# Energy loss of heavy and light quarks in holographic magnetized background

Zhou-Run Zhu  College of Science, China Three Gorges University, Yichang
443002, China  Sheng-Qin Feng<EMAIL_ADDRESS>College of Science, China
Three Gorges University, Yichang 443002, China  Key Laboratory of Quark and
Lepton Physics (MOE) and Institute of Particle Physics,
Central China Normal University, Wuhan 430079, China  Ya-Fei Shi  College of
Science, China Three Gorges University, Yichang 443002, China  Yang Zhong
College of Science, China Three Gorges University, Yichang 443002, China

###### Abstract

We systematically study holographic effects on the magnetic field dependence
of the drag force, diffusion coefficient, jet quenching parameter of heavy
quarks, and the shooting string energy loss of light quarks in the RHIC and
LHC energy regions by using the AdS/CFT correspondence in this paper. This
study is motivated by the phenomena of a strong magnetic field and jet
quenching, which have been found in relativistic heavy ion collisions. The
probe’s direction of motion is perpendicular and parallel to the direction of
magnetic field $B$. The effects of a magnetic field on energy loss when moving
perpendicular to the magnetic field direction are larger than moving parallel
to the magnetic field direction, which implies that the magnetic field tends
to suppress more quarks and jets when moving in the transverse direction than
in the parallel direction. It is found that the diffusion coefficient
decreases with the magnetic field in the transverse direction, but increases
with the magnetic field in the parallel direction, which indicates that the
quark may diffuse farther when moving parallel to the magnetic field
direction. We also find that the magnetic field will enhance the energy loss
of the light quarks when moving in the transverse direction than in the
parallel direction.

##  I Introduction

It is well known that the experiments at the Relativistic Heavy Ion Collider
(RHIC) and the Large Hadron Collider (LHC) can generate a new state of matter
so-called quark gluon plasma (QGP)Adams  _et al._ (2005); Adcox  _et al._
(2005); Shuryak (2005); Aamodt  _et al._ (2010). One of the important
properties of QGP is jet quenching: when a high energy parton propagates
through the medium, the presence of the medium in which the energetic parton
finds itself has two significant effects: it causes the parton to lose energy
and it changes the direction of the parton’s momentum Wang and Gyulassy
(1992). In the study of relativistic heavy ion collisions, besides jet
quenching, another important phenomenon is the generation of a strong magnetic
field of noncentral heavy ion collisions at the RHIC and the LHCVoronyuk  _et
al._ (2011); Skokov  _et al._ (2009); Bzdak and Skokov (2012); Deng and Huang
(2012); Mo  _et al._ (2013); She  _et al._ (2018); Zhong  _et al._ (2014).
Besides the phenomenological significance in theoretical sides of strong
interaction, strong magnetic fields in relativistic heavy-ion collisions also
provide some deep investigations of the dynamics of quantum chromodynamics
(QCD), of which the vacuum structure is of numerous interests.

In order to study the important features of jet quenching，which defines the
energy loss as a high-energy parton passes through the QGP during RHIC and LHC
energy regions, one should make it work by passing some colored objects
through the finite temperature $N=4$ super-Yang-Mills plasma. Readiest to hand
is an external quark, which in the framework of AdS/CFTWitten (1998); Gubser
_et al._ (1998); Maldacena (1999) is represented as a string dangling from the
boundary of $\mathrm{AdS}_{5}$-Schwarzschild black holeGubser (2006); Rey and
Yee (2001); Brandhuber  _et al._ (1998); Maldacena (1998); Rey  _et al._
(1998). Its point of attachment on the boundary carries a fundamental charge
under the gauge group $SU(N)$, and it is infinitely massive. The magnetic
field is introduced into the background geometry by solving the Einstein-
Maxwell systemLi  _et al._ (2017); Dudal  _et al._ (2016); Chelabi  _et al._
(2016). After embedding the magnetized background geometry into the modified
soft-wall model, the magnetic field dependent behaviors of jet quenching and
energy loss can be worked out numerically.

AdS/CFT correspondence or the gauge/string duality has yielded many important
explorations into the dynamics of strongly coupled gauge theoriesBrustein and
Medved (2009); Demir and Bass (2009); Pourhassan and Bagheri-Mohagheghi
(2017); Herzog  _et al._ (2006); Sadeghi and Pourhassan (2012). The jet
quenching parameter for $N=4$ SYM plasma has been carried out by Liu et al. in
their seminal workLiu  _et al._ (2006). On the other hand, gauge/string
duality can be taken as an insightful tool in this issue and many quantities
have already been studied, such as heavy quarkonium entropyChen  _et al._
(2018), shear viscosity to entropy density ratioCritelli  _et al._ (2014) and
energy lossMamo (2016); Zhang  _et al._ (2018); Finazzo  _et al._ (2016);
Rougemont  _et al._ (2016). A new study for light quark energy loss by using
shooting strings in SYM plasma to overcome the difficulties of previous
falling string holographic scenarios was carried out by the authors of
Refs.Ficnar  _et al._ (2014); Ficnar and Gubser (2014); Chesler  _et al._
(2009); Abelev  _et al._ (2013).

The study of the QCD features for strong magnetic field $B$ has attracted
considerable attentionEvans  _et al._ (2011); Alam  _et al._ (2012); Preis
_et al._ (2011); Ballon-Bayona (2013); Bali  _et al._ (2012); Kharzeev  _et
al._ (2013). Recently, the jet quenching parameter in a strongly coupled $N=4$
SYM plasma with a strong magnetic field was analyzed inLi  _et al._ (2016);
Zhang and Ma (2018). The inverse magnetic catalysis was analyzed inMamo
(2015). The main motivation for studying the magnetic field holographic QCD
features is that strong magnetic field
$\mathfrak{B}$($\mathfrak{B}(0.02-0.25)\textrm{GeV}^{2}$) is generated in
relativistic heavy ion collisions experiments at the RHIC and the LHCVoronyuk
_et al._ (2011); Skokov  _et al._ (2009); Bzdak and Skokov (2012); Deng and
Huang (2012); Mo  _et al._ (2013); She  _et al._ (2018); Zhong  _et al._
(2014), which has amounted in effects on the QGP created during these heavy
ion collision experimentsKharzeev  _et al._ (2008); Abelev (2009);
Selyuzhenkov (2012).

Holographic effects on the magnetic field dependence of the drag force,
diffusion coefficient, jet quenching parameter of heavy quarks and the
shooting string energy loss of light quarks are studied in the RHIC and LHC
energy regions by using the AdS/CFT correspondence in this article. The paper
is organized as follows. In Sec. II, we introduce the gravity background with
a backreaction of a magnetic field through the Einstein-Maxwell (EM) system.
In Secs. III and IV, we calculate the drag force and diffusion coefficient.
The jet quenching parameter is computed in Sec. V. The shooting string energy
loss of the light quarks is computed in Sec. VI. A short discussion and
conclusion are given in Sec. VII.

##  II Background geometry

The gravity background with a backreaction of a magnetic field through the
Einstein-Maxwell system was introduced byLi  _et al._ (2017); Dudal  _et al._
(2016); Mamo (2015), and the action is as follows:

$\ S=\frac{1}{16\pi
G_{5}}\int\differential{x}^{5}{\sqrt{-g}(L-F^{MN}F_{MN}+\frac{12}{R^{2}})},$
(1)

where $L$ represents the scalar curvature, $G_{5}$ represents $5D$ Newton
constant, $g$ is the determinant of metric $g_{\mu\nu}$, $R$ represents the
AdS radius, and $F_{MN}$ is the U(1) gauge field Li  _et al._ (2017).

Since we assume that the magnetic field is along the $x_{3}$ axis, which
breaks the rotation symmetry, the ansatz for metric can be taken as

$\
ds^{2}=\frac{R^{2}}{z^{2}}[-f(z)dt^{2}+h(z)(dx_{1}^{2}+dx_{2}^{2})+q(z)dx_{3}^{2}+\frac{dz^{2}}{f(z)}].$
(2)

When $z=z_{h}$, a black hole solution is $f(z=z_{h})=0$.

It has been pointed out Mamo (2015) that the perturbative solution can work
well when $B\ll T^{2}$. The physical magnetic field $\mathfrak{B}$ at the
boundary is related with $B$ that we use in this article by the equation
$\mathfrak{B}=\sqrt{3}B$. We take $B\leq 0.15\textrm{GeV}^{2}$, and the
physical magnetic field $\mathfrak{B}\leq 0.26\textrm{GeV}^{2}$ which conforms
to the RHIC and LHC magnetic field. As a first approximation, one can only
take the leading expansion inLi  _et al._ (2017) as

$f(z)=1-\frac{z^{4}}{z_{h}^{4}}\left(1+\frac{2}{3}B^{2}z_{h}^{4}\log(\frac{z}{z_{h}})\right),$
(3) $q(z)=1+\frac{2}{3}B^{2}\ln(\mu z)z^{4},$ (4)
$h(z)=1-\frac{1}{3}B^{2}\ln(\mu z)z^{4},$ (5)

where $z_{h}$ is the horizon of a black hole, and $\mu$ is a constant and
varies from 0.25-1 GeV, we take it as 0.5 GeV in this article. Since the
element $q(z)$ is not equal to $h(z)$, it allows us to study the anisotropic
cases in the presence of the magnetic field. The Hawking temperature with
magnetic field $B$ is calculated as

$T=\frac{1}{\pi z_{h}}-\frac{B^{2}z_{h}^{3}}{6\pi}.$ (6)

The Hawking temperature $T=T(z_{h})$, which is a function of the position of
the horizon, corresponds to the temperature of the thermal bath in the gauge
theory. In this article, we will expand this method to study the effects on
the magnetic field and temperature of the drag force, diffusion coefficient,
jet quenching parameter of heavy quarks, and the shooting string energy loss
of light quarks.

##  III Drag force in a magnetized background

When a heavy quark moves though the strongly coupled QGP with an unchanging
velocity $v$, it loses energy via drag force from the trailing string model
Gubser (2006); Herzog  _et al._ (2006). It can also be analyzed by the
Langevin coefficient Giataganas and Soltanpanahi (2014a, b). When a quark
moves on the boundary of the AdS, the end of the string hangs down into the
bulk of the AdS space. The shape of the trailing string does not change with
time when the quark has been moving at a constant velocity for a long time.
The drag force is correlated with the damping rate $\mu$ (or friction
coefficient), and the Langevin equation is

$\frac{dp}{dt}=-\mu p+f_{1},$ (7)

where $f_{1}$ is the driving force. The driving force is equal to the drag
force for $dp/dt=0$. The effects on the magnetic field of the drag force while
moving perpendicular and parallel to the magnetic field are discussed as
follows.

###  III.1 Moving perpendicular to the magnetic field

When the heavy quark is moving perpendicularly to the magnetic field, the
coordinates are parametrized by

$\ t=\tau,\ x_{1}=vt+\xi(z),\ x_{2}=x_{3}=0,\ z=\sigma.$ (8)

A classical trailing string can be described by the Nambu-Goto action

$S=-\frac{1}{2\pi\alpha^{\prime}}\int d\sigma d\tau\sqrt{-\det
g_{\alpha\beta}},$ (9)

where $g_{\alpha\beta}$ is the determinant of the induced metric,

$\ g_{\alpha\beta}=g_{\mu\nu}\frac{\partial
X^{\mu}}{\partial\sigma^{\alpha}}\frac{\partial
X^{\nu}}{\partial\sigma^{\beta}},$ (10)

where $g_{\mu\nu}$ and $X^{\mu}$ are the brane metric and target space
coordinates, respectively.

By plugging Eq.(8) into Eq.(2), one gets the metric as

$\ d{s}^{2}=g_{tt}\
d{t}^{2}+g_{xx}\differential{x_{1}}^{2}+g_{zz}\differential{z}^{2},$ (11)

and the induced metric is

$\ g_{tt}=-\frac{R^{2}}{z^{2}}f(z),\ g_{xx}=\frac{R^{2}}{z^{2}}h(z),\
g_{zz}=\frac{R^{2}}{z^{2}}\frac{1}{f(z)}.$ (12)

The Lagrangian density is given by

$\begin{split}\mathcal{L}&=\sqrt{-g_{zz}g_{tt}-g_{zz}g_{xx}\upsilon^{2}-g_{tt}g_{xx}\xi^{\prime
2}}\\\
&=\sqrt{(\frac{R^{2}}{z^{2}})^{2}-(\frac{R^{2}}{z^{2}})^{2}\frac{h(z)}{f(z)}\upsilon^{2}+(\frac{R^{2}}{z^{2}})^{2}h(z)f(z)\xi^{\prime
2}},\end{split}$ (13)

where $\xi^{\prime}=d\xi/d\sigma$. From Eq.(13), one finds that the action
does not rely on $\xi$ explicitly, which means
$\partial\mathcal{L}/\partial\xi^{\prime}$ is a constant. The canonical
momentum is given as

$\
\Pi_{\xi}=\frac{\partial\mathcal{L}}{\partial\xi^{\prime}}=-\xi^{\prime}\frac{g_{tt}g_{xx}}{\sqrt{-g_{\alpha\beta}}}=\frac{\xi^{\prime
2}(\frac{R^{2}}{z^{2}})^{2}h(z)f(z)}{\sqrt{(\frac{R^{2}}{z^{2}})^{2}-(\frac{R^{2}}{z^{2}})^{2}\frac{h(z)}{f(z)}\upsilon^{2}+(\frac{R^{2}}{z^{2}})^{2}h(z)f(z)\xi^{\prime
2}}},$ (14)

which leads to

$\xi^{\prime
2}=\frac{\Pi_{\xi}^{2}[1-\frac{h(z)}{f(z)}\upsilon^{2}]}{h(z)f(z)[(\frac{R^{2}}{z^{2}})^{2}h(z)f(z)-\Pi_{\xi}^{2}]}.$
(15)

It is emphasized that ${\xi^{\prime}}^{2}$ must be positive everywhere,
therefore, the numerator and denominator on the right-hand side of Eq.(15) are
both positive for small $z$ and negative for large $z$ near the horizon. With
these, the critical point $z_{c}$ can be written as

$\ h(z_{c})\upsilon^{2}=f(z_{c}),$ (16)

and

$\Pi_{\xi}^{2}=(\frac{R^{2}}{z_{c}^{2}})^{2}f(z_{c})h(z_{c}).$ (17)

The current density for momentum $p_{1}$ along the $x_{1}$ direction can be
given as

$\pi^{r}_{x_{1}}=-\frac{1}{2\pi\alpha^{\prime}}\xi^{\prime}\frac{g_{tt}g_{xx}}{-g_{\alpha\beta}}.$
(18)

The the drag force can be obtained as

$f_{\perp}=\frac{dp_{1}}{dt}=\sqrt{-g_{\alpha\beta}}\pi^{r}_{x_{1}}=-\frac{1}{2\pi\alpha^{\prime}}\Pi_{\xi}=-\frac{1}{2\pi\alpha^{\prime}}\frac{R^{2}}{z_{c}^{2}}h(z_{c})\upsilon,$
(19)

where the minus sign denotes the opposite direction of momentum.

The drag force of the isotropic SYM result at zero magnetic field Gubser
(2006) was given by

$f_{SYM}=-\frac{\pi T^{2}\sqrt{\lambda}}{2}\frac{v}{\sqrt{1-v^{2}}},$ (20)

where $\sqrt{\lambda}=\sqrt{g^{2}_{YM}N_{c}}=\frac{R^{2}}{\alpha^{\prime}}$.

###  III.2 Moving parallel to the magnetic field

When the heavy quark moves parallel to the magnetic field, the corresponding
coordinates are parametrized by

$\ t=\tau,\ x_{3}=vt+\xi(z),\ x_{1}=x_{2}=0,\ z=\sigma.$ (21)

By repeating the previous deduction, one can get the drag force as

$f_{\parallel}=-\frac{1}{2\pi\alpha^{\prime}}\frac{R^{2}}{z_{c}^{2}}q(z_{c})\upsilon.$
(22)

###  III.3 The calculated results of drag force

In order to study the anisotropic effect on the magnetic field dependence of
the drag force, we study the anisotropic drag force $f/f_{\textrm{SYM}}$ in
the magnetized background normalized by the isotropic SYM result at zero
magnetic field in Fig. 1. It is found that the drag force is generally
stronger when the heavy quark is moving perpendicular to the magnetic field
direction than when it is moving parallel to the magnetic field direction,
which indicates that the magnetic field tends to suppress more quarks in the
transverse than in the parallel direction.

Figure 1:  Anisotropic effect on the magnetic field dependence of the drag
force normalized by the isotropic SYM result at zero magnetic field (a) for a
low temperature ($T=0.15\textrm{GeV}$) and (b) for a higher one
($T=0.3\textrm{GeV}$). The solid line indicates the heavy quark moving
parallel to the magnetic field direction, and the dashed line denotes the
heavy quark moving perpendicular to the magnetic field direction.

The anisotropic effect on temperature dependence of the drag force
$f/f_{\textrm{SYM}}$ in the magnetized background is given in Fig. 2. It is
found that the drag force in the magnetized background is obviously
temperature dependent. When the temperature is relatively low ($T\leq
0.3\textrm{GeV}$), the magnetic field can change the isotropic phase while
both moving parallel and transverse to the magnetic field, but at relatively
high temperature($T>0.3$), $f/f_{\textrm{SYM}}$ tends to be 1, which suggests
the magnetic field hardly changes the isotropic phase. The anisotropy
$f/f_{\textrm{SYM}}<1$ is computed in the case of moving parallel to the
magnetic field with ultrafast motion($v=0.95$).

Figure 2:  Anisotropic effect on temperature dependence of the drag force in
the magnetized background normalized by the isotropic SYM result at zero
magnetic field (a) for $B=0.05\textrm{GeV}^{2}$, (b) for
$B=0.1\textrm{GeV}^{2}$, and (c) for $B=0.15\textrm{GeV}^{2}$. The solid line
indicates the heavy quark moving parallel to the magnetic field direction, and
the dashed line indicates it moving perpendicular to the magnetic field
direction. The red line denotes a low velocity ($\nu=0.5$) and the black line
denotes a higher one ($\nu=0.95$).

##  IV Diffusion coefficient in a magnetic field background

In this section, we focus on the study of the diffusion coefficient which can
be derived from the drag force.

The drag force with zero magnetic field in the Eq.(20) can be rewritten as

$f_{SYM}=-\frac{\pi
T^{2}\sqrt{\lambda}}{2m}\frac{vm}{\sqrt{1-v^{2}}}=-\eta_{D}p,$ (23)

where $m$ represents the mass of the heavy quark, $\eta_{D}$ is the drag
coefficient, and $p=\frac{mv}{\sqrt{1-v^{2}}}$ is the momentum.

The diffusion time $t_{\textrm{SYM}}$ is given as

$t_{SYM}=\frac{1}{\eta_{D}}=\frac{2m}{\pi T^{2}\sqrt{\lambda}},$ (24)

and the diffusion coefficient can be given by

$D_{SYM}=\frac{T}{m}t_{SYM}=\frac{2}{\pi T\sqrt{\lambda}}.$ (25)

When the quark is moving perpendicular to the magnetic field, Eq.(19) can be
rewritten as

$f_{\perp}=-\frac{h(z_{c})\sqrt{1-v^{2}}}{\pi^{2}T^{2}z_{c}^{2}}\frac{\pi
T^{2}\sqrt{\lambda}}{2m}\frac{vm}{\sqrt{1-v^{2}}},$ (26)

and the diffusion time $t_{\perp}$ is given as

$t_{\perp}=\frac{2m}{\pi
T^{2}\sqrt{\lambda}}\frac{\pi^{2}T^{2}z_{c}^{2}}{h(z_{c})\sqrt{1-v^{2}}}.$
(27)

The diffusion coefficient can be given by

$D_{\perp}=\frac{T}{m}t_{\perp}=\frac{2}{\pi
T\sqrt{\lambda}}\frac{\pi^{2}T^{2}z_{c}^{2}}{h(z_{c})\sqrt{1-v^{2}}}.$ (28)

From Eqs.(25) and (28), one can get

$\frac{D_{\perp}}{D_{\textrm{SYM}}}=\frac{\pi^{2}T^{2}z_{c}^{2}}{h(z_{c})\sqrt{1-v^{2}}}.$
(29)

Then the diffusion coefficient moving parallel to the magnetic field direction
can be given as

$D_{\parallel}=\frac{2}{\pi
T\sqrt{\lambda}}\frac{\pi^{2}T^{2}z_{c}^{2}}{q(z_{c})\sqrt{1-v^{2}}}.$ (30)

The anisotropic diffusion coefficient $D/D_{\textrm{SYM}}$ in the magnetized
background is given in Fig. 3. It is found that the diffusion coefficient
decreases with the magnetic field when moving perpendicular to the magnetic
field direction, but increases with the magnetic field when the probe is
moving parallel to the magnetic field direction in the high temperature and
high velocity, which indicates that the quark may diffusion farther when
moving parallel to the magnetic field direction.

Figure 3:  Anisotropic effect on the magnetic field dependence of the
diffusion coefficient normalized by the isotropic SYM result at zero magnetic
field (a) for a low temperature ($T=0.15\textrm{GeV}$) and (b) for a higher
one ($T=0.3\textrm{GeV}$). The solid line indicates the heavy quark moving
parallel to the magnetic field direction, and the dashed line denotes it
moving transverse to the magnetic field direction.

The anisotropic effect on the temperature dependence of the diffusion
coefficient $D/D_{\textrm{SYM}}$ in the magnetized background is given in Fig.
4. One can see that the diffusion coefficient in the magnetized background is
obviously temperature dependent. When the temperature is relatively low
($T\leq 0.3\textrm{GeV}$), the magnetic field will change the isotropic phase,
but at relatively high temperature ($T>0.3$), $D/D_{\textrm{SYM}}$ tends to be
1 with both moving parallel and transverse to the magnetic field, which means
the magnetic field hardly changes the isotropic phase at relatively high
temperature. A special result with the anisotropy of $D/D_{\textrm{SYM}}>1$ is
shown in the case of moving parallel to the magnetic field with ultrafast
motion ($v=0.95$).

Figure 4:  Anisotropic effect on temperature dependence of the diffusion
coefficient in the magnetized background normalized by the isotropic SYM
result at zero magnetic field (a) for $B=0.05\textrm{GeV}^{2}$, (b) for
$B=0.1\textrm{GeV}^{2}$, and (c) for $B=0.15\textrm{GeV}^{2}$. The solid line
indicates the heavy quark moving parallel to the magnetic field direction, and
the dashed line denotes it moving perpendicular to the magnetic field
direction. The red line denotes a low velocity ($\nu=0.5$) and the black line
denotes a higher one ($\nu=0.95$).

##  V Jet quenching parameter in magnetic field background

The strong jet quenching and the elliptic flowAdler  _et al._ (2003);
Ackermann  _et al._ (2001); Kolb  _et al._ (2001) suggest that the matter of
relativistic heavy ion collisions is strongly interacting. AdS/CFT
correspondence has produced many important insights into the dynamics of
strongly coupled gauge theories. Liu, Rajagopal and Wiedemann Liu  _et al._
(2006) have studied the jet quenching parameter $\hat{q}$ for $N=4$ SYM
plasma. Motivated by this, there are many attempts to study the jet quenching
parameter in this approach. For example, the effects of an electromagnetic
field and the chemical potential on $\hat{q}$ have been analyzed inLin and
Matsuo (2006); Armesto  _et al._ (2006); Avramis and Sfetsos (2007); Sadeghi
and Pourhassan (2011); Bitaghsir Fadafan  _et al._ (2011). The anisotropy
effects on $\hat{q}$ are investigated inGiataganas (2012), and some
worksPourhassan and Sadeghi (2013); Zhang  _et al._ (2013); Bitaghsir Fadafan
(2010) have used some of the results and formulas of Giataganas (2012) to
apply them on other anisotropic theories etc.

In this section we will discuss the jet quenching parameter $\hat{q}$ in the
magnetized background. It is well known that the jet quenching parameter
$\hat{q}$ is related to the Wilson loop with the following equationLiu  _et
al._ (2006):

$\langle W^{A}[C]\approx exp(-\frac{1}{4\sqrt{2}}\hat{q}L^{-}L^{2}),$ (31)

where $W^{A}[C]$ is the adjoint Wilson loop and $C$ is a rectangular contour
of size $L\times L^{-}$. The quark and antiquark are separated by a small $L$
and travel along the $L^{-}$.

Meanwhile, one can use the following equations

$\langle W^{A}[C]\rangle\approx\langle W^{F}[C]\rangle^{2},$ (32)

and

$\langle W^{F}[C]\rangle\approx exp[-S_{I}],$ (33)

where $W^{F}[C]$ is the fundamental representation of the Wilson loop and
$S_{I}=S-S_{0}$ ($S$ is the total energy of the quark and antiquark pair, and
$S_{0}$ is the self-energy of the isolated quark and antiquark).

Then the general relation of the jet quenching parameter is given as

$\hat{q}=8\sqrt{2}\frac{S_{I}}{L^{-}L^{2}}.$ (34)

###  V.1 Moving perpendicular to the magnetic field

There are two cases for the probe moving perpendicular to magnetic field
direction, the first case is that the jet moves along the $x_{1}$ direction
and the momentum broadening occurs along the $x_{3}$ direction(also the
magnetic field direction), and the second is that the jet moves along the
$x_{1}$ direction and the momentum broadening occurs along the $x_{2}$
direction.

By using the the light-cone coordinate $x^{\mu}=(z,x^{+},x^{-},x_{2},x_{3})$,
we start with the first case. One can rewrite metric(2) as

$\begin{split}ds^{2}=&\frac{R^{2}}{z^{2}}\bigg{\\{}-\frac{f(z)}{2}[(dx^{+})^{2}+(dx^{-})^{2}]+\frac{h(z)}{2}[(dx^{+})^{2}+(dx^{-})^{2}]-f(z)dx^{+}dx^{-}\\\
&-h(z)dx^{+}dx^{-}+h(z)dx^{2}_{2}+q(z)dx^{2}_{3}\bigg{\\}}+\frac{R^{2}}{z^{2}f(z)}dz^{2},\end{split}$
(35)

then chooses the following static gauge coordinate

$\ x^{-}=\tau,\ x_{3}=\sigma,\ x^{+}=x_{2}=const.$ (36)

If one adopts a profile of $z=z(\sigma)$, then Eq. (35) becomes

$\
ds^{2}=\frac{R^{2}}{2z^{2}}[h(z)-f(z)]d\tau^{2}+\frac{R^{2}}{z^{2}}[q(z)+\frac{\dot{z}}{f(z)}d\sigma^{2}],$
(37)

where $\dot{z}=\frac{dz}{d\sigma}$.

The Nambu-Goto action can be given as

$\
S=\frac{\sqrt{2}L^{-}}{2\pi\alpha^{\prime}}\int^{\frac{L}{2}}_{0}d\sigma\frac{R^{2}}{z^{2}}\sqrt{[h(z)-f(z)][q(z)+\frac{\dot{z}}{{f(z)}}]},$
(38)

and the Lagrangian density can be written as

$\
\mathcal{L}=\frac{R^{2}}{z^{2}}\sqrt{[h(z)-f(z)][q(z)+\frac{\dot{z}}{{f(z)}}]}.$
(39)

Since the Lagrangian density does not rely on $\sigma$ explicitly, one has a
conserved quantity as

$\ \frac{\partial\mathcal{L}}{\dot{z}}-\mathcal{L}=E,$ (40)

where $E$ is the constant energy of motion. One can derive the following
formulas

$\
\dot{z}=\sqrt{\frac{f(z)q(z)}{E^{2}}}\sqrt{(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]-E^{2}}.$
(41)

The separation parameter $L$ of a quark and antiquark pair can be given by

$\begin{split}\ L&=2\int^{z_{h}}_{0}dz\cdot\frac{1}{\dot{z}}\\\
&=2\int^{z_{h}}_{0}dz\frac{E}{\sqrt{q(z)f(z)}}\frac{1}{\sqrt{(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}}[1-\frac{E^{2}}{(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}]^{-\frac{1}{2}}.\end{split}$
(42)

In the low limit of $E$, Eq.(42) turns into

$\
L=2\int^{z_{h}}_{0}dz\frac{E}{\sqrt{q(z)f(z)}}\frac{1}{\sqrt{(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}}[1+\frac{E^{2}}{2(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}].$
(43)

By ignoring $E^{2}$, one gets

$\begin{split}\
L&=2E\int^{z_{h}}_{0}dz\frac{1}{q(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[h(z)-f(z)]}}\\\
&=2EI,\end{split}$ (44)

where

$\
I=\int^{z_{h}}_{0}dz\frac{1}{q(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[h(z)-f(z)]}}.$
(45)

Substituting Eq.(41) into Eq.(38) in the small limit $E$, one calculates the
Nambu-Goto action as

$\
S=\frac{\sqrt{2}L^{-}}{2\pi\alpha^{\prime}}\int^{z_{h}}_{0}dz\sqrt{\frac{1}{f(z)}[h(z)-f(z)](\frac{R^{2}}{z^{2}})^{2}}[1+\frac{E^{2}}{2(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}].$
(46)

The self-energy $S_{0}$ is

$\
S_{0}=\frac{\sqrt{2}L^{-}}{2\pi\alpha^{\prime}}\int^{z_{h}}_{0}dz\sqrt{\frac{1}{f(z)}[h(z)-f(z)](\frac{R^{2}}{z^{2}})^{2}}.$
(47)

By subtracting Eq.(47) from Eq.(46), one can get

$\begin{split}\ S&=S-S_{0}\\\
&=\frac{\sqrt{2}L^{-}}{2\pi\alpha^{\prime}}\int^{z_{h}}_{0}dz\sqrt{\frac{1}{f(z)}[h(z)-f(z)](\frac{R^{2}}{z^{2}})^{2}}\frac{E^{2}}{2(\frac{R^{2}}{z^{2}})^{2}q(z)[h(z)-f(z)]}\\\
&=\frac{\sqrt{2}L^{-}E^{2}}{4\pi\alpha^{\prime}}\int^{z_{h}}_{0}dz\frac{1}{q(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[h(z)-f(z)]}}\\\
&=\frac{\sqrt{2}L^{-}E^{2}}{4\pi\alpha^{\prime}}I.\end{split}$ (48)

By inserting Eqs.(44) and (48) into Eq.(34), one can get the jet quenching
parameter as

$\begin{split}\hat{q}_{\perp(\parallel)}&=8\sqrt{2}\frac{S_{I}}{L^{-}L^{2}}\\\
&=\frac{1}{\pi\alpha^{\prime}}\frac{1}{I},\end{split}$ (49)

where

$\
I=\int^{z_{h}}_{0}dz\frac{1}{q(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[h(z)-f(z)]}}.$
(50)

The jet quenching parameter of an isotropic SYM result at zero magnetic field
Liu  _et al._ (2006) has been given by

$\
\hat{q}_{SYM}=\frac{\sqrt{\lambda}T^{3}\pi^{\frac{3}{2}}\Gamma(\frac{3}{4})}{\Gamma(\frac{5}{4})},$
(51)

where $\sqrt{\lambda}=\sqrt{g^{2}_{YM}N_{c}}=\frac{R^{2}}{\alpha^{\prime}}$.

By considering the jet moving along the $x_{1}$ direction and the momentum
broadening occurring along the $x_{2}$ direction, we will study the second
situation. One chooses the following static gauge:

$\ x^{-}=\tau,\ x_{2}=\sigma,\ x^{+}=x_{3}=const.$ (52)

The jet quenching parameter is calculated as

$\begin{split}\hat{q}_{\perp(\perp)}&=8\sqrt{2}\frac{S_{I}^{\prime}}{L^{-}L^{2}}\\\
&=\frac{1}{\pi\alpha^{\prime}}\frac{1}{I_{\perp(\perp)}},\end{split}$ (53)

where

$\
I_{\perp(\perp)}=\int^{z_{h}}_{0}dz\frac{1}{h(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[h(z)-f(z)]}}.$
(54)

###  V.2 Moving parallel to the magnetic field

By considering the jet moving along the $x_{3}$ direction and the momentum
broadening occurring along the $x_{1}$ direction, we will study the jet
quenching parameter of the parallel case. One chooses the following static
gauge:

$\ x^{-}=\tau,\ x_{1}=\sigma,\ x^{+}=x_{2}=const.$ (55)

The jet quenching parameter of the parallel case is

$\begin{split}\hat{q}_{\parallel(\perp)}&=8\sqrt{2}\frac{S_{I}^{\prime\prime}}{L^{-}L^{2}}\\\
&=\frac{1}{\pi\alpha^{\prime}}\frac{1}{I_{\parallel(\perp)}},\end{split}$ (56)

where

$\
I_{\parallel(\perp)}=\int^{z_{h}}_{0}dz\frac{1}{h(z)}\frac{z^{2}}{R^{2}\sqrt{f(z)[q(z)-f(z)]}}.$
(57)

###  V.3 The calculated results of jet quenching parameter in a magnetized
background

In order to study the effects on the magnetic field dependence of the jet
quenching parameter, we study the dependence of
$\hat{q}/\hat{q}_{\textrm{SYM}}$ on a magnetic field for various temperatures
in Fig. 5. It is found that the jet quenching parameter when the probe is
moving perpendicular to magnetic field direction is larger than when it is
moving parallel to the magnetic field direction. The result suggests that the
magnetic field inclines to suppress more jets in the transverse direction than
in the parallel direction.

Figure 5:  Anisotropic effect on the magnetic field dependence of the jet
quenching parameter normalized by the isotropic SYM result at zero magnetic
field (a) for a low temperature ($T=0.15\textrm{GeV}$) and (b) for a higher
one ($T=0.3\textrm{GeV}$). The dashed line indicates
$\hat{q}_{\perp(\perp)}/\hat{q}_{\textrm{SYM}}$, the dash-dotted line
indicates $\hat{q}_{\perp(\parallel)}/\hat{q}_{\textrm{SYM}}$, and the solid
line denotes $\hat{q}_{\parallel(\perp)}/\hat{q}_{\textrm{SYM}}$.

The anisotropic effect on the temperature dependence of the jet quenching
parameter $\hat{q}/\hat{q}_{\textrm{SYM}}$ in the magnetized background is
given in Fig. 6. One can see that the jet quenching parameter in the
magnetized background is obviously temperature dependent when $T\leq
0.3\textrm{GeV}$, which shows that the magnetic field can change the isotropic
phase of jet quenching at low temperature. But at relatively high temperature
($T>0.3$), $\hat{q}/\hat{q}_{\textrm{SYM}}$ always tends to be 1, which means
that the magnetic field hardly changes the isotropic phase of jet quenching.
The authors of Ref. Zhang  _et al._ (2018) investigated the dependence of a
jet quenching parameter on $B/T^{2}$ at large magnetic field but did not study
the dependencies of a jet quenching parameter on a magnetic field and
temperature, separately. The dependencies of a jet quenching parameter on a
magnetic field and temperature have been studied in the article.

Figure 6:  Anisotropic effect on temperature dependence of the jet quenching
parameter in the magnetized background normalized by the isotropic SYM result
at zero magnetic field (a) for $B=0.05\textrm{GeV}^{2}$, (b) for
$B=0.1\textrm{GeV}^{2}$, and (c) for $B=0.15\textrm{GeV}^{2}$. The dashed line
indicates $\hat{q}_{\perp(\perp)}/\hat{q}_{\textrm{SYM}}$, the dash-dotted
line indicates $\hat{q}_{\perp(\parallel)}/\hat{q}_{\textrm{SYM}}$, and the
solid line denotes $\hat{q}_{\parallel(\perp)}/\hat{q}_{\textrm{SYM}}$.

##  VI The energy loss of light quarks in a magnetized background

In this section, we will pay attention to the energy loss of the light quarks
in a magnetized background. A light quark-antiquark pair by an initially
pointlike open string created with endpoints that propagate away from each
other and fall from the boundary toward the horizon has been discussed by
using the falling stringChesler  _et al._ (2009). The endpoints must travel
transversely to the string. It means no endpoint momentum or say there is no
part of the string has momentum upward toward the boundary during the process
of moving. But inFicnar  _et al._ (2014); Ficnar and Gubser (2014), there is a
development for the endpoint’s trajectory that starts close to the horizon
rather than close to the boundary in the previous treatments of the falling
string model.

The authors of Ref.Ficnar and Gubser (2014) considered the endpoints
representing the energetic quarks which were created though a hard scattering
event and the string representing the color field generated by the quarks. The
string is to start with packs of energy into the endpoints which were located
close to the horizon. It is termed finite-endpoint-momentum shooting
string(“the shooting string” for short): adding finite momentum at the
endpoints and the trajectories of the endpoints follow the null geodesics
while the rest of the string sags behind the endpoints. One can consider the
endpoints are close to the horizon initially and “shot” towards the boundary.
As it first reaches to a minimal value $z_{\ast}$ of the radial coordinate, it
falls back into the horizon. There is a shooting limit that the energy loss
can be approximated by using the null geodesic with $L$ = 1. During the
process of endpoints rising, the energy and momentum are gradually bled off.
The string performs the process of a “snap-back” or “rising-and-falling”. It
may offer a more natural description of the energetic light quarks passing
through the QGP medium. Meanwhile the finite momentum endpoints can travel
further than in the falling string model.

A general expression of the instantaneous energy loss of light quarks proposed
inFicnar  _et al._ (2014)is taken as

$\ \frac{dE}{dx}=-\frac{|L|}{2\pi\alpha^{\prime}}G_{xx}(z),$ (58)

where the constant $L$ represents the null geodesics that the endpoint
follows. In order to make Eq.(58) into an usable expression, one needs to
relate $L$ to some observable quantity and express $z$ in terms of $x$. From
the Eq.(58) one can see that if the endpoints starts close to the boundary($z$
is very small), the energy loss will be large. It means the jets will be
quenched in a short time and will not be observable. So it needs to start
close to the horizon in order to be observable.

###  VI.1 Moving perpendicular to the magnetic field

By assuming the light quark moves in the $x_{1}$ direction and magnetic field
along the $x_{3}$ direction and using metric $(2)$, we study the energy loss
of light quarks in a magnetized background through the EM system with Eq.(2).
The energy and momentum of a probe are conserved as

$\ E=-\frac{1}{\eta}\frac{R^{2}}{z^{2}}f(z),$ (59)

and

$\ p_{x_{1}}=\frac{1}{\eta}\frac{R^{2}}{z^{2}}h(z)\frac{dx}{dt}.$ (60)

where $\eta(t)$ is an auxiliary field. The null geodesics $L$ read as

$\ L=\frac{E}{p_{x_{1}}}=-\frac{f(z)dt}{h(z)dx}.$ (61)

The finite momentum endpoints will move along null geodesics $ds^{2}=0$, and
one gets

$\ (\frac{dx}{dz})^{2}=\frac{1}{h(z)[h(z)L^{2}-f(z)]}.$ (62)

If the endpoints follow the null geodesics, then the denominator of Eq.(62)
vanishes at $z=z_{\ast}$. One can relate it to $L$ as

$\ L=-\sqrt{\frac{f(z_{\ast})}{h(z_{\ast})}}.$ (63)

Then one can get the energy loss as

$\
\frac{dE}{dx}=-\frac{\sqrt{\lambda}}{2\pi}\frac{h(z)}{z^{2}}\sqrt{\frac{f(z_{\ast})}{h(z_{\ast})}},$
(64)

and

$\
\frac{dx}{dz}=\sqrt{\frac{h(z_{\ast})}{h^{2}(z)f(z_{\ast})-f(z)h(z)h(z_{\ast})}}.$
(65)

As one assumes that the endpoint is at $x=0$ and $z=z_{h}$ as the initial
moment, then the endpoint is shot towards the boundary and reaches to a
minimal value $z_{\ast}$ of the radial coordinate. Note that $z_{\ast}$ is
very small. In the shooting limit, $z_{\ast}\rightarrow 0$, and large $x$
corresponds to the fact that the endpoint is closer to the boundary.

In order to calculate the energy loss $dE/dx$, we use the numerical simulation
method to solve Eq.(65) in the next section. In order to compare with the
conformal case, we compute the ratio of energy loss with the magnetic field to
the conformal field. The conformal case Ficnar  _et al._ (2014) is

$\ (\frac{dE}{dx})_{SYM}=-\frac{\pi\sqrt{\lambda}}{2}T^{2}(1+\pi Tx)^{2}.$
(66)

where $\sqrt{\lambda}=\sqrt{g^{2}_{YM}N_{c}}=\frac{R^{2}}{\alpha^{\prime}}$.

###  VI.2 Moving parallel to the magnetic field

We assume the light quark moves in the $x_{3}$ direction which is parallel to
the direction of the magnetic field. The energy and momentum of a probe are
conserved in metric (2)

$\ E=-\frac{1}{\eta}\frac{R^{2}}{z^{2}}f(z),$ (67)

and

$\ p_{x_{3}}=\frac{1}{\eta}\frac{R^{2}}{z^{2}}q(z)\frac{dx}{dt},$ (68)

where $\eta(t)$ is an auxiliary field.

By using the same procedure as above, one can get

$\
\frac{dE}{dx}=-\frac{\sqrt{\lambda}}{2\pi}\frac{q(z)}{z^{2}}\sqrt{\frac{f(z_{\ast})}{q(z_{\ast})}},$
(69)

and

$\
\frac{dx}{dz}=\sqrt{\frac{q(z_{\ast})}{q^{2}(z)f(z_{\ast})-f(z)q(z)q(z_{\ast})}}.$
(70)

###  VI.3 The calculated results of the shooting string

In a search for the holographic effect on a magnetic field dependence of the
energy loss of light quarks, the dependence of
$(dE/dx)/(dE/dx)_{\textrm{SYM}}$ on the magnetic field at some fixed
temperatures and $x$ are provided in Fig. 7. It is found that the energy loss
of light quarks increases with the magnetic field continuously, and it is
larger than that of $N=4$ SYM theory especially at low temperature. It
suggests that the magnetized background enhances the energy loss of the light
quarks. One also finds that in early times (small $x$), the effects on the
energy loss of light quarks when moving perpendicular to the magnetic field
direction is more obvious than moving parallel to the magnetic field
direction, which implies that the magnetic field tends to suppress more quarks
and jets when moving in the transverse direction than in the parallel
direction in the early times. But in later times(large $x$), the effects on
energy loss of light quarks of moving perpendicular to the magnetic field
direction is nearly the same as that of moving parallel to the magnetic field
direction, which suggests that the effect on the magnetic field of the energy
loss in the transverse direction is almost the same as that moving in the
parallel direction in the later times.

Figure 7:  Anisotropic effect on the magnetic field dependence of the energy
loss of light quarks normalized by the isotropic SYM result at zero magnetic
field (a) for a small distance $x$ ($x=0.1fm$) and (b) for a bigger
one($x=10fm$). The solid line indicates the light quark moving parallel to the
magnetic field direction, and the dashed line indicates the light quark moving
perpendicular to the magnetic field direction.The red line denotes a low
temperature($T=0.15\textrm{GeV}$) and the black line denotes a higher
one($T=0.3\textrm{GeV}$).

Figure. 8 shows the effect on temperature dependence of the energy loss of
light quarks $(dE/dx)/(dE/dx)_{\textrm{SYM}}$ for various magnetic field and
distance $x$. The ratio decreases rapidly with the increase of temperature at
$T\leq 0.3$, which expresses a strong temperature dependence at low
temperature. But at relatively high temperature ($T>0.3$), the ratio always
tends to be 1, which means the magnetic field hardly changes the isotropic
phase at high temperature.

Figure 8:  Anisotropic effect on temperature dependence of the energy loss of
light quarks in the magnetized background normalized by the isotropic SYM
result at zero magnetic field. (a) for a small distance $x$($x=0.1fm$) and (b)
for a bigger one($x=10fm$). The solid line indicates the light quark moving
parallel to the magnetic field direction, and the dashed line indicates the
light quark moving perpendicular to the magnetic field direction. The red line
denotes $B=0.15\textrm{GeV}^{2}$ , the blue line denotes
$B=0.1\textrm{GeV}^{2}$ and the black line denotes $B=0.05\textrm{GeV}^{2}$.

##  VII Conclusion and discussion

Some RHIC and LHC data indicate the production of jet quenching and a strong
magnetic field. As is well known noncentral heavy ion collisions at the RHIC
and the LHC can produce a very strong magnetic field. Besides the
phenomenological significance in theoretical sides of strong interaction,
strong magnetic fields in relativistic heavy-ion collisions also provide some
deep investigations of the dynamics of QCD, of which the vacuum structure is
of numerous interest. The magnetic field is introduced into the background
geometry by solving the Einstein-Maxwell system in this paper. After embedding
the magnetized background geometry into the modified soft-wall model, we study
the magnetic field dependent behaviors of jet quenching and energy loss
numerically.

In summary, the holographic effects on the magnetic field dependence of the
drag force, diffusion coefficient, jet quenching parameter of heavy quarks,
and the energy loss of the light quarks were systematically studied in the
paper. It was found that the perpendicular case is larger than that of the
parallel case, which implies that the magnetic field tends to suppress more
quarks and jets in the transverse direction than in the parallel direction.
One also finds that the magnetic field will enhance the energy loss of the
light quarks. The diffusion coefficient decreases with the magnetic field in
the transverse direction, but in the high temperature and velocity case the
diffusion coefficient increases with the magnetic field when moving parallel
to the magnetic field direction, which indicates that the quark may diffusion
farther when moving along the parallel to the magnetic field direction.

The dependencies of energy loss of heavy and light quarks on temperature for
various magnetic fields were studied in this article. We found some important
phenomena with the increase of temperature. When the temperature rises to
$0.3\textrm{GeV}$, the ratio approaches to 1, which suggests that the magnetic
field hardly changes the isotropic phase in high temperature.

## ACKNOWLEDGMENTS

This work was supported by National Natural Science Foundation of China
(Grants No. 11875178, No. 11475068, and No. 11747115) and the CCNU-QLPL
Innovation Fund (Grant No. QLPL2016P01).

## References

## References

  * Adams  _et al._ (2005) J. Adams _et al._ (STAR), Nucl. Phys. A757, 102 (2005).
  * Adcox  _et al._ (2005) K. Adcox _et al._ (PHENIX), Nucl. Phys. A757, 184 (2005).
  * Shuryak (2005) E. V. Shuryak,  _Quark gluon plasma. New discoveries at RHIC: A case of strongly interacting quark gluon plasma. Proceedings, RBRC Workshop, Brookhaven, Upton, USA, May 14-15, 2004_ , Nucl. Phys. A750, 64 (2005).
  * Aamodt  _et al._ (2010) K. Aamodt _et al._ (ALICE), Phys. Rev. Lett. 105, 252302 (2010).
  * Wang and Gyulassy (1992) X.-N. Wang and M. Gyulassy, Phys. Rev. Lett. 68, 1480 (1992).
  * Voronyuk  _et al._ (2011) V. Voronyuk, V. D. Toneev, W. Cassing, E. L. Bratkovskaya, V. P. Konchakovski, and S. A. Voloshin, Phys. Rev. C83, 054911 (2011).
  * Skokov  _et al._ (2009) V. Skokov, A. Yu. Illarionov, and V. Toneev, Int. J. Mod. Phys. A24, 5925 (2009).
  * Bzdak and Skokov (2012) A. Bzdak and V. Skokov, Phys. Lett. B710, 171 (2012).
  * Deng and Huang (2012) W.-T. Deng and X.-G. Huang, Phys. Rev. C85, 044907 (2012).
  * Mo  _et al._ (2013) Y.-J. Mo, S.-Q. Feng, and Y.-F. Shi, Phys. Rev. C88, 024901 (2013).
  * She  _et al._ (2018) D. She, S.-Q. Feng, Y. Zhong, and Z.-B. Yin, Eur. Phys. J. A54, 48 (2018).
  * Zhong  _et al._ (2014) Y. Zhong, C.-B. Yang, X. Cai, and S.-Q. Feng, Adv. High Energy Phys. 2014, 193039 (2014).
  * Witten (1998) E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  * Gubser  _et al._ (1998) S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B428, 105 (1998).
  * Maldacena (1999) J. M. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999).
  * Gubser (2006) S. S. Gubser, Phys. Rev. D74, 126005 (2006).
  * Rey and Yee (2001) S.-J. Rey and J.-T. Yee, Eur. Phys. J. C22, 379 (2001).
  * Brandhuber  _et al._ (1998) A. Brandhuber, N. Itzhaki, J. Sonnenschein, and S. Yankielowicz, Phys. Lett. B434, 36 (1998).
  * Maldacena (1998) J. M. Maldacena, Phys. Rev. Lett. 80, 4859 (1998).
  * Rey  _et al._ (1998) S.-J. Rey, S. Theisen, and J.-T. Yee, Nucl. Phys. B527, 171 (1998).
  * Li  _et al._ (2017) D. Li, M. Huang, Y. Yang, and P.-H. Yuan, JHEP 02, 030 (2017).
  * Dudal  _et al._ (2016) D. Dudal, D. R. Granado, and T. G. Mertens, Phys. Rev. D93, 125004 (2016).
  * Chelabi  _et al._ (2016) K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, JHEP 04, 036 (2016).
  * Brustein and Medved (2009) R. Brustein and A. J. M. Medved, Phys. Rev. D79, 021901 (2009).
  * Demir and Bass (2009) N. Demir and S. A. Bass, Phys. Rev. Lett. 102, 172302 (2009).
  * Pourhassan and Bagheri-Mohagheghi (2017) B. Pourhassan and M. M. Bagheri-Mohagheghi, Eur. Phys. J. C77, 759 (2017).
  * Herzog  _et al._ (2006) C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaffe, JHEP 07, 013 (2006).
  * Sadeghi and Pourhassan (2012) J. Sadeghi and B. Pourhassan, Acta Phys. Polon. B43, 1825 (2012).
  * Liu  _et al._ (2006) H. Liu, K. Rajagopal, and U. A. Wiedemann, Phys. Rev. Lett. 97, 182301 (2006).
  * Chen  _et al._ (2018) X. Chen, S.-Q. Feng, Y.-F. Shi, and Y. Zhong, Phys. Rev. D97, 066015 (2018).
  * Critelli  _et al._ (2014) R. Critelli, S. I. Finazzo, M. Zaniboni, and J. Noronha, Phys. Rev. D90, 066006 (2014).
  * Mamo (2016) K. A. Mamo, Phys. Rev. D94, 041901 (2016).
  * Zhang  _et al._ (2018) Z.-q. Zhang, K. Ma, and D.-f. Hou, J. Phys. G45, 025003 (2018).
  * Finazzo  _et al._ (2016) S. I. Finazzo, R. Critelli, R. Rougemont, and J. Noronha, Phys. Rev. D94, 054020 (2016).
  * Rougemont  _et al._ (2016) R. Rougemont, A. Ficnar, S. Finazzo, and J. Noronha, JHEP 04, 102 (2016).
  * Ficnar  _et al._ (2014) A. Ficnar, S. S. Gubser, and M. Gyulassy, Phys. Lett. B738, 464 (2014).
  * Ficnar and Gubser (2014) A. Ficnar and S. S. Gubser, Phys. Rev. D89, 026002 (2014).
  * Chesler  _et al._ (2009) P. M. Chesler, K. Jensen, and A. Karch, Phys. Rev. D79, 025021 (2009).
  * Abelev  _et al._ (2013) B. Abelev _et al._ (ALICE), Phys. Rev. Lett. 110, 012301 (2013).
  * Evans  _et al._ (2011) N. Evans, T. Kalaydzhyan, K.-y. Kim, and I. Kirsch, JHEP 01, 050 (2011).
  * Alam  _et al._ (2012) M. S. Alam, V. S. Kaplunovsky, and A. Kundu, JHEP 04, 111 (2012).
  * Preis  _et al._ (2011) F. Preis, A. Rebhan, and A. Schmitt, JHEP 03, 033 (2011).
  * Ballon-Bayona (2013) A. Ballon-Bayona, JHEP 11, 168 (2013).
  * Bali  _et al._ (2012) G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, A. Schafer, and K. K. Szabo, JHEP 02, 044 (2012).
  * Kharzeev  _et al._ (2013) D. E. Kharzeev, K. Landsteiner, A. Schmitt, and H.-U. Yee, Lect. Notes Phys. 871, 1 (2013).
  * Li  _et al._ (2016) S. Li, K. A. Mamo, and H.-U. Yee, Phys. Rev. D94, 085016 (2016).
  * Zhang and Ma (2018) Z.-q. Zhang and K. Ma, Eur. Phys. J. C78, 532 (2018).
  * Mamo (2015) K. A. Mamo, JHEP 05, 121 (2015).
  * Kharzeev  _et al._ (2008) D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A803, 227 (2008).
  * Abelev (2009) B. I. e. a. Abelev (STAR), Phys. Rev. Lett. 103, 251601 (2009).
  * Selyuzhenkov (2012) I. Selyuzhenkov (ALICE),  _Proceedings, 41st International Symposium on Multiparticle Dynamics (ISMD 2011): Miyajima, Hiroshima, Japan, September 26-30, 2011_ , Prog. Theor. Phys. Suppl. 193, 153 (2012).
  * Giataganas and Soltanpanahi (2014a) D. Giataganas and H. Soltanpanahi, Phys. Rev. D89, 026011 (2014a).
  * Giataganas and Soltanpanahi (2014b) D. Giataganas and H. Soltanpanahi, JHEP 06, 047 (2014b).
  * Adler  _et al._ (2003) S. S. Adler _et al._ (PHENIX), Phys. Rev. Lett. 91, 182301 (2003).
  * Ackermann  _et al._ (2001) K. H. Ackermann _et al._ (STAR), Phys. Rev. Lett. 86, 402 (2001).
  * Kolb  _et al._ (2001) P. F. Kolb, U. W. Heinz, P. Huovinen, K. J. Eskola, and K. Tuominen, Nucl. Phys. A696, 197 (2001).
  * Lin and Matsuo (2006) F.-L. Lin and T. Matsuo, Phys. Lett. B641, 45 (2006).
  * Armesto  _et al._ (2006) N. Armesto, J. D. Edelstein, and J. Mas, JHEP 09, 039 (2006).
  * Avramis and Sfetsos (2007) S. D. Avramis and K. Sfetsos, JHEP 01, 065 (2007).
  * Sadeghi and Pourhassan (2011) J. Sadeghi and B. Pourhassan, Int. J. Theor. Phys. 50, 2305 (2011).
  * Bitaghsir Fadafan  _et al._ (2011) K. Bitaghsir Fadafan, B. Pourhassan, and J. Sadeghi, Eur. Phys. J. C71, 1785 (2011).
  * Giataganas (2012) D. Giataganas, JHEP 07, 031 (2012).
  * Pourhassan and Sadeghi (2013) B. Pourhassan and J. Sadeghi, Can. J. Phys. 91, 995 (2013).
  * Zhang  _et al._ (2013) Z.-q. Zhang, D.-f. Hou, and H.-c. Ren, JHEP 01, 032 (2013).
  * Bitaghsir Fadafan (2010) K. Bitaghsir Fadafan, Eur. Phys. J. C68, 505 (2010).


#  Vid2Real HRI: Align video-based HRI study designs with real-world settings

Elliott Hauser1, Yao-Cheng Chan1, Sadanand Modak2, Joydeep Biswas2, Justin
Hart2 *This research is part of an ongoing collaboration supported by NSF
Award 2219236, Living and Working with Robots, a core research project of Good
Systems, a UT Grand Challenge, and an unrestricted gift from The MITRE
Corporation. Dr. Hart is additionally supported by Cisco Research and Army
Futures Command.1School of Information, The University of Texas at Austin,
{eah13<EMAIL_ADDRESS>of Computer Science, The University of
Texas at Austin, {sadanandm, joydeepb<EMAIL_ADDRESS>
###### Abstract

HRI research using autonomous robots in real-world settings can produce
results with the highest ecological validity of any study modality, but many
difficulties limit such studies’ feasibility and effectiveness. We propose
Vid2Real HRI, a research framework to maximize real-world insights offered by
video-based studies. The Vid2Real HRI framework was used to design an online
study using first-person videos of robots as real-world encounter surrogates.
The online study ($n=385$) distinguished the within-subjects effects of four
robot behavioral conditions on perceived social intelligence and human
willingness to help the robot enter an exterior door. A real-world, between-
subjects replication ($n=26$) using two conditions confirmed the validity of
the online study’s findings and the sufficiency of the participant recruitment
target ($22$) based on a power analysis of online study results. The Vid2Real
HRI framework offers HRI researchers a principled way to take advantage of the
efficiency of video-based study modalities while generating directly
transferable knowledge of real-world HRI. Code and data from the study are
provided at vid2real.github.io/vid2realHRI.

##  I Introduction

Human-Robot Interaction (HRI) research is intimately shaped by the nature of
robots as technical artifacts. As robots are not part of daily life for most
people around the world, studies of robots in real-world settings are thus
limited to existing uses of robots or researcher-constructed scenarios, which
are oriented towards validating new designs or robot behaviors [1], and often
involve real-world designs where humans are state-of-the-art research robots.
While these may gain direct applicability to expanding the frontiers of
robotics, they often lose ecological validity [2]. The difficulties this
dynamic presents call for a new research framework that is applicable to novel
forms of autonomous robot HRI phenomena, such as fully autonomous robotics and
incidental human-robot encounters (HRE) research in pedestrian settings.

HRI of autonomous robots in real-world settings presents the methodological
challenge of deriving precise knowledge of a highly complex subject in a high-
dimensional space of potential variables. Incidental encounters with robots,
the scenario studied here, are fleeting yet increasingly common events with
potentially profound social impact. Without directly addressing these
challenges, the field of HRI risks delaying or forgoing the technical [3] and
theoretical [4] opportunities of better understanding and reacting to them.

The present study proposes a new research framework, Vid2Real HRI, to guide
researchers studying HRI with autonomous robots in real-world settings seeking
to use video-based studies. Vid2Real HRI, described in Section III, allows
researchers to better align video-based study designs with the real-world
conditions they seek to understand.

We illustrate the application of the Vid2Real HRI framework to an HRE research
study on the effects of socially compliant autonomous robot behaviors on
pedestrians. The results of the application study demonstrated that Vid2Real
HRI improved the video study’s alignment with real-world settings, produced
HRI knowledge with real-world applicability, and provides a compelling path
towards specific follow-up studies. In addition to the statistical best
practices it encourages [5], the Vid2Real HRI framework provides principled
epistemological grounding for HRI research programs seeking to effectively and
efficiently generate and build upon knowledge of complex sites, phenomena, and
robotic systems.

##  II Related Work

Amidst longstanding calls for standard metrics and heightened scientific rigor
in the field of HRI [6, 7], an increasing number of researchers are conducting
methodologically oriented studies, seeking to better understand and improve
the scientific knowledge generated from HRI research practices. These have
included studies of reproducibility [8], the relative validity of lab-based
and online studies [9], and the effects of different stimulus media, such as
static images, moving images, and videos upon research results [10].

A range of frameworks have been advanced to guide research in ever-more
situated and specialized contexts [11, 12]. Kunold [13], for instance, notes a
lack of principled ways for turning research insights into design principles
as the rationale for a framework for studying communication with social
robots. Frameworks have been advanced to guide research on complex topics like
group dynamics [14] or the formation of expectations of social robots [15].

HRI with mobile autonomous robots in real-world settings faces a range of
methodological difficulties arising from the high dimensionality of potential
factors. Factors found to have influenced real-world HRI with autonomous
robots range from the robot characteristics [16] to robot physical behavior
[17] to human-robot communication [18]. While real-world HRI knowledge
continues to advance, isolation and control of variables and context remains a
substantial challenge, posing risks to the applicability of HRI research.

A potential solution to this problem is to use more highly controlled
experimental setups in the laboratory or online [19]. The established validity
of online studies for specific categories of HRI research questions [9, 10] is
mitigated by its lack of fidelity of experience: seeing a video of an
autonomous robot will rarely involve the full range of experiences present in
real-world encounters. Laboratory studies, on the other hand, gain the ability
to control variables and present in-person robotic stimuli to participants,
but must trade the ecological validity of study setting inherent to research.
Online studies have high statistical power and can be relatively well-
controlled between participants, but have low ecological validity for studies
of autonomous mobile robots specifically. Lab-based studies have the complex
interactional possibilities of in-person studies, but trade statistical power
to do so. Real-world studies’ extremely high ecological validity is mitigated
substantially. This situation, summarized in Table I, forces researchers to
make difficult choices about the strengths and weaknesses of different study
modalities.

TABLE I: Summary of tradeoffs between video-based study and real-world study. |  Video-based Online Study |  Real-world Study
---|---|---
Pros |  • Reproducibility of stimulus • Fast recruitment • Ease of isolating factors Higher Statistical Power |  • Multimodal data (e.g. sensors, observation) • Longitudinal potential • Site-specific context Higher Ecological validity
Cons |  • Skills for creating video encounters required • Potential disconnection from specific contexts • Homogenous data (e.g. no sensors, observation) Lower Ecological Validity |  • Inherently Between subjects • Labor-intensive • Difficult to isolate factors Lower Statistical Power
Example Studies |  Babel _et al_. [9], Randall and Sabanovic [10] |  Liang _et al_. [16], Chen _et al_. [18]

Attempts to move outside the online/real-world dichotomy have yielded a range
of partial solutions, including realistic laboratory settings, ad hoc
incorporation of various modalities in a single study, or estimates of real-
world validity based on published studies of very different design. While
these approaches may increase real-world applicability, they can be difficult
to evaluate and compare. HRI-specific study design frameworks responsive to
the general move towards standardization [20] in the field are needed to
improve the efficiency and validity of real-world HRI studies of autonomous
robots.

##  III Vid2Real HRI Framework

The Vid2Real HRI framework offers HRI researchers a principled way to use the
complementary strengths of video-based and real-world research modalities in
studies such as Human-Robot Interaction or incidental Human-Robot Encounters
with autonomous robots. It characterizes the methodological particularities of
each modality for HRI studies of autonomous robots in real-world settings; and
defines the epistemological relationships between them. This section describes
the framework’s rationale, design, and potential and recommended uses.

###  III-A Statistical and Epistemological Rationale

Statistical best practice for performing a study requires a power analysis to
inform the estimated sample size required to achieve the desired statistical
power [6, 21]. Past HRI research has utilized this practice, which becomes
much easier if similar instruments are used for most studies. Wasted effort
due to insignificant results is potentially avoidable through statistical
techniques: accurate effect size estimates and power calculations can help
inform researchers whether their design is likely to observe the intended
effect. Statistical discipline, as urged by leading HRI methods reference
sources [22] dramatically increases the efficiency and quality of research
activity.

However, statistical best practice isn’t enough. Without a principled
framework for when and how to conduct a study online or in the field,
researchers risk a non-optimial blend of these modalities’ tradeoffs, shown in
table I. In contrast, the Vid2Real HRI framework is designed to enhance real-
world study outcomes by aligning the hypothesis and design of a video-based
study with untested assumptions of a target real-world study. This alignment,
described below and exemplified in section IV, is designed to achieve
commensurable results, wherein results from each study are informative and
predictive of the other. Vid2Real HRI thus takes an epistemological approach
to the design of research studies, focusing on producing knowledge of unknowns
and testing assumptions. In addition to facilitating statistical rigor, the
framework enables a research team to efficiently and iteratively improve their
knowledge of their subject and of their experimental intervention over a
series of studies, within or across research publications. The Vid2Real HRI
framework’s focus on alignment helps to identify and realize the synergistic
value of commensurable results in single studies and within a broader research
program. Video-based studies are used to produce highly specific knowledge
that help explain and isolate phenomena of interest in real-world HRI studies.
Unexpected results or events in real-world studies generate hypotheses for
refinement in future online studies. The Vid2Real HRI framework thus helps
researchers use their current state of knowledge to determine which modality
is most informative at a given stage of inquiry.

###  III-B Framework Description

Figure 1 provides an overview of the Vid2Real HRI framework. We specify that
video-based study designs should be aligned with a specific real-world study’s
hypotheses, design, and scenario, regardless of whether such a real-world
study is actually performed. Deliberate alignment with a real-world study
design makes video-based study results commensurable with and informative
about the real-world settings of interest.

We define _commensurable_ as a relative property that obtains between video
and real-world studies that produce directly comparable and mutually
predictive results. The framework aims to acheive commensurability between
video-based and real-world study designs by aligning variable(s), scenario,
and settings. This alignment ensures that similar results are obtainable, in
principle, in real-world settings. The degree of commensurability realized
between two studies aligned in this way is primarily a function of the
fidelity with which the video-based encounter surrogate evokes the real-world
encounter of interest for study participants.

We define _informative_ as a property of the hypothesis tested in the video-
based study, whereby the results have significant implications for real-world
study design. The sense of information invoked here is from an information-
theoretic sense: novel information is gained. Informativeness is, roughly, the
expected surprise weighted by expected frequency. Informative study designs
should thus test both assumptions, which are rarely expected to be violated
but produce large amounts of novel information when they are, and empirical
measurements, which produce small amounts of novel information reliably.

The _hypothetical real-world study design_ is defined as a version of the
video-based study able to be conducted in person using the same variable(s),
scenario, and setting. This study design is not carried out in all cases,
would be carried out after the online results are obtained, and likely would
be revised if carried out. The hypothetical real-world study design’s primary
function in the framework is as an alignment target for the video-based
design, enabling the accomplishment of commensurability and informativeness.
Follow-up real-world studies, if any, should have designs informed by the
Vid2Real HRI study results (otherwise, the real-world study’s value would be
primarily methodological, as they are in the present research).

The following paragraphs reference and explain the Vid2Real HRI phase labels
shown in fig. 1.

Figure 1: A schematic of the Vid2Real HRI process

a. Design. Beginning with an HRI research question, researchers identify a
_hypothesis_ and operationalize it in a _hypothetical real-world study design_
(Figure 1a). Researchers then develop a _commensurable_ video study hypothesis
and study design, iteratively revising the designs as needed. The video
stimulus is conceived as an encounter surrogate, and can be judged by its
capability to replicated participant experience intended in the hypothetical
real-world study. The characteristics of videos may vary significantly by
research question, so the Vid2Real HRI framework does not specify standard
methods. An example of creating videos for human-robot encounters research is
provided in Section IV.

b. Conduct and c. Evaluate. Once a commensurable video hypothesis and study
design are ready and tested, the study can be conducted (Figure 1b). Note that
standard best practices, such as obtaining institutional review board (IRB)
approval and piloting the design should be followed, and are not shown in
Figure 1. Due to the speed and relative cost-efficiency of participant
recruitment, a large amount of data can be collected in a short amount of
time. With this data collected, researchers can evaluate the commensurable
video study hypothesis (Figure 1c), producing findings (these may be
publishable or contribute to future publications, depending on their
significance).

The findings of Vid2Real HRI study can of course be published without real-
world replication if they are significant and novel. The insights produced by
the alignment of study design with a specific real-world setting aid in
interpretation of findings, the selection of future research questions, and
design of real-world of video-based studies of the same or related real-world
settings and scenarios. When warranted, the hypothetical real-world study
design may be modified in light of the online video study results,
supplementing the original results or constituting an independent research
contribution. Conducting the hypothetical real-world study design with little
modification, as done in the present paper, can characterize the
methodological validity of the framework in specific applications where the
applicability of the framework’s validity (demonstrated below) is uncertain.

##  IV Vid2Real HRI Online Study

The Vid2Real HRI framework was applied to a specific HRE research study on the
effects of socially compliant robot behavior conditions, operationalized as
mixtures of verbal cues and body language, on pedestrian perceptions of the
robot’s social intelligence and willingness to open a door for the robot. The
application study’s illustrative value and relevance to the strengths of the
Vid2Real HRI framework is the focus of its presentation in this paper; full
analysis of results and their implications for HRE research is presented
elsewhere.

###  IV-A Application Online Study Design

The study scenario is an incidental encounter with a quadruped robot requiring
human assistance to enter a building. Specifically, the robot is assisted by a
human pushing a button to automatically open the doors. Since the nearby human
has no obligation to assist the robot, we hypothesized that increased
perceived social intelligence would increase human compliance with the robot’s
need for assistance.

Four robot behavioral conditions operationalized differentially socially
compliant behaviors using verbal cues and body language:

  * •

Baseline: The walking robot stops at the entrance and waits for the nearby
human to push the button, without offering any indications that it needs
assistance.

  * •

Verbal: The walking robot stops at the entrance and says, _“Excuse me, can you
open the door for me?”_ to the nearby human, then waits for the human to push
the button.

  * •

Body Language: The walking robot stops at the entrance and turns its head
facing the nearby human, then turns its head back to look at the door, then
waits for the human to push the button.

  * •

Body Language + Verbal: The walking robot stops at the entrance and turns its
head facing the nearby human and says, _“Excuse me, can you open the door for
me?”_ , then turns its head back to look at the door and waits for the human
to push the button.

Figure 2: Sample frames from the videos of the Body Language (top) and Verbal
(Bottom) conditions.

####  IV-A1 Video and Real-World Alignment

To ensure the alignment of the video settings and the real-world scenarios,
the videos are shot from a first-person point-of-view. This decision is mainly
to support the need for the participants to imagine that they are the person
encountering the robot. The robot motion is also reproduced across the
conditions in order to maintain consistency. Additionally, the location where
the videos are shot is the same as the place where the future in vivo HRE
research will be conducted. Therefore, the ecological validity of this online
study is reserved, and the results are commensurable. The videos and a
detailed description of the study design are publicly available [23].

####  IV-A2 Questionnaire

The Perceived Social Intelligence (PSI) scale [24] was adopted as the
measurement of the effects of robot body language and verbal cues. According
to the authors’ suggestions, research can adopt a subset of PSI that suits the
research context and goals. We selected 8 of PSI’s 13 Social Information
Processing scales: (1) Social Competence, (2) Identifies Humans, (3)
Identifies Individuals, (4) Recognizes Human Behaviors, (5) Adapts to Human
Behaviors, (6) Predicts Human Behaviors, (7) Recognizes Human Cognitions, and
(8) Adapts to Human Cognitions. Other scales were not chosen because they were
not applicable to a first-person point-of-view video-based study.

In addition to PSI, two exploratory questions were presented with each study
condition. The first was a five-point Likert question, ”The person in the
video represents how you would have responded in the situation”, which was
included to assess the participants’ perceptions of the fidelity of the
human’s actions in the video to their own. The second was a free-form text
response question that asked the participants to answer how they would have
behaved in the situation that they just watched.

####  IV-A3 Study procedure

The participants were recruited on Prolific. They had to have no visual and
hearing difficulties, a high level of English fluency, at least a 95% approval
rate on Prolific, and currently live in the United States. The online study
used a within-subject design, and the order of the study conditions was
randomized to avoid the learning effect. The participants had to first consent
to participate, and then they would be presented with one study video and the
questionnaire. This step was randomly repeated four times. The total study
lasted around 10 minutes. The University of Texas at Austin IRB reviewed and
approved this study.

###  IV-B Application Study Results

####  IV-B1 Participants

The dataset of the application online study is publicly available [23] for
review and reuse. The Prolific platform recruited 420 participants. However,
upon careful investigation of response quality, 35 participants were excluded
due to incomplete answers or cheating behaviors, leaving 385 valid responses
for result analyses. Among the 385 participants, 194 participants identified
as female, and 191 as male, the age ranged from 19 to 75 (M = 38.53, SD =
12.86).

####  IV-B2 Human Compliance

The human compliance was measured using the 5-point Likert exploratory
question reported above. The average score are as follows: Baseline M = 3.371,
SD = 1.35, Verbal: M= 4.283, SD = 1.038, Body Language M = 3.698, SD = 1.281,
Body Language + Verbal M = 4.376, SD = 0.992. Using the one-way repeated
measures ANOVA test with Bonferroni correction (corrected significance level
is 0.008333)), the results showed that there was a significant main effect
(F(3, 1552) = 129.88, p <0.001, $\eta_{p}^{2}$ = 0.252). Pairwise comparisons
were also used as ad-hoc analyses. The results showed that only the pair of
Body Language + Verbal condition and Verbal condition did not have a
significant difference (p = 0.03497). Based on these findings, it was clear
that adding body language and verbal commands were efficient ways of
increasing human compliance in an HRE context. Meanwhile, the verbal command
had a significantly stronger effect than the body language.

####  IV-B3 PSI ratings

Given the within-subject design, the one-way repeated measures ANOVA test with
Bonferroni correction was used to evaluate the differences. The Body Language
+ Verbal condition was rated the highest (M = 3.826, SD = 0.661), followed by
the Verbal condition (M = 3.611, SD = 0.657), followed by the Body Language
condition (M = 3.601, SD = 0.595), and the Baseline condition was rated the
lowest (M = 3.151, SD = 0.784). The ANOVA test showed a main effect on PSI
overall rating (F(3, 1552) = 144.26, p <0.001, $\eta_{p}^{2}$ = 0.272),
indicating the robot’s socially compliant behaviors had positive influences on
its perceived social intelligence. Additionally, higher PSI seemed to indicate
higher human compliance. Therefore, the higher socially intelligent a robot
is, the more likely humans would comply and offer help when the robot asks for
one. Please note that full analyses, such as pairwise comparisons and ANOVA
tests on the subscales, are omitted from the scope of this study.

TABLE II: Power analyses and the estimated _n_ Intervention | Control |  $n$ for $\beta=.95$ | $\eta_{p}^{2}$ | Needed increase of $n$
---|---|---|---|---
Body language + Verbal | Baseline | 22 | 0.413 | 0.00%
Verbal | Baseline | 32 | 0.3043 | 45.45%
Body language | Baseline | 36 | 0.2782 | 63.64%
Body language + Verbal | Body language | 70 | 0.164 | 218.18%
Body language | Verbal | 6902 | 0.0019 | 31,272.73%

####  IV-B4 Power analyses

An initial contribution of the Vid2Real HRI framework is a reliable estimation
of the number of participants needed to observe a significant effect. Real-
world studies of incidental human-robot encounters almost always require
between-subject designs due to the nature of the scenario. Between-subject
designs typically require a larger sample size than within-subject designs,
threatening researchers’ ability to achieve their research goals. Drawing from
the average of the 8 PSI scale ratings, power analyses of the Baseline
condition compared to other conditions, and the Body Language condition
compared to the Body Language + Verbal condition were conducted. The results
are summarized in Table II. The results showed that 22 people would be
required to reach a power of 0.95 in a between-subject study of Baseline and
Body Language + Verbal condition. We also conducted an analysis of the Body
Language condition compared to the Verbal condition, and the result was that
6902 people (${F}(1,384)=0.723$, ${p}<0.395$, $\eta_{p}^{2}=0.00188$) would be
required. Please note that a between-subject design is chosen because it can
better reflect the natural settings of real-world scenarios than a within-
subject design.

##  V Real-World study

###  V-A Study Design

Following the Vid2Real HRI framework and the knowledge obtained from the
online video study, the Baseline and Body Language + Verbal conditions with a
between-subject design were chosen for the real-world study due to its
achievable sample size. The real-world study took place at the exact same
location where the videos were shot. The participants were instructed to start
at the same location as in the video and walk in the same direction. After
encountering the robot, the participants had the freedom to do whatever they
felt natural as pedestrians who incidentally encountered the robot. After this
interaction, the participants had to answer a questionnaire, which contained
the same items, except for the two exploratory questions, which were excluded
as they were not applicable. In replacement of the exploratory questions, a
camera was set up to record the interaction session, specifically focused on
how the participants reacted to the robot (_i.e_., whether or not they
complied).

The robot behaviors were also the same as in the video studies. However, given
the challenges of achieving full robot autonomy in such a real-world scenario,
and more importantly to ensure that the robot behaviour is as close as
possible to the video, the robot was teleoperated using a Wizard-of-Oz method.
One author of the present study was designated as the study manager, who faced
and gave instructions to the participants and pretended to start the study
session using a laptop that was visible to them, while another author of this
paper teleoperated the robot staying at a place where they could perfectly
view the study process while being hidden from the participants. The process
and setup were validated with pilot tests. The real-world study was approved
by The University of Texas at Austin IRB. Upon successful completion of the
study, all participants were entered into a draw to stand a chance to win a
$100 gift card, with one of them finally receiving the gift card.

###  V-B Study Result

A total of 26 participants were recruited, 13 experienced the Baseline
condition and 13 had the Body Language + Verbal condition, 13 identified as
males, 13 as females. The age ranged from 18 to 28 (M = 21.04, SD = 3.01).
Given the sample size and the between-subject design, the Mann-Whitney U test
was used to compare the PSI ratings between the conditions (Baseline: M =
3.433, SD = 0.680, Body Language + Verbal: M= 3.952, SD = 0.630). As expected,
the results showed a significant difference (z = 1.9801, p = 0.047, r = 0.39).
In terms of human compliance, 11 out of 13 participants opened the door in the
Body Language + Verbal condition, whereas only one participant did so in the
Baseline condition. Using Fisher’s exact test, the Body Language + Verbal
condition had a significantly higher proportion of participants who opened the
door (p <0.001).

##  VI Discussion

###  VI-A Vid2Real HRI Benefits in the Application Study

The benefits of the Vid2Real HRI’s Online Video modality on the application
HRE study are demonstrated through the data results and the accumulated
knowledge gained in the study material preparation process.

####  VI-A1 Aligned results

The video study’s statistical results serve as both independent findings and
empirical foundations for future in vivo research of autonomous robot HRI. The
Vid2Real HRI process of designing a video-based study commensurable with a
target real-world study shown in fig. 1 enabled this advantage by keeping
real-world application a central concern in video study design. Aligning an
online video study with a specific real-world study design is an effective way
to disentangle the high-dimensionality nature of HRI research of autonomous
robots in real-world settings. Future HRE research may also build upon the
findings obtained from online video studies and expand its scope to examine
other factors underlying social environments.

The results of the PSI scale comparisons and the power analyses are sources
for condition selection, especially for the between-subject design nature of
research in real-world settings. For instance, in a research context the same
as the application study, we learn that a study able to use the Baseline and
Body Language + Verbal conditions results for effect size estimation leads to
a reasonable sample size ($n=22$). This could inform future real-world studies
or enable researchers to confidently select a multi-condition $NxM$ design
without losing statistical significance by dividing their online study
population too finely.

Small effect sizes or non-significance between conditions revealed by our
approach were also informative. A comparison between the effect of body
language and verbal cues on pedestrian perceptions would be drastically
informed by the small effect size, the ${p}$ value, and the extremely large
sample size ($n=6,902$) implied by these results. This suggests that a new
study design would be required to distinguish the effects of body language and
verbal forms of socially compliant behavior upon human compliance. A Vid2Real
HRI study could rapidly inform selection of behavioral conditions suitable for
investigating such a question.

###  VI-B Optimizing Modality Strengths

Vid2Real HRI helped us navigate the strengths and weaknesses of video and
real-world study modalities (in table I). This section surveys our approach
and highlights insights for researchers seeking to adopt the Vid2Real HRI
framework in their research.

Preparing the video encounter surrogate in situ helped us refine the study
design and proactively control the eventual real-world encounters. Our first
videos revealed that pedestrians might not realize that the robot is
attempting to have their attention, the door might be opened from inside,
pedestrians might walk in front of the robot or follow it without interacting
with it (in our case, offering help). During the real-world study, several of
these issues happened again, making maintaining identical behavior across all
study sessions difficult. These led to small variations to the location and
timing of the robot’s behavior. Participants’ pace also naturally varied as
well, causing the robot to miss the opportune moment to perform its behaviors.
Some participants didn’t see the body language, instead only hearing the
verbal command. These exigencies are components of real-world studies’
ecological validity, but could obscure valid findings if they obscure the
effects of the study conditions. Confirming the effect using online study
before entering the field helped us anticipate and mitigate these potential
confounds through study design, while the power analysis helped us scope the
study with confidence. The seemingly ‘methodologically better’ alternative,
starting with a real-world study, would have risked selecting conditions
requiring infeasible sample sizes, resorting to a between-subjects design
(diminishing ecological validity), and/or recruiting too few participants.

We view our online study videos as encounter surrogates, aiming to replicated
the conditions of incidental encounters with high fidelity. We thus used a
first-person perspective of the encounter, rather than a third-person view of
someone encountering a robot. This removed the variable of the appearance of
the human as a potential confound, and the possibility of the participants
trying to interpret the human actor’s behaviors and be biased. Additionally,
the questionnaire instructed participants to imagine that they were the person
encountering the robot.

###  VI-C Summary of Framework Benefit

The Vid2Real HRI research framework offered a principled way to design a
video-based study of encounters with a quadruped robot aligned to a specific
real-world setting. The online study’s alignment with a specific real-world
study design enabled it to efficiently produce valid knowledge of real-world
encounters in a specific site. The online study results produced power
analysis-based estimates of required sample size that accurately represented
the statistical power obtained in the real-world study. Finally, the
researchers’ experiential insight into the importance of the direct ‘gaze’ of
the robot for the effectiveness of body language cues as perceived by humans
suggests limitations of the chosen platform that can be directly targeted in
future research. Together, these improvements increased the validity of
application study results to a specific real-world setting and clarified the
ways the results can directly inform future work.

###  VI-D Limitations and Future Work

While our real-world results suggest that our encounter surrogate was
sufficient to predict real-world encounter data, future research is needed to
understand effects of video different techniques upon surrogates’ fidelity.
This study only used video-based encounter surrogates due to their simplicity
and suitability for HRE research. Video-based surrogates will likely be less
informative to studies involving extensive user interaction with robots.
Interactive study modalities such as simulation and VR/AR experiences may be
effective encounter surrogates, but were not evaluated in this study.

##  VII Conclusion

Vid2Real HRI is a research framework that leverages the complementary benefits
of video-based and real-world autonomous robot HRI study designs. The Vid2Real
HRI framework was used to design an online, video-based study aligned with a
real-world study design in a specific site. The online study videos, conceived
of as encounter surrogates, utilized a first-person video of autonomous
behavior conditions planned for the real-world study. This validated key study
assumptions about the body language and verbal conditions’ effectiveness,
provided valuable characterization of the chosen survey scales over potential
alternatives, and enabled targeted refinement of the autonomy. The aligned
online and real-world study designs produced commensurable and informative
findings, as demonstrated by similarity of results and accuracy of sample size
estimates. The framework’s benefits compared favorably to potential
alternatives, such as lab-based studies or longitudinal in-situ
instrumentation of real-world sites. The Vid2Real HRI framework offers HRI
researchers a principled way to use the complementary strengths of video-based
and real-world research modalities to understand and improve real-world
encounters with autonomous robots.

## References

  * [1] E. Hauser, Y.-C. Chan, P. Chonkar, G. Hemkumar, H. Wang, D. Dua, S. Gupta, E. M. Enriquez, T. Kao, J. Hart, R. Mirsky, J. Biswas, J. Jiao, and P. Stone, ““what’s that robot doing here?”: Perceptions of incidental encounters with autonomous quadruped robots,” in _Proceedings of the First International Symposium on Trustworthy Autonomous Systems_. New York, NY, USA: ACM, July 2023.
  * [2] L. Dole and W. Ju, “Face and ecological validity in simulations: Lessons from Search-and-Rescue HRI,” in _Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems_ , ser. CHI ’19, no. Paper 451. New York, NY, USA: Association for Computing Machinery, May 2019, pp. 1–8.
  * [3] A. Biswas, A. Wang, G. Silvera, A. Steinfeld, and H. Admoni, “SocNavBench: A grounded simulation testing framework for evaluating social navigation.” [Online]. Available: https://doi.org/10.1145/3476413
  * [4] A. M. H. Abrams, P. S. C. Dautzenberg, C. Jakobowsky, S. Ladwig, and A. M. Rosenthal-von der Pütten, “A theoretical and empirical reflection on technology acceptance models for autonomous delivery robots,” in _Proceedings of the 2021 ACM/IEEE International Conference on Human-Robot Interaction_ , ser. HRI ’21. Association for Computing Machinery, pp. 272–280. [Online]. Available: https://doi.org/10.1145/3434073.3444662
  * [5] H. Kang, “Sample size determination and power analysis using the G*Power software,” _J. Educ. Eval. Health Prof._ , vol. 18, p. 17, July 2021.
  * [6] C. L. Bethel and R. R. Murphy, “Review of human studies methods in HRI and recommendations,” vol. 4, pp. 347–359. [Online]. Available: https://www.infona.pl//resource/bwmeta1.element.springer-6b23bd21-1cd1-3179-b67e-ad4cda63b545
  * [7] S. N. Woods, M. L. Walters, K. L. Koay, and K. Dautenhahn, “Methodological issues in HRI: A comparison of live and video-based methods in robot to human approach direction trials,” in _ROMAN 2006 - The 15th IEEE International Symposium on Robot and Human Interactive Communication_ , pp. 51–58. [Online]. Available: http://dx.doi.org/10.1109/ROMAN.2006.314394
  * [8] H. Gunes, F. Broz, C. S. Crawford, A. R.-v. der Pütten, M. Strait, and L. Riek, “Reproducibility in human-robot interaction: Furthering the science of HRI,” vol. 3, pp. 281–292. [Online]. Available: http://dx.doi.org/10.1007/s43154-022-00094-5
  * [9] F. Babel, J. Kraus, P. Hock, H. Asenbauer, and M. Baumann, “Investigating the validity of online robot evaluations: Comparison of findings from an one-sample online and laboratory study,” in _Companion of the 2021 ACM/IEEE International Conference on Human-Robot Interaction_ , ser. HRI ’21 Companion. Association for Computing Machinery, pp. 116–120. [Online]. Available: https://doi.org/10.1145/3434074.3447141
  * [10] N. Randall and S. Sabanovic, “A picture might be worth a thousand words, but it’s not always enough to evaluate robots,” in _Proceedings of the 2023 ACM/IEEE International Conference on Human-Robot Interaction_ , ser. HRI ’23. Association for Computing Machinery, pp. 437–445. [Online]. Available: https://doi.org/10.1145/3568162.3576970
  * [11] A. Rosenthal-von der Pütten and A. M. H. Abrams, _Empirical Methods in the Social Science for Researching Socially Interactive Agents_ , 1st ed. Association for Computing Machinery, vol. 37, pp. 19–76. [Online]. Available: https://doi.org/10.1145/3477322.3477325
  * [12] M. F. Damholdt, C. Vestergaard, and J. Seibt, “Testing for ‘anthropomorphization’: A case for mixed methods in human-robot interaction,” in _Springer Series on Bio- and Neurosystems_. Cham: Springer International Publishing, 2020, pp. 203–227.
  * [13] L. Kunold, “Seeing is not feeling the touch from a robot,” in _2022 31st IEEE International Conference on Robot and Human Interactive Communication (RO-MAN)_. ieeexplore.ieee.org, pp. 1562–1569. [Online]. Available: http://dx.doi.org/10.1109/RO-MAN53752.2022.9900788
  * [14] A. M. H. Abrams and A. M. R.-v. der Pütten, “I–C–E framework: Concepts for group dynamics research in human-robot interaction,” vol. 12, pp. 1213–1229. [Online]. Available: https://doi.org/10.1007/s12369-020-00642-z
  * [15] J. M. Berzuk and J. E. Young, “Clarifying social robot expectation discrepancy: Developing a framework for understanding how users form expectations of social robots,” in _Companion of the 2023 ACM/IEEE International Conference on Human-Robot Interaction_ , ser. HRI ’23. Association for Computing Machinery, pp. 231–233. [Online]. Available: https://doi.org/10.1145/3568294.3580078
  * [16] C. Liang, A. E. Ricci, H. Kress-Gazit, and M. F. Jung, “Lessons from a robot asking for directions in-the-wild,” in _Companion of the 2023 ACM/IEEE International Conference on Human-Robot Interaction_ , ser. HRI ’23. Association for Computing Machinery, pp. 617–620. [Online]. Available: https://doi.org/10.1145/3568294.3580159
  * [17] Y. Okafuji, Y. Ozaki, J. Baba, J. Nakanishi, K. Ogawa, Y. Yoshikawa, and H. Ishiguro, “Behavioral assessment of a humanoid robot when attracting pedestrians in a mall,” _Adv. Robot._ , vol. 14, no. 7, pp. 1731–1747, July 2022.
  * [18] Z. Chen, T. Fan, X. Zhao, J. Liang, C. Shen, H. Chen, D. Manocha, J. Pan, and W. Zhang, “Autonomous social distancing in urban environments using a quadruped robot,” _IEEE Access_ , vol. 9, pp. 8392–8403, 2021.
  * [19] B. Holman, A. Anwar, A. Singh, M. Tec, J. Hart, and P. Stone, “Watch where you’re going! gaze and head orientation as predictors for social robot navigation.” IEEE, 2021, pp. 3553–3559.
  * [20] M. Schrum, M. Ghuy, E. Hedlund-botti, M. Natarajan, M. Johnson, and M. Gombolay, “Concerning trends in likert scale usage in human-robot interaction: Towards improving best practices,” vol. 12, pp. 1–32. [Online]. Available: https://doi.org/10.1145/3572784
  * [21] A. Kahng, M. K. Lee, R. Noothigattu, A. Procaccia, and C.-A. Psomas, “Statistical foundations of virtual democracy,” in _Proceedings of Machine Learning Research_ , K. Chaudhuri and R. Salakhutdinov, Eds., vol. 97. PMLR, pp. 3173–3182. [Online]. Available: http://proceedings.mlr.press/v97/kahng19a.html
  * [22] C. L. Bethel, Z. Henkel, and K. Baugus, _Conducting Studies in Human-Robot Interaction_. Springer International Publishing, pp. 91–124. [Online]. Available: https://doi.org/10.1007/978-3-030-42307-0˙4
  * [23] Y.-C. Chan, S. Modak, E. Hauser, J. Biswas, and J. Hart, “Community embedded robotics: Vid2Real an online video dataset about perceived social intelligence in human robot encounters,” 2024.
  * [24] K. A. Barchard, L. Lapping-Carr, R. S. Westfall, A. Fink-Armold, S. B. Banisetty, and D. Feil-Seifer, “Measuring the perceived social intelligence of robots,” _J. Hum.-Robot Interact._ , vol. 9, no. 4, pp. 1–29, Sept. 2020.
  * [25] C. Bartneck, D. Kulić, E. Croft, and S. Zoghbi, “Measurement instruments for the anthropomorphism, animacy, likeability, perceived intelligence, and perceived safety of robots,” _International Journal of Social Robotics_ , vol. 1, no. 1, pp. 71–81, Jan. 2009.
  * [26] Contributors, “Openpcdet: An open-source toolbox for 3d object detection from point clouds,” 2020.
  * [27] M. F. Damholdt, C. Vestergaard, and J. Seibt, “Testing for ‘anthropomorphization’: a case for mixed methods in human-robot interaction,” _Human-robot interaction: evaluation methods and their standardization_ , pp. 203–227, 2020.

###  -A Pairwise Comparisons of Conditions by PSI Scores

Tables VIII, XII, IV, V, X, VI, XI, XIII and III show the pairwise comparison
of different interventions based on PSI scores.

TABLE III: Pairwise comparison - Social Competence Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.885 | 226.977 | <0.001
Base-Body | 0.348 | 18.212 | <0.001
Base-BL+V | 1.226 | 401.571 | <0.001
Verb-Body | 0.537 | 51.017 | <0.001
Verb-BL+V | 0.340 | 45.713 | <0.001
Body-BL+V | 0.877 | 118.539 | <0.001
TABLE IV: Pairwise comparison - Identifies Humans Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.802 | 190.848 | <0.001
Base-Body | 0.831 | 177.925 | <0.001
Base-BL+V | 1.018 | 258.512 | <0.001
Verb-Body | 0.028 | 0.481 | 0.488
Verb-BL+V | 0.215 | 34.166 | <0.001
Body-BL+V | 0.187 | 28.961 | <0.001
TABLE V: Pairwise comparison - Identifies Individuals Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.582 | 113.824 | <0.001
Base-Body | 0.571 | 93.503 | <0.001
Base-BL+V | 0.797 | 163.145 | <0.001
Verb-Body | 0.010 | 0.046 | 0.829
Verb-BL+V | 0.215 | 24.443 | <0.001
Body-BL+V | 0.226 | 27.822 | <0.001
TABLE VI: Pairwise comparison - Recognizes Human Behaviors Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.316 | 47.377 | <0.001
Base-Body | 0.351 | 58.324 | <0.001
Base-BL+V | 0.454 | 86.911 | <0.001
Verb-Body | 0.033 | 0.718 | 0.397
Verb-BL+V | 0.137 | 14.029 | <0.001
Body-BL+V | 0.104 | 9.507 | 0.002
TABLE VII: Godspeed [25] questions and response types Category | Question | Response
---|---|---
Anthropomorphism | Fake - Natural | 6 pt. bipolar
| Machinelike - Humanlike | 6 pt. bipolar
| Unconscious - Conscious | 6 pt. bipolar
| Artificial - Likelike | 6 pt. bipolar
|  Moving rigidly - Moving elegantly | 6 pt. bipolar
TABLE VIII: Pairwise comparison - Adapts to Human Behaviors Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.330 | 35.193 | <0.001
Base-Body | 0.270 | 25.814 | <0.001
Base-BL+V | 0.478 | 75.702 | <0.001
Verb-Body | 0.059 | 1.535 | 0.216
Verb-BL+V | 0.148 | 9.244 | 0.003
Body-BL+V | 0.207 | 22.368 | <0.001
TABLE IX: PSI [24] questionnaire questions and response type Scale |  Question | Response
---|---|---
Social Competence (SOC) |  This robot is socially competent | 5 pt. Likert
Identifies Humans (IH) |  This robot notices human presence | 5 pt. Likert
Identifies Individuals (II) |  This robot recognizes individual people. | 5 pt. Likert
Recognizes Human Behaviors (RB) |  This robot notices when people do things. | 5 pt. Likert
Adapts to Human Behaviors (AB) |  This robot adapts effectively to different things people do. | 5 pt. Likert
Predicts Human Behaviors (PB) |  This robot anticipates people’s behavior. | 5 pt. Likert
Recognizes Human Cognitions (RC) |  This robot can figure out what people think. | 5 pt. Likert
Adapts to Human Cognitions (AC) |  This robot adapts its behavior based upon what people around it know. | 5 pt. Likert
Exploratory questions |  |
Compliance likelihood |  The person in the video represents how you would have responded in the situation. | 5 pt. Likert
|  How would you have behaved in this situation? | Free Text
TABLE X: Pairwise comparison - Predicts Human Behaviors Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.143 | 5.415 | 0.021
Base-Body | 0.379 | 45.561 | <0.001
Base-BL+V | 0.358 | 34.13 | <0.001
Verb-Body | 0.236 | 18.793 | <0.001
Verb-BL+V | 0.216 | 17.303 | <0.001
Body-BL+V | 0.021 | 0.177 | 0.6739
TABLE XI: Pairwise comparison - Recognizes Human Cognitions Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.259 | 24.09 | <0.001
Base-Body | 0.400 | 68.286 | <0.001
Base-BL+V | 0.413 | 52.605 | <0.001
Verb-Body | 0.140 | 7.086 | 0.008
Verb-BL+V | 0.153 | 9.186 | 0.003
Body-BL+V | 0.013 | 0.063 | 0.802
TABLE XII: Pairwise comparison - Adapts to Human Cognitions Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.368 | 37.269 | <0.001
Base-Body | 0.340 | 36.078 | <0.001
Base-BL+V | 0.522 | 71.693 | <0.001
Verb-Body | 0.028 | 0.274 | 0.601
Verb-BL+V | 0.153 | 8.387 | 0.004
Body-BL+V | 0.181 | 12.954 | <0.001
TABLE XIII: Pairwise comparison - All Pair | Mean Difference | F statistic | p-value
---|---|---|---
Base-Verb | 0.461 | 167.924 | <0.001
Base-Body | 0.436 | 147.988 | <0.001
Base-BL+V | 0.658 | 271.385 | <0.001
Verb-Body | 0.024 | 0.723 | 0.395
Verb-BL+V | 0.197 | 50.745 | <0.001
Body-BL+V | 0.222 | 75.328 | <0.001
Figure 3: Overview of the methodology for recording videos

###  -B Questionnaire 1: PSI

Table IX shows the questions chosen from the PSI questionnaire’s various
scales, as well as the two exploratory questions that we added.

###  -C Questionnaire 2 - Godspeed

Table VII shows the questions chosen from the Godspeed questionnaire.

###  -D Questionnaire 3 - AMPH

Table XIV shows the questions chosen from the AMPH questionnaire.

###  -E Video Recording Methodology for Online Video Study

For the purposes of this study, the Wizard-of-Oz design was used. More
specifically, the robot operation was semi-autonomous, with the navigation
being manually teleoperated by an operator. These modules supplemented manual
operation:

  * •

Speech: This uses the python libraries (gTTs and pydub) to produce audio from
text on the fly.

  * •

Bodypose: Uses pointcloud-based object detection [26] to detect the observer
and leverages the Clearpath Spot-ROS wrapper (built upon Boston Dynamics API)
to modify the pose of the robot in a way that its head is “looking” at the
observer.

  * •

Motreplay: It uses a recorded bagfile and republishes the stream of motion
commands required to generate identical navigation motion for the robot.

TABLE XIV: AMPH [27] questionnaire questions and response type AMPH |  Question | Response
---|---|---
|  Would you name an everyday object? | 4 pt. Likert-like
|  Do you ever blame your computer for being uncooperative? | 4 pt. Likert-like
|  Do you believe that sometimes your computer sabotages your actions on purpose? | 4 pt. Likert-like
|  Do you find it understandable when people treat their car as if it were human? I.e. by giving it a name and referring to it as `reliable` and `helpful`? | 4 pt. Likert-like
|  Do you tend to feel grateful toward a technological object (your car, your computer, your mobile) if it has rescued you from a dangerous or difficult situaiton? | 4 pt. Likert-like
|  Would you ever believe that a mountain (such as Mount Everest) would set off a series of avalanches on mountain climbers if they disturb the peace of the mountain? | 4 pt. Likert-like
|  Do you believe that a tree can feel pain? | 4 pt. Likert-like
|  Do you believe that an insect has a soul that you need to respect? | 4 pt. Likert-like

Figure 3 shows the high-level overview of the methodology followed for
recording videos. To make the different conditions perfectly comparable, the
videos were shot in a way that preserves this consistency between the videos.
To do so, robot motion was reproduced across different conditions. The main
idea was to record a bagfile with the relevant rostopics while the robot
performs the baseline behavior, and then use Motreplay to generate the same
motion while we add other required behaviors depending on the condition we
were recording the video for on the fly. However, due to differing robot
behaviors among the conditions, the Baseline condition and Verbal condition
used one bagfile, while the Body Language condition and the Body Language +
Verbal condition used another bagfile as they required additional behaviors.