elementary set theory to describe the
well-known effect of electron-spin asymmetry in neutron decay. The concept of
a partial decay constant and a partial lifetime are refined as characteristics
of a subset of particles that have the property of decay into a given channel.
It is shown that the total neutron lifetime is a weighted average of the
partial lifetimes, which leads to a more accurate formulation of the full
width rule. Analytical expressions are obtained that relate the basic neutron
lifetimes and the weighted average value of the neutron lifetime with the
integral parameter of the neutron beta decay asymmetry. Numerical estimates of
the weighted average value of the neutron lifetime are obtained on the basis
of the developed concept and known experimental data. Convincing agreement
with the known independent experimental results was noted, which is proof of
the validity of the concept of two lifetimes in the neutron beta decay. The
dependence of the key parameters of the neutron beta decay on the split
-parameter and the central lifetime are obtained. The ways of transition to a
new level of precision are shown and substantiated due to the detailed study
of the neutron beta decay. Theoretical estimates are given for the expected
values for the two basic lifetimes of neutrons. The estimates agree with the
preliminary experimental results [18].

##  6 Acknowledgements

In this work, the author used the results obtained during the processing of
experimental data on neutron beams from the ITEP heavy water reactor, and
developed some approaches that were the subject of discussions in the ITEP
laboratory of neutron physics more than 15 years ago.

The author is grateful to all the participants in those discussions, the
memory of which became an incentive for this work.

No funding sources have been involved in this research.

## References

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  * [18] V.V. Vasiliev. Neutron lifetime splitting in beta-decay. ArXiv: 1903.12515 (2019).


# Audience-specific Explanations for Machine Translation

###### Abstract

In machine translation, a common problem is that the translation of certain
words even if translated can cause incomprehension of the target language
audience due to different cultural backgrounds. A solution to solve this
problem is to add explanations for these words. In a first step, we therefore
need to identify these words or phrases. In this work we explore techniques to
extract example explanations from a parallel corpus. However, the sparsity of
sentences containing words that need to be explained makes building the
training dataset extremely difficult. In this work, we propose a semi-
automatic technique to extract these explanations from a large parallel
corpus. Experiments on English$\to$German language pair show that our method
is able to extract sentence so that more than 10$\%$ of the sentences contain
explanation, while only 1.9$\%$ of the original sentences contain
explanations. In addition, experiments on English$\to$French and
English$\to$Chinese language pairs also show similar conclusions. This is
therefore an essential first automatic step to create a explanation dataset.
Furthermore we show that the technique is robust for all three language pairs.

Keywords: keyword1, keyword2, keyword3

Audience-specific Explanations for Machine Translation

Renhan Lou, Jan Niehues
---
Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology
Karlsruhe, Germany
<EMAIL_ADDRESS><EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

With different neural network models proposed, neural machine translation
(NMT) is now becoming the dominant approach in machine translation. Especially
new neural network models, such as Transformer (Vaswani et al., 2017), improve
significantly the performance of machines in translation tasks. While NMT
achieves a very good quality in the direct translation of source text into the
target language, in practical application scenarios additional challenges need
to be address in order to enable a successful communication across language
barriers.

One of the most common problems is that the translation of certain words can
cause incomprehension of the audience in the target language. Because some
words are common in the source language, but not common in the target
language. This leads to the fact that when the audience of the target language
sees the translation of these words, they cannot understand the meaning of the
translation.

A simple example is the Super Bowl, the annual championship game of the
National Football League in the United States. The Super Bowl is one of the
most famous games in the United States. However, in some countries in Europe
and Asia, only a few people who like American football know about it.
Therefore, when the Super Bowl is translated into another language, such as
German or Chinese, the audience in the target language will simply understand
it as a kind of tableware according to the literal meaning of the translation.

Thus, when these words are translated into another language, how to eliminate
the incomprehension of the target language audience is a problem that cannot
be ignored in machine translation. Different solutions have been proposed to
address the translation difficulties of uncommon words or rare words. The
method proposed by (Luong et al., 2014) uses external dictionaries to overcome
the difficulty of rare word translation. Afterwards, (Sennrich et al., 2015)
utilize the BPE (byte pair encoding) algorithm to encode rare words into
subword units, thereby reducing the number of rare words and improving
translation quality. (Wu et al., 2016) also use subword units to improve the
translation quality of rare words. (Pham et al., 2018) introduce external
expert models such as terminology lists to improve the performance of rare
word translation.

However, the above work only focuses on the translation of rare words in the
source language. Moreover, they cannot eliminate the incomprehension of the
target language audience during machine translation. To solve this problem, we
can learn from human translation. In human translation, a simple solution to
solve this problem is to add explanations when translating these words. With
the help of this additional information, the incomprehension of the target
language audience can be well eliminated.

The purpose of our paper is to explore whether it is possible to find a
suitable model that can accurately predict which words need to be explained
when performing machine translation tasks. In order to train the model the
first step is to build a high quality training dataset. However, sentences
containing words that need to be explained are extremely uncommon. The
sparsity of the target sentence makes it difficult to build the training
dataset.

Therefore, we propose a method for finding sentences with words that need to
be explained by utilizing external knowledge sources. We conducted experiments
on English$\to$German, English$\to$French and English$\to$Chinese language
pairs. The results show that the method we propose can greatly reduce the
final manual selection work, and at the same time, it can stably and
efficiently find the target sentence in the last remaining sentences for all
three language pairs. This reduces the difficulty of building a training
dataset and also facilitates the training of models in the future. 111Code and
data available at: https://github.com/RHL1014/Audience-specific-Explanations-
for-MT

The contributions of our work are as follows:

  1. 1.

We propose a method for finding sentences with words that need to be
explained. Using this method we can find the target sentences stably and
efficiently.

  2. 2.

This method works for multiple language pairs, and the final effect is
independent of the input data distribution. This shows that this method has
robustness.

## 2\. Audience-specific Explanations

We want to solve the problem of how to eliminate the target language
audience’s incomprehension during the translation. With the help of the human
translation solution, this problem can be transformed into another more
specific problem, that is, how can we model audiences’ specific needs for
additional information during translation? This means we need to develop a
model that can predict which words will cause incomprehension to the target
language audience during translation. In order to accurately predict the words
that need to be explained when doing machine translation tasks, it is
necessary to build a dataset for training and evaluation. In this paper we
develop a methodology to identify these words in a parallel corpus. In a
second step this data can then be used to train and test models that are able
to predict these words.

Here is an example of translation with explanation for English$\to$German:

  1. 1.

En: John Bunyan said , “ He who runs from God in the morning will scarcely
find Him the rest of the day . ”
De: John Bunyan , der Autor der bekannten Pilgerreise , hat einmal gesagt : „
Wer morgens vor Gott wegläuft , wird Ihn den Rest des Tages kaum noch finden .
“

In German translation, , der Autor der bekannten Pilgerreise , is the
explanation for John Bunyan, which tells the German audience that John Bunyan
is a writer.

We started with an initial manual inspection of explanation. The main
challenge thereby is that these explanations are extremely infrequent. On the
other hand, the uncertainty in the position of the explanation also increases
the difficulty of finding sentence pairs with explanations. To reduce the
complexity of finding sentence pairs with explanations, we only consider the
most common form of sentence pairs with explanations, that is, the explanation
part immediately follows the word that needs to be explained. Based on our
initial investigate we identified several key characteristics of sentences
containing explanations. Based on these characteristics we build filters to
find the sentences:

  1. 1.

The word being explained or the word in the phrase being explained is rare in
the target language.

  2. 2.

The explanation is a redundant part of the sentence in the target language.

  3. 3.

The explanation follows the word or phrase being explained.

  4. 4.

The explanation contains punctuation.

  5. 5.

Words that differ from the word or phrase being explained are also included in
the explanation.

  6. 6.

The word or phrase being explained is more likely to be a named entity.

  7. 7.

Information about words or phrases that need to be explained can be found
using Wikipedia.

## 3\. Identifying candidate source phrases

Based on the summarized characteristics of sentence pairs with explanations, a
heuristic method for efficiently searching sentence pairs with explanations is
proposed. Considering the sparsity of the sentence pairs with explanations
that need to be found, the goal of this method is to find as many sentence
pairs with explanations as possible while minimizing the number of sentence
pairs without explanations.

This heuristic method is divided into four processes. The first process is to
identify words that may need explanation based on corpus statistics. The
second process is to identify sentence pairs that may have explanation with
the help of word alignment. After utilizing the internal knowledge we also
integrated external knowledge. The third process is to use the named entity
recognition (NER) model to identify the words that need to be explained. The
last process is to exploit Wikipedia to more accurately identify target
sentence pairs.

### 3.1. Filtering based on corpus statistics

Intuitively, when translating, if a word is rare in the target language, it is
more likely to be explained than other words. In order to decide which words
are rare, the word count within a certain range can be used. A word can be
considered rare if its count is below a certain threshold. For the purpose of
finding as many rare words as possible, the word count in all Wikipedia
articles is used to check whether a word is rare. Meanwhile, if only the
uncommon words in the target language are considered, it is found that many
non-candidates are introduced in the experiment. So not only the word count in
the target language but also the word count in the source language must be
considered.

### 3.2. Integrating word alignment inference

While the model to identify the words that need to be explained does not have
access to the translation, we can use the target side for identifying examples
in the parallel data, in this case, this is even the most valuable way. With
the help of the word alignment of the determined rare word and the word
following it, the corresponding words in the target language sentence and
their position in the sentence can be found. If there is a redundant part
between the corresponding words in the target language sentence, it can be
considered that there may be an explanation for the rare word in the redundant
part.

The explanation part is often accompanied by punctuation marks, such as commas
and parentheses. This means that it is possible to determine whether a
redundant part contains an explanation by checking for possible punctuation in
the redundant part. In addition, as the explanation contains additional
information about the object being explained, the explanation should contain
other words besides the explained word, so it can be judged whether there is
an explanation in the redundant part by checking the words in the redundant
part and their word alignment. If the redundant part also contains words other
than the explained word, and none of the words in the redundant part have a
word alignment, the redundant part can be considered as likely to contain the
true explanation.

Depending on the form of the sentence pair that need to be identified and the
summarized characteristics, we can visualize the candidate sentence pair with
explanations. Figure 1 shows an ideal candidate sentence pair.

Figure 1: Candidate sentence pair

Given the source language sentence $\boldsymbol{s}$ and the corresponding
target language translation sentence $\boldsymbol{t}$. The length of sentence
$\boldsymbol{s}$ is $\boldsymbol{N}$, which means it is composed of
$\boldsymbol{N}$ tokens. Similarly, the length of sentence $\boldsymbol{t}$ is
$\boldsymbol{M}$. In sentence $\boldsymbol{s}$, the _k-th_ token
$\boldsymbol{token_{k}}$ is an uncommon word, meanwhile, the _m-th_ token
$\boldsymbol{token_{m}}$ aligned with $\boldsymbol{token_{k}}$ in sentence
$\boldsymbol{t}$ is also a rare word. The next token
$\boldsymbol{token_{k+1}}$ of token $\boldsymbol{token_{k}}$ in sentence
$\boldsymbol{s}$ is aligned with token $\boldsymbol{token_{m+n+1}}$ in
sentence $\boldsymbol{t}$. And in sentence $\boldsymbol{t}$
$\boldsymbol{token_{m+n+1}}$ is not the next token of
$\boldsymbol{token_{m}}$, which means that there is a redundant part of length
$\boldsymbol{n}$ after $\boldsymbol{token_{m}}$ in sentence $\boldsymbol{t}$.
In the redundant part from $\boldsymbol{token_{m+1}}$ to
$\boldsymbol{token_{m+n}}$, there are punctuation marks, such as
$\boldsymbol{token_{m+1}}$ is likely to be a comma, or a parenthesis. All
tokens from $\boldsymbol{token_{m+1}}$ to $\boldsymbol{token_{m+n}}$ in the
redundant part should have no word alignment results, and should contain other
words except $\boldsymbol{token_{m}}$.

### 3.3. Using NER

From the summarized characteristics about the target sentence pair we know
that the word or phrase being explained is more likely to be a named entity.
This provides another way to determine candidate sentence pairs. If the named
entities in a sentence, such as person names, place names or organization
names, can be identified and located, then the range of candidate sentences
can be narrowed down better. Named entity recognition (NER) is an effective
tool for identifying named entity in a sentence. NER can also give the
location of each named entity. So NER can be used to further identify possible
candidates while also reducing the number of non-candidates.

The word being explained is either itself a named entity, or it is part of a
named entity. So the candidate sentence pairs can be further determined by
comparing the recognized named entities with the previously confirmed words
that may be explained.

### 3.4. Using Wikipedia

All the named entities in a sentence can be recognized after NER. Based on
named entities, another method that can further to identify target sentence
pairs with explanations is using Wikipedia. This step is also inspired by the
work of Nothman et al. (2008, 2009, 2013). Their work confirms that Wikipedia
can be used to build dataset for training NER models and NER models can also
achieve optimal results.

For most phrases that need to be explained, the corresponding articles can be
searched in Wikipedia, so the titles of Wikipedia articles can be used to
determine target sentence pairs. If a source language named entity is a title
of a Wikipedia article, then it is likely a candidate that needs to be
explained. However, this only considers the aspect of the source language, if
the consideration for the target language is added, candidates can be further
identified. If a source language named entity is the title of a Wikipedia
article, and the corresponding target language named entity is not the title
of a Wikipedia article, this means that the source language audience has a
source of information to understand this named entity, while the target
language audience does not have a corresponding information source. In this
case, this named entity is more likely to be a good candidate that needs to be
explained.

On the other hand, in addition to the title of the Wikipedia article can be
used to determine candidates, the Wikipedia article itself can also be used to
determine candidates. If both the named entity in the source language and the
corresponding named entity in the target language are the titles of Wikipedia
articles, then the articles corresponding to the titles can be compared. More
precisely, candidates can be determined by comparing the size of Wikipedia
articles. If the size of the Wikipedia article in the source language is
larger than the size of Wikipedia article in the target language, this
situation means that while both the source and target language audiences have
a source of information to understand the candidate, but the candidate is less
common in target language, then the title of the source language Wikipedia
article might be a good candidate that needs to be explained. Figure 2 shows
the process of using Wikipedia to identify candidates.

There are many text comparisons in this step, for example, the comparisons
between named entities and Wikipedia titles. The possible form inconsistencies
between them will make the comparison difficult. In order to simplify the text
comparison when using Wikipedia, the stemming algorithm will be applied.

Figure 2: An example of identifying candidates using Wikipedia

## 4\. Evaluation

### 4.1. Setup

We choose CCMatrix (Schwenk et al., 2019; Fan et al., 2021) as the corpus
required for the experiment. All CCMatrix data are downloaded from OPUS
(Tiedemann, 2012). The version of Wikipedia database backup dumps used in the
experiments is 20221101. We use wikiextractor
222https://github.com/attardi/wikiextractor to extract Wikipedia articles.
Meanwhile, we use the tool wikipedia-parallel-titles
333https://github.com/clab/wikipedia-parallel-titles to create the Wikipedia
parallel titles corpus. For preprocessing, we choose spaCy (Honnibal et al.,
2020) as the word tokenization tool. For Chinese word tokenization, we use
pkuseg (Luo et al., 2019) under the framework of spaCy. We use awesome-align
(Dou and Neubig, 2021) to extract word alignment results. We choose the
Snowball algorithm from NLTK (Bird et al., 2009) to perform stemming to
simplify text comparison. When using word alignment to find the target
sentence pair, the length of the redundant part in the target language
sentence is set to be greater than or equal to 3.

### 4.2. Evaluation Metric

Filter the target sentences from the corpus to construct the training dataset
is a classification problem. Therefore, the metric BLEU does not work here.
For a classification problem, F1-score is a good evaluation metric. The
calculation of the F1-score requires the number of positive examples and the
number of negative examples. However, due to the sparsity of sentences with
explanations, we only focus on whether the target sentence can be found, which
means that in our experiments, the evaluation of the method for finding target
sentences only involves sentences with explanation, i.e. only the number of
positive examples is considered. This means that we just selected a subset of
F1-score as the evaluation metric for our experiments.

### 4.3. Initial Result

We first focus only on the English$\to$German (En$\to$De) language pair. In
order to compare and evaluate the subsequent steps of our proposed method, we
first run our method to the step before NER, i.e., using only word counts and
word alignments to find target sentence pair candidates. The first 5 million
sentence pairs from the corpus are taken as the input, and the word count
thresholds for both source and target languages are set to 15000. This means
that if a word, its word count is below 15000, it is considered a rare word.
The results are in Table 1.

En$\to$De | Num. of sentences | F1
---|---|---
Total | 5000000 | -
1\. Initial result | 8977/173 | $3.78\%$
Table 1: The initial results of the En$\to$De

It can be found from the Table 1 that for En$\to$De there are still 8977
sentence pairs remaining. On the basis of the remaining sentence pairs, manual
work is performed to select out the sentence pairs that contain explanations.
Finally, 173 sentence pairs with explanations are found out of 8977 remaining
sentence pairs. This means that only 1.92$\%$ of the original sentences
contain explanations. F1-score is also calculated and given in the table.

### 4.4. Follow-up results

Based on the results in Table 1, the subsequent experiments can be performed.
Since the models provided by different NER tools and different word count
thresholds will affect the final experimental results, different combinations
of NER models and thresholds need to be considered and compared to obtain the
best results. We compared the performance of the NER models from Flair (Akbik
et al., 2019), spaCy (Honnibal et al., 2020), and Stanza (Qi et al., 2020). We
also tried five different word count thresholds for both source and target
languages under each NER model: 100, 1000, 5000, 10000 and 15000. We found
that for En$\to$De, optimal results can be obtained when using the NER model
provided by Flair with a word count threshold of 5000 (i.e., the word count is
under 5000) for both the source and target languages. The final overall
results are in Table 2.

Step | Num. of sent. | F1
---|---|---
Initial result | 8977/173 | $3.78\%$
1\. Using word count and alignment | 3102/134 | $8.18\%$
2\. Using NER | 791/93 | $19.29\%$
3\. Using Wiki | 323/44 | $17.74\%$
Table 2: The final result of the En$\to$De

Comparing the initial result and the result of the first step, we can find
that as the word count threshold becomes smaller, the number of remaining
sentence pairs decreases, and the number of target sentence pairs with
explanations in the remaining sentence pairs also decreases. But on the other
hand, the F1-score increased from $3.78\%$ to $8.18\%$. Comparing the results
of the first step and the second step, we can find that after using NER, the
number of remaining sentence pairs and target sentence pairs both decreased,
but the F1-score increased from $8.18\%$ to $19.29\%$. The significant
improvement in the F1-score shows that NER is a powerful and effective tool
for identifying target sentence pairs.

Finally, comparing the results of the second step with the third step, we can
find that after using Wikipedia to continue to identify target sentence pairs,
the number of remaining sentence pairs and target sentence pairs are reduced.
Meanwhile, the F1-score is also decreased from $19.29\%$ to $17.74\%$. This
shows that Wikipedia can greatly reduce manual work while losing a relatively
small F1-score.

The results in Table 2 prove that our proposed method can greatly improve the
efficiency of finding target sentence pairs. In order to verify the general
effectiveness of our method, we also test the effect of our method on other
inputs. We randomly select 5 million sentence pairs from all remaining
sentence pairs in the corpus except for the first 5 million sentence pairs.
These randomly selected sentence pairs are used as input. The same
configurations are also used for test. In order to avoid accidental errors, we
conduct five experiments for testing. The results of the five experiments for
testing are very similar, so we only provide the results of one of them. The
results of the experiments for testing are in Table 3 and Table 4.

Step | Num. of sent.
---|---
1\. Using word count & align. | 17271
2\. Using NER | 7176
3\. Using Wiki | 2832
Table 3: The results of the experiment for testing (En$\to$De) En$\to$De | Num. of sent. | Perc.
---|---|---
3\. Wiki (First 5M) | 323/44 | 13.62$\%$
3\. Wiki (Rand. 5M) | 2832/294 | 10.38$\%$
Table 4: The percentage results of En$\to$De

If we compare the results in Table 3 with those in Table 2, we can find a non-
negligible gap between the two results regarding the number of remaining
sentence pairs. In order to check the proportion of target sentence pairs with
explanations in the remaining sentence pairs, we also check the number of
target sentence pairs among the last remaining sentence pairs. We select the
results of the last step (i.e. the step to use Wikipedia) for validation. The
proportion results are in Table 4.

When the input is the first 5 million sentence pairs of the corpus, 44
sentence pairs with explanations can be found in the remaining 323 sentence
pairs. When 5 million randomly selected sentence pairs are taken as input, we
found 294 target sentence pairs with explanations out of 2832 remaining
sentence pairs. This means that when the input is random, the number of
remaining sentence pairs and the sentence pairs with explanations are all
increased. However, when we check the proportion results, we can find that for
the random input, among the remaining sentence pairs we can find $10.38\%$
target sentence pairs. And for the first 5 million sentence pairs, the
proportion is $13.62\%$. Although the proportion result of the random input is
lower than that of the first 5 million sentence pairs, it is still higher than
$10\%$, which is an acceptable result.

The results in Table 4 illustrate that our proposed method for finding
sentence pairs with explanations is robust against different input data and
efficient for the En$\to$De. Our proposed method is independent of the
distribution of data, and a large number of non-target sentence pairs can be
removed. Therefore, the number of last remaining sentence pairs is extremely
small. Among the last remaining sentences, no matter how the number of
remaining sentences changes, more than $10\%$ of the target sentence pairs can
always be found.

Finally, we also check whether each named entity that is explained in the
found target sentence pairs also always needs to be explained in other
sentences. Based on 44 named entities that require explanation found in
experiments, in the input of 5 million sentence pairs, for each named entity,
we check whether each sentence pair containing this named entity also contains
an explanation for it. The result is in Figure 3 and Figure 4.

Figure 3: Probability distribution of NE to be explained Figure 4: Explanation
frequency of NE that is always explained

After removing duplicate named entities, there are 42 explained named entities
left for En$\to$De. From the Figure 3 we can find that not all named entities
always need to be explained. Only 15 named entities are always explained (with
100$\%$ probability). Based on these 15 named entities that always require
explanation, we also examine how often these named entities are explained, the
result is in the Figure 4. Among the 15 named entities that are always
explained, 14 named entities are explained only once, and only 1 named entity
is explained 4 times.

### 4.5. Multi-language results

We also conduct experiments for English$\to$French (En$\to$Fr) and
English$\to$Chinese (En$\to$Zh) language pairs. The first 5 million sentence
pairs in the corpus are still used as the input. For initial results, the word
count thresholds for both the source and target languages are set to 15000. We
found that for En$\to$Fr, optimal results can be obtained when using the NER
model provided by Stanza (Qi et al., 2020) with a word count threshold of 5000
for both the source and target languages. And for En$\to$Zh, optimal results
can be obtained when using the NER model provided by HanLP (He and Choi, 2021)
with a word count threshold of 5000 for both the source and target languages.
Although the word count threshold to obtain the optimal results is the same
for all language pairs. However, for each language pair, the results of the
number of remaining sentence pairs and the number of sentence pairs with
explanations are different.

Table 5 is the result for En$\to$Fr. The result for En$\to$Zh is in Table 6.
The results for these two language pairs are similar to those for En$\to$De.
As the word count threshold gets smaller, the number of remaining and target
sentence pairs decreases, while the F1-score rises. NER is also a powerful and
effective tool for identifying target sentence pairs for both language pairs.
After using NER, although the number of remaining sentence pairs and target
sentence pairs are further reduced, the F1-score is significantly improved.
And the use of Wikipedia can still achieve an acceptable F1-score while
greatly reducing manual work.

Step | Num. of sent. | F1
---|---|---
Initial Result | 6982/122 | $3.43\%$
1\. Using word count and alignment | 3350/95 | $5.47\%$
2\. Using NER | 1332/76 | $10.45\%$
3\. Using Wiki | 395/18 | $6.96\%$
Table 5: The final results of En$\to$Fr language pair Step | Num. of sent. | F1
---|---|---
Initial Result | 13541/402 | $5.77\%$
1\. Using word count and alignment | 7360/302 | $7.78\%$
2\. Using NER | 2557/194 | $13.11\%$
3\. Using Wiki | 1083/87 | $11.72\%$
Table 6: The final results of En$\to$Zh language pair

Similarly, we also test the effect of our method on random inputs for
En$\to$Fr and En$\to$Zh language pairs. The results are in Table 7 and Table
8. In order to avoid accidental errors, we also conduct five experiments. The
results of the five experiments for En$\to$Fr and En$\to$Zh are also very
similar, so we also provide the results of one of them. Compared to the
experimental results of the first five million sentence pairs as input, when
the input are random five million sentence pairs, a non-negligible gap
regarding the number of remaining sentence pairs can be always found.

Step | Num. of sent.
---|---
1\. Using word count & align. | 22679
2\. Using NER | 12420
3\. Using Wiki | 4051
Table 7: The results of the experiments for testing (En$\to$Fr) Step | Num. of sent.
---|---
1\. Using word count & align. | 16267
2\. Using NER | 7451
3\. Using Wiki | 3149
Table 8: The results of the experiments for testing (En$\to$Zh)

We also calculated the proportion of target sentence pairs with explanations
in the results of experiments for validation for En$\to$Fr and En$\to$Zh. The
proportion results are in Table 9 and Table 10. For En$\to$Fr, a surprising
result is obtained. For the results with the random input, $8.24\%$ of the
target sentence pairs can be found in the last remaining 4051 sentence pairs,
which is much higher than the $4.56\%$ of the results with the first 5 million
sentence pairs as the input. Due to the identical experimental parameters, the
significant difference in proportion results is presumably caused by the
distribution of input data. For En$\to$Zh, $7.40\%$ of the target sentence
pairs can be found in the remaining 3149 sentence pairs when the input is
random, which is very close to the $8.03\%$ of the results when the input is
the first 5 million sentence pairs. This means that our proposed method is
also robust against different input data and efficient for En$\to$Fr and
En$\to$Zh. The number of last remaining sentence pairs is extremely small. For
En$\to$Fr, more than $5\%$ of the target sentence pairs can always be found
among the last remaining sentence pairs. While for En$\to$Zh, more than $7\%$
of the target sentence pairs can always be found in the last remaining
sentence pairs.

En$\to$Fr | Num. of sent. | Perc.
---|---|---
3\. Wiki (First 5M.) | 395/18 | 4.56$\%$
3\. Wiki (Rand. 5M.) | 4051/334 | 8.24$\%$
Table 9: The percentage results of En$\to$Fr En$\to$Zh | Num. of sent. | Perc.
---|---|---
3\. Wiki (First 5M.) | 1083/87 | 8.03$\%$
3\. Wiki (Rand. 5M.) | 3149/233 | 7.40$\%$
Table 10: The percentage results of En$\to$Zh

We can also provide some examples with explanations found for En$\to$Fr and
En$\to$Zh.

  1. 1.

En: ‘ Even if WMO agrees , I will still not pass on the data .
Fr: « Même si la WMO [ Organisation mondiale de la météorologie ] est d’
accord , je ne vais toujours pas transmettre les données .

  2. 2.

En: I looked at Raytheon ’s annual report and they lost a lot of money in this
area , but they ’re selling their own planes so maybe they do n’t care .
Zh: 我 看 了 Raytheon [ 美国 主要 的 军事 承包 商] 的 年报 ， 它们 在 这个 领域 亏 了 很多 钱 ， 但 他们 销售 自己
的 飞机 ， 因此 可能 并不 在意 。

## 5\. Conclusion

We propose a heuristic method to find target sentence pairs with explanations.
In this method, both internal and external knowledge are utilized: word count,
word alignment, named entity recognition, and Wikipedia. We conduct
experiments on three language pairs: English$\to$German, English$\to$French
and English$\to$Chinese. The results show that for each language pair, our
proposed method can reduce the number of remaining sentence pairs to an
extremely low number. Moreover, our method is robust, among the remaining
sentence pairs, a certain proportion of target sentence pairs can always be
found for each language pair. Among the remaining sentence pairs, more than
$10\%$ of the target sentence pairs can be found for the English$\to$German,
more than $7\%$ of the target sentence pairs can be found for the
English$\to$Chinese, and for the English$\to$French, more than $5\%$ of the
target sentence pairs can be found. This means that a sufficient number of
target sentence pairs can be efficiently found using our method so that we can
construct a training dataset for the training of the model in the future.

## 6\. Bibliographical References

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