This paper is dedicated to the memory of Gerard Baur, one of the founders of
the UPC physics, who passed away recently.]

# Light-by-light scattering in ultraperipheral collisions of heavy ions with
future FoCal and ALICE 3 detectors

Paweł Jucha<EMAIL_ADDRESS>Institute of Nuclear Physics Polish
Academy of Sciences,
ul. Radzikowskiego 152, PL-31-342 Kraków, Poland  Mariola Kłusek-Gawenda
<EMAIL_ADDRESS>Institute of Nuclear Physics Polish Academy of
Sciences,
ul. Radzikowskiego 152, PL-31-342 Kraków, Poland  Antoni Szczurek
<EMAIL_ADDRESS>Institute of Nuclear Physics Polish Academy of
Sciences,
ul. Radzikowskiego 152, PL-31-342 Kraków, Poland  College of Mathematics and
Natural Sciences, University of Rzeszów,
ul. Pigonia 1, PL-35-310 Rzeszów,Poland

###### Abstract

We discuss possible future studies of photon-photon (light-by-light)
scattering using a planned FoCal and ALICE 3 detectors. We include different
mechanisms of $\gamma\gamma\to\gamma\gamma$ scattering such as double-hadronic
photon fluctuations, $t/u$-channel neutral pion exchange or resonance
excitations ($\gamma\gamma\to R$) and deexcitation ($R\to\gamma\gamma$). The
broad range of (pseudo)rapidities and lower cuts on transverse momenta open a
necessity to consider not only dominant box contributions but also other
subleading contributions. Here we include low mass resonant $R=\pi^{0}$,
$\eta$, $\eta^{\prime}$ contributions. The resonance contributions give
intermediate photon transverse momenta. However, these contributions can be
eliminated by imposing windows on di-photon invariant mass. We study and
quantify individual box contributions (leptonic, quarkish). The
electron/positron boxes dominate at low $M_{\gamma\gamma}~{}<$ 1 GeV di-photon
invariant masses. The PbPb$\to$PbPb$\gamma\gamma$ cross section is calculated
within equivalent photon approximation in the impact parameter space. Several
differential distributions are presented and discussed. We consider four
different kinematic regions. We predict cross section in the (mb-b) range for
typical ALICE 3 cuts, a few orders of magnitude larger than for the current
ATLAS or CMS experiments. We also consider the two-$\pi^{0}$ background which
can, in principle, be eliminated at the new kinematical range for the ALICE 3
measurements by imposing dedicated cuts on di-photon transverse momentum
and$/$or so-called vector asymmetry.

Light-by-light scattering, ALICE 3, FoCal

##  I  Introduction

The photon-photon scattering, often called light-by-light scattering, is an
interesting quantum effect. Till recently, it was not studied experimentally.
It was a dream for the laser community. The works in this direction by the
laser community are going on Doyle et al. (2022). The possibility of light-by-
light studies in ultraperipheral heavy ion collisions was proposed in
d’Enterria and da Silveira (2013); Kłusek-Gawenda et al. (2016a). Inspired by
the theoretical analyses it was then studied experimentally by the ATLAS
Aaboud and others (ATLAS Collaboration) and CMS Sirunyan and others (CMS
Collaboration) collaborations. Statistics improved data were presented in Aad
and others (ATLAS Collaboration, ATLAS Collaboration). The experimental data
can be almost explained taking into account only QED box contributions. The
ATLAS and CMS measurements can register only transverse momenta of photons
larger than about $2-2.5$ GeV, i.e. automatically large diphoton masses. As
matter of course, this means small statistics of several tens of events. It
was discussed in Kłusek-Gawenda et al. (2019) what the ALICE and LHCb
collaborations could do for smaller di-photon invariant masses. According to
our knowledge, the experimental analysis of the ALICE collaboration is in
progress. The previous studies of nuclear reactions considered almost
exclusively so-called box contributions. Other underlying mechanisms were
discussed rather only for $\gamma\gamma\to\gamma\gamma$ scattering in Kłusek-
Gawenda et al. (2016a, 2019, b); Lebiedowicz and Szczurek (2017a). The authors
of Coelho et al. (2020) considered also diffractive mechanisms of production
of two photons associated however with extra hadronic emissions. The
$\gamma\gamma\to\gamma\gamma$ is also interesting in the context of searching
for effect beyond Standard Model Baldenegro et al. (2018).

In this analysis, we explore what future FoCal Loizides et al. (2020) and
ALICE 3 Musa et al. (2022) detectors could do in this respect. A forward
electromagnetic calorimeter is planned as an upgrade to the ALICE experiment
for data-taking in 2027-2029 at the LHC. The FoCal will cover pseudorapidities
range of $3.4<\eta<5.8$. Runs 5 and 6 will allow to measure more than five
times the present Pb-Pb luminosity. This increase of luminosity, in
combination with improved detector capabilities, will enable the success of
the physical program planned in ALICE 3. A significant feature of FoCal and
ALICE 3 programs is the ability to measure photons in relatively low (starting
from a few MeV) transverse momenta.

In the present paper we will consider not only box contributions but also
contributions of the other mechanisms (double photon hadronic fluctuations,
$\pi^{0}$ t$/$u-channel exchanges, two-gluon exchange, etc.). We will explore
whether the other mechanisms that are less under theoretical control (non-
perturbative pQCD domain), can be observed experimentally with the future
apparatus. We will try to find conditions how to relatively enhance them
compared to the box contributions to be observed in heavy ion UPC.

##  II  Sketch of the formalism

###  II.1 Elementary cross section and general remarks

The Weizsäcker-Williams formula (see subsection II.3) is based on the
knowledge of the elementary $\gamma\gamma\to\gamma\gamma$ cross section. The
angular distribution of $\gamma\gamma\to\gamma\gamma$ depends on
$z=\cos(\theta)$ where $z$ is in range $(-1,1)$, and $\theta$ is the
scattering angle, and the mass of the particles produced in the process
$M_{\gamma\gamma}$. Determination of the elementary cross section requires a
calculation of photon-photon scattering amplitudes derived from Feynman
diagrams of fermion loops. As shown in Kłusek-Gawenda et al. (2016b), higher-
order processes such as VDM-Regge and 2-Gluon exchange can be important at
energies above 30 GeV, while in the low-energy regime, these processes should
not play a significant role.

The distribution of the elementary cross section for low energies is known and
has been shown at least in Kłusek-Gawenda et al. (2016a), but so far, no one
has used this for light-by-light scattering calculation below 5 GeV due to
experimental limitations. Moreover, this is the first paper where the
influence of the different types of particles generated in the loop on total
cross section is shown explicitly.

In the present work, the minimum mass of invariant produced photons is $10$
MeV, which, according to the formula $p_{t,min}=M_{min}/2$, means that the
minimum value of the transverse momentum can be 5 MeV. The elementary cross
section here is calculated for unpolarised photons. To do this, all $16$
photon helicity combinations of the cross section$/$amplitude must be added
up. In fact, due to symmetries, it is sufficient to count only five
combinations and then add them up with the corresponding weights:

$\displaystyle\sum_{{\lambda_{1},\lambda_{2},\lambda_{3},\lambda_{4}}}\left|\mathcal{A}^{\gamma\gamma\rightarrow\gamma\gamma}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}\right|^{2}$
$\displaystyle=$ $\displaystyle
2\left|\mathcal{A}_{++++}^{fermions}\right|^{2}+2\left|\mathcal{A}_{+--+}^{fermions}\right|^{2}$
(1) $\displaystyle+$ $\displaystyle
2\left|\mathcal{A}_{+-+-}^{fermions}\right|^{2}+2\left|\mathcal{A}_{++--}^{fermions}\right|^{2}+8\left|\mathcal{A}_{+-++}^{fermions}\right|^{2}\;.$

Elementary cross section calculations for the box contribution were carried
out using FormCalc and LoopTools libraries based on Mathematica software.

###  II.2 Double-photon hadronic fluctuations

This component was calculated for the first time in Kłusek-Gawenda et al.
(2016a, b) assuming vector dominance model. In this approach, the amplitude
for the process is given as:

$\displaystyle{\cal M}$ $\displaystyle=$
$\displaystyle\Sigma_{i,j}C_{i}^{2}C_{j}^{2}\left(C_{{\bf
I\\!P}}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!P}}(t)-1}F(t)+C_{{\bf
I\\!R}}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!R}}(t)-1}F(t)\right)\;,$
(2) $\displaystyle+$ $\displaystyle\Sigma_{i,j}C_{i}^{2}C_{j}^{2}\left(C_{{\bf
I\\!P}}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!P}}(u)-1}F(u)+C_{{\bf
I\\!R}}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!R}}(u)-1}F(u)\right)\;.$

In the simplest version of the model $i,j=\rho^{0},\omega,\phi$ (only light
vector mesons are included). The couplings $C_{i},C_{j}$ describe the
$\gamma\to V_{i/j}$ transitions that are calculated based on vector meson
dilepton width. $C_{{\bf I\\!P}}$ and $C_{{\bf I\\!R}}$ are extracted from the
Regge factorization hypothesis (see e.g. Szczurek et al. (2002); Szczurek and
Speth (2003)).

It was shown in Kłusek-Gawenda et al. (2016a) that the component is
concentrated mainly at small photon transverse momenta which at not too small
subsystem energies corresponds to $z\approx\pm$ 1\. The Regge trajectories are
usually written in a linear form:

$\displaystyle\alpha_{{\bf I\\!P}}(t/u)=\alpha_{{\bf I\\!P}}(0)+\alpha_{{\bf
I\\!P}}^{\prime}t/u\;,$ $\displaystyle\alpha_{{\bf I\\!R}}(t/u)=\alpha_{{\bf
I\\!R}}(0)+\alpha_{{\bf I\\!R}}^{\prime}t/u\;.$ (3)

These linear forms are valid at not too large $|t|$ or $|u|$. At large $|t|$
or $|u|$ the energy dependent factors are artificially small. Therefore here
where we explore it more, we propose to smoothly switch off the $t/u$
dependent terms in (3) at $t\sim$ -0.5 GeV2 and $u\sim$ -0.5 GeV2. The actual
place where it should be done is not known precisely. Another option would be
to use $\sqrt{t/u}$ trajectories Brisudová et al. (2000); Brisudova et al.
(2003).

We also wish to analyze whether more heavy vector mesons such as $J/\psi$ can
give a sizeable contribution.

For example, for the double $J/\psi$ fluctuations (both photons fluctuate into
virtual $J/\psi$ mesons) we take the following Ansatz for the helicity
conserving amplitude:

$\displaystyle{\cal M}_{VDM}^{J/\psi J/\psi}$ $\displaystyle=$ $\displaystyle
g_{J/\psi}^{2}C_{{\bf
I\\!P}}^{J/\psi}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!P}}^{J/\psi
J/\psi}(t)-1}F_{J/\psi J/\psi{\bf I\\!P}}^{H}(t)F_{J/\psi J/\psi{\bf
I\\!P}}^{H}(t)$ (4) $\displaystyle+$ $\displaystyle g_{J/\psi}^{2}C_{{\bf
I\\!P}}^{J/\psi}\left(\frac{s}{s_{0}}\right)^{\alpha_{{\bf I\\!P}}^{J/\psi
J/\psi}(u)-1}F_{J/\psi J/\psi{\bf I\\!P}}^{H}(u)F_{J/\psi J/\psi{\bf
I\\!P}}^{H}(u)\;.$

In this case (double $J/\psi$ fluctuations) only pomeron can be exchanged (no
subleading reggeons are possible due to the $c\bar{c}$ structure of $J/\psi$
mesons). In this case, for simplicity, we take the simplified trajectories as

$\alpha_{{\bf I\\!P}}^{J/\psi J/\psi}(t)=\alpha_{{\bf I\\!P}}^{J/\psi
J/\psi}(u)=\alpha_{{\bf I\\!P}}^{J/\psi J/\psi}(0)\;.$ (5)

Here the $t/u$ dependencies of the trajectories are totally ignored. In
numerical calculations we take $\alpha_{{\bf I\\!P}}^{J/\psi
J/\psi}(0)=1.3-1.4$ (typical hard pomeron). Since the $J/\psi$ mesons are far
off-mass-shell and more compact than light vector mesons also the form factors
must be modified. Here we take them in the form:

$\displaystyle F_{J/\psi J/\psi{\bf
I\\!P}}^{H}(t)=\exp\left(\frac{t-m_{J/\psi}^{2}}{\Lambda_{J/\psi}^{2}}\right)\;,$
(6) $\displaystyle F_{J/\psi J/\Psi{\bf
I\\!P}}^{H}(u)=\exp\left(\frac{u-m_{J/\psi}^{2}}{\Lambda_{J/\psi}^{2}}\right)\;.$
(7)

Please note that the form factors are normalized to 1 on the meson ($J/\psi$)
mass shell. One could also use monopole-like form factors. These form factors
drastically reduce the $J/\psi J/\psi$ component of the amplitude in
comparison to light vector meson components. However, due to compactness of
$J/\psi$ we expect $\Lambda_{J/\psi}$ to be large. In the calculations
presented here, we take $\Lambda_{J/\psi}=2$ GeV for illustration. The actual
number is not well known. Also the normalization parameter $C_{{\bf
I\\!P}}^{J/\psi}$ is not well known. It is expected to be smaller than for
light vector mesons.

In a similar fashion, one could include one $J/\psi$ fluctuation and one light
vector meson fluctuation. However, there the choice of trajectories is
unclear. We will leave these components for future detailed studies.

Finally, let us discuss the helicity structure of the double photon hadronic
fluctuation amplitude. We write:

$\displaystyle{\cal
M}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}^{(t)}$ $\displaystyle=$
$\displaystyle
A(t)\;\delta_{\lambda_{1}\lambda_{3}}\delta_{\lambda_{2}\lambda_{4}}\;,$ (8)
$\displaystyle{\cal
M}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}^{(u)}$ $\displaystyle=$
$\displaystyle
A(u)\;\delta_{\lambda_{1}\lambda_{4}}\delta_{\lambda_{2}\lambda_{3}}\;.$ (9)

$A(t)$ and $A(u)$ are given explicitly in (2). Then the total double VDM
amplitude, including $t$ and $u$ processes, reads:

${\cal
M}^{VDM}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}=\frac{1}{\sqrt{2}}\left({\cal
M}^{VDM,(t)}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}+{\cal
M}^{VDM,(u)}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}\right)\;.$ (10)

Having the double VDM helicity amplitudes, we can add different mechanisms
coherently:

${\cal M}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}={\cal
M}^{boxes}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}+{\cal
M}^{VDM}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}+{\cal
M}^{\pi^{0}}_{\lambda_{1}\lambda_{2}\to\lambda_{3}\lambda_{4}}+...\;.$ (11)

In the following, we shall discuss the sum of the larger two components (boxes
and VDM) and quantify their interference effects.

###  II.3 Nuclear cross section

In the present paper, the nuclear cross section is calculated using equivalent
photon approximation (EPA) in the b-space. In this approach, the di-photon
cross section can be written as (see Kłusek-Gawenda and Szczurek (2010)):

$\displaystyle\frac{d\sigma(PbPb\to
PbPb\gamma\gamma)}{dy_{\gamma_{1}}dy_{\gamma_{2}}dp_{t,\gamma}}$
$\displaystyle=$
$\displaystyle\int\frac{d\sigma_{\gamma\gamma\to\gamma\gamma}(W_{\gamma\gamma})}{dz}N(\omega_{1},b_{1})N(\omega_{2},b_{2})S^{2}_{abs}(b)$
(12) $\displaystyle\times$ $\displaystyle
d^{2}bd\bar{b_{x}}d\bar{b_{y}}\frac{W_{\gamma\gamma}}{2}\frac{dW_{\gamma\gamma}dY_{\gamma\gamma}}{dy_{\gamma_{1}}dy_{\gamma_{2}}dp_{t,\gamma}}dz\;,$

where $\bar{b}_{x}=\left(b_{1x}+b_{2x}\right)/2$ and
$\bar{b}_{y}=\left(b_{1y}+b_{2y}\right)/2$. The relation between
$\vec{b}_{1}$, $\vec{b}_{2}$ and impact parameter:
$b=|\vec{b}|=\sqrt{|\vec{b}_{1}|^{2}+|\vec{b}_{2}|^{2}-2|\vec{b}_{1}||\vec{b}_{2}|\cos\phi}$.
Absorption factor $S^{2}_{abs}(b)$ is calculated as:

$\displaystyle S^{2}_{abs}(b)=\Theta(b-b_{max})$ (13)

or

$\displaystyle S^{2}_{abs}(b)=exp\left(-\sigma_{NN}T_{AA}(b)\right)\;,$ (14)

where $\sigma_{NN}$ is the nucleon-nucleon interaction cross section, and
$T_{AA}(b)$ is related to the so-called nuclear thickness, $T_{A}(b)$,

$T_{AA}\left(|\vec{b}|\right)=\int d^{2}\rho
T_{A}\left(\vec{\rho}-\vec{b}\right)T_{A}\left(\rho\right),$ (15)

and the nuclear thickness is obtained by integrating the nuclear density

$T_{A}\left(\vec{\rho}\right)=\int\rho_{A}\left(\vec{r}\right)dz,\hskip
14.22636pt\vec{r}=\left(\vec{\rho},z\right)\;,$ (16)

where $\rho_{A}$ is the nuclear charge distribution. The nuclear photon fluxes
$N(\omega_{1},b_{1})$ and $N(\omega_{2},b_{2})$ are calculated with realistic
charge distribution, as described in Kłusek-Gawenda and Szczurek (2013).

So far, in our previous works, we presented UPC results only with a sharp cut
on the impact parameter, which reflects the distance between two nuclei with a
value equal to exactly two radii of the nuclei, i.e. $b>14$ fm for Pb+Pb
collisions. Due to the no homogeneous nuclear charge distribution, it seems to
be more reasonable to use the absorption factor given by Eq. (14).

###  II.4 Background contribution

It was discussed in Kłusek-Gawenda et al. (2019) that the
$\gamma\gamma\to\pi^{0}(\to 2\gamma)\pi^{0}(\to 2\gamma)$ reaction constitutes
a difficult background for the $\gamma\gamma\to\gamma\gamma$ measurements at
intermediate $M_{\gamma\gamma}$. How to calculate the cross section for
$\gamma\gamma\to\pi^{0}\pi^{0}$ reaction was discussed in Klusek-Gawenda and
Szczurek (2013) and will be not repeated here. The calculation of the
background proceeds in three steps. First the cross section for
$\gamma\gamma\to\pi^{0}\pi^{0}$ is calculated (for details see Klusek-Gawenda
and Szczurek (2013)). Next the cross section for $AA\to AA\pi^{0}\pi^{0}$ is
computed in the equivalent photon approximation in an analogous way as
described in the previous subsection. Finally the simulation of both $\pi^{0}$
decays is performed and combined distributions of one photon from the first
$\pi^{0}$ and one photon from the second $\pi^{0}$ are constructed.

##  III  Results - Elementary cross section

(a) (b)

Figure 1:  Elementary cross section (in pb) as a function of energy. Results
for fermionic boxes are shown over a wide range of energies (a) - linear scale
and focusing on the MeV range (b) - where logarithmic scale is used. The total
cross section (blue solid line) is split somewhat artificially into quarks
(green solid line), electrons (red dashed line), electrons and muons (red
dotted line), and leptons (red solid line) contributions.

Treating photons as massless particles, one can expect the absence of a
minimum energy value, which is determined by the kinematical threshold. In
Fig. 1 we show the dependence of the elementary cross section on energy in the
$\gamma\gamma$ system. Fig. 1(a) demonstrates that putting a cut on the energy
of the two-photon system (the red dashed vertical line indicates the value of
$W_{\gamma\gamma}=5$ GeV), we automatically get rid of a significant signal
contribution. The pointed limitation is due to the existing restriction of the
detectors measuring light-by-light scattering in the ATLAS and CMS
experiments. Focusing on the details of box contribution, Fig. 1(b), we show
individual contributions of different boxes (electron, muon, quarks). One can
see that at low diphoton invariant masses, the electronic loops dominate. The
quarkish loops become sizeable only at $W_{\gamma\gamma}>$ 1 GeV. At an energy
of $W_{\gamma\gamma}>2m_{\tau}$ one can observe a slight enhancement of the
fermionic contribution, which illustrates the presence of $\tau$ leptons in
the loop.

In Fig. 2 we show $d\sigma/dz$ for $\gamma\gamma\to\gamma\gamma$ for (a)
boxes, (b) double hadronic fluctuation calculated within the VDM-Regge
approach and (c) the $\pi^{0}$-exchange calculated as in Ref. Lebiedowicz and
Szczurek (2017b). Results are presented for five fixed values of energy in the
range of $(1-50)$ GeV. At larger energies the VDM contribution peaks at $z=\pm
1$. On the other hand, the $\pi^{0}$ exchange contribution has minima at
$z=\pm 1$ which is due to the structure of corresponding vertices. The latter
contribution is relatively small. In general, the box contributions dominate,
especially for low photon-photon scattering energies. At larger scattering
energies ($W_{\gamma\gamma}>2$ GeV) the VDM contribution competes with the box
contributions only at $z\sim\pm 1$. Can one expect in this context sizeable
interference effects of both mechanisms?

(a) (b) (c)

Figure 2: $cos(\theta)$ distributions for (a) boxes, (b) double hadronic
fluctuations and (c) $\pi^{0}$ exchange for different energies
$W=1,2,5,10,20,50$ GeV.

Now we wish to concentrate briefly on second biggest in Fig.2 contribution,
double photon fluctuations. We include both light vector mesons $\rho^{0}$,
$\omega$, $\phi$) as well as $J/\psi$ (one or two) as decribed in the
theoretical section. Our results, for two collision energies ($W=2,5$ GeV),
are shown in Fig.3. The dotted line includes only light vector meson
fluctuations, the dashed line in addition double $J/\psi$ fluctuations and the
solid line all combinations of photon fluctuations. Inclusion of $J/\psi$
meson fluctuations leads to an enhancement of the cross section at -0.5 $<z<$
0.5. The enhancement is more spectacular for larger collsion energy. The
corresponding cross section there is, however, much smaller than the box
contribution (see Fig.2).

(a) (b)

Figure 3: Modification of $d\sigma/dz$ due to including fluctuations with
virtual $J/\psi$ mesons: (a) $W=2$ GeV, (b) $W=5$ GeV. The top solid line
includes all components (light (l) and heavy (h) vector mesons), the dotted
line only light vector mesons.

Now we wish to quantify how much is the box result changed when adding the
VDM-Regge contribution. In Fig. 4 we show the ratio of cross sections when
including the VDM-Regge contribution to that for box contribution only. In
this calculation, only the helicity contributions that are active in the VDM
component (6 combinations) are included. The red line represents the
incoherent sum, while the blue line also includes interference effects. In
this calculation, the so-called “sqrt” trajectories Brisudova et al. (2003);
Brisudová et al. (2000) were used. We observe a negative interference effect.
Adding the remaining contributions would lead to additional deviations.

Figure 4: The ratio of the coherent (blue) and incoherent (red) sum of the box
and VDM-Regge contributions divided by the cross section for the box
contribution alone for $W=5$ GeV.

##  IV  Results - nuclear cross section

Now we go to nuclear UPC and will show our results for four experimental
kinematic conditions, each in a separate subsection.

####  IV.0.1 ATLAS and CMS kinematics

(a)

(b)

(c)

Figure 5:  Differential cross section as a function of two-photon invariant
mass at $\sqrt{s_{NN}}=5.02$ TeV. (a) The ATLAS experimental data are
collected with theoretical results including a sharp cut on impact parameter
($b>14$ fm - solid black line) and smooth nuclear absorption factor $S^{2}(b)$
(dash-dotted red line). For completeness, results that are obtained with the
help of Eq. (12) are compared with results from SuperChic Harland-Lang et al.
(2020). The right panel shows two ratios: (b) results from our approach
comparing sharp and smooth cut-off on impact parameter and (c) SuperChic
outcome to our results, using a smooth representation of the gap survival
factor.

We start by confronting our calculations with the current ATLAS data Aad and
others (ATLAS Collaboration). Fig. 5(a) shows di-photon invariant mass
distribution Aad and others (ATLAS Collaboration). This result slightly
depends on the treatment of absorption corrections in the $b$-space. The
results of the two different approximations (as described in the figure
caption) almost coincide. For comparison, we show results obtained with
SuperChic generator Harland-Lang et al. (2020). We get a reasonable agreement
taking into account relatively large error bars of experimental data (small
statistics). Right panel of Fig. 5 presents the ratio of nuclear results from
our approach (Eq. (12)) comparing smooth cut-off (Eq. (14)) and sharp cut on
impact parameter ($b>14$ fm) corresponds to results from SuperChic generator
Harland-Lang et al. (2020). The difference between results including smooth
and sharp cut in ultraperipheral condition becomes larger with larger value of
invariant mass, Fig. 5(b). However, applying the same type of the condition to
the impact parameter, i.e. comparing the results from the SuperChic generator
and our calculation, gives a difference of about $2\%$. A similar conclusion
arises after comparing the total cross sections listed in Tab. 1. Taking into
account the possibility of different initial UPC condition, the used methods
describe the experimental data of ATLAS Aaboud and others (ATLAS
Collaboration); Aad and others (ATLAS Collaboration, ATLAS Collaboration) and
CMS Sirunyan and others (CMS Collaboration) in a similar way.

Experiment |  $p_{t,min}$ [GeV] | UPC condition |  $\sigma_{tot}$ [nb] |
---|---|---|---|---
ATLAS | 2.5 | b $>$ 14 fm | 81.062 $\pm$ 0.05 |
|  | S2(b) Eq. (14) | 78.092 $\pm$ 0.05 |
|  | SuperChick | 76.421 $\pm$ 0.074 |
CMS | 2 | b $>$ 14 fm | 105.986 $\pm$ 0.067 |
|  | S2(b) | 102.104 $\pm$ 0.057 |
|  | SuperChick | 100.101 $\pm$ 0.144 |
Table 1: Total cross section for PbPb$\rightarrow$PbPb$\gamma\gamma$ in nb
obtained in different approaches for experimental ATLAS/CMS kinematics:
collision energy $\sqrt{s_{NN}}=5.02$ TeV, di-photon invariant mass
$M_{\gamma\gamma}>5$ GeV, photon rapidity $|y|<2.4$. ATLAS and CMS have
detected photons in different range of transverse momenta.

In Fig. 6 we show results with a sharp cut-off, $b>14$ fm, and when including
the smooth dependence of $S^{2}_{abs}(b)$ on impact parameter. In Fig. 6(a),
we show somewhat academic impact parameter distribution (not measureable)
while in Fig. 6(b), rapidity distribution of outgoing system,
$Y_{\gamma\gamma}=(y_{1}+y_{2})/2$. Only small differences due to the
treatment in the $b$-space (about $(3-4)\%$) at midrapidities can be observed.

(a) (b)

Figure 6:  (a) Impact parameter and (b) rapidity distribution for UPC of lead-
lead at collision energy $\sqrt{s_{NN}}=5.02$ TeV. The solid line corresponds
to a sharp cut on the impact parameter and the red dash-dotted line is for the
absorption factor as given by Eq. (14).

Having described the ATLAS data, we wish to discuss new unexplored kinematics
regions.

####  IV.0.2 Broad range of rapidity, full phase space

Now we go to the somewhat broader range of rapidity and allow for very small
transverse momenta. In Fig.7 we show two-dimensional distribution in
$(M_{\gamma\gamma},p_{t,\gamma})$. We observe a strong enhancement for
$M_{\gamma\gamma}\approx 2p_{t}$, which infers that small $p_{t,\gamma}$ means
automatically small $M_{\gamma\gamma}$ and vice versa.

Figure 7:  Two-dimensional distribution in photon transverse momentum and di-photon invariant mass for UPC of lead-lead in a wide photon rapidity range $y\in(-8,8)$, starting from $p_{t}>5$ MeV. |  $\sigma_{tot}$ [mb] |
---|---|---
Total | 91.675 $\pm$ 0.023 |
electrons+muons | 41.597 $\pm$ 0.010 |
electrons | 39.163 $\pm$ 0.010 |
quarks | 12.483 $\pm$ 0.003 |
Table 2: Total cross section in mb for PbPb$\rightarrow$PbPb$\gamma\gamma$ for
different fermionic contributions artificially separated. Here collision
energy $\sqrt{s_{NN}}=5.02$ TeV, di-photon invariant mass
M${}_{\gamma\gamma}=(0.01-1)$ GeV, photon transverse momentum p${}_{t}>5$ MeV
and photon rapidity $|y|<8$.

In Fig.8 we show different distributions in (a) $M_{\gamma\gamma}$, (b)
$p_{t}$ and in (c) $y_{\gamma}$. In this figure we present decomposition into
different loop contributions (leptons, quarks). The electron/positron loops
dominate at low $M_{\gamma\gamma}$ and low $p_{t}$. Despite the noticeable
difference between leptonic and quarkonic contribution, their coherent sum
contributes much more than the leptonic contribution alone. Looking at the
total cross section values in Tab. 2, although the quark contribution is more
than twice as small as the lepton contribution ($\sigma_{tot}^{quarks}\approx
30\%\,\sigma_{tot}^{leptons}$), summing over the helicities for leptonic and
quarkish boxes, yields a result that is more than twice bigger than the lepton
contribution ($\sigma_{tot}^{leptons}\approx 45\%\,\sigma_{tot}^{fermions}$).
These cross sections are calculated for the di-photon invariant mass range up
to $1$ GeV.

(a) (b) (c)

Figure 8:  (a) Di-photon invariant mass, (b) photon transverse momentum and
(c) rapidity distribution in mb for different fermionic contributions in
ultraperipheral lead-lead collisions at energy $\sqrt{s_{NN}}=5.02$ TeV. The
blue solid line corresponds to a sum of all contributions, the red solid line
is a sum for leptons, the dashed red line relates to electrons, and the green
solid line represents quarks contribution.

In Fig. 9 and Fig. 10 we show corresponding two-dimensional distributions
($y_{1}$, $y_{2}$) for three different mechanisms separately: boxes, double-
hadronic fluctuations and two-gluon exchange. In this inclusive case
(integration over $p_{t}=p_{1t}=p_{2t}$ and $W_{\gamma\gamma}$) we observe
absolute dominance of the box contribution over the other mechanisms. The red
contours represent the rapidity limit for ALICE 3: $-1.6<y_{\gamma}<4$ and
$3<y_{\gamma}<5$. The largest cross section occurs in the midrapidity of both
photons. Within this rapidity range, it is expected to be able to detect
photons with $p_{t,\gamma}>100$ MeV. Our predictions show that in the forward
range of the calorimeter, $3<y_{\gamma}<5$, even though the VDM-Regge
contribution is about three orders of magnitude smaller than fermionic boxes,
it should be included to determine the coherent sum of these two processes.

(a) (b) (c)

Figure 9:  Distribution in ($y_{1}$,$y_{2}$) in mb for photon transverse
momentum $p_{t}>5$ MeV, di-photon invariant mass $M_{\gamma\gamma}>1$ GeV. (a)
Boxes, (b) VDM-Regge and (c) two-gluon exchange.

(a) (b)

Figure 10:  Distribution in ($y_{1}$,$y_{2}$) in mb for transverse momentum
$p_{t}>5$ MeV, di-photon invariant mass $M_{\gamma\gamma}>5$ GeV. (a) Boxes,
(b) VDM-Regge mechanism.

In Fig.11 we present di-photon invariant mass distributions for different
mechanisms including (a) $\pi^{0}$, $\eta$ and $\eta^{\prime}$ resonances as
well as (b) VDM-Regge and two-gluon exchange mechanism. While the resonances
stick over the box-continuum they can be easily eliminated imposing windows
around the resonance positions. Although at first glance the contribution from
higher order mechanisms seems insignificant, it is important to be aware that
the contribution from VDM-Regge is only an order of magnitude smaller than the
leading contribution from the fermionic boxes.

(a) (b)

Figure 11:  Di-photon invariant mass distribution for photon transverse
momentum $p_{t}>5$ MeV and photon rapidities $y_{1/2}\in(-8,8)$. (a) Boxes vs
resonances, $M_{\gamma\gamma}<1$ GeV (b) Boxes vs VDM-Regge and vs two-gluon
exchange contribution, $M_{\gamma\gamma}>1$ GeV.

(a) (b)

Figure 12:  Transverse momentum distribution for photon transverse momentum
$p_{t}>5$ MeV, di-photon invariant mass $W_{\gamma\gamma}<1$ GeV and photon
rapidities $y_{1/2}\in(-8,8)$. (a) Boxes vs resonances; (b) boxes vs VDM-Regge
vs two-gluon exchange.

The corresponding distributions in $p_{t}=p_{1t}=p_{2t}$ are shown in Fig.12.
We observe huge enhancements of the cross section at $p_{t}\sim M_{R}/2$
(jacobian peak). It would be interesting to see such enhancements
experimentally for controlling the general situation. Imposing the windows
around resonances would allow to eliminate the resonance contributions.
However, this would probably distort to some extent other distributions, in
particular, those for $p_{t}=p_{1t}=p_{2t}$. Therefore it is not clear to us
whether such cuts would be welcomed.

(a) (b)

Figure 13:  Distribution in $y_{diff}$ for light-by-light scattering processes
in PbPb$\to$PbPb$\gamma\gamma$. Here the transverse momentum cut is equal to 5
MeV. The blue solid line relates to the boxes, and the green dotted line to
the VDM-Regge contribution. Here the range of measured di-photon invariant
mass is: (a) $(1-5)$ GeV, (b) $>5$ GeV.

For completeness, in Fig.13 we show distributions in rapidity difference
hoping it could distinguish different mechanisms. Indeed the shape of the
distributions corresponding to two-photon hadronic fluctuations seems somewhat
broader than that for boxes. There is a region of $y_{diff}$ where the VDM-
Regge contribution is as big as that for fermionic boxes. This region of phase
space is, however, not easy to measure at the LHC. The resonance
contributions, not shown here explicitly, are concentrated at $-2<y_{diff}<2$
but for $M_{\gamma\gamma}>5$ GeV the light mesons are automatically removed.
We shall discuss the resonance contribution for ALICE 3.

####  IV.0.3 ALICE and FoCal

The FoCal detector planned for Run 4 was described in Loizides et al. (2020).
It is a general purpose detector. It can also measure photons.

(a) (b)

Figure 14:  Invariant mass distribution for the nuclear process. Predictions
are made for the future FoCal acceptance, i.e. (a) $E_{t,\gamma}>200$ MeV and
$3.4<y_{\gamma_{1/2}}<5.8$, (b) $p_{t,\gamma}>200$ MeV and
$3.4<y_{\gamma_{1/2}}<5.8$. Here, both photons are ”measured” in FoCal. The
background contribution is presented for different elimination cuts.

We start our presentation from the results when in addition both photons are
measured by FoCal. In Fig.14 (a) we show results when both photons have
energies bigger than 200 MeV. In addition, we show the $\pi^{0}\pi^{0}$
background. In this case, only two photons are measured. Without additional
cuts, the background is clearly bigger than the signal. However, by imposing
extra conditions on vector asymmetry, we can lower the background
contribution. The vector asymmetry defined in Ref. Kłusek-Gawenda et al.
(2019) as:

$A_{V}=|\vec{p}_{t,1}-\vec{p}_{t,2}|/|\vec{p}_{t,1}+\vec{p}_{t,2}|\;,$ (17)

reflects a convolution of each photon transverse momentum vector.

At very low $M_{\gamma\gamma}$ the $\pi^{0}\pi^{0}$ background is negligible,
which opens a new window to measure the $\gamma\gamma\to\gamma\gamma$
scattering at $M_{\gamma\gamma}<1$ GeV while for the ATLAS experiment it was
$M_{\gamma\gamma}>5$ GeV. In Fig.14(b) we show similar results when imposing
$p_{t,\gamma}$ condition. In this case, it is rather difficult to eliminate
the $\pi^{0}\pi^{0}$ background. Here the VDM-Regge component is relatively
small. Only at $W_{\gamma\gamma}\approx 5$ GeV some effect of the VDM-Regge
component could potentially be observed. Comparing the results for the same
cut on the energy of each outgoing photon, Fig. 14(a), and on the transverse
momentum of the photon, Fig. 14(b), one can observe that the limit on
$p_{t,\gamma}$ removes a very large contribution to the total cross section,
which is located in a small di-photon invariant mass.

Figure 15:  Di-photon invariant mass distribution for
PbPb$\to$PbPb$\gamma\gamma$ process for ALICE, FoCal and their combination.

Another option is to use simultaneously the FoCal and the main ALICE detector.
In Fig.15, we simultaneously show the box and two-gluon exchange
contributions. In this calculation, we assumed that the transverse momenta of
both photons have $p_{t}$ $>$ 1 GeV. In this case, the separated two-gluon
exchange contribution is only an order of magnitude smaller than the box
contribution. The shaded band is due to ”unknown” effective gluon mass.

(a) (b)

Figure 16:  Prediction for the FoCal detector in association with mid-rapidity
ALICE detector for photons: $p_{t}>200$ MeV, di-photon mass $M_{\gamma\gamma}$
$>$ 400 MeV and photon rapidities $|y_{1}|<0.9$ and $y_{2}\in(3.4,5.8)$. The
blue line corresponds to fermionic loops and the green lines to the VDM-Regge
contribution. (a) Di-photon invariant mass, (b) photon transverse momentum
distribution.

In Fig.16 we show similar distributions but for $p_{t}$ $>$ 0.2 GeV and
combined ALICE and FoCal rapidity region. Here in some regions of the phase
space, the VDM-Regge contribution could be seen as $~{}10\%$ modification of
the cross section with respect to the calculations with only boxes. Here the
separated VDM-Regge component is even bigger. We conclude that already at Run
4 one could indirectly observe a signature of other mechanisms than fermionic
boxes.

####  IV.0.4 ALICE 3 kinematics

Now we wish to show distributions relevant for the ALICE 3 detector.

Figure 17:  Di-photon invariant mass distribution for ALICE 3, i.e. rapidity
$y_{\gamma}\in(-4,4)$ and photon energy E${}_{\gamma}>50$ MeV. Here the blue
solid line relates to the box contribution, the dotted line to the VDM-Regge
component and the dashed lines are for double-$\pi^{0}$ background
contribution. Here we impose several extra conditions on di-photon transverse
momenta and vector asymmetry.

In Fig. 17 we show distributions in di-photon invariant mass for photons
$-4<y_{1},y_{2}<4$ and $E_{\gamma}>50$ MeV (see Ref. Musa et al. (2022)). We
show the light-by-light box contribution (solid line) as well as the
$\pi^{0}\pi^{0}$ background contribution (red lines). At di-photon invariant
masses, $0.5$ GeV $<M_{\gamma\gamma}<1$ GeV, the background contribution is
almost as big as the signal contribution. As discussed in Kłusek-Gawenda et
al. (2019) it can be to some extent reduced. Although the background is
smaller than fermionic boxes in the full range of di-photon invariant mass, it
can be further reduced by imposing the cut on
$|\vec{p_{1t}}+\vec{p_{2t}}|<0.1$ GeV and vector asymmetry $A_{V}<0.02$.
Imposing a limit on the background causes that the background in the whole di-
photon invariant mass range is much smaller than the signal.

Figure 18:  Differential cross section as a function of $y_{diff}=y_{1}-y_{2}$
for extended ALICE 3 kinematics: $|y_{\gamma}|<4$ and $E_{\gamma}>50$ MeV.
Results are presented for boxes, resonances, VDM-Regge and double-$\pi^{0}$
background.

In Fig. 18 we show analogous distribution in $y_{diff}=y_{1}-y_{2}$. Again
different contributions are shown separately. The results for the
double-$\pi^{0}$ background contribution are particularly interesting. It has
a maximal contribution at $y_{diff}=0$ and drops quickly for larger
$|y_{diff}|$. An extra cut on $y_{diff}$ could therefore considerably reduce
the unwanted double-$\pi^{0}$ contribution. In Fig. 19 we show what happens
when we impose the cut on $y_{diff}$. The effect of such a cut on box
contribution is relatively small but leads to huge reduction of the
background. The effect of the cut is much larger for small $M_{\gamma\gamma}$
and therefore should be avoided if one is interested in this region of
energies.

Figure 19:  Influence of extra conditions on $y_{diff}=y_{1}-y_{2}$
($|y_{diff}|>1,2$) on di-photon invariant mass distribution for ALICE 3. Here
the solid lines relate to the box contribution and the dashed lines are for
double-$\pi^{0}$ background contribution.

(a) (b)

Figure 20:  Prediction for the ALICE 3 experiment for soft photons:
$p_{t}=(5-50)$ MeV and photon rapidities $y_{i}\in(3,5)$ . The blue line
corresponds to fermionic loops, the red line relates to the double-$\pi^{0}$
background. (a) di-photon invariant mass distribution, (b) photon transverse
momentum distribution.

In Fig.20 we show distribution in $M_{\gamma\gamma}$ (a) and $p_{t}$ (b) for a
planned special photon detector $3<y_{\gamma}<5$. Here $p_{t}>5$ MeV was
imposed as described in Ref. Musa et al. (2022). We show that at low
$M_{\gamma\gamma}$ and low $p_{t}$ the LbL signal by far exceeds the
$\pi^{0}\pi^{0}$ background, even without including any background suppression
condition. Here we have assumed 2 $\pi$ azimuthal coverage of the special
photon detector.

In principle, there is an option to leave the FoCal detector Loizides et al.
(2020) when running the ALICE 3 detector. This option will be explored
elsewhere.

(a) (b)

Figure 21:  Prediction for the ALICE 3 experiment for photons: $p_{t}>100$ MeV
and photon rapidities $y_{i}\in(-1.6,4)$. The blue line corresponds to
fermionic loops, the red line relates to the double-$\pi^{0}$ background. (a)
Di-photon invariant mass, (b) photon transverse momentum distribution.

At somewhat larger $M_{\gamma\gamma}$ and/or $p_{t}$ the background
contribution becomes as big as the signal (box) contribution (see Fig.21).
Imposing a cut $|\vec{p}_{1,t}+\vec{p}_{2,t}|<$ 0.1 GeV reduces the background
contribution. It can be further reduced by imposing a cut on so-called vector
asymmetry $A_{V}$ (see Kłusek-Gawenda et al. (2019)). However, assuming no
background constraints, the cross section for this rapidity range is twice as
large as the signal contribution, see Tab. 3. The comparison of the total
cross-sections for the three scenarios shows that the most optimistic scenario
is the photon forward detection and $p_{t,\gamma}=(1-50)$ MeV. Here, the
double-$\pi^{0}$ background does not play significant role.

kinematical limitation |  $\sigma(\pi^{0}\pi^{0}$ bckg) $\mu b$ |  $\sigma($boxes) $\mu b$
---|---|---
$p_{t}>$5 MeV |  $E_{\gamma}>50$ MeV | $-4<\eta_{\gamma}<4$ | 112.824 | 952.590
$p_{t}>100$ MeV |  $E_{\gamma}>50$ MeV | $-1.6<\eta_{\gamma}<4$ | 159.231 | 82.682
$p_{t}=(1-50)$ MeV |  $E_{\gamma}>50$ MeV | $3<\eta_{\gamma}<5$ | 105.301 | 3095.795
Table 3: Fermionic box signal contribution versus double-$\pi^{0}$ background
given in $\mu$b at PbPb collision energy $\sqrt{s_{NN}}=5.02$ TeV, with three
considered scenarios of ALICE 3 detector limitations.

##  V  Conclusions

We have discussed different mechanisms of $\gamma\gamma\to\gamma\gamma$
scattering such as leptonic/quarkish boxes, double hadronic fluctuations,
neutral $t/u$-channel pion exchanges and two-gluon exchanges. Possible effects
of the subleading mechanisms have been discussed. The latter contributions
turned out difficult to be identified in previous ATLAS and CMS measurements.
We have discussed possible interference effect of box and double-hadronic
fluctuations for $\gamma\gamma\to\gamma\gamma$ scattering.

We have calculated several differential distributions for diphotons in the
equivalent photon approximation such as $d\sigma/dp_{t}$, $d\sigma/dy$,
$d\sigma/dM_{\gamma\gamma}$, $d\sigma/dy_{diff}$, $d\sigma/dy_{1}dy_{2}$ for
PbPb$\to$PbPb$\gamma\gamma$. Imposing cuts on $y_{diff}$ and transverse
momenta of each of the photons ($p_{t}<$ 0.2 GeV) or $M_{\gamma\gamma}>$ 20
GeV and cut on transverse momenta of photons we have found regions of the
phase space with the dominance of the hadronic excitation of both photons,
called in this paper VDM-Regge for brevity. Identification of this mechanism
at ALICE 3 would be very interesting and would allow to verify the concept of
the VDM-Regge experimentally.

We have also considered the two-$\pi^{0}$ background, one photon from one
$\pi^{0}$ and a second photon from the other $\pi^{0}$, which gives a
relatively large cross section which could be misidentified as the
$\gamma\gamma\to\gamma\gamma$ process. Imposing lower cuts on
$|\vec{p}_{1t}+\vec{p}_{2t}|$ or alternatively azimuthal angle between photons
eliminates a big part of the unwanted two-$pi^{0}$ background but still some
contribution at $M_{\gamma\gamma}\sim 1$ GeV survives.

We have also explored an option to use the planned FoCal detector. When used
simultaneously with the ALICE main detector it may allow to study the
$\gamma\gamma\to\gamma\gamma$ scattering for $W_{\gamma\gamma}$ $<$ 1 GeV, a
new unexplored region of the subsystem energies. Therefore we conclude that
the measurement of $\gamma+\gamma\to\gamma+\gamma$ in a unique region of
relatively small energies and small transverse momenta (much lower than those
for ATLAS or CMS) will be possible.

We have made also predictions for the ALICE 3 ($-4<y_{\gamma}<4$) and for a
planned special soft photon detector ($3<y_{\gamma}<5$). We have shown that
imposing a cut on $y_{diff}=y_{1}-y_{2}$ one can eliminate the unwanted double
$\pi^{0}$ background. The soft photon detector can be used to measure the
$\gamma\gamma\to\gamma\gamma$ scattering at extremely small energies,
$W_{\gamma\gamma}<0.05$ GeV. Therefore we conclude that the ALICE 3
infrastructure will be an extremely useful to study the
$\gamma\gamma\to\gamma\gamma$ scattering in a new, not yet explored, domain of
energies and transverse momenta. In this domain the double-$\pi^{0}$
background can to large extent be eliminated.

For photon-photon energies (diphoton invariant masses) 1 GeV $<W<$ 2 GeV the
tensor meson exchanges may play an important role (see Lebiedowicz and
Szczurek (2017a)). They would lead to deviations from the box component. This
effect may be difficult to eliminate by imposing cuts on diphoton invariant
mass.

In the present calculations we used EPA in the impact parameter space. In the
future one can try to use also so-called Wigner function approach (never used
for the di-photon production). This goes, however, beyond the scope of the
present exploratory paper.

##  VI Acknowledgments

This work was partially supported by the Polish National Science Center grant
UMO-2018/31/B/ST2/03537 and by the Center for Innovation and Transfer of
Natural Sciences and Engineering Knowledge in Rzeszów.

We are indebted to Adam Matyja and Jacek Otwinowski for a discussion on ALICE
3 and FoCAL projects.

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# Beyond Toxic: Toxicity Detection Datasets are Not Enough for Brand Safety

Elizaveta Korotkova1111Work done during internship at Clarifai, Isaac Kwan Yin
Chung2

###### Abstract

The rapid growth in user generated content on social media has resulted in a
significant rise in demand for automated content moderation. Various methods
and frameworks have been proposed for the tasks of hate speech detection and
toxic comment classification. In this work, we combine common datasets to
extend these tasks to brand safety. Brand safety aims to protect commercial
branding by identifying contexts where advertisements should not appear and
covers not only toxicity, but also other potentially harmful content. As these
datasets contain different label sets, we approach the overall problem as a
binary classification task. We demonstrate the need for building brand safety
specific datasets via the application of common toxicity detection datasets to
a subset of brand safety and empirically analyze the effects of weighted
sampling strategies in text classification.

##  1 Introduction

As the amount of user generated content on social media continues to grow, a
need to automate content moderation to address the scale problem has arisen,
and many turn to using Deep Learning models and frameworks. In particular,
harmful sources like hate speech and toxic comments have been targeted for
moderation (Mondal, Silva, and Benevenuto 2017; Kwak, Blackburn, and Han
2015). Thus, various and often overlapping text moderation tasks, such as Hate
Speech Detection, Toxic Comment Classification, and Offensive Language
Detection (Basile et al. 2019; Fortuna and Nunes 2018; Ranasinghe and Zampieri
2020), have received increasing attention from the NLP research community.
Here we will refer to the broad task as toxicity detection.

Deep learning models often perform well on specialized datasets when they are
evaluated on their respective train-test splits; however, these models are
unable to generalize to new hate speech content (Wullach, Adler, and Minkov
2021; Arango, Pérez, and Poblete 2019). Datasets often differ in their class
definitions and labelling criteria, leading to poor model performance when
predicting across new domains and datasets. One way to address this problem is
to collect more data from the target domain, but in reality quality data is
often scarce. Thus, a common technique is to include additional data from
related sources.

Brand safety is an industry application of content moderation that has
received increasing attention. It refers to understanding and identifying
contexts in which advertisements should not appear.222In this work, we
consider the textual aspect of brand safety, while acknowledging that brand
safety is typically evaluated in a multi-modal setting. While hate speech and
toxic comments are certainly part of most brand safety applications, other
moderation criteria such as spam, crime, and illegal drug use are also present
in the widely adopted GARM Brand Safety Floor and Suitability Framework (WFA
2022). Although the need to automate brand safety is undeniable, this field
remains under-explored in literature as there are, to our knowledge, no
existing publications or current benchmarks.

We perform an initial case study of methods that could leverage existing
datasets to generalize well in a different and potentially wider domain such
as brand safety. We apply these methods in a binary classification problem to
classify text into offensive and non-offensive categories. Our contributions
are:

  * •

We demonstrate the need for building brand safety specific datasets via the
application of common toxicity detection datasets to a subset of brand safety.

  * •

We empirically analyze the effects of weighted sampling strategies in text
classification.

##  2 Related Work

### Toxicity Detection

Works on toxicity detection often cover a large variety of domains such as
social media platform contents (Rosenthal et al. 2021), news comments
(Korencic et al. 2021) and hate speech from online forums (de Gibert et al.
2018). There are also works that focus on culture-, region- or language-
specific applications, such as Almerekhi et al. (2019) and Li and Ning (2022).
Arango et al. (2019) showed that cross-dataset performance can be improved by
removing bias from the training data, and adding data from another source.
Waseem et al. (2018) proposed a multi-task learning approach to integrate
different datasets into a single training process to construct a generalized
hate speech detection model. Multi-task learning (Waseem, Thorne, and Bingel
2018; Yuan and Rizoiu 2022) has been previously used to improve generalization
of hate speech detection models. Yuan and Rizoiu (2022) also binarize the
class labels from multiple datasets into harmful vs non-harmful labels.

### Weighted Sampling

Previous works have shown empirically that various sampling techniques can
improve classification of imbalanced image data (Masko and Hensman 2015; Byrd
and Lipton 2018) and imbalanced text data (Padurariu and Breaban 2019).
Oversampling has been shown to be effective in overcoming the class imbalance
in SemEval top submissions (Zampieri et al. 2020). In this work, we explore
weighted sampling by class and datasets (when multiple datasets are combined).

##  3 Data

In this section, we describe the datasets used in our experiments. Aiming to
explore the effectiveness of existing toxicity detection datasets, we focus on
readily available datasets distributed under permissive licenses. Some
challenges of using such data are their differing label sets and varying,
often unclear, labeling criteria. Train and test data statistics are shown in
Table 1.

Figure 1: PCA projection of embeddings extracted from the 4th Transformer layer of the pre-trained DistilBERT model (200 examples sampled from each dataset). Each example’s embedding is the average of its token embeddings.  Dataset |  #Train |  #Test |  *#Positives |  *AvgTextLen
---|---|---|---|---
AHS** | 22,305 | **2,478 | 2,062 | 85.4
SOLID | - | 3,887 | 1,080 | 78.1
Surge | - | 1,000 | 501 | 135.6
KTC | 159,571 | 63,978 | 6,243 | 383
JUB | 1,804,874 | 97,320 | 29,052 | 296
Private | - | 37,352 | 6,534 | 81.3
Table 1:  Description of the toxicity detection and brand safety datasets.
Average text length is measured in characters.
Note *: For test sets. **: train-test split was 90-10.

### Common Toxicity Detection Datasets

“Automated Hate Speech Detection and the Problem of Offensive Language” by
Davidson et al. (2017) (AHS) is comprised of examples where 77.4% are
categorized as offensive language, 5.8% as hate speech, and 16.8% as neither.
Annotators were instructed that the presence of a particular word, however
offensive, did not necessarily indicate that a tweet is hate speech. Labels
are assigned according to the majority decision.

Semi-Supervised Offensive Language Identification Dataset (SOLID) (Rosenthal
et al. 2021) was created for the SemEval-2020 task on Multilingual Offensive
Language Identification in Social Media (Zampieri et al. 2020). The labelling
is hierarchical, but we only operate at the highest level and consider its two
classes: NOT (neither offensive, nor profane), and OFF (inappropriate
language, insults, or threats). The dataset is imbalanced, with 84% of
training labels below 0.5.

Surge AI free Toxicity dataset333https://github.com/surge-ai/toxicity is a
sample of a larger, commercially distributed
set444https://www.surgehq.ai/datasets/toxicity-dataset. The data is from “a
variety of social media platforms”. Annotators had “to identify comments that
they personally found toxic” without a strict definition of toxicity. Due to
this, use of profanity by itself does not mean that an example is toxic, and
intended meaning is taken into account.

Toxic Comment Classification Challenge
dataset555https://www.kaggle.com/competitions/jigsaw-toxic-comment-
classification-challenge/data (KTC) was published within a Kaggle competition.
The data is sourced from Wikipedia comments and labeled by human raters for
toxic behavior. The dataset is multi-labeled using 6 toxicity classes, with an
additional negative class that can be defined for non-toxic texts. The
training set is imbalanced: 89.8% of instances are negative.

Jigsaw Unintended Bias in Toxicity
Classification666https://www.kaggle.com/competitions/jigsaw-unintended-bias-
in-toxicity-classification/data (JUB) was also published within a Kaggle
competition and was sourced from the Civil Comments platform. The target
toxicity label is between 0.0 and 1.0, showing what fraction of annotators
marked the instance as either toxic or very toxic. The dataset also contains
multi-class annotation similar to that of KTC. For each of the toxicity
subtypes, a label between 0.0 and 1.0 is provided. The training set is
imbalanced: 92% of the data has a toxicity label below 0.5.

### Private Dataset

This dataset was sampled from a real-world customer application in brand
safety text moderation. It consists of 55,755 user-generated text captions
posted alongside videos on a social media platform. We only use the 37,352
English examples in our experiments. Annotators were instructed to indicate
all brand safety classes that are present. Positive class counts are shown in
Figure 2. See Table 2 for examples.

Figure 2: Counts of brand safety classes in the Private dataset. The dataset is multi-labeled, i.e. one example may belong to more than one class. Additionally, there are 29,596 negative examples in the dataset (not shown here). Pos |  Yikes….(this was pre covid btw) #racist #homophopic #exposed #fyp #foryou #awkward #lgbtq #blm
---|---
oomf.. u caused this #danganronpa #byakuyatogami #makotonaegi
#yasuhirohagakure #genocidersyo #aoiasahina
Neg |  im carrying this family on my back????
#greenscreensticker #swordsman000 #animethings #hiddenanimesociety
Table 2:  Examples from the Private dataset

##  4 Methodology

### Datasets

We use the AHS, KTC, and JUB datasets to train our models. We implement two
settings: 1) train a model using a single dataset, and 2) concatenate all
three datasets to form the combined training set. We randomly select 10% of
each dataset for validation. We evaluate our models on all test sets. The full
Surge dataset sample is used for testing due to its small size. For SOLID, we
do not collect the training examples (for which only tweet IDs are provided)
and use the provided test split for evaluation. AHS does not have a designated
test split, and we report results on its validation split. For KTC and JUB, we
use the pre-defined training and test splits. The private dataset is treated
as unseen and only used for testing. We extract an additional subset from it
by combining negative (safe) examples and examples labelled as containing hate
speech or obscenity, while excluding other brand safety classes.

### Preprocessing

As the datasets have different classes and labeling criteria, we unify them by
treating the task as a binary classification problem. We map all labels
corresponding to hateful, toxic, and otherwise offensive texts to offensive
(positive) class, and the rest to non-offensive (negative) class. If a value
between 0.0 and 1.0 is provided instead of a discrete class label, we consider
instances with toxicity scores strictly below 0.5 negative, and the rest
positive. We do not apply any additional cleaning or filtering to the
datasets.

### Models

To obtain our classification models, we fine-tune the pre-trained DistilBERT
model (Sanh et al. 2019) using the Hugging Face Transformers library (Wolf et
al. 2019). We fine-tune each model for 3 epochs, keeping all other
hyperparameters at their default values. For each model, we do 3 restarts of
fine-tuning and report the average scores. We use 3 NVIDIA GeForce GTX TITAN X
GPUs for each training run with a batch size of 16 instances per GPU.

### Weighted Sampling

A strong class imbalance is seen across all training datasets, and the
datasets differ significantly in size. This suggests that weighted sampling of
instances during training may significantly influence the results shown by the
models. In the default setting, we combine all training datasets into one
dataset and sample its instances with equal probability. Additionally, we
implement 3 variants of weighted sampling: with an equal probability of
sampling from each of the 2 classes (to account for class imbalance), from
each of the 3 datasets (to account for different datasets being unequally
represented), and with equal weight given to each class of each dataset (the
two previous strategies combined).

### Evaluation

For each of the models, we report the F1-score on each of the test sets,
averaged over 3 training runs.

Test set | Training set
---|---
KTC | JUB | AHS
KTC | 0.674 | 0.666 | 0.592
JUB | 0.508 | 0.691 | 0.296
AHS | 0.897 | 0.846 | 0.995
SOLID | 0.873 | 0.874 | 0.782
Surge | 0.762 | 0.739 | 0.613
Private | 0.253 | 0.135 | 0.189
Private-Subset | 0.280 | 0.199 | 0.275
Table 3:  Cross-dataset performance in F1 scores. In most cases, the results are clearly worse on out-of-domain data. Highest results for each test set are shown in bold. For AHS, we report results on the validation set. Test set | Sampling strategy
---|---
Combined | By label | By dataset | Both
KTC | 0.690 | 0.652 | 0.686 | 0.669
JUB | 0.687 | 0.676 | 0.675 | 0.646
AHS | 0.989 | 0.989 | 0.998 | 0.998
SOLID | 0.879 | 0.879 | 0.858 | 0.873
Surge | 0.751 | 0.800 | 0.740 | 0.837
Private | 0.162 | 0.198 | 0.194 | 0.203
Private-Subset | 0.273 | 0.240 | 0.261 | 0.223
Table 4:  F1 scores on different test sets achieved by fine-tuning on the
combined training set with different weighted sampling strategies. ”Combined”
has no weighted sampling. ”Both” samples by both label and dataset. Highest
results for each test set are shown in bold. For AHS, we report results on the
validation set. Figure 3: Heatmap of F1 scores $\times 100$ per class
breakdown over all models on the Brand Safety test set. Obscenity and Hate
Speech correspond to the toxicity detection domain better than the rest of the
classes.

##  5 Results

Results of models trained on different training sets are shown in Table 3. As
expected, models perform best on their own respective test sets. The model
trained on KTC yields better results than other training sets on all test-only
sets except for SOLID. However, on the Private test set, all models show a
large drop in metrics.

Table 4 shows the performance of various weighted sampling strategies over the
combined dataset on the test sets. Simply combining all datasets without
balancing yields the highest F1 scores in 4 test sets. Balancing by both label
and dataset yields highest metrics in 3 test sets.

##  6 Discussion

In general, all fine-tuned models perform reasonably well on toxicity
detection test sets. Weighted sampling is able to offer marginal boosts in
performance.

FP |  For real ep 6 is what took the show from ”pretty good” to ”i fucking love this show” for me
---|---
FN |  Can’t wait to see you dressed in an orange jumpsuit
Table 5:  False positive (FP) and false negative (FN) examples from the Surge
dataset

Table 5 shows two challenging examples from the Surge dataset misclassified by
the model fine-tuned on all data. In the first example, profanity is used to
convey a positive sentiment. While in the Surge dataset profanity does not
mean the example will be labeled as toxic, in some other datasets it does.
Such differences in labelling are undeniably problematic for our models. For
the false negative, world knowledge (which is also culture-specific in this
case) is needed to recognize the text as toxic/offensive.

Our hypothesis is that the hate speech and obscenity portions of the Private
dataset would correspond the closest to the toxicity detection datasets, which
is confirmed by higher F1 scores across all models on the Private-Subset than
on the Private test set in Tables 3 and 4. From the per-class breakdown shown
in Figure 3, we also observe that the aforementioned portions are indeed
relatively closer compared to the rest of the GARM classes. Debated social
issues and explicit sexual content portions correspond the next closest to the
toxicity detection datasets. These scores are still much lower compared to the
results achieved on the other test sets. This suggests many further
differences, and we observe this dissimilarity in Figure 1 as well.

In general, brand safety in text moderation remains an under-explored area
without many prior publications, which prompted us to explore the
applicability of the related task of toxicity detection. Empirical results
suggest that even though the two domains are related, this only applies to a
small portion of brand safety aspects. Additional data collection and
continuing to align brand safety-focused data to the current toxicity
definitions will benefit future work. This is important because harmful
content moderation is frequently driven in part by the pragmatic desire to
protect commercial branding, thus creating a need to understand both tasks and
how they relate.

##  7 Conclusion and Future Work

In this work, we perform an initial case study of extending toxicity detection
to the task of brand safety. Our results reveal various challenges in using
common toxicity detection datasets for solving this task, including domain
differences between the datasets and a coverage mismatch between the tasks’
label sets. We begin to address this gap using multi-dataset training and
weighted sampling.

The scope of this work is limited to English data. In future work, it could be
extended to other languages by using multilingual large language models and
exploring relevant available data. Methods for bridging the gap between
different domains and tasks could also be explored and may include combining
the toxicity detection and brand safety data in various ratios.

##  8 Social Impact

Research on brand safety can help in the moderation of potentially harmful
content in addition to hate speech, including illegal drug use and illegal
arms use, taking a step towards a safer digital media environment.

##  9  Acknowledgments

We thank David Eigen, Michael Gormish, and Eran Nussinovitch for their support
and guidance in this study, and Karen Herder and Michael Tolbert for their
support in gathering the private dataset.

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corresponds to the 3 main columns of the table. The works by Zhong et al.
(2019, 2021) are classified in several cells, as inference of the conformation
$z_{i}$ is performed via a VAE, but the inference of the poses $R_{i},t_{i}$
is performed with an optimization algorithm. The notation (*) specifies that
the optimization associated with this step is fully performed (until
convergence to local extremum) while its absence indicates that only a
gradient step is taken toward the optimum.