# Multipole Photon Radiation in the Vincia Parton Shower

Peter Skands  Rob Verheyen<EMAIL_ADDRESS>School of Physics &
Astronomy, Monash University, Clayton VIC 3800, Australia  University College
London, WC1E 6BT London, United Kingdom

###### Abstract

We present algorithms that interleave photon radiation from the final state
and the initial state with the QCD evolution in the antenna-based Vincia
parton shower. One of the algorithms incorporates the complete soft and
collinear structure associated with photon emission, but may be
computationally expensive, while the other approximates the soft structure at
a lower cost. Radiation from fermions and $W$ bosons is included, and a
strategy for photon radiation off leptons below the hadronization scale is set
up. We show results of the application of the shower algorithms to Drell-Yan
and $W^{+}W^{-}$ production at the LHC, showing the impact of the inclusion of
the full soft structure and treatment of radiation off $W$ bosons.

###### keywords:

Parton Showers, Quantum Electrodynamics , Hadron Collisions

††journal: Physics Letters B

##  1 Introduction

Parton-shower algorithms are an essential component of Monte Carlo event
generators [1], providing a means of resumming radiative corrections in a
fully exclusive and universal manner. While the focus is typically on the
simulation of QCD branching processes, the effects of the radiation of photons
are in some cases substantial. For instance, photon radiation from the initial
state and its interference with radiation from the final state has been shown
to be significant for precision measurements at the LHC [2, 3] and at future
colliders [4, 5, 6].

Treatments of QED radiation based on collinear approximations are included in
all of the standard general-purpose event-generator programs [7, 8, 9]. Modulo
corrections from fixed-order process-specific QED matrix elements, these
approaches neglect the eikonal interference structure. On the other hand, YFS
exponentiation [10] is used in some cases [11, 12] as a means of including the
soft interference structure in a universal process-independent way, but the
QCD and QED showers are then not interleaved. In an interleaved evolution
[13], different branching types (here, QED and QCD ones) are allowed to
compete with each other for phase space during the shower evolution. This
produces an arguably more physical relative ordering of evolution scales in
the resulting joint resummation, compared to the non-interleaved case. In
[14], the first algorithm allowing QCD showers to be interleaved with a fully
coherent (multipole) treatment of final-state QED radiation off fermions was
set out, in the Vincia [15, 16, 17] antenna-based parton-shower formalism.
This letter describes the extension of that algorithm to initial-state
radiation and photon radiation off $W$ bosons, and the implementation in the
Vincia parton shower.

The singularity structure associated with soft and collinear photon emission
is recounted in Section 2. Next, two versions of our QED shower are presented
in Section 3: one that incorporates the full soft interference structure, and
one that includes only dipole terms. The latter is computationally faster but
does not account for multipole effects beyond the dipole level. A description
of the treatment of photon radiation below the hadronization scale is also
included, though without attempting to account for hadronic form factors.
Finally, section 4 shows the impact of the soft structure and treatment of
radiation off $W$ bosons in the context of LHC processes. Some further details
may be found in [18].

##  2 Photon Emission Singularity Structure

We first review the factorization properties of an $n+1$-particle matrix
element that includes a photon. In the soft limit [19], the squared matrix
element factorizes according to

$|M_{n+1}(\\{p\\},p_{j})|^{2}=-8\pi\alpha\Bigg{[}\sum_{x,y}^{n}\sigma_{x}Q_{x}\sigma_{y}Q_{y}\frac{s_{xy}}{s_{xj}s_{yj}}+\sum_{x}^{n}Q_{x}^{2}\frac{m_{x}^{2}}{s_{xj}^{2}}\Bigg{]}|M_{n}(\\{p\\})|^{2},$
(1)

where $\alpha$ is the fine-structure constant, $p_{j}$ is the momentum of the
emitted photon and the sums run over all charged particles with momenta in the
set $\\{p\\}$. The quantities $s_{xy}\equiv 2p_{x}{\cdot}p_{y}$ signify the
Lorentz-invariance of the eikonal factor. The factors $Q_{x}$ are the charges
of particle $x$, while $\sigma_{x}=\pm 1$ is a sign factor that has
$\sigma_{x}=1$ for final-state particles and $\sigma_{x}=-1$ for initial-state
particles. Charge conservation for the total event is then given by

$\sum_{x}Q_{x}\sigma_{x}=0.$ (2)

The quasi-collinear limit [20, 21] with charged particle $i$ leads to

$|M_{n+1}(p_{1},..,p_{i},..,p_{n},p_{j})|^{2}=4\pi\alpha\,Q_{i}^{2}\frac{2}{s_{ij}}P_{I\rightarrow
ij}(z)|M_{n}(p_{1},..,p_{i}+p_{j},..,p_{n})|^{2},$ (3)

where the DGLAP splitting functions are given in terms of $z=E_{i}/E_{i+j}$ by

$\displaystyle P_{f\rightarrow f\gamma}(z)$
$\displaystyle=\frac{1+z^{2}}{1-z}-2\frac{m_{i}^{2}}{s^{2}_{ij}}$
$\displaystyle P_{W^{\pm}\rightarrow W^{\pm}\gamma}(z)$
$\displaystyle=2\frac{z}{1-z}-2\frac{m_{i}^{2}}{s_{ij}^{2}}+\frac{4}{3}\left(\frac{1-z}{z}+z(1-z)\right).$
(4)

Note that the first two terms in the $W^{\pm}$ splitting function constitute
the soft-collinear contribution that reduce to the eikonal factor in the soft
limit. The remaining pieces are purely collinear, and are weighted with a
factor of $4/3$ because they are absent for the longitudinal $W$ polarization.
For initial-state radiation, the quasi-collinear limit is similar, with the
exception of the inclusion of an additional factor $1/z$.

The branching kernels of the shower should capture the soft and quasi-
collinear singularity structure of the matrix element factorization. In the
QCD evolution of Vincia, they are incorporated in antenna functions spanned
between pairs of partons. In the photon emission case, the singularities may
similarly be captured by the expression

$a_{\mbox{\tiny{Emit}}}\left(\\{p\\},p_{j}\right)=-\sum_{\\{x,y\\}}\sigma_{x}Q_{x}\sigma_{y}Q_{y}a_{\mbox{\tiny{Emit}}}(s_{xj},s_{yj},s_{xy}),$
(5)

where ${\\{x,y\\}}$ indicates that the sum runs over all _pairs_ of charged
particles. The definition of the antenna-like functions
$a_{\mbox{\tiny{Emit}}}(s_{xj},s_{yj},s_{xy})$ spanned between two charged
particles depend on $x$ and $y$ being in the initial state or the final state.
They are given by

$\displaystyle
a_{\mbox{\tiny{Emit}}}^{\mbox{\tiny{FF}}}(s_{ij},s_{jk},s_{ik})$
$\displaystyle=4\frac{s_{ik}}{s_{ij}s_{jk}}-4\frac{m_{i}^{2}}{s_{ij}^{2}}-4\frac{m_{k}^{2}}{s_{jk}^{2}}+\delta_{if}\frac{2}{s_{IK}}\frac{s_{jk}}{s_{ij}}+\delta_{kf}\frac{2}{s_{IK}}\frac{s_{ij}}{s_{jk}}$
$\displaystyle+\delta_{iW}\frac{8}{3}\frac{1}{s_{ij}}\left(\frac{s_{jk}}{s_{IK}-s_{jk}}+\frac{s_{jk}(s_{IK}-s_{jk})}{s_{IK}^{2}}\right)$
$\displaystyle+\delta_{kW}\frac{8}{3}\frac{1}{s_{jk}}\left(\frac{s_{ij}}{s_{IK}-s_{ij}}+\frac{s_{ij}(s_{IK}-s_{ij})}{s_{IK}^{2}}\right)$
$\displaystyle
a_{\mbox{\tiny{Emit}}}^{\mbox{\tiny{IF}}}(s_{aj},s_{jk},s_{ak})$
$\displaystyle=4\frac{s_{ak}}{s_{aj}s_{jk}}-4\frac{m_{a}^{2}}{s_{aj}^{2}}-4\frac{m_{k}^{2}}{s_{jk}^{2}}+\delta_{af}\frac{2}{s_{AK}}\frac{s_{jk}}{s_{aj}}+\delta_{kf}\frac{2}{s_{AK}}\frac{s_{aj}}{s_{jk}}$
$\displaystyle+\delta_{aW}\frac{8}{3}\frac{1}{s_{aj}}\left(\frac{s_{jk}}{s_{AK}+s_{jk}}+\frac{s_{jk}}{s_{AK}}+\frac{s_{jk}^{2}}{s_{AK}^{2}}\right)$
$\displaystyle+\delta_{kW}\frac{8}{3}\frac{1}{s_{jk}}\left(\frac{s_{aj}}{s_{ak}+s_{jk}}+\frac{s_{aj}}{s_{AK}+s_{jk}}-\frac{s_{aj}^{2}}{(s_{AK}+s_{jk})^{2}}\right)$
$\displaystyle
a_{\mbox{\tiny{Emit}}}^{\mbox{\tiny{II}}}(s_{aj},s_{bj},s_{ab})$
$\displaystyle=4\frac{s_{ab}}{s_{aj}s_{bj}}+\frac{2}{s_{AB}}\left(\frac{s_{aj}}{s_{bj}}+\frac{s_{bj}}{s_{aj}}\right),$
(6)

where initial state particles are labelled by $a$ and $b$, final state
particles are labelled by $i$, $j$, and $k$, and capital letters indicate the
pre-branching momenta. The Kronecker delta functions then check if the
particle is a $W$ or a fermion. Note that they are absent from the initial-
initial antenna, because $W$ bosons do not appear in hadronic or fermionic
initial states. They are however present in the initial-final antenna, because
the $W$ may appear as the initial state of a resonance decay, which is
showered as described in [22].

The parton shower approximation to the radiative matrix element is

$|M_{n+1}\left(\\{p\\},p_{j}\right)|^{2}\approx 4\pi\alpha
a_{\mbox{\tiny{Emit}}}\left(\\{p\\},p_{j}\right)|M_{n}\left(\\{\bar{p}\\}\right)|^{2},$
(7)

where $\\{\bar{p}\\}$ are the pre-branching momenta of the charged particles,
related to the post-branching antennae by the kinematic maps [23, 17].
Considering the $s_{ij}$-collinear limit of eq. (5) leads to

$\displaystyle a_{\mbox{\tiny{Emit}}}\left(\\{p\\},p_{j}\right)$
$\displaystyle=-\sigma_{i}Q_{i}\sum_{x\neq
i}\sigma_{x}Q_{x}a_{\mbox{\tiny{Emit}}}(s_{ij},s_{xj},s_{ix})+\mathcal{O}(1)$
$\displaystyle\mathrel{\overset{\makebox[0.0pt]{\mbox{\tiny
col.}}}{=}}-\sigma_{i}Q_{i}\frac{2}{s_{ij}}P_{I\rightarrow ij}(z)\sum_{x\neq
i}\sigma_{x}Q_{x}$ $\displaystyle=Q_{i}^{2}\frac{2}{s_{ij}}P_{I\rightarrow
ij}(z).$ (8)

As such, all collinear limits are automatically included in eq. (5). In a
similar fashion, it may be shown that the mass terms in eq. (1) are also
properly incorporated. Finally, in the soft limit, each oppositely-charged
particle pair (modulo the effects of crossing) contributes a positive term to
the sum in eq. (5) while each like-sign pair contributes a negative one; this
produces the full pattern of constructive and destructive interference effects
in the soft limit.

##  3 Showering Algorithms

In this section, we present two algorithms that are currently implemented in
the Vincia parton shower. The first one captures the full soft structure
indicated by eq. (1), but is at risk of becoming computationally expensive in
certain situations. In the second algorithm, only the dominant dipole term is
kept in each phase-space point. This allows for a more efficient, and hence
faster, algorithm, at the price of neglecting (subleading) corrections from
quadrupole and higher multipole terms.

###  3.1 Coherent Algorithm

Our aim is to distribute emissions according to eq. (5) while maintaining a
structure that is as similar as possible to the QCD shower. In particular, its
ordering variable should regulate all singular limits simultaneously, but it
should be directly comparable with the QCD ordering variable. Furthermore, the
kinematic mappings should be infrared safe, meaning that in all collinear
limits all other charged particles should remain unaffected and in the soft
limit no particle momenta should be modified.

To meet the above requirements, we modify the parton shower approximation of
eq. (7) to

$|M_{n+1}\left(\\{p\\},p_{j}\right)|^{2}\approx
a_{\mbox{\tiny{Emit}}}\left(\\{p\\},p_{j}\right)\sum_{\\{x,y\\}}\Theta\left(Q^{2}_{xy}\right)|M_{n}\left(\\{\bar{p}\\}_{xy}\right)|^{2},$
(9)

where

$Q^{2}_{xy}=\begin{cases}s_{xj}s_{jk}/s_{XY}&\mbox{ for final-final }\\\
s_{xj}s_{yj}/(s_{XY}+s_{yj})&\mbox{ for initial-final}\\\
s_{xj}s_{yj}/s_{xy}&\mbox{ for initial-initial.}\end{cases}$ (10)

is the transverse mometum in the antenna rest frame which is also used as the
ordering scale in the QCD shower [17]. Eq. (9) then includes the step function

$\Theta\left(Q^{2}_{xy}\right)=\begin{cases}1&\text{if }\forall\text{ pairs
}\\{v,w\\}\,\,Q^{2}_{xy}\leq Q^{2}_{vw}\\\ 0&\text{otherwise.}\end{cases}$
(11)

which divides the emissive phase space into sectors111See [24] for a sector-
based approach to QCD antenna showers.. Only a single term of the sum in eq.
(9) thus contributes to each phase space point. For each such term, the
argument of the non-radiative matrix element $\\{\bar{p}\\}_{xy}$ indicates
that only the momenta $p_{x}$ and $p_{y}$ are modified; i.e., the recoil from
the photon emission is shared by the pair of charged particles that has the
lowest transverse momentum with the photon. Eq. (9) is relatively simple to
implement in a shower using the usual Sudakov veto algorithm [25, 26, 27].
Competing trial emissions are generated in every sector using the appropriate
local transverse momentum. An additional veto is included that checks the
condition imposed by the step function in eq. (11).

This procedure in fact orders emissions with ordering variable

$Q^{2}=\min\left(Q^{2}_{xy}\right),$ (12)

which has the required property of ensuring that all soft and collinear
regions are contained in the limit $Q^{2}\rightarrow 0$, while still allowing
for the use of regular $2\rightarrow 3$ shower kinematics. However, this
algorithm may become prohibitively expensive in situations where the number of
charged particles in an event grows rapidly.

###  3.2 Pairing Algorithm

To tackle the large computational cost of the above algorithm, the parton-
shower approximation eq. (7) may instead be replaced by

$|M_{n+1}\left(\\{p\\},p_{j}\right)|^{2}\approx
4\pi\alpha\sum_{[x,y]}Q^{2}_{[x,y]}a_{\mbox{\tiny{Emit}}}(s_{xj},s_{yk},s_{xy})|M_{n}\left(\\{\bar{p}\\}_{xy}\right)|^{2}.$
(13)

The sum now runs over _pairings_ $[x,y]$ that have identical but opposite
charge $Q_{[x,y]}$. Eq. (13) trivially reduces to the correct collinear
limits, but only contains a subset of eikonal factors. By choosing a suitable
method to pair up the charges, the missing interference structure may however
be approximated.

Figure 1: An illustration of a $2e^{+}2e^{-}$ configuration where the
electron-positron pairs are moving into roughly the same direction. The blue
lines indicate antennae with positive sign while the orange lines indicate
antennae with negative signs.

To illustrate how this may be done, Figure 1 shows a configuration of charges
consisting of two boosted $e^{+}e^{-}$ pairs moving in opposite directions. In
this situation, one pairing performs much better than the other. Since the
components of the pairs move in roughly the same direction, the charges of the
electrons and positrons should be shielded and the radiation of photons should
be suppressed. Equivalently, contributions to eq. (7) between the pairs should
largely cancel, and the remaining contributions are those inside the pair
where the radiative phase space is restricted by the small invariant mass of
the pair. In this case, the soft structure would be mismodelled badly if the
charges were paired up between pairs. We therefore opt to pair up charges to
minimize the sum of invariant masses of the pairs. The combinatorial problem
of finding the optimal pairing is known as the _assignment problem_ , which
may be solved in $\mathcal{O}(n^{3})$ time-complexity using the Hungarian
algorithm [28, 29, 30]. Vincia makes used of an open-source implementation
that may be found in [31]. Note that it may not always be possible to pair up
all charged particles with an opposite charged partner. For example, in a
$W^{+}\rightarrow u\bar{d}$ resonance decay, no pairing is possible at all. In
these cases, the algorithm pairs up as many charges as possible, and employs
the coherent algorithm on the remainder.

###  3.3 Photon Emission Below the Hadronization Scale

In the parton-shower formalism, a natural separation of scales occurs at
$\Lambda_{\mbox{\tiny{QCD}}}$. Above that scale, coloured partons radiate
gluons and multiple separate systems may radiate as a consequence of the
simulation of resonance decays and multiple particle interactions in hadron
collisions. Below $\Lambda_{\mbox{\tiny{QCD}}}$, coloured partons hadronize
and the evolution should continue as a single QED (multipole) system composed
of leptons and charged hadrons, down to values beyond experimental precision.
A detailed treatment of QED radiation off hadrons is beyond the scope of this
work. However, even if we were to focus exclusively on radiation off leptons,
the algorithm described in section 3.1 is complicated by the fact that the
system of leptons is not necessarily charge-conserving by itself. We therefore
continue the QED evolution below $\Lambda_{\mbox{\tiny{QCD}}}$ by using the
algorithm of section 3.2 and supplementing the pool of charges with the
available colour-neutral strings that are entering the hadronization stage.
Strings that have an overall electric charge can thereby act as recoilers for
photon emission off leptons. Since we do not attempt to describe photon
radiation off the strings themselves, we replace the antenna function in eq.
(13) by the final-state dipole function

$a^{\mbox{\tiny{FF}}}_{\mbox{\tiny{Dipole}}}(s_{ij},s_{jk},s_{ik})=4\frac{s_{ik}}{s_{ij}(s_{ij}+s_{jk})}-4\frac{m_{i}^{2}}{s_{ij}^{2}}+\frac{2}{s_{IK}}\frac{s_{jk}}{s_{ij}}$
(14)

which only contains the soft and quasi-collinear singularity structure of the
lepton $i$.

##  4 Results

In this section, we apply the new QED shower algorithms implemented in Vincia
to Drell-Yan and $W^{+}W^{-}$ production at the LHC and investigate their
differences. We also compare to the default (DGLAP-based) Pythia QED shower,
whose dipole kinematics are based on a principle of “maximum screening”
similar to that of our pairing algorithm. The Pythia results are produced with
Pythia 8.2 [7] using the default tune and the NNPDF2.3 PDF sets [32]. The
Vincia results are produced using Vincia 2.3 [17] with Pythia 8.2, using the
default tune and the same PDF set.

###  4.1 Drell-Yan

We first consider dilepton invariant-mass observables for Drell-Yan at centre-
of-mass energy $\sqrt{s}=14$ TeV with the cuts

$p_{\perp}>25\text{ GeV and }\eta<3.5$ (15)

applied to the final-state leptons. Invariant-mass distributions are good
candidates to probe the effects of the QED shower because the QCD evolution of
the initial state only affects the final state through recoil imparted by a
Lorentz boost. As such, invariant mass observables are unaffected by initial-
state QCD radiation and isolate the QED corrections.

Drell-Yan production serves as a suitable test-case to probe the differences
between coherent and incoherent approaches to photon radiation. While the
initial state and final state are both charged, the scope of interference
between the two is suppressed by a factor of the order of the off-shellness of
the $Z$ [6, 33]. This is a result of the relatively long-lived nature of the
$Z$-boson close to its mass peak, causing the production and decay to remain
separated. Pythia approximates this separation by showering the initial state
and final state of Drell-Yan production separately. This is equivalent to
making the narrow-width approximation. However, a more physical treatment may
be considered where the initial state and final state are showered
incoherently up to scales of the order of the off-shellness of the $Z$, and
coherently from there on.

To investigate the differences between these approaches, we generate Born-
level events with Madgraph5 [34] using the same PDF sets and shower them with
Pythia and Vincia. The results are shown in Figure 2. On the left-hand side,
the invariant-mass distribution of the lepton pair is shown. The leptons are
dressed by clustering them with photons within a cone distance $\Delta R=0.2$.
The blue and red lines show the result of the application of the pairing and
coherent algorithms for the complete shower evolution, while the orange line
refers to a mix of the two, allowing for only incoherent radiation at scales
above the off-shellness of the $Z$ and coherent radiation below it. To show
the importance of QED radiation on this observable, the result without QED
showering is also included.

Figure 2: Invariant mass spectra of the $e^{+}e^{-}$ pair (left) and the
$e^{+}e^{-}$ pair with an isolated photon (right) for Drell-Yan at
$\sqrt{s}=14$ TeV. Made using RIVET [35].

We observe that the results from the Pythia shower and the pairing algorithm
match closely while the coherent and mixed algorithms show deviations of a few
percent in the lower end of the spectrum. These differences are a consequence
of the forward-backward asymmetry due to the axial nature of the $Z$ boson.
For values of $\hat{s}<m_{z}^{2}$, the matrix element is enhanced for small
values of the angle $\theta_{e\bar{q}}$ between the electron and the
antiquark, while for $\hat{s}>m_{z}^{2}$ it is enhanced for large values of
$\theta_{e\bar{q}}$. Due to the PDF weights, the initial-state quarks are most
likely to be of up-type, which also have a larger electromagnetic charge than
down-type quarks. As a consequence, for values $\hat{s}<m_{z}^{2}$ the
branching kernel of eq. (5) is more often suppressed, leading to fewer events
being pushed toward the left-hand tail of the distribution.

On the right-hand side of Figure 2, the spectrum of the invariant mass of the
lepton pair with an additional isolated photon is shown. The isolated photon
is required to have an energy of at least $1$ GeV, and no other particles that
have a combined energy of 7% of the photon energy may be present in a cone of
$\Delta R=0.2$ around the photon. In this observable, differences between the
pairing algorithm and the Pythia shower appear, but these remain minor
compared with the difference with the coherent and mixed algorithms.

###  4.2 $W^{+}W^{-}$ Production

We now consider invariant-mass observables for $pp\to W^{+}W^{-}$ production
with the leptonic decays $W^{+}\rightarrow e^{+}\nu_{e}$ and
$W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}$ at center-of-mass energy
$\sqrt{s}=14$ TeV. The cuts

$p_{\perp}>25\text{ GeV and }\eta<3.5$ (16)

are applied to the charged leptons, as well as the missing transverse energy
cuts

$E_{\perp}>20\text{ GeV}$ (17)

applied to the neutrinos. Figure 3 shows the spectra of the invariant mass of
$W^{+}W^{-}$ pair and the $W^{+}$ with an additional isolated photon. In this
case, due to the more complex structure of the hard-scattering matrix element
and the application of the phase space cuts, effects due to coherence are not
visible. However, differences between the Vincia showers and Pythia do appear,
which are due to significant differences in the treatment of photon radiation
off $W$ bosons and treatment of showers in resonance decays. The Pythia shower
radiates photons from $W$ bosons using the fermionic DGLAP $f\to f\gamma$
splitting function, while the Vincia antenna functions include the full Yang-
Mills coupling and the effects of the longitudinal $W$ boson polarization.

Figure 3: Invariant mass spectra of the $W^{+}W^{-}$ pair (left) and the
$W^{+}$ with an isolated photon (right) for $pp\to W^{+}W^{-}$ production at
$\sqrt{s}=14$ TeV. Made using RIVET [35].

##  5 Conclusion

In this letter, we have presented and implemented algorithms that interleave
photon radiation in the Vincia parton shower, incorporating the full or
approximate soft structure at varying computational cost. The QED shower,
which also includes photon splitting as described in [14] and radiation in
resonance decays as described in [22], is available in Vincia 2.3 which has
been incorporated into the Pythia event generator starting from Pythia version
8.3. We have shown that the inclusion of interference effects between
radiation from the initial state and final state affect the invariant mass
spectrum of Drell-Yan production at the LHC, and that the use of antenna
functions for photon emission off $W$ bosons with the correct collinear limit
leads to perceptible differences with the Pythia QED shower.

##  6 Acknowledgements

We are grateful to Ronald Kleiss for many useful discussions. RV acknowledges
support by the Foundation for Fundamental Research of Matter (FOM) via program
156 ”Higgs as Probe and Portal” and by the Science and Technology Facilities
Council (STFC) via grant award ST/P000274/1. PS acknowledges support from the
Australian Research Council via Discovery Project DP170100708. This work was
also supported in part by the European Union’s Horizon 2020 research and
innovation programme under the Marie Sklodowska-Curie grant agreement No
722105 – MCnetITN3.

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