# Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) event rates for Ge,
Zn and Si detector materials

T. S. Kosmas<EMAIL_ADDRESS>Division of Theoretical Physics, University of
Ioannina, GR 45110 Ioannina, Greece  V. K. B. Kota<EMAIL_ADDRESS>Physical Research Laboratory, Ahmedabad 380 009, India  D. K. Papoulias
<EMAIL_ADDRESS>Division of Theoretical Physics, University of Ioannina, GR
45110 Ioannina, Greece  R. Sahu<EMAIL_ADDRESS>National Institute of
Science and Technology, Palur Hills, Berhampur 761 008, Odisha, India

###### Abstract

Realistic nuclear structure calculations are presented for the event rates due
to coherent elastic neutrino-nucleus scattering (CE$\nu$NS), assuming
neutrinos from pion decay at rest, from nuclear reactors, and from Earth’s
interior. We focus on the currently interesting germanium isotopes,
70,73,76Ge, which constitute detector materials of the recently planned
CE$\nu$NS experiments. We study in addition the potential use of 64,70Zn and
28Si isotopes as promising CE$\nu$NS detectors. From nuclear physics
perspectives, recently, calculations have been carried out within the
framework of the deformed shell model (DSM), based on realistic nuclear
forces, and assessed on the reproducibility of spectroscopic nuclear
properties. The high confidence level acquired by their agreement with
experimental results and by their comparison with other mostly
phenomenological calculations encouraged the use of DSM to extract predictions
for the CE$\nu$NS event rates of the above isotopes. Our detailed estimation
of the nuclear physics aspects of the recently observed neutral current
coherent neutrino-nucleus scattering may shed light on unravelling the still
remaining uncertainties for the CE$\nu$NS process within and beyond the
standard model.

##  1 Introduction

More than four decades ago, Freedman Freedman:1973yd  proposed the measurement
of the neutral current coherent elastic neutrino-nucleus scattering
(CE$\nu$NS) when low-energy neutrinos scatter off nuclei. This process,
however, was observed for the first time very recently by the COHERENT
collaboration Akimov:2017ade  using the sodium-doped CsI detector at the
Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. The process
was, subsequently, observed at the SNS using also a liquid argon (LAr)
detector Akimov:2020pdx . The observation of CE$\nu$NS has opened up new
opportunities to test the predictions of the standard model (SM)
Cadeddu:2017etk ; Papoulias:2019lfi ; Sahu:2020kwh ; Tomalak:2020zfh ;
Co:2020gwl , while a precise measurement of this process may offer a way to
constrain the particle physics parameters of theories beyond the SM
Papoulias:2017qdn  (the recent constraints extracted from CE$\nu$NS are
summarized in Ref. Papoulias:2019xaw ).

The detection signal of CE$\nu$NS, i.e., the low-energy recoil of the target
nucleus, is an experimental challenge while the uncertainties associated with
the relevant measurements should be minimized and the accuracy of CE$\nu$NS
experimental method must be improved. Toward this purpose, many planned
experiments for measuring CE$\nu$NS are based on the well known germanium
detectors Yuri-Efremenko , while zinc and silicon are also promising detector
materials for neutrino-nucleus cross section measurements Tsakstara:2012yd .
Such ongoing and designed detectors are CONUS CONUS:2020skt , $\nu$GEN
Belov:2015ufh , TEXONO TEXONO:2020vnv , COHERENT COHERENT:2018gft , RICOCHET
Billard:2016giu , MINER MINER:2016igy , NUCLEUS NUCLEUS:2019igx , CONNIE
CONNIE:2019xid , Coherent Captain-Mills (CCM) CCM , European Spallation Source
(ESS) Baxter:2019mcx , vIOLETA Fernandez-Moroni:2020yyl  and SBC SBC:2021yal
experiments. The employment of pure Ge detectors in measuring rare event
processes has shown appreciably good sensitivity, while in CE$\nu$NS some
combinations of detection media have been chosen and proposed to be utilized
due to other experimental criteria Galindo-Uribarri:2020huw . Toward the
latter purposes, Zn and Si isotopes may offer advantageous combinations to
reduce the systematic errors of CE$\nu$NS experiments instead of a single
element Yuri-Efremenko .

Theoretically, it was known that roughly speaking the CE$\nu$NS cross section
has a quadratic dependence on the neutron number of the target nucleus
($\propto N^{2}$) which is attributed to the different strength of the
respective couplings with which the protons and the neutrons of the atomic
nuclei interact with the intermediate $Z_{0}$ boson; see, e.g., Ref.
Drukier:1984vhf . The ground-state to ground-state transition channel, which
is possible in neutral current neutrino-nucleus scattering, appears enhanced
due to the fact that the proton and neutron amplitude phases corresponding to
a neutrino scattering off nucleons are added coherently Lindner:2016wff , and
dominates the process at low energies. On the other hand, the incoherent
scattering cross sections are much smaller and demonstrate some well
pronounced peaks of specific multipole excitations Pirinen:2018gsd . Such
detailed calculations have been performed previously for various nuclear
isotopes (see, e.g., Refs. Tsakstara:2011zzc ; Tsakstara:2011zzd ).

With respect to physics beyond the SM, nonstandard interactions (NSIs) is a
widely used formalism that can phenomenologically describe a large family of
new physics interactions, in particular those involving novel vector or axial
vector processes Flores:2020lji . Constraints on NSIs exist from the analysis
of available CE$\nu$NS data by COHERENT with CsI Liao:2017uzy ;
Papoulias:2017qdn ; Giunti:2019xpr  and LAr Miranda:2020tif . Moreover,
extensions of the NSI formalism, namely neutrino generalized interactions
(NGIs) can accommodate scalar, pseudoscalar and tensor interactions
AristizabalSierra:2018eqm .

Over the years, the deformed shell model (DSM) based on Hartree-Fock states
with angular momentum projection and band mixing has been found to be quite
successful in describing several nuclear properties like spectroscopic
properties including spectroscopy of $N=Z$ odd-odd nuclei with isospin
projection Srivastava:2017elr , the coherent and incoherent neutral current
$\mu\rightarrow e$ conversion in the field of nuclei Kosmas:2003xr  and
double-$\beta$ decay half-lives Sahu:2013yna ; Sahu:2014nga . Recently, we
have calculated event rates for weakly interacting massive particle (WIMP)
scattering off 73Ge Sahu:2017czz  and elastic and inelastic scattering of
neutrinos and WIMPs on nuclei Papoulias:2018uzy ; Sahu:2020kwh . Our aim in
this work is to provide reliable theoretical predictions for event rates of
neutrino-nucleus scattering involving 70,73,76Ge, 64,70Zn and 28Si isotopes by
using DSM for the nuclear structure functions needed for the event rate
calculations. Motivated by the various experimental facilities, first, we
focus on pion decay at rest ($\pi$-DAR) and reactor antineutrino sources. We
furthermore consider geoneutrinos, which are expected to contribute sizable
the overall neutrino background signal at the next-generation large-scale
detectors planned to look for light WIMPs Gelmini:2018gqa .

Finally, we quantify the percentage differences on the expected number of
events obtained with the DSM, as compared to those relying on the widely used
approximate form factor parametrizations, at different energy regimes, as well
as to those obtained with different nuclear physics methods VanDessel:2020epd
. We stress that, in extracting the percentage differences we rely on the
number of events of the CE$\nu$NS which is the most relevant experimental
observable.

The paper has been organized as follows: In Sec. 2, we discuss the CE$\nu$NS
formalism and our adopted nuclear structure method calculated in the framework
of the DSM. Then, in Sec. 3, we present the theoretical event rates and we
discuss the level of inconsistency with respect to similar calculations
involving effective nuclear form factors. Finally, our conclusions are
summarized in Sec. 4.

##  2 basic formalism

In this section, we present the basic formalism for calculating the CE$\nu$NS
event rates at different facilities aiming to detect signals induced by
$\pi$-DAR, reactor or geoneutrinos. We pay special attention to discussing the
key ingredients of the nuclear physics aspects that have been taken into
consideration. In particular, the nuclear form factors are obtained using
nuclear wavefunctions determined by DSM, of which the confidence level is
well-established through the reproducibility of spectroscopic results for the
nuclear isotopes of interest (see below).

Before embarking to the nuclear physics calculations, it is worth mentioning
that, interesting studies of physics beyond the standard model include
deviations from unitarity Miranda:2020syh , sterile neutrinos Kosmas:2017zbh ;
Canas:2017umu ; Miranda:2020syh , neutrino magnetic moments Wong:2005vg ;
Miranda:2019wdy ; Papoulias:2019txv , nonstandard interactions
AristizabalSierra:2018eqm ; Giunti:2019xpr ; Miranda:2020zji ; Denton:2020hop
, light new physics Abdullah:2018ykz ; Flores:2020lji , dark matter
Dutta:2019nbn ; delaVega:2021wpx , etc.

###  2.1 CE$\nu$NS differential cross section

Neutrinos with energies below some tens of MeV predominately conserve the
integrity of nucleons in neutrino-quark interactions with $Z_{0}$-boson
exchange, allowing us to consider the CE$\nu$NS process using an effective
neutrino nucleon interaction in which the nucleon current is a sum of vector
and axial currents. The differential CE$\nu$NS cross section with respect to
the nuclear recoil energy $T_{A}$ (the axial vector contributions is neglected
in this work) reads Papoulias:2017qdn

$\frac{{\text{d}}\sigma}{{\text{d}}T_{A}}=\frac{G_{\text{F}}^{2}m_{A}}{2\pi}\mathcal{Q}_{W}^{2}\left(2-\frac{m_{A}T_{A}}{E_{\nu}^{2}}\right)\,,$
(1)

where $G_{\text{F}}$ is the Fermi’s constant, $E_{\nu}$ is the incoming
neutrino energy, while $Z$ and $N=A-Z$ denote the number of protons and
neutrons, respectively. The vector weak charge, $\mathcal{Q}_{W}$,
encapsulates the information from the nuclear structure and is written in
terms of the proton and neutron form factors $F_{p,n}(q^{2})$ as

$\mathcal{Q}_{W}=g^{V}_{p}ZF_{p}(q^{2})+g^{V}_{n}NF_{n}(q^{2})\,,$ (2)

where the proton and neutron couplings are expressed as
$g^{V}_{p}=1/2-2\sin^{2}\theta_{W}$ and $g^{V}_{n}=-1/2$, respectively, and
$q=\displaystyle\sqrt{2m_{A}T_{A}}$ denotes the magnitude of the 3-momentum
transfer.

For the low energies involved in CE$\nu$NS, our calculations consider the low-
energy limit of the weak mixing angle running, and hence we assume
$\sin^{2}\theta_{W}=0.2381$ Kumar:2013yoa . Note, that due to the smallness of
the proton coupling, the CE$\nu$NS cross section scales with a characteristic
$N^{2}$ dependence. Finally, the nuclear mass is calculated as
$m_{A}=Zm_{p}+Nm_{n}-B$, where the nuclear binding energy $B$ is taken from
Ref. Wang:2017  (the nucleon masses are taken to be $m_{p}=938.28$ MeV and
$m_{n}=939.57$ MeV).

###  2.2 CE$\nu$NS event rates

The differential and integrated event rates of CE$\nu$NS , after defining all
the parameters in Eq.(1), are calculated by

$\frac{{\text{d}}R}{dT_{A}}=\mathcal{K}\displaystyle\int_{E_{\nu,\text{min}}}^{E_{\nu,\text{max}}}\left[\displaystyle\frac{{\text{d}}\sigma}{{\text{d}}T_{A}}\left(E_{\nu},T_{A}\right)\right]\;\;\lambda_{\nu}(E_{\nu})\,dE_{\nu}$
(3)

where $\lambda_{\nu}(E_{\nu})$ represents the relevant neutrino energy
distribution function characterizing the specific neutrino source. The
normalization factor $\mathcal{K}$ is given by
$\mathcal{K}=t_{\text{run}}\Phi_{\nu}N_{\text{targ}}$, with
$N_{\text{targ}}=\displaystyle\frac{m_{\text{det}}\,N_{A}}{M_{r}}$. Here,
$t_{\text{run}}$ is taken as $1\;$yr, $N_{\text{targ}}$ is the number of
target nuclei and $\Phi_{\nu}$ is the neutrino flux normalization. In the
calculation of $N_{\text{targ}}$, the detector mass $m_{\text{det}}$ is
assumed to be 1 kg for $\pi$-DAR and reactor neutrinos and 1 ton for
geoneutrinos. Similarly, $M_{r}$ is the molar mass (atomic weight) and $N_{A}$
is the Avogadro number ($N_{A}=6.022\times 10^{23}$) Cadeddu:2017etk .

For the case of $\pi$-DAR neutrinos, we consider the specifications of the SNS
at Oak Ridge with $r=0.08$ being the number of emitted neutrinos per flavor
for each proton on target (POT) and $N_{\text{POT}}\approx 2.1\times 10^{23}$
denoting the number of protons on target per year Akimov:2017ade . The SNS
flux is then obtained as $\Phi_{\nu}=\displaystyle\frac{r\cdot
N_{\text{POT}}}{4\pi L^{2}}$, which for a typical detector baseline of
$L\approx 20$ m, evaluates to $\Phi_{\nu}\approx 1\times
10^{7}~{}\mathrm{s^{-1}~{}cm^{-2}}$. Finally, the neutrino energy distribution
functions $\lambda_{\nu}(E_{\nu})$ for SNS neutrinos are Louis:2009zza ,

$\lambda_{\nu}(E_{\nu})=\left\\{\begin{array}[]{llc}&\delta\left(E_{\nu}-\frac{m^{2}_{\pi}-m^{2}_{\mu}}{2m_{\pi}}\right)&\text{prompt}\quad\nu_{\mu}\,,\\\
&\frac{64E^{2}_{\nu}}{m^{3}_{\mu}}\left(\frac{3}{4}-\frac{E_{\nu}}{m_{\mu}}\right)&\text{delayed}\quad\nu_{e}\,,\\\
&\frac{192E^{2}_{\nu}}{m^{3}_{\mu}}\,,\left(\frac{1}{2}-\frac{E_{\nu}}{m_{\mu}}\right)&\text{delayed}\quad\bar{\nu}_{\mu}\,.\end{array}\right.$
(4)

In the present work, the reactor antineutrino energy-distribution which
assumes the fission products of 235U, 238U, 239Pu and 241Pu is taken from Ref.
Mention:2011rk . We note that, due to the lack of experimental data for
$E_{\nu}<2~{}\text{MeV}$, the theoretical calculation of Ref. Kopeikin:1997ve
is employed, while we assume a typical flux of $\Phi_{\nu}\approx 1\times
10^{13}~{}\mathrm{s^{-1}\,cm^{-2}}$. Similarly, for the case of geoneutrinos
the corresponding antineutrino energy distributions for the K, Th and U chains
are taken from Ref. huang:2013 . It is worth noting that presently the flux
uncertainties are quite large due to low statistics Ludhova:2013hna  while the
geoneutrino flux depends largely on the location Gelmini:2018gqa . Here, we
comply with the normalizations quoted in Ref. OHare:2020lva  which correspond
to the location of the Gran Sasso National Laboratory (LNGS).

The differential number of events is obtained through the convolution of the
differential cross section with the neutrino-energy distribution
$\lambda_{\nu}(E_{\nu})$. The lower integration limit in Eq.(3) is trivially
obtained from the CE$\nu$NS kinematics and reads

$E_{\nu,\text{min}}=\frac{1}{2}\left(T_{A}+\sqrt{T_{A}^{2}+2m_{A}T_{A}}\right)\approx\displaystyle\sqrt{\frac{m_{A}T_{A}}{2}}\,.$
(5)

Note that $E_{\nu,\text{max}}=m_{\mu}/2=52.8$ MeV for the case of $\pi$-DAR
neutrinos, while $E_{\nu,\text{max}}\approx 9.5$ MeV for reactor neutrinos and
$E_{\nu,\text{max}}\approx(1.3,~{}2.3,4.5)$ MeV for the (K, Th, U)
geoneutrinos, respectively.

Finally, an additional integration over the nuclear recoil energy $T_{A}$,
from a threshold energy $T_{A}^{\text{thres}}$ up to a maximum energy
$T_{A}^{\text{max}}=\frac{2E_{\nu,\text{max}}^{2}}{2E_{\nu,\text{max}}+m_{A}}\approx\frac{2E_{\nu,\text{max}}^{2}}{m_{A}}$,
needs to be performed in order to obtain the expected number of events.

###  2.3 Deformed shell model

The details of the deformed shell model have been described in our earlier
publications (for details see Ref. ks-book ). In this model, for a given
nucleus, starting with a model space consisting of a given set of spherical
single particle (sp) orbitals with single-particle energies (spe) and an
effective two-body interaction specified by its two-body matrix elements
(TBME), the lowest energy intrinsic states are obtained by solving the
Hartree-Fock (HF) single-particle equation self-consistently. We assume axial
symmetry, while excited intrinsic configurations are obtained by making
particle-hole excitations over the lowest intrinsic state. Since the intrinsic
states denoted by $\chi_{K}(\eta)$ do not have definite angular momenta,
states of good angular momentum are projected from the latter which can be
written in the form

$|\psi^{J}_{MK}(\eta)\rangle=\frac{2J+1}{8\pi^{2}\sqrt{N_{JK}}}\int d\Omega
D^{J^{*}}_{MK}(\Omega)R(\Omega)|\chi_{K}(\eta)\rangle\,,$ (6)

where $N_{JK}$ is the normalization constant given by

$N_{JK}=\frac{2J+1}{2}\int^{\pi}_{0}d\beta\sin\beta
d^{J}_{KK}(\beta)\langle\chi_{K}(\eta)|e^{-i\beta
J_{y}}|\chi_{K}(\eta)\rangle\,.$ (7)

In Eq.(6), $\Omega$ represents the Euler angles ($\alpha$, $\beta$, $\gamma$),
and $R(\Omega)=\exp(-i\alpha J_{z})\exp(-i\beta J_{y})\exp(-i\gamma J_{z})$
represents the general rotation operator. However, it is worth noting that the
good angular momentum states, projected from different intrinsic states, are
not in general orthogonal to each other. Hence they are orthonormalized and
then band mixing calculations are performed. The resulting eigenfunctions are
of the form

$|\Phi^{J}_{M}(\eta)\rangle\,=\,\sum_{K,\alpha}S^{J}_{K\eta}(\alpha)|\psi^{J}_{MK}(\alpha)\rangle\,,$
(8)

with $S^{J}_{K\eta}(\alpha)$ being the expansion coefficients. The nuclear
matrix elements occurring in the calculation of event rates are evaluated
using the wave functions $|\Phi^{J}_{M}(\eta)\rangle$. We finally stress that
the DSM is well established enough to be a successful model for transitional
nuclei with $A$=60–90 ks-book , while recently, it has also been used
successfully for heavier nuclei like 127I, 133Cs and 133Xe Sahu:2020kwh .

##  3 Results for CE$\nu$NS event rates

The nuclei selected in the present study, 70,73,76Ge, 64,70Zn and 28Si, are of
current experimental interest and therefore calculations for CE$\nu$NS event
rates that take into account the details of the nuclear structure are
important. Firstly, the Ge isotopes are discussed in Ref. Galindo-
Uribarri:2020huw  with the most relevant experiments being the COHERENT
Akimov:2017ade ; Akimov:2020pdx , the CONUS Bonet:2020ntx ; Lindner:2016wff ,
$\nu$GEN Belov:2015ufh  and the TEXONO Wong:2005vg  which use ionization-based
Ge-semiconductors. Similarly, the (Si, Zn, Ge) isotopes have been chosen as
the detector materials of the MINER MINER:2016igy , NUCLEUS NUCLEUS:2019igx ,
and RICOCHET Billard:2016giu , which employ cryogenic detectors.

We should, moreover, add that high-purity germanium (HPGe) detectors are used,
for example, in CONUS experiment where the detector is located at $17.1$ m
from the reactor core (4 detectors each with $\approx 1$ kg) and the expected
$\bar{\nu}_{e}$ flux is $2.3\times 10^{13}~{}\mathrm{s^{-1}cm^{-2}}$; see
e.g., Ref. Bonet:2020ntx . Also, for the Chooz experiment Ge-based and
metallic Zn-based detectors of mass $m_{\text{det}}\approx 10$ kg are under
deployment, with a reported threshold as low as 100 eV Billard:2016giu .

Figure 1: Square of proton (solid line) and neutron (dotted line) form factors
for 70,73,76Ge, 64,70Zn and 28Si as a function of $u=q^{2}b_{\ell}^{2}/2$.

###  3.1 Nuclear structure calculations within the DSM

As is well known, the largest source of theoretical uncertainty in CE$\nu$NS
originates from the nuclear physics Papoulias:2019lfi  (see also Ref.
Cadeddu:2017etk ). In this subsection, we evaluate the corresponding nuclear
form factors with high reliability by incorporating our realistic nuclear
structure DSM calculations. In Table 1, some useful nuclear structure
properties of the isotopes studied in the present work are tabulated.

Property Nucleus | Germanium | Zinc | Silicon
---|---|---|---
|  70Ge |  73Ge |  76Ge |  64 Zn |  70 Zn |  28 Si
ground state spin ($J^{\pi}$) | $0^{+}$ | $9/2^{+}$ | $0^{+}$ | $0^{+}$ | $0^{+}$ | $0^{+}$
isotopic abundance (%) | 20.52 | 7.76 | 7.75 | 49.2 | 0.6 | 92.2
h.o. length (fm) | 1.894 | 1.907 | 1.920 | 1.865 | 1.894 | 1.625
Table 1: Nuclear structure properties of the studied isotopes (for details
regarding the model space chosen, the sp energies, etc., see the text).

In the following paragraphs, for the benefit of the reader we describe briefly
some basic properties of the studied CE$\nu$NS detector materials.

####  3.1.1 The studied isotopes as CE$\nu$NS detectors

(1) For the 70Ge isotope, in our earlier double-$\beta$ decay (DBD) study
using DSM Sahu:2014nga , calculations have been carried out for spectroscopic
properties such as the energy spectra (band structures), the B(E2) values and
occupancies. For this isotope, the $jj$44b effective interaction in a model
space consisted of the ${}^{2}p_{3/2}$, ${}^{1}f_{5/2}$, ${}^{2}p_{1/2}$,
${}^{1}g_{9/2}$ $j$-levels with single particle (sp) energies ($-9.6566$,
$-9.2859$, $-8.2695$,$-5.8944$) MeV respectively Cheal:2010zza , gave good
agreement with data. Additional isotopic properties are listed in Table 1. We
note that for the harmonic oscillator (h.o.) size (length) parameter we used
the simple expression $b_{\ell}=0.933\,A^{1/6}=1.894$ fm for all the nuclei
studied.

(2) For the 73Ge, the DSM calculations have been assessed through the
spectroscopic properties in Ref. Sahu:2017czz  by employing the modified Kuo
effective interaction ABS  in the model space: ${}^{2}p_{3/2}$,
${}^{1}f_{5/2}$, ${}^{2}p_{1/2}$, ${}^{1}g_{9/2}$, with the sp energies ($0$,
$0.78$, $1.08$, $4.9$) MeV, respectively. Band structures and other
spectroscopic properties are well reproduced with the aforementioned
ingredients. We also mention that, in our recent CE$\nu$NS results for 73Ge in
Ref. Sahu:2020kwh  we have adopted the same model parameter values with
$b_{\ell}=1.907$ fm.

(3) For the 76Ge isotope, which is a well-known neutrinoless double-$\beta$
decay (DBD) detector material, the DSM calculations have been performed with
the modified Kuo interaction and the same model space as well as sp energies
as in the case of the 73Ge isotope above ($b_{\ell}=1.920$ fm) Sahu:2013yna .
Low-lying bands, $B(E2)$ values and orbit occupancies are well reproduced for
this isotope too.

(4) The DSM calculations for the 64Zn isotope have been carried out using
GXPF1A effective interaction Sahu:2013yna . The model space consisted of the
(${}^{1}f_{7/2}$, ${}^{2}p_{3/2}$, ${}^{1}f_{5/2}$, ${}^{2}p_{1/2}$) orbits
with sp energies ($-8.6240$, $-5.6793$, $-1.3829$, $-4.1370$) MeV,
respectively Honma:2004xk . The energy spectra, the $B(E2)$ values and
occupancies of sp orbits (with $b_{\ell}=1.865$ fm) agree very well with the
corresponding experimental data Sahu:2013yna .

(5) For 70Zn, the DSM spectroscopic results have been obtained with the
ingredients of 70Ge as described above ($b_{\ell}=1.894$) Sahu:2014nga .

(6) For the 28Si, the spectroscopic calculations within DSM have been
performed ($b_{\ell}=1.625$ fm) by using the recently determined USD effective
interaction Brown:2006gx ; Magilligan:2020bbd . The calculated energy spectra,
the $B(E2)$’s and also the $B(M1)$ values agree reasonably well with the
experimental data and they will be discussed elsewhere Kosmas-in-preparation .

Although we have used a formula for $b_{\ell}$ following the DSM study of 72Ge
in Ref. Kosmas:2003xr , it is desirable to deduce the values of $b_{\ell}$ for
each isotope from proton charge radii obtained by electron scattering
experiments. The experimental values for the charge radii (in fm) are 4.041,
4.063, 4.081, 3.928, 3.985 and 3.122 for 70,73,76Ge, 64,70Zn and 28Si as given
in Ref. ANGELI201369 . However, theoretical calculations for charge radii (see
Ref. BROWN1983313  for shell model and Ref. Mukherjee:1984zz  for HFB
examples) involve not only $b_{\ell}$ as a parameter but also effective
charges. A consistent analysis of experimental data for charge form factors,
charge radii, quadrupole moments and $B(E2)$ values using DSM for the nuclei
studied here, will be considered in a future work. Finally, we note that the
length parameter $b_{\ell}=0.933\,A^{1/6}$ (in fm) used (see Table 1) is
slightly smaller than the conventional parametrization
$\hbar\omega=41\,A^{1/3}$ giving $b_{\ell}=0.994\,A^{1/6}$.

###  3.2 DSM calculations of the nuclear form factors needed for CE$\nu$NS
event rates

The proton and neutron nuclear form factors, $F_{p,n}(u)$, in terms of the
dimensionless parameter $u=q^{2}(b_{\ell})^{2}/2$, are illustrated in Fig. 1.
As can be seen from this figure, for the even-even isotopes 76Ge, 70Ge and
70Zn, the neutron form factor peaks shift toward smaller values of $u$. Again,
the second neutron peak is larger than the corresponding proton peak. For the
other three nuclear isotopes, the neutron and proton form factors are almost
similar. Further details for the nuclei of interest, on the chosen nuclear
configuration, the effective interaction, the $b_{\ell}$ value, etc., are
listed in Table 1 and are discussed previously.

Figure 2: Differential (left) and integrated (right) event rates as a function
of the nuclear recoil energy for 70,73,76Ge, 64,70Zn and 28Si. The results are
presented for CE$\nu$NS process with $\pi$-DAR neutrinos.

Figure 3: Differential (left) and integrated (right) event rates as a function
of the nuclear recoil energy for 70,73,76Ge, 64,70Zn and 28Si. The results are
presented for CE$\nu$NS process with reactor neutrinos.

Figure 4: Differential (left) and integrated (right) event rates as a function
of the nuclear recoil energy for 70,73,76Ge, 64,70Zn and 28Si. The results are
presented for CE$\nu$NS process with reactor neutrinos.

Figure 5: Percentage difference between DSM calculations and those involving
the effective Klein-Nystrand form factor parametrization (for details see the
text). The results are presented for the case of $\pi$-DAR neutrinos (left)
and reactor neutrinos (right) as a function of the nuclear recoil energy for
70,73,76Ge, 64,70Zn and 28Si.

By employing the form factors shown in Fig. 1, the differential and integrated
event rates are calculated utilizing Eq.(3) for neutrinos of the SNS, reactor
and geoneutrino sources and the results are illustrated in Figs. 2, 3 and 4.
In these plots, we have used different isotopes of the same element which is
crucial for reducing the systematic errors as pointed out in Ref. Galindo-
Uribarri:2020huw . For example, for SNS the proportion of differential event
rates for 70,73,76Ge at recoil energy 0.1 keV is 2.96:3.64:4.0 which is
equivalent to 1:1.230:1.351.

Assuming that the $N^{2}$ dependence is approximately valid, the corresponding
proportions are $38^{2}$:$41^{2}$:$44^{2}$, which is equivalent to
1:1.164:1.340. For the case of reactor neutrons, the corresponding proportions
are 1:1.213:1.316. For other cases also, we obtain similar results. Use of
detectors made up of a set of isotopes of an element may help in precision
measurements at different experimental facilities.

Turning to large-scale dark matter direct detection detectors, our current
results indicate sizable geoneutrino-induced event rates, especially for sub-
keV thresholds. Even though the detectable geoneutrino background signal will
be completely dominated by solar neutrino events, it is expected to become a
crucial component in the overall neutrino background at future ton-scale
detectors looking for weakly interacting massive particles (WIMPs), especially
for those aiming to detect low mass WIMPs with $m_{\chi}\leq
10~{}\mathrm{GeV/c^{2}}$. As a concrete example, we discuss the SuperCDMS
experiment at SNOLAB which aims to reach nuclear recoil thresholds as low as
40 eV (78 eV) using a germanium (silicon) detector SuperCDMS:2016wui  for
which our present calculations are particularly relevant and of significant
importance.

Finally, we are interested to quantify the percentage difference on the number
of events calculated using our nuclear structure DSM calculations or involving
effective form factor approximations. As a benchmark test case, we consider
the Klein-Nystrand form factor approximation Klein:1999qj  that has been
recently adopted by the COHERENT Collaboration Akimov:2017ade . We illustrate
the difference between the two calculations by evaluating the quantity

$\mathcal{R}=\frac{|R_{\text{DSM}}-R_{\text{KN}}|}{R_{\text{DSM}}}$ (9)

and our corresponding results are shown in Fig. 5. As can be seen, reactor
neutrino experiments looking for CE$\nu$NS will not suffer from nuclear
structure uncertainties, even at the sub-percentage level. On the other hand,
for the case of $\pi$-DAR neutrinos which involve larger values of the
momentum transfer, $\mathcal{R}$ can be as high as 8% for 64Zn and 76Ge. We
finally note that here we do not present the corresponding results for
geoneutrinos since the signal uncertainty will be dominated by the flux
uncertainties, while also the momentum transfer is lower compared to reactor
neutrinos. For solar, diffused supernova background and atmospheric neutrinos,
such results have been presented in a previous study Papoulias:2018uzy .

###  3.3 Application to nonstandard interactions

Figure 6: Projected sensitivity to NSIs for a 10-kg 76Ge detector at a
$\pi$-DAR facility. A comparison of the expected sensitivities is given
assuming DSM and KN nuclear form factors.

Focusing on vector-type NSIs only, our goal is to explore the impact of DSM
form factors to the projected NSI sensitivities. In order to quantify the
effect of nonzero NSI contributions to the CE$\nu$NS cross section, it is
sufficient to replace the SM weak charge of Eq.(2) with the corresponding NSI
charge according to the substitution
$\mathcal{Q}_{W}\to\mathcal{Q}_{\text{NSI}}$, with

$\displaystyle\mathcal{Q}^{V}_{\text{NSI}}=$
$\displaystyle\left[\left(g_{V}^{p}+2\varepsilon_{\alpha\alpha}^{uV}+\varepsilon_{\alpha\alpha}^{dV}\right)ZF_{p}(Q^{2})+\left(g_{V}^{n}+\varepsilon_{\alpha\alpha}^{uV}+2\varepsilon_{\alpha\alpha}^{dV}\right)NF_{n}(Q^{2})\right]$
$\displaystyle+$
$\displaystyle\sum_{\alpha}\left[\left(2\varepsilon_{\alpha\beta}^{uV}+\varepsilon_{\alpha\beta}^{dV}\right)ZF_{p}(Q^{2})+\left(\varepsilon_{\alpha\beta}^{uV}+2\varepsilon_{\alpha\beta}^{dV}\right)NF_{n}(Q^{2})\right].$

Our sensitivity analysis is based on a simple $\chi^{2}$ function

$\chi^{2}=\sum_{i=1}^{50}\left(\frac{R_{\text{SM}}^{i}-(1+a)R_{\text{NSI}}^{i}(\epsilon_{ee}^{uV},\epsilon_{ee}^{dV})}{\sigma_{\text{stat}}^{i}}\right)^{2}+\left(\frac{a}{\sigma_{a}}\right)^{2}\,,$
(10)

for which we consider 50 equal-size bins of recoil energy in the range 5–80
keV, allowing for non-zero NSIs with the $\nu_{e}$ flux only. The statistical
uncertainty is defined as
$\sigma^{i}_{\text{stat}}=\sqrt{R^{i}_{\text{SM}}+R^{i}_{\text{bkg}}}$,
assuming a flat background
$R^{i}_{\text{bkg}}=\sigma_{\text{bkg}}R^{i}_{\text{SM}}$. We furthermore
consider a conservative scenario taking the background and signal
uncertainties to be $\sigma_{\text{bkg}}=\sigma_{a}=30\%$. For our statistical
analysis, we assume a $\pi$-DAR neutrino source with a 10-kg 76Ge target
nucleus for which we expect the impact of nuclear form factors to be maximized
(see left panel of Fig. 5).

Taking one nonvanishing NSI parameter at a time, our results are presented in
Fig. 6. As can be seen from the $\chi^{2}$ profiles, the use of DSM or KN form
factors will not alter the sensitivities on $\epsilon_{ee}^{uV}$. On the other
hand, for the case of $\epsilon_{ee}^{dV}$ our fit clearly prefers the trivial
solution over the nonzero one when relying on DSM nuclear structure
calculations. This is found to be in contrast to the case of KN calculations
where there is absence of a best-fit point preference. A few comments are in
order. As expected, the sensitivity on $\epsilon_{ee}^{dV}$ is stronger
compared to $\epsilon_{ee}^{uV}$, and hence the implications of DSM
calculations are more pronounced in the former case, which might be helpful
for resolving the LMA dark degeneracy Coloma:2017egw . As a final remark, we
have checked that the neutrino-floor explored in Ref.
AristizabalSierra:2021kht , due to the currently large uncertainties, is not
affected by the choice of phenomenological or nuclear structure form factors.

##  4 Conclusions

Our main aim in the present study was to perform calculations of the CE$\nu$NS
event rates for the Ge-detectors chosen in ongoing and designed CE$\nu$NS
experiments. We also studied Zn and Si which are considered promising target
materials of experiments aiming to measure CE$\nu$NS events. The nuclear
structure calculations have been carried out (for the specific isotopes
70,73,76Ge, 64,70Zn and 28Si) with a high level of reliability, by taking into
account crucial information from the nuclear structure. The detailed nuclear
physics aspects came out of the DSM method which involves realistic two-body
interactions and is assessed on the reproducibility of experimental
microscopic nuclear properties.

Highly accurate calculations such as those provided here, are valuable for
discriminating the expected signal from the various isotopic admixtures
contained in germanium or zinc detectors, the use of which has been proposed
for reducing the experimental uncertainties. We have considered typical
experimental configurations, exposed to neutrinos from $\pi$-DAR, reactor
antineutrinos and geoneutrinos, while to the best of our knowledge, the
present work is the first nuclear-physics-based study with regards to
geoneutrino signals.

We compared our theoretical event rates with those calculated on the basis of
the widely adopted form factors (e.g., the phenomenological Klein-Nystrand)
and we concluded that especially for the SNS neutrinos the differences can be
of the order of 10%. On the other hand, we have verified that reactor
antineutrino facilities with sub-keV thresholds as well as large-scale direct
dark matter detection experiments looking for light WIMPs uncertainties may be
neglected for very low momentum transfer involved in the CE$\nu$NS process. We
have finally discussed the robustness of the attainable sensitivities on NSI
with regards to phenomenological and DSM nuclear form factors.

###### Acknowledgements.

The research of D.K.P. is co-financed by Greece and the European Union
(European Social Fund- ESF) through the Operational Programme «Human Resources
Development, Education and Lifelong Learning» in the context of the project
“Reinforcement of Postdoctoral Researchers - 2nd Cycle” (MIS-5033021),
implemented by the State Scholarships Foundation (IKY). R.S. is thankful to
SERB of Department of Science and Technology (Government of India) for
financial support. The work of T.S.K. is implemented through the Operational
Program “Human Resources Development, Education and Lifelong Learning - cycle
B” (MIS-5047635) and is co-financed by the European Union (European Social
Fund) and Greek national funds.

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# Towards Emotion-Aware Agents For Negotiation Dialogues ††thanks: Research
was sponsored by the National Science Foundation and Army Research Office
under Cooperative Agreement W911NF-20-2-0053. The views and conclusions
contained in this document are those of the authors and should not be
interpreted as representing the official policies, either expressed or
implied, of the Army Research Office or the U.S. Government. The U.S.
Government is authorized to reproduce and distribute reprints for Government
purposes notwithstanding any copyright notation herein.

Kushal Chawla1 Rene Clever2 Jaysa Ramirez3 Gale Lucas1 Jonathan Gratch1
1University of Southern California, Los Angeles, USA
2CUNY Lehman College, Bronx, USA 3Rollins College, Winter Park, USA
1{chawla, lucas<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Negotiation is a complex social interaction that encapsulates emotional
encounters in human decision-making. Virtual agents that can negotiate with
humans are useful in pedagogy and conversational AI. To advance the
development of such agents, we explore the prediction of two important
subjective goals in a negotiation – outcome satisfaction and partner
perception. Specifically, we analyze the extent to which emotion attributes
extracted from the negotiation help in the prediction, above and beyond the
individual difference variables. We focus on a recent dataset in chat-based
negotiations, grounded in a realistic camping scenario. We study three degrees
of emotion dimensions – emoticons, lexical, and contextual by leveraging
affective lexicons and a state-of-the-art deep learning architecture. Our
insights will be helpful in designing adaptive negotiation agents that
interact through realistic communication interfaces.

##  I Introduction

Negotiation is a core task for studying emotional feelings and expressions in
human decision-making [1]. Being a mixed-motive task, it creates both
interpersonal and intrapersonal conflicts for the negotiators. Motivational
tensions often arise when negotiations pit aspirations for individual
accomplishments against the demands of sustaining social connections. This
leaves difficult decisions for the negotiators about working towards their own
self-oriented outcomes or making sacrifices for others. Such situations can be
fraught with emotional encounters. For instance, as a negotiator strives to
get as much as possible for themselves, in doing so, they need their partner
to go along as well. However, the partner’s willingness to go along is
essentially an emotional decision. A negotiator that tries to take too much
can annoy their partner, and in turn, hurt their likeability in the eyes of
their partners and also the partner’s affective evaluation of the outcome
(that is, their satisfaction). Instead, it is desirable for the negotiator to
strive for maximum performance while ensuring that the partner is satisfied
[2] and leaves with a positive perception of the partner [3, 4]. Therefore,
predicting the partner’s satisfaction and perception in advance can be crucial
for an AI assistant that aims to negotiate with its users. These virtual
negotiation agents find broad applications in advancing conversational AI such
as the Google Duplex agent that books a haircut appointment over the phone
[5]. Further, such agents can also be useful in increasing access to social
skills training [6].

A number of prior studies rely on user individual difference attributes to
explain negotiation behaviors and outcomes. For instance, this includes
studies based on gender [7] and personality traits such as Social Value
Orientation and Machiavellianism [8]. This research is crucial from the
perspective of practical negotiation agents that interact with users on social
media platforms since research suggests that demographic and personality
attributes can be inferred from past user interactions [9, 10, 11]. Thus, they
can be used to adapt the behavior of the deployed automated systems. However,
relying only on these variables misses out on all the other available
information such as affective attributes in the negotiation itself, which may
further help in predicting the outcomes. While one might expect that such
affect variables would help merely because they are manifestations of the
individual differences, it is instead possible that affective factors reflect
the recent interaction with the partner and might predict in their own right.
This leads us to our key research question in this work: For predicting a
negotiator’s satisfaction and liking for their partners, is there value in
leveraging affective attributes from the negotiation, above and beyond the
individual difference variables?

Most prior efforts in negotiations focus on a menu-driven communication
between the human and the agent. Such interfaces allow button clicks for
sharing offers or preferences, which helps to keep the design tractable. This
concreteness, however, comes at a cost – it hinders the analysis of several
realistic aspects in a negotiation such as persuasion and free-form emotion
expression. Due to the inherent design restrictions, emotion expression merely
reduces to the use of emoticons and predefined sentence templates [12].
Instead, recent efforts have explored a fundamentally different, chat-based
interaction that allows human-agent communication in free-form natural
language such as English [13, 14], having the potential to fill the gap
between existing emotion research and the challenges in real-world
negotiations.

To this end, we analyze a large-scale, linguistically rich dataset [14] that
is grounded in a realistic campsite negotiation task. The associated metadata
about the participants enables us to study individual differences and
linguistic dialogue behaviors in the same setup. Going beyond the capabilities
of restrictive menu-driven interfaces, we develop three degrees of emotion
recognition techniques: emoticons, lexical, and contextual emotion by
leveraging recent advancements in deep learning (Section III). Using
correlational and step-wise regression analysis, we quantify the extent to
which affective attributes help to account for the variance in the outcomes,
beyond just the individual user attributes (Section V). We further discuss how
our analysis can guide the development of automated negotiation agents and
briefly summarise the ethical considerations around such systems (Section VI).

##  II Related Work

How humans negotiate has been extensively studied in multiple disciplines:
Game Theory for identifying optimal behaviors [15], Psychology for
understanding human decision-making [16], and Computer Science for building
automated negotiation agents [17, 18]. Demographics, personality and affective
behaviors have played a central role in improving our understanding around
negotiations [7, 8] and similar decision-making social interactions [19, 20].
For instance, de Melo and colleagues studied human-agent prisoner’s dilemma
interaction and found that the display of guilt after exploitation can elicit
more cooperative responses as compared to an agent that smiled [20].

Both satisfaction and the relationship with the negotiation partner are seen
as crucial metrics of negotiation performance. Oliver and colleagues studied
how profit expectations relate to satisfaction after the bargaining in buyer-
seller interactions, finding that higher expectations had the effect of
decreased satisfaction [2]. Maintaining a positive relationship with the
partner is especially crucial in repeated interactions, where poor relations
in earlier negotiations can adversely impact the results of future ones [4].
Relationship also manifests in the context of rapport building [21], favor
exchange [22], and reputation effects [23].

However, most efforts in human-agent negotiations are based on highly
structured menu-driven designs such as the IAGO negotiation platform [12]. In
many cases, the negotiation is seen as simply an exchange of offers [24].
Towards more realistic modes of communication, limited efforts have studied
chat-based dialogue systems, that are fundamentally different than menu-driven
systems and hence, must be studied separately. Initial datasets in this
direction looked at game settings [25], which allow free-form language use but
the lack of any semantic context in such negotiations inhibits any rich
personal conversations. He and colleagues focused on more realistic buyer-
seller price negotiations for the product listings on Craigslist [13].
Unfortunately, none of these datasets incorporated the demographics or the
personality of the users. Further, all of them looked only at the objective
outcomes of the negotiation performance such as the points scored or the final
agreed price. Our focus is on the recently released CaSiNo dataset that
enables linguistically rich conversations in a constrained, tractable
environment [14]. The dataset further contains the metadata of the
participants, that we use to develop our measures in this work (Section III).

Finally, we note that researchers have also looked at face-to-face
negotiations [26], including speech and embodied agents that can be natural
extensions to our current analysis in chat-based negotiations.

##  III Dataset and Methods

Figure 1: Screenshot from the CaSiNo data collection interface. Taken from
[14].

Our analysis is based on the recently released CaSiNo dataset [14]. The design
is an instance of Multi-Issue Bargaining Task (MIBT), which is a popular model
for studying negotiations computationally [27, 12]. MIBT provides a concrete
structure to the negotiation and thus, it helps to keep the conversations
focused. Further, the task is grounded in a real-world campsite scenario that
promotes rich personal conversations in free-form natural language. Unlike
prior datasets in chat-based negotiation systems [28, 25, 13], this design
enables the study of a number of realistic aspects in negotiations such as
persuasion and emotion expression in a constrained, tractable environment.

###  III-A Participants

A total of $846$ unique participants were recruited on Amazon Mechanical Turk
for collecting the CaSiNo dataset. The participant pool was restricted to the
United States. They were paid for their time and also with a performance based
bonus. Among the participants, $472$ identified themselves as Female, $372$
were Male, and 2 belonged to Other category. $73.9\%$ of the participants were
White American, $1.5\%$ were Native or Islander, $8.7\%$ were Asian American,
$8.6\%$ were Black or African American, $4.1\%$ were of Hispanic or Latino
origin, and remaining $3.1\%$ belonged to Other category.

###  III-B Design and Procedure

The CaSiNo dataset contains a total of $1030$ negotiation dialogues in
English. In each dialogue, two participants take the role of campsite
neighbors and negotiate for additional packages of camping essential items.
Following the MIBT structure, there are three issues: Food, Water, and
Firewood. Each issue has an available quantity of three, thereby resulting in
four levels from $0$ to $3$. Before the negotiation begins, each participant
is randomly assigned a priority order for the three issues, which is a
permutation of {High, Medium, Low}. Once the priorities are assigned, the
participants also come up with their own justifications for needing or not
needing a particular issue such as needing more water for a planned hike or
food for the kids. This exercise prepares the participants for their upcoming
negotiation, and subsequently results in the collection of linguistically rich
conversations.

The dialogues in CaSiNo contain $11.6$ utterances with $22$ tokens per
utterance, on average. The participants were also allowed to use emoticons for
four basic emotions: Joy, Sadness, Anger, and Surprise. We provide a
screenshot from the chat interface in Figure 1. Once the negotiation is over,
the researchers record the performance of the participants based on the number
of items that they are able to negotiate for. Alongside, the participants are
also asked to report their satisfaction with the outcome, and their perception
of the negotiation partner. Analyzing these subjective measures of negotiation
performance is the primary focus of this work. The dataset further contains
the demographics and personality traits for the participants, which are
collected prior to the negotiation. We refer the readers to the original
CaSiNo paper [14] for more information on the data collection procedure and a
sample dialogue from the dataset.

###  III-C Measures

We cluster the variables into three categories: 1) Individual difference,
which captures the demographics and personality of the participants, 2) Affect
Variables, which comprises all the affective attributes extracted from the
negotiation utterances, and 3) Negotiation Outcomes, where we describe the two
primary dependent variables in our analysis.

####  III-C1 Individual Difference

These variables are based on the responses reported by the participants in a
survey before their negotiation. The participants self-identified their
demographic attributes while the personality traits are based on the standard
tests from the psychology literature.

Demographics: There are two continuous variables: Age111One participant
reported the age of $3$, which we believed to be in error and was removed from
all our analysis that uses Age. and Education. We encoded Education as a
continuous variable, leveraging the inherent order in the highest level of
education. It takes a value from $0$ to $8$, with an increasing level of
education.

Further, there are two discrete demographic variables: Gender and Ethnicity.
For our regression analysis, we dummy-coded these variables based on the
categories discussed earlier.

Personality: There are two available measures of individual personality
differences: Social Value Orientation [29] and the Big-$5$ personality traits
[30]. These personality attributes have been extensively studied in the
context of negotiation research [31, 32]. The Social Value Orientation (SVO)
is defined as the stable preferences for certain patterns of outcomes for
oneself or others [33]. A participant can either be categorized as Prosocial,
that tend to be cooperative in their interactions, or Proself, that tend to
serve their individual interests. In the CaSiNo data collection study, SVO was
computed using the Triple Dominance Measure [29]. $463$ participants were
classified as Prosocial, $364$ as Proself, while $19$ were Unclassified. The
Big-$5$ test consists of five personality dimensions: Extraversion,
Agreeableness, Conscientiousness, Emotional Stability, and Openness to
Experiences. These dimensions were computed using the Ten-Item Personality
Inventory [34]. Each dimension takes a value between $1$ and $7$.

####  III-C2 Capturing Affect

Natural language based negotiations provide exciting avenues for Affective
Computing research. Unlike menu-driven systems, where communication is highly
restricted, language allows free expression of emotion and other affective
attributes. In order to capture these attributes in CaSiNo, we consider three
different degrees of affect recognition techniques: emoticon counts, use of
emotive vocabulary based on affect lexicons (specifically LIWC [35]), and
utterance-level emotion expressions (based on a pretrained deep learning model
called T5 [36]). We discuss these approaches below. We will later compare
these methods through our regression analysis for predicting satisfaction and
likeness.

Emoticons: Emoticons provide a structured way for emotion expression. Due to
this reason, emoticons have been heavily used in menu-driven negotiation
research. For instance, the IAGO platform for human-agent negotiations allows
human participants to use the emoticons via button clicks [12]. For CaSiNo,
the participants were allowed to use shorthands for typing emoticons directly
in the chat interface for four basic emotions: Joy, Sadness, Anger, and
Surprise (see Figure 1). For a given participant and the negotiation dialogue,
we count the number of emoticons used by the participant for each of these
types and use that as a continuous measure of emotion expression.
Approximately $15\%$ of the utterances in CaSiNo make use of one or more
emoticons. Among those that use it, nearly $80\%$ use Joy emoticon.

Based on a manual inspection of the utterances, we find that the participants
tend to use Joy emoticon in a number of scenarios, including small talk at the
beginning or end of the conversation when showing agreement, and in some
cases, interestingly, also when rolling out a strict offer. Sadness tends to
be used when showing disagreement, showing empathy, or emphasizing personal
needs. Some cases where the participants expressed Surprise are when pointing
out strange behavior from their partner or showing empathy towards a specific
need of their partner. Anger is used in the cases of strong disagreement where
for instance, the partner does not empathize with the personal requirements of
the participants or when they receive a very unfair offer that largely
benefits the negotiation partner.

LIWC: We now go beyond the capabilities of menu-driven systems by extracting
emotion attributes from the text in the utterances of the participants.
Specifically, we look at word-level expressions by leveraging affect lexicons
from the literature. Specifically, we make use of the Linguistic Inquiry and
Word Count lexicon, popularly referred to as LIWC in the literature [35]. LIWC
consists of a number of word vocabularies corresponding to everyday use that
reflect our feelings and personality. Given our focus on affective attributes,
we use four LIWC dimensions in this work: Positive Emotions, Sadness, Anger,
and Anxiety. To compute the corresponding scores for a participant in a given
dialogue, we simply count the number of words in the utterances of the
participant that are present in the corresponding LIWC lexicons.

As one might expect, we find a number of instances where the participants
express emotions without explicitly making use of emoticons. For instance, an
excerpt where the participant clearly expresses anger without using the anger
emoticon: ‘Are you mad. with out water what we do…’. Hence, with LIWC
lexicons, we are able to capture more emotive utterances than by simply
looking at the emoticon usage. Nearly $60\%$ of the utterances make use of at
least one emotive word from our four LIWC categories.

Since LIWC variables are based on word usage, they provide a highly
interpretable way of extracting emotions directly from the text. However,
merely relying on word-level traits can still miss out on phrase-level or
utterance-level emotion expressions. Hence, we next discuss how we make use of
a state-of-the-art deep learning model from Natural Language Processing (NLP)
to identify emotion in CaSiNo dialogues.

Utterance-level emotion: Large deep learning models based on the highly
parallelizable Transformer architecture have gained enormous popularity in the
field of NLP in recent years [37]. These models have achieved huge success on
a variety of tasks ranging from sentiment analysis to machine translation,
fundamentally changing the way researchers approach these tasks. The primary
way of training a model for a specific task consists of two steps: 1) Pre-
train a large language model with freely available text data on the web in an
unsupervised or a self-supervised manner, and then 2) Fine-tune the model on
the task-specific dataset based on supervised learning.

Leveraging these recent advancements, we make use of the Text-to-Text Transfer
Transformer (T5) model [36]. T5 is an encoder-decoder architecture that is
pretrained on a variety of NLP tasks by converting all the tasks in the same
text-to-text format. No matter the task, the input to the model is a text
sequence along with a task identifier prefix, and the target output is also a
text sequence. Classification tasks can also be converted in this way by
simply using a target output sequence that consists of a single word
corresponding to the ground-truth label. This approach swiftly unifies a
number of tasks, paving the way for parameter sharing throughout the model
architecture. T5 achieves the state-of-the-art performance on a number of NLP
tasks such as classification, text summarization, and question answering.

For our purpose, we first pre-process the utterances in CaSiNo by removing all
the emoticons. We then use the publicly available T5
model222https://huggingface.co/mrm8488/t5-base-finetuned-emotion for making
predictions. This model is fine-tuned on an emotion recognition dataset based
on social interactions on Twitter [38]. Given an input text sequence, the
model classifies it into one of the six classes: Joy, Love, Sadness, Fear,
Anger, and Surprise. The model performs well on the test set of the emotion
data, achieving an accuracy of $93\%$ and a macro F1 score of $90\%$.

The output prediction of the model is based on the confidence scores that it
generates for all the emotion labels, such that the label with the highest
confidence is chosen as the prediction. In our case, since we are primarily
interested in extracting the emotion scores for the utterances, we do not rely
on the final predictions of the model. Instead, we directly use these
confidence scores (probability values between $0$ and $1$) as the
corresponding scores for each label. Given a negotiation dialogue and a
participant, we simply sum up these confidence scores for all the
participant’s utterances and use these as the continuous measures for the six
emotion dimensions. We refer to these dimensions (and interchangeably, this
method) as T5-Emotion in this paper.

All the three methods described above capture the emotion expression in CaSiNo
dataset, in fundamentally very different ways. To gain further insight into
these methods, in Section IV, we will analyze the relationship between them
through a combination of quantitative and qualitative techniques. First, we
complete our description for measures by elaborating on the subjective
negotiation outcomes.

TABLE I: Correlations of T5-Emotion variables (a) among each other, and (b)
with corresponding Emoticon and LIWC variables. We only consider the
dimensions that are common across all methods. * denotes $p<0.05$. ** denotes
$p<0.01$.

(a)

| Joy | Sadness | Anger
---|---|---|---
Joy | $1$ |  $-.288$** |  $-.295$**
Sadness |  $-.288$** | $1$ |  $.277$**
Anger |  $-.295$** |  $.277$** | 1

(b)

T5-Emotion | Emoticon Usage | LIWC Variables
---|---|---
| Joy | Sadness | Anger | Positive Emotions | Sadness | Anger
Joy |  $.062$** | $-.043$ | $-.040$ |  $.387$** |  $-.125$** |  $-.106$**
Sadness | $-.010$ |  $.213$** |  $.086$** | $-.033$ |  $.550$** | $.033$
Anger |  $-.052$* |  $.113$** |  $.111$** |  $-.185$** |  $.114$** |  $.169$**

TABLE II: Top 5 words based on log-odds ratio for (a) Emoticon (b) LIWC and
(c) T5-Emotion methods. * denotes $p<0.05$. ** denotes $p<0.01$. *** denotes
$p<0.001$.

(a)

Joy | Sadness | Anger | Surprise
---|---|---|---
Word | Z-score | Word | Z-score | Word | Z-score | Word | Z-score
hope |  $2.89$** | sorry |  $2.10$* | animal | $1.36$ | drive | $1.43$
buddy |  $2.72$** | spilled | $1.84$ | unacceptable | $0.98$ | bargain | $1.43$
awesome |  $2.71$** | n’t | $1.82$ | covid-$19$ | $0.84$ | awful | $1.32$
great |  $2.60$** | reconsider | $1.38$ | word | $0.84$ | function | $1.32$
thank |  $2.53$* | stopped | $1.30$ | joking | $0.84$ | snack | $1.23$

(b)

Positive Emotions | Sadness | Anger | Anxiety
---|---|---|---
Word | Z-score | Word | Z-score | Word | Z-score | Word | Z-score
good |  $11.89$*** | sorry |  $9.93$*** | hate |  $2.08$* | worried |  $7.18$***
well |  $11.87$*** | low |  $6.16$*** | greedy | $1.58$ | afraid |  $4.07$***
okay |  $9.90$*** | alone |  $4.43$*** | critical | $1.35$ | worry |  $3.5$***
great |  $9.86$*** | sugar |  $2.44$* | tricky | $1.19$ | risk |  $3.22$**
ok |  $9.68$*** | hear |  $2.43$* | bother | $1.06$ | confused |  $2.54$*

(c)

Joy | Love | Sadness | Fear | Anger | Surprise
---|---|---|---|---|---
Word | Z-score | Word | Z-score | Word | Z-score | Word | Z-score | Word | Z-score | Word | Z-score
you |  $8.62$*** | hot |  $6.4$*** | sorry |  $10.63$*** | worried |  $8.72$*** | cold |  $11.5$*** | funny | $1.93$
good |  $7.68$*** | generous |  $3.04$** | unfortunately |  $4.68$*** | afraid |  $7.05$*** | no |  $5.76$*** | interesting | $1.89$
great |  $7.33$*** | hotter | $1.89$ | dehydrated |  $4.03$*** | concerned |  $4.48$*** | need |  $4.77$*** | surprise | $1.08$
hello |  $6.84$*** | lovely | $1.56$ | low |  $3.12$*** | dark |  $3.88$*** | thirsty |  $4.63$*** | ha | $1.03$
sounds |  $6.81$*** | liking | $1.34$ | suffer |  $2.98$** | scared |  $3.58$*** | hungry |  $4.36$*** | status | $0.85$

TABLE III: High confidence sample predictions for T5-Emotion model that went
undetected for both Emoticon and LIWC methods.

Prediction |  Sample Utterances
---|---
Joy |  1) I think that sounds reasonable to me.
|  2) I can make that deal work.
|  3) You sound very resourceful! Sounds like we have a deal then, yes?
Sadness |  1) I feel like this deal just keeps getting worse for me. I won’t take less than 2 waters.
|  2) That is unfortunate. How about I give you all my firewood for all your
food?
|  3) Oh, that would make things difficult!
Anger |  1) You are not getting everything, thats just selfish
|  2) I am about to walk, you are being so unfair
|  3) You gave me one on each, thats unfair man!

####  III-C3 Negotiation Outcomes

We focus on two outcome variables: 1) Satisfaction (How satisfied are you with
the negotiation outcome?), and 2) Likeness (How much do you like your
opponent?). Both variables were self-reported by the participants after the
negotiation, using a 5-point Likert scale. We coded the responses from $1$ to
$5$ to create the continuous measures. We present the means and standard
deviations for all the continuous variables in Table IV.

TABLE IV: Statistics and correlations with outcome variables for all
continuous measures. * denotes $p<0.05$. ** denotes $p<0.01$.

Variable | Mean | Std. | Correlations
---|---|---|---
|  |  | Satisfaction | Likeness
Individual Difference
Age | $36.97$ | $10.81$ |  $.110$** |  $.158$**
Education | $5.23$ | $1.67$ | $-.004$ | $-.009$
Extraversion | $3.69$ | $1.70$ |  $.055$* |  $.060$**
Agreebleness | $5.27$ | $1.29$ |  $.067$** |  $.099$**
Conscientiousness | $5.60$ | $1.26$ | $.026$ |  $.046$*
Emotional Stability | $4.91$ | $1.56$ |  $.062$** |  $.087$**
Openness to Experiences | $5.04$ | $1.31$ | $.027$ | $.042$
Emoticons
Joy | $.77$ | $1.24$ | $.040$ |  $.075$**
Sadness | $.13$ | $.42$ |  $-.151$** |  $-.170$**
Anger | $.02$ | $.18$ |  $-.074$** |  $-.108$**
Surprise | $.07$ | $.27$ |  $-.062$** |  $-.059$**
LIWC
Positive Emotions | $5.58$ | $3.36$ | $.033$ |  $.061$**
Sadness | $.22$ | $.52$ |  $-.057$** |  $-.091$**
Anger | $.05$ | $.25$ |  $-.047$* | $-.043$
Anxiety | $.18$ | $.52$ | $-.040$ | $-.014$
T5-Emotion
Joy | $3.89$ | $1.09$ | $.010$ | $.026$
Love | $.22$ | $.21$ | $-.010$ | $-.030$
Sadness | $.35$ | $.42$ |  $-.141$** |  $-.172$**
Fear | $.43$ | $.43$ |  $-.121$** |  $-.117$**
Anger | $.81$ | $.66$ |  $-.217$** |  $-.295$**
Surprise | $.03$ | $.08$ | $-.011$ | $-.016$
Negotiation Outcomes
Satisfaction | $4.17$ | $1.03$ | $1$ | $.702$
Likeness | $4.11$ | $1.12$ | $.702$ | $1$

##  IV Analysis of Emotion Variables

Before presenting our results for predicting participant satisfaction and
likeness, we first validate T5-Emotion measures by understanding how they
relate to Emoticon and LIWC.

###  IV-A Correlation among emotion dimensions

Table I(b) presents the correlations of T5-Emotion measures among each other
and with Emoticons and LIWC dimensions. For this analysis, we only focus on
the dimensions that appear in all three models: Joy, Sadness, and Anger. For
LIWC, we incorporate the Positive dimension. In general, we find significant
positive correlations of the emotion dimensions with their own counterparts
across the three models, which aligns well with our expectations and validates
the model predictions on the CaSiNo dataset. We observe that although
significant, most correlation values are weak to moderate, indicating the
fundamental differences in what is captured by these three models. We also
note that Anger shows significant positive correlations with Sadness as well.
Since these measures are based on the confidence scores of the model, this
suggests that the model might get confused between these two negative emotion
dimensions.

###  IV-B Lexical correlates of emotion

To gain more insights, we perform additional qualitative analysis by
generating lexical correlates for the emotion measures. We assigned an emotion
label to each utterance for all three methods. For Emoticons and LIWC, this
was based on the label that is reflected in the majority in the utterance. For
T5-Emotion dimensions, we simply used the final predictions from the model. We
next compute the log-odds ratio, informative Dirichlet prior [39] of all the
tokens for each emotion dimension relative to all other dimensions. This
allows us to study the associations between the tokens and each emotion
dimension. We present the top $5$ words in each category in Table II(c) along
with scaled Z-scores. We observe a number of highly significant associations
across all categories that align with our intuition such as words like
‘awesome’, ‘great’, ‘thank’ for Joy and Positive Emotions categories. We found
these words to be common in the beginning and end of the negotiation where
participants engage in small talk, resulting in such utterances being
classified as Joy or Positive. Further, the associations are higher for LIWC
and T5-Emotion which, as we observe, are able to recognize many other emotive
utterances. Although significant, we observe that some words are less
meaningful such as in the case of Anger. This suggests that some emotion
dimensions may require more utterance-level context for better interpretation.

###  IV-C Sample Predictions

For a more contextual analysis, we explicitly observe the sample predictions
for T5-Emotion. We still focus on the three dimensions that are the most
common and are present in all the three emotion methods. Table III presents a
few of the most confident predictions by the model. To analyze the utterances
that are specifically captured by the deep learning model, we only look at the
utterances that are undetected by the other two methods. As the table depicts,
the model is able to capture contextual emotion, beyond just the lexical or
emoticon usage. Based on these observations, we expected the affective
attributes extracted using the deep learning model to be better predictors
than Emoticons and LIWC measures.

##  V Results

We now present our main results.

###  V-A Correlation with outcomes

Table IV summarizes the correlations of all the continuous measures defined in
Section III with the negotiation outcomes. Overall, we observe a number of
significant trends across individual differences and emotion variables. We
find that satisfaction and partner likeness both improve with age
($r$=$0.110$, $p<0.01$). The outcomes are also positively correlated with
Agreebleness and Emotional Stability ($ps<0.01$). We observe that positive
emotions tend to relate positively with both the outcomes, showing significant
trends for likeness in the case of Emoticon usage ($r$=$0.075$, $p<0.01$) and
LIWC ($r$=$0.061$, $p<0.01$). We do not observe similar results for
T5-Emotion. This may be due to the inherent bias that the deep learning model
shows towards Joy label, reducing its precision. However, trends show
significant negative correlations for both Sadness and Anger that are usually
expressed when the negotiation is not going favorably. This is naturally
associated with lower satisfaction of the participants and liking for their
negotiation partners.

Among the discrete variables, we find that females are significantly more
satisfied ($t$=$3.6$, $p<0.001$) and significantly more like their partners
($t$=$4.1$, $p<0.001$) than males. We do not observe any significant
associations with SVO and Ethnicity, based on t-test and one-way ANOVA
respectively.

###  V-B Regression Analysis

We now discuss the results of our regression analysis that answers whether
emotion variables extracted from the negotiation dialogue collectively explain
more variance in satisfaction and likeness, above and beyond the individual
difference variables. To achieve this, we perform regression with three steps
where each subsequent step incorporates the following set of variables: 1)
Individual difference, 2) Affect variables of the participant, and 3) Affect
variables for the negotiation partner. The affect variables come from one of
the emotion methods defined in Section III, which also helps to compare their
performance. As discussed earlier, these variables only encompass the
information about the negotiation that would be entirely visible to an
automatic negotiation agent, either explicitly from the negotiation dialogue,
or implicitly by inferring the individual difference attributes from past
online behaviors of the users on social media platforms. Hence, our insights
from such an analysis can practically aid in designing sophisticated
negotiation agents that incorporate user satisfaction and their perception of
the agent itself in their modelling.

Table V and VI summarize the results for satisfaction and likeness
respectively. Overall, we observe that the predictions are highly significant
with just using the individual difference variables. However, incorporating
the affective attributes of the participant and the negotiation partner
explains significantly more variance.

For satisfaction, the individual difference variables account for minimal yet
significant variance (F($14$, $1997$)=$3.46$, $p<.001$, R2=$.024$). Adding the
participant’s affect variables based on the T5-Emotion model in the second
step, helps to account for a much higher variance (F($20$, $1991$)=$10.41$,
$p<.001$, R2=$.095$), such that this increase in the proportion is itself
highly significant ($\Delta$F($6$, $1991$)=$26.02$, $p<.001$,
$\Delta$R2=$.071$). Yet, further variance is explained when the partner’s
affect variables are incorporated (F($26$, $1985$)=$10.88$, $p<.001$,
R2=$.125$: $\Delta$F($6$, $1985$)=$11.38$, $p<.001$, $\Delta$R2=$.030$).

Similar trends can be observed for likeness as well. Individual difference
variables alone account for a significant proportion (F($14$, $1997$)=$6.05$,
$p<.001$, R2=$.041$) but adding the participant’s T5-Emotion attributes
further improves the prediction performance (F($20$, $1991$)=$18.16$,
$p<.001$, R2=$.154$) with a significant increase ($\Delta$F($6$,
$1991$)=$44.58$, $p<.001$, $\Delta$R2=$.114$). Finally, when the partner’s
attributes are also incorporated as predictors, this again shows significant
improvements in the explained variance (F($26$, $1985$)=$19.07$, $p<.001$,
R2=$.200$: $\Delta$F($6$, $1985$)=$18.83$, $p<.001$, $\Delta$R2=$.046$).

Lastly, we note that in line with our linguistic analysis, the ability for
T5-Emotion to capture more contextual emotive utterances helps to account for
more variance, as compared to Emoticons and LIWC independently. In our
experiments, we also observed that even when Emoticons and LIWC are combined,
T5-Emotion still achieves a much better performance.

TABLE V: Regression results for predicting Satisfaction. ** denotes $p<0.01$.
*** denotes $p<0.001$.

Variables | $\mathbf{R^{2}}$ | df | F |  $\mathbf{R^{2}}$ Change | F Change
---|---|---|---|---|---
Affect Variables: Emoticons
Individual Difference | $.024$ | ($14$, $1997$) |  $3.46$*** | $-$ | $-$
+Participant Affect | $.051$ | ($18$, $1993$) |  $5.92$*** | $.027$ |  $14.20$***
+Partner Affect | $.063$ | ($22$, $1989$) |  $6.04$*** | $.012$ |  $6.34$***
Affect Variables: LIWC
Individual Difference | $.024$ | ($14$, $1997$) |  $3.46$*** | $-$ | $-$
+Participant Affect | $.032$ | ($18$, $1993$) |  $3.61$*** | $.008$ |  $4.07$**
+Partner Affect | $.051$ | ($22$, $1989$) |  $4.85$*** | $.019$ |  $10.14$***
Affect Variables: T5-Emotion
Individual Difference | $.024$ | ($14$, $1997$) |  $3.46$*** | $-$ | $-$
+Participant Affect | $.095$ | ($20$, $1991$) |  $10.41$*** | $.071$ |  $26.02$***
+Partner Affect | $.125$ | ($26$, $1985$) |  $10.88$*** | $.030$ |  $11.38$***

TABLE VI: Regression results for predicting Likeness. *** denotes $p<0.001$.

Variables | $\mathbf{R^{2}}$ | df | F |  $\mathbf{R^{2}}$ Change | F Change
---|---|---|---|---|---
Affect Variables: Emoticons
Individual Difference | $.041$ | ($14$, $1997$) |  $6.05$*** | $-$ | $-$
+Participant Affect | $.080$ | ($18$, $1993$) |  $9.68$*** | $.040$ |  $21.50$***
+Partner Affect | $.097$ | ($22$, $1989$) |  $9.70$*** | $.017$ |  $9.12$***
Affect Variables: LIWC
Individual Difference | $.041$ | ($14$, $1997$) |  $6.05$*** | $-$ | $-$
+Participant Affect | $.055$ | ($18$, $1993$) |  $6.39$*** | $.014$ |  $7.32$***
+Partner Affect | $.072$ | ($22$, $1989$) |  $7.06$*** | $.018$ |  $9.56$***
Affect Variables: T5-Emotion
Individual Difference | $.041$ | ($14$, $1997$) |  $6.05$*** | $-$ | $-$
+Participant Affect | $.154$ | ($20$, $1991$) |  $18.16$*** | $.114$ |  $44.58$***
+Partner Affect | $.200$ | ($26$, $1985$) |  $19.07$*** | $.046$ |  $18.83$***

##  VI Discussion and Conclusions

Our aim was to empirically investigate the extent to which the affect
variables extracted from the negotiation itself are helpful for prediction of
two important metrics for negotiation agents – participant’s outcome
satisfaction and liking for the partner. We presented an extensive analysis
based on a large-scale dataset of human-human negotiation dialogues, grounded
in a realistic camping scenario. We devised three degrees of emotion
dimensions, from leveraging emoticon usage similar to prior work in menu-
driven systems, to going beyond and extracting emotion expression directly
from the textual chat utterances. Our results show that such affect variables
explain variance in these subjective outcomes, above and beyond the impact of
individual difference variables that are available before the negotiation
begins333We also tried controlling for the objective negotiation performance
of the partner in the regression analysis. We still observed similar
significant trends for both satisfaction and likeness..

One might expect that the affect variables would help merely because they are
manifestations of the individual difference such as the social value
orientation, agreeableness, or gender. If this was indeed the case, there
would have been no need to incorporate such affective variables, but merely
the individual difference variables would have sufficed. However, to the
extent to which the affect variables help in predictions, above and beyond
these individual differences, this suggests that there is utility in
extracting these emotion dimensions explicitly for improved agent’s
performance, being especially well-suited for more subjective outcomes in a
negotiation.

We further note that the individual difference variables that we use are based
on self-identification and standard personality tests from the psychology
literature. This makes these variables more reliable than if they were to be
implicitly inferred from past social behaviors of the users, as attempted in a
number of previous works analysing interactions on social media platforms [9,
10, 11]. If affective factors show significant improvements above the
individual differences measured with minimal error, this further attests to
their utility when the demographics and personality information is inferred,
and thus, less reliable.

Since negotiations and other mixed-motive situations can be fraught with
emotional decisions, our findings suggest that it would be useful for
designers of agents that negotiate with humans to be armed with algorithms for
understanding the unfolding emotions displayed by users in terms of their
emoticon use and natural language. Our work suggests that demographic and
personality attributes inferred from past social interactions (such as on
social media) are not sufficient, and that providing information to
negotiating agents from affective channels tracked during the negotiation
itself is important for developing agents that can predict or understand if
their human counterpart is satisfied and likes them. Ultimately, outcomes like
satisfaction and likeness will be essential for such agents to cultivate if
they, like human negotiators, hope to successfully negotiate with that same
partner in the future [4].

In light of the theme for this year’s ACII on Ethical Affective Computing, we
briefly discuss the ethical considerations around the development of automated
negotiation agents. There has been a significant amount of work on ethics in
negotiation literature. The acts of emotion manipulation, deception, bias, and
misinterpretation have been central concerns [40]. It is plausible that these
behaviors also get reflected in the negotiation agents that are grounded in
the insights gained from human-human negotiation datasets such as CaSiNo. To
mitigate the impact of these ethical concerns when automated negotiation
systems are deployed to the end users, we lay out a few recommendations. We
believe that transparency is the key. Being upfront and open about the
identity, capabilities, and any known misbehaviors of the agent would prevent
any misinterpretation and would set the right expectations for the end users.
Further, we note that our work encourages the agent to adapt its behavior by
incorporating affective attributes along with user demography and personality.
If the deployed agent is indeed adaptive towards these traits, we recommend a
regular monitoring cycle for unexpected behaviors of the agent, preventing
against any offensive or discriminative actions.

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