EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-008 LHCb-PAPER-2014-069 April 13, 2015

Measurement of indirect $C\\!P$ asymmetries in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays using semileptonic $B$
decays

The LHCb collaboration†††Authors are listed at the end of this paper.

Time-dependent $C\\!P$ asymmetries in the decay rates of the singly Cabibbo-
suppressed decays ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ are measured in $pp$ collision
data corresponding to an integrated luminosity of 3.0$\mbox{\,fb}^{-1}$
collected by the LHCb experiment. The ${D}^{0}$ mesons are produced in
semileptonic $b$-hadron decays, where the charge of the accompanying muon is
used to determine the initial state as ${D}^{0}$ or ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$. The asymmetries in effective
lifetimes between ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decays, which are sensitive to
indirect $C\\!P$ violation, are determined to be

$\displaystyle A_{\Gamma}({{K}^{-}}{{K}^{+}})=(-0.134\pm
0.077\;{}^{+0.026}_{-0.034})\%\ ,$ $\displaystyle
A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})=(-0.092\pm 0.145\;{}^{+0.025}_{-0.033})\%\
,$

where the first uncertainties are statistical and the second systematic. This
result is in agreement with previous measurements and with the hypothesis of
no indirect $C\\!P$ violation in ${D}^{0}$ decays.

Submitted to JHEP

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

In neutral meson systems, mixing may occur between the particle and anti-
particle states. This mixing is very small in the charm-meson (${D}^{0}$)
system. Experimentally, a small, non-zero ${D}^{0}$–${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing is now firmly
established by several experiments [1, 2, 3, 4, 5, 6], where the average of
these measurements excludes zero mixing at more than 11 standard deviations
[7]. This opens up the possibility to search for a breaking of the charge-
parity ($C\\!P$) symmetry occurring in the ${D}^{0}$–${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing alone or in the
interference between the mixing and decay amplitudes. This is called indirect
$C\\!P$ violation and the corresponding asymmetry is predicted to be ${\cal
O}(10^{-4})$ [8, 9], but can be enhanced in theories beyond the Standard Model
[10]. Indirect $C\\!P$ violation can be measured in decays to $C\\!P$
eigenstates such as the singly Cabibbo-suppressed decays
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ (the inclusion of charge-
conjugate processes is implied hereafter) from the asymmetry between the
effective ${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$
lifetimes, $A_{\Gamma}$. The effective lifetime is the lifetime obtained from
a single exponential fit to the decay-time distribution. Several measurements
of $A_{\Gamma}$ exist [1, 11, 12]. The most precise determination was made by
LHCb with data corresponding to 1.0$\mbox{\,fb}^{-1}$ of integrated
luminosity, resulting in $A_{\Gamma}({{K}^{-}}{{K}^{+}})=(-0.035\pm 0.062\pm
0.012)\%$, and $A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})=(0.033\pm 0.106\pm
0.014)\%$ [11]. When indirect $C\\!P$ violation is assumed to be the same in
the two modes, the world average becomes $A_{\Gamma}=(-0.014\pm 0.052)\%$ [7].
In all previous measurements of $A_{\Gamma}$, the initial flavour of the
neutral charm meson (i.e., whether it was a ${D}^{0}$ or ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ state) was determined (tagged)
by the charge of the pion in a ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$
decay. In this paper, the time-dependent $C\\!P$ asymmetry is measured in
${D}^{0}$ decays originating from semileptonic $b$-hadron decays, where the
charge of the accompanying muon is used to tag the flavour of the ${D}^{0}$
meson. These samples are dominated by
${{{B}^{-}}}\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ and
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$
decays, where $X$ denotes other particle(s) possibly produced in the decay.
The same data samples as for the measurement of time-integrated $C\\!P$
asymmetries [13] are used.

##  2 Formalism and method

The time-dependent $C\\!P$ asymmetry for a neutral $D$ meson decaying to a
$C\\!P$ eigenstate, $f$, is defined as

$\displaystyle A_{{C\\!P}}(t)\equiv\frac{\Gamma({{D}^{0}}\rightarrow
f;t)-\Gamma({{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow
f;t)}{\Gamma({{D}^{0}}\rightarrow f;t)+\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow f;t)}\ ,$ (1)

where $\Gamma({{D}^{0}}\rightarrow f;t)$ and $\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow f;t)$ are the time-
dependent partial widths of initial ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons to final state $f$. The
$C\\!P$ asymmetry can be approximated as [14]

$\displaystyle A_{{C\\!P}}(t)\approx A_{{C\\!P}}^{\rm
dir}-A_{\Gamma}\frac{t}{\tau}\ ,$ (2)

where $A_{{C\\!P}}^{\rm dir}$ is the direct $C\\!P$ asymmetry and $\tau$ is
the ${D}^{0}$ lifetime. The linear decay-time dependence is determined by
$A_{\Gamma}$, which is formally defined as

$\displaystyle
A_{\Gamma}\equiv\frac{\hat{\Gamma}_{{{D}^{0}}}-\hat{\Gamma}_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}}{\hat{\Gamma}_{{{D}^{0}}}+\hat{\Gamma}_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}}\ ,$ (3)

where $\hat{\Gamma}$ is the effective partial decay rate of an initial
${D}^{0}$ or ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ state to
the $C\\!P$ eigenstate. Furthermore, $A_{\Gamma}$ can be approximated in terms
of the ${D}^{0}$–${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing
parameters, $x$ and $y$, as [15]

$\displaystyle A_{\Gamma}\approx(A_{{C\\!P}}^{\rm mix}/2-A_{{C\\!P}}^{\rm
dir})\,y\,\cos\phi-x\,\sin\phi\ ,$ (4)

where $A_{{C\\!P}}^{\rm mix}=|q/p|^{2}-1$ describes $C\\!P$ violation in
${D}^{0}$–${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing, with
$q$ and $p$ the coefficients of the transformation from the flavour basis to
the mass basis, $|D_{1,2}\rangle=p|{{D}^{0}}\rangle\pm q|{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rangle$. The weak phase $\phi$
describes $C\\!P$ violation in the interference between mixing and decay, and
is specific to the decay mode. Finally, $A_{\Gamma}$ receives a contribution
from direct $C\\!P$ violation as well [16].

The raw asymmetry is affected by the different detection efficiencies for
positive and negative muons, and the different production rates of ${D}^{0}$
and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons. These
effects introduce a shift to the constant term in Eq. (2), but have a
negligible effect on the measurement of $A_{\Gamma}$ (see Sect. 6). The decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$, also flavour-tagged by the muon
from a semileptonic $b$-hadron decay, is used as a control channel. Since this
is a Cabibbo-favoured decay mode, direct $C\\!P$ violation is expected to be
negligible. More importantly, any indirect $C\\!P$ violation is heavily
suppressed as the contribution from doubly Cabibbo-suppressed
${{D}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}$ decays is small.

##  3 Detector and simulation

The LHCb detector [17, 18] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The polarity of the magnetic field is regularly reversed during data
taking. The tracking system provides a measurement of momentum, $p$, with a
relative uncertainty that varies from 0.5% at low momentum to 1.0% at
200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex, the impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is the component
of the momentum transverse to the beam, in
${\mathrm{Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photon, electron and hadron candidates are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers,
situated behind the hadronic calorimeter. The trigger [19] consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

In the simulation, $pp$ collisions are generated using Pythia [20,
*Sjostrand:2007gs] with a specific LHCb configuration [22]. Decays of hadronic
particles are described by EvtGen [23], in which final-state radiation is
generated using Photos [24]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [25,
*Agostinelli:2002hh] as described in Ref. [27].

##  4 Data set and selection

This analysis uses a data set corresponding to an integrated luminosity of
$3.0\mbox{\,fb}^{-1}$. The data were taken at two different $pp$ centre-of-
mass energies: 7$\mathrm{\,Te\kern-1.00006ptV}$ in 2011
($1.0\mbox{\,fb}^{-1}$) and 8$\mathrm{\,Te\kern-1.00006ptV}$ in 2012
($2.0\mbox{\,fb}^{-1}$). The data sets recorded with each dipole magnet
polarity are roughly equal in size.

At the hardware trigger stage, the events are triggered by the presence of the
muon candidate in the muon system. This requires the muon $p_{\rm T}$ to be
greater than $1.64{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
($1.76{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) for the 2011 (2012) data. At the
software trigger stage, one of the final-state particles is required to have
enough momentum and be significantly displaced from any primary $pp$ vertex.
In addition, the candidates must be selected by a single-muon trigger or by a
topological trigger that requires the muon and one or two of the ${D}^{0}$
daughters to be consistent with the topology of $b$-hadron decays [19].

To further suppress background, the ${D}^{0}$ daughters are required to have
$\mbox{$p_{\rm T}$}>300{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. All final-state
particles are required to have a large impact parameter and be well identified
by the particle identification systems. The impact parameter requirement on
the muon reduces the contribution from ${D}^{0}$ mesons produced directly in
the $pp$ interaction to below $2\%$. The scalar $p_{\rm T}$ sum of the
${D}^{0}$ daughters should be larger than
$1.4{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and the $p_{\rm T}$ of the
${D}^{0}$ candidate should be larger than
$0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The two tracks from the ${D}^{0}$
candidate and the ${{D}^{0}}\mu$ combination are required to form good
vertices and the latter vertex should be closer to the primary vertex than the
${D}^{0}$ vertex. The ${D}^{0}$ decay time is determined from the distance
between these two vertices, and the reconstructed ${D}^{0}$ momentum. The
invariant mass of the ${{D}^{0}}\mu$ combination is required to be between
$2.5$ and $5.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, where the upper bound
suppresses hadronic $b$-hadron decays into three-body final states.
Backgrounds from inclusive $b$-hadron decays into charmonium are suppressed by
vetoing candidates where the invariant mass of the muon and the oppositely
charged ${D}^{0}$ daughter, misidentified as a muon, is consistent with the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ or $\psi{(2S)}$ mass.
Additionally, the invariant mass of the muon and same-charge ${D}^{0}$
daughter, under the muon mass hypothesis, is required to be larger than
$240{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ to remove events where a single
charged particle is reconstructed as two separate tracks. For most selection
requirements, the efficiency is roughly independent of the ${D}^{0}$ decay
time, giving efficiency variations of ${\cal O}(1\%)$. The largest dependence
on the decay time comes from the topological trigger, which introduces an
efficiency profile that decreases with ${D}^{0}$ decay time, resulting in
about 20% relative efficiency loss at large decay times.

##  5 Determination of $A_{\Gamma}$

The mass distributions for the selected
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$,
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ candidates are shown in Fig. 1.
The numbers of signal candidates are determined from unbinned extended
maximum-likelihood fits in the range 1810 to
1920${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The signal for all three decay
modes is modelled by a sum of three Gaussian functions. The first two have the
same mean, but independent widths; the third is used to describe a small
radiative tail, and has a lower mean and larger width. The effective width of
the signal ranges from $7.1{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ candidates to
$9.3{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ candidates. As the final
states ${{K}^{-}}{{K}^{+}}$ and ${{\pi}^{-}}{{\pi}^{+}}$ are charge symmetric,
the shape parameters for the signal are the same for both ${D}^{0}$ and
${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ candidates. The
combinatorial background is modelled by an exponential function. In the
${{\pi}^{-}}{{\pi}^{+}}$ invariant mass distribution, a reflection from
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays is visible in the region
below $1820{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. This background
component is modelled by a single Gaussian function and the fit range is
extended from 1795 to 1930${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The
shape parameters and overall normalisation of the background components are
allowed to differ between ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ candidates. The numbers of
signal candidates obtained from these global fits are $2.34\times 10^{6}$ for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$, $0.79\times 10^{6}$ for
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and $11.31\times 10^{6}$ for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays. The latter number
corresponds to only half of the available
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ candidates, randomly selected,
to reduce the sample size.

(a)(b)

(c)

Figure 1: Invariant mass distributions for (a)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$, (b)
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and (c)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ candidates. The results of the
fits are overlaid. Underneath each plot the pull in each mass bin is shown,
where the pull is defined as the difference between the data point and total
fit, divided by the corresponding uncertainty.

The raw $C\\!P$ asymmetry is determined from fits to the mass distributions in
50 bins of the ${D}^{0}$ decay time. The fits are performed simultaneously for
${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$
candidates and the asymmetry is determined for each decay-time bin. The shape
parameters and relative normalisation for the third Gaussian function and for
the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ reflection background are
fixed from the global fit. All other parameters are allowed to vary in these
fits. In particular, since both the amount and the composition of background
depend on the decay time, the background parameters are free to vary in each
decay-time bin. For decay times larger than $1{\rm\,ps}$ the relative
contribution from combinatorial background increases. This is due to the
exponential decrease of the signal and a less steep dependence of the
combinatorial background on the decay time. The mass distribution in each
decay-time bin is well described by the model.

Events at large ${D}^{0}$ decay times have a larger sensitivity to
$A_{\Gamma}$ compared to events at small decay times, which is balanced by the
fewer signal candidates at large decay times. The binning in ${D}^{0}$ decay
time is chosen such that every bin gives roughly the same statistical
contribution to $A_{\Gamma}$. The value of $A_{\Gamma}$ is determined from a
$\chi^{2}$ fit to the time-dependent asymmetry of Eq. (2). The value of
$A_{\Gamma}$ and the offset in the asymmetry are allowed to vary in the fit,
while the ${D}^{0}$ lifetime is fixed to $\tau=410.1\rm\,fs$ [28]. Due to the
exponential decay-time distribution, the average time in each bin is not in
the centre of the bin. Therefore, the background-subtracted [29] average decay
time is determined in each bin and used in the fit. This fit procedure gives
unbiased results and correct uncertainties, as is verified by simulating many
experiments with large samples.

The measured asymmetries in bins of decay time are shown in Fig. 2, including
the result of the time-dependent fit. The results in the three decay channels
are

$\displaystyle A_{\Gamma}({{K}^{-}}{{K}^{+}})$ $\displaystyle=(-0.134\pm
0.077)\%\ ,$ $\displaystyle A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})$
$\displaystyle=(-0.092\pm 0.145)\%\ ,$ $\displaystyle
A_{\Gamma}({{K}^{-}}{{\pi}^{+}})$ $\displaystyle=(\phantom{-}0.009\pm
0.032)\%\ ,$

where the uncertainties are statistical only. The values for $A_{\Gamma}$ are
compatible with the assumption of no indirect $C\\!P$ violation. The fits have
good $p$-values of $54.3\%$ (${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$),
$30.8\%$ (${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$) and $14.5\%$
(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$). The measured values for the
raw time-integrated asymmetries, which are sensitive to direct $C\\!P$
violation, agree with those reported in Ref. [13].

(a)
(b)
(c)

Figure 2: Raw $C\\!P$ asymmetry as function of ${D}^{0}$ decay time for (a)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$, (b)
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and (c)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ candidates. The results of the
$\chi^{2}$ fits are shown as blue, solid lines with the $\pm 1$ standard-
deviation ($\sigma$) bands indicated by the dashed lines. The green, dashed
lines indicate one ${D}^{0}$ lifetime ($\tau=410.1\rm\,fs$). Underneath each
plot the pull in each time bin is shown.

##  6 Systematic uncertainties and consistency checks

The contributions to the systematic uncertainty on $A_{\Gamma}$ are listed in
Table 1. The largest contribution is due to the background coming from random
combinations of muons and ${D}^{0}$ mesons. When the muon has the wrong charge
compared to the real ${D}^{0}$ flavour, this is called a mistag. The mistag
probability ($\omega$) dilutes the observed asymmetry by a factor
$(1-2\omega)$. This mistag probability is measured using
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays, exploiting the fact that
the final state determines the flavour of the ${D}^{0}$ meson, except for an
expected time-dependent wrong-sign fraction due to ${D}^{0}$–${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing and doubly Cabibbo-
suppressed decays. The mistag probability before correcting for wrong-sign
decays is shown in Fig. 3. After subtracting the (time-dependent) wrong-sign
ratio [3], the mistag probability as function of ${D}^{0}$ decay time is
obtained. The mistag probability is small, with an average around $1\%$, but
it is steeply increasing, reaching 5% at five ${D}^{0}$ lifetimes. This is due
to the increase of the background fraction from real ${D}^{0}$ mesons from
$b$-hadron decays combined with a muon from the opposite-side $b$-hadron
decay. This random-muon background is reconstructed with an apparently longer
lifetime. The time-dependent mistag probability is parameterised by an
exponential function, which is used to determine the shift in $A_{\Gamma}$.
The systematic uncertainty from this time-dependent mistag probability is
$0.006\%$ for the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and $0.008\%$
for the ${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decay mode, with a
supplementary, multiplicative scale uncertainty of $0.05$ for both decay
modes.

Table 1: Contributions to the systematic uncertainty of $A_{\Gamma}({{K}^{-}}{{K}^{+}})$ and $A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})$. The constant and multiplicative scale uncertainties are given separately. Source of uncertainty | ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ | ${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$
---|---|---
| constant | scale | constant | scale
Mistag probability | $0.006\%$ | 0.05 | $0.008\%$ | 0.05
Mistag asymmetry | $0.016\%$ |  | $0.016\%$ |
Time-dependent efficiency | $0.010\%$ |  | $0.010\%$ |
Detection and production asymmetries | $0.010\%$ |  | $0.010\%$ |
${D}^{0}$ mass fit model | $0.011\%$ |  | $0.007\%$ |
${D}^{0}$ decay-time resolution |  | 0.09 |  | 0.07
${B}^{0}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mixing | $0.007\%$ |  | $0.007\%$ |
Quadratic sum | $0.026\%$ | 0.10 | $0.025\%$ | 0.09
Figure 3: Mistag probability, before subtracting the contribution from wrong-
sign (WS) decays, determined with
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ candidates. The result of the
fit to the data points with an exponential function is overlaid (solid, blue
line). The red, dashed line indicates the expected mistag contribution from WS
decays.

The mistag probabilities can potentially differ between positive and negative
muons. Such a mistag asymmetry would give a direct contribution to the
observed asymmetry. The slope of the mistag asymmetry is also obtained from
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays. This slope is consistent
with no time dependence, and its statistical uncertainty ($0.016\%$) is
included in the systematic uncertainty on $A_{\Gamma}$.

The selection of signal candidates, in particular the topological software
trigger, is known to introduce a bias in the observed lifetime. Such a bias
could be charge dependent, thus biasing the measurement of $A_{\Gamma}$. It is
studied with the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ sample and a
sample of ${{D}^{-}}\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ decays from
semileptonic $b$-hadron decays. No asymmetry of the topological triggers in
single-muon-triggered events is found within an uncertainty of $0.010\%$. This
number is propagated as a systematic uncertainty.

The detection and production asymmetries introduce a constant offset in the
raw time-dependent asymmetries. Since these asymmetries depend on the muon or
$b$-hadron momentum, they can also introduce a time dependence in case the
momentum spectrum varies between decay-time bins. This effect is tested by
fitting the time-dependent asymmetry after weighting the events so that all
decay-time bins have the same ${D}^{0}$ or muon momentum distribution. The
observed shifts in $A_{\Gamma}$ are within the statistical variations. The
shift ($0.010\%$) observed in the larger
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ sample, which has the same
production asymmetry and larger detection asymmetry, is taken as a measure of
the systematic uncertainty.

An inaccurate model of the mass distribution can introduce a bias in
$A_{\Gamma}$. The effect on the observed asymmetries is studied by applying
different models in the fits to the invariant mass distributions. For the
signal, a sum of two Gaussian functions with and without an exponential tail,
and for the background a first and a second-order polynomial are tested. The
maximum variation from the default fit for each decay mode ($0.011\%$ for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$; $0.007\%$ for
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$) is taken as a systematic
uncertainty on $A_{\Gamma}$.

The ${D}^{0}$ decay-time resolution affects the observed time scale, and
therefore changes the measured value of $A_{\Gamma}$. For each decay mode, the
resolution function is obtained from the simulation, which shows that for the
majority of the signal ($90\%$) the decay time is measured with an RMS of
about $103\rm\,fs$. The remaining candidates ($10\%$) are measured with an RMS
of about $312\rm\,fs$. The theoretical decay rates are convolved with the
resolution functions in a large number of simulated experiments. The effect of
the time resolution scales linearly with the size of $A_{\Gamma}$. The
corresponding scale uncertainty on $A_{\Gamma}$ is $0.09$ for the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ decay mode and $0.07$ for the
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decay mode. Decays where the
muon gives the correct tag but the decay time is biased, e.g., when the muon
originates from a $\tau$ lepton in the semileptonic $b$-hadron decay, are
studied and found to be negligible.

About 40% of the muon-tagged ${D}^{0}$ decays originate from neutral $B$
mesons [30]. Due to ${B}^{0}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mixing the observed production
asymmetry depends on the ${B}^{0}$ decay time [31]. A correlation between the
${B}^{0}$ and ${D}^{0}$ decay times may result in a shift in the measured
value of $A_{\Gamma}$. The effect of this correlation, determined from
simulation, together with a $1\%$ ${B}^{0}$ production asymmetry [32, 31], is
estimated to be a shift of $0.007\%$ in the observed value of $A_{\Gamma}$.
This is taken as systematic uncertainty.

Possible shifts in $A_{\Gamma}$ coming from the $1.5\rm\,fs$ uncertainty on
the world-average ${D}^{0}$ lifetime [28], from the uncertainty on the
momentum scale and detector length scale [33, 34] and from potential biases in
the fit method are negligible.

The scale uncertainty (cf. Table 1) gives a small contribution to the overall
systematic uncertainty, which depends on the true value of $A_{\Gamma}$. In
order to present a single systematic uncertainty, the effect of the scale
uncertainty is evaluated with a Neyman construction [35]. For each true value
of $A_{\Gamma}$, the absolute size of the scale uncertainty is known and added
in quadrature to the constant uncertainty. In this way, a confidence belt of
observed values versus true values is constructed. This procedure gives a
slightly asymmetric systematic uncertainty, which is ${}^{+0.026}_{-0.034}\%$
for the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ decay channel and
${}^{+0.025}_{-0.033}\%$ for the
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decay channel. Except for the
contribution from the mass fit model, all contributions to the systematic
uncertainty are fully correlated, resulting in an overall correlation
coefficient of $89\%$ between the systematic uncertainties of
$A_{\Gamma}({{K}^{-}}{{K}^{+}})$ and $A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})$.

Additional checks have been performed to determine potential sensitivity of
the measurements on the data-taking conditions, detector configuration, and
analysis procedure. Changing to a finer decay-time binning yields compatible
results. Potential effects on the measurement of $A_{\Gamma}$ coming from
detection asymmetries are expected to appear when dividing the data set by
magnet polarity and data-taking period. Detection asymmetries originating from
a left-right asymmetric detector change sign when reversing the magnet
polarity. Similarly, during the two data-taking periods, detection asymmetries
and production asymmetries might have changed due to different running
conditions. As shown in Fig. 4, there is no significant variation of
$A_{\Gamma}$ across various configurations. Also splitting the data set
according to the number of primary vertices or in bins of the $B$ decay time
does not show any deviation in the measured values of $A_{\Gamma}$.

(a)(b)

(c)

Figure 4: Measured values of $A_{\Gamma}$ for different magnet polarities and
data-taking periods for (a) ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$, (b)
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ and (c)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays. The vertical line and
error band indicate the average $A_{\Gamma}$ obtained from the combined data
set. The error bars indicate the statistical uncertainty only.

##  7 Conclusions

The time-dependent $C\\!P$ asymmetries in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays are measured using
muon-tagged ${D}^{0}$ mesons originating from semileptonic $b$-hadron decays
in the 3.0$\mbox{\,fb}^{-1}$ data set collected with the LHCb detector in 2011
and 2012. The asymmetries in the effective lifetimes are measured to be

$\displaystyle A_{\Gamma}({{K}^{-}}{{K}^{+}})=(-0.134\pm
0.077\;{}^{+0.026}_{-0.034})\%\ ,$ $\displaystyle
A_{\Gamma}({{\pi}^{-}}{{\pi}^{+}})=(-0.092\pm 0.145\;{}^{+0.025}_{-0.033})\%\
,$

where the first uncertainty is statistical and the second systematic. Assuming
that indirect $C\\!P$ violation in ${D}^{0}$ decays is universal [10], and
accounting for the correlation in the systematic uncertainties, the average of
the two measurements becomes $A_{\Gamma}=(-0.125\pm 0.073)\%$. The results in
this paper are uncorrelated with the time-integrated asymmetries reported in
Ref. [13]. The results are consistent with other $A_{\Gamma}$ measurements [1,
11, 12], and independent of the $A_{\Gamma}$ measurements [11] from LHCb using
${D}^{0}$ mesons from ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ decays. They
are consistent with the hypothesis of no indirect $C\\!P$ violation in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy);
FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are
supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted
to the communities behind the multiple open source software packages on which
we depend. We are also thankful for the computing resources and the access to
software R&D tools provided by Yandex LLC (Russia). Individual groups or
members have received support from EPLANET, Marie Skłodowska-Curie Actions and
ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and
OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain),
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

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Spaan9, P. Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl38, O.
Steinkamp40, O. Stenyakin35, F Sterpka59, S. Stevenson55, S. Stoica29, S.
Stone59, B. Storaci40, S. Stracka23,t, M. Straticiuc29, U. Straumann40, R.
Stroili22, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4,
M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J.
van Tilburg41, V. Tisserand4, M. Tobin39, J. Todd57, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, K Trabelsi39, M.T. Tran39, M. Tresch40, A. Trisovic38, A.
Tsaregorodtsev6, P. Tsopelas41, N. Tuning41,38, M. Ubeda Garcia38, A.
Ukleja28, A. Ustyuzhanin65, U. Uwer11, C. Vacca15,e, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez
Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M.
Vesterinen11, J.V. Viana Barbosa38, B. Viaud7, D. Vieira2, M. Vieites Diaz37,
X. Vilasis-Cardona36,p, A. Vollhardt40, D. Volyanskyy10, D. Voong46, A.
Vorobyev30, V. Vorobyev34, C. Voß63, J.A. de Vries41, R. Waldi63, C.
Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59, D.R. Ward47,
N.K. Watson45, D. Websdale53, M. Whitehead48, D. Wiedner11, G. Wilkinson55,38,
M. Wilkinson59, M.P. Williams45, M. Williams56, H.W. Wilschut67, F.F.
Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M. Witek26, G. Wormser7,
S.A. Wotton47, S. Wright47, K. Wyllie38, Y. Xie61, Z. Xing59, Z. Xu39, Z.
Yang3, X. Yuan34, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b, L. Zhang3,
W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Yandex School of Data Analysis, Moscow, Russia, associated to 31
66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
67Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41
68Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy


# PhishChain: A Decentralized and Transparent System to Blacklist Phishing
URLs

Shehan Edirimannage†, Mohamed Nabeel‡, Charith Elvitigala†, Chamath
Keppitiyagama† †University of Colombo School of Computing‡Qatar Computing
Research InstituteSri Lanka, Qatar

(2021)

###### Abstract.

Blacklists are a widely-used Internet security mechanism to protect Internet
users from financial scams, malicious web pages and other cyber attacks based
on blacklisted URLs. In this demo, we introduce PhishChain, a transparent and
decentralized system to blacklisting phishing URLs. At present, public/private
domain blacklists, such as PhishTank, CryptoScamDB, and APWG, are maintained
by a centralized authority, but operate in a crowd sourcing fashion to create
a manually verified blacklist periodically. In addition to being a single
point of failure, the blacklisting process utilized by such systems is not
transparent. We utilize the blockchain technology to support transparency and
decentralization, where no single authority is controlling the blacklist and
all operations are recorded in an immutable distributed ledger. Further, we
design a page rank based truth discovery algorithm to assign a phishing score
to each URL based on crowd sourced assessment of URLs. As an incentive for
voluntary participation, we assign skill points to each user based on their
participation in URL verification.

Phishing URLs, Blacklisting, Blockchain, Smart Contracts, Crowdsourcing, Truth
Inference

††copyright: acmcopyright††journalyear: 2021††conference: ; April 25-29, 2022;
The Web Conference 2022

##  1\. Introduction

Crowdsourced phishing blacklists such as PhishTank, CryptoScamDB and APWG are
quite useful in practice to defend against phishing attacks. Out of these
services, PhishTank, has been the longest serving and most widely used crowd-
sourced phishing blacklist. While it has been instrumental in maintaining a
ledger of phishing URLs, it suffers from several limitations: (1) centralized
architecture with a single point of failure, (2) lack of transparency, (3)
lack of incentive to participate and (4) prone to manipulations. In fact,
these are common issues for all existing centralized blacklisting systems.
Focusing on PhishTank and for example, Figure 1 shows inconsistent assignment
of final labels to URLs in PhishTank. The figure on the left shows a URL
marked as phishing even though all 5 crowd sourced verifiers ascertain it is
phishing. The figure on the right, on the other hand, shows that a URL is
marked as not phishing even though no one has verified it. It is not clear how
PhishTank arrived at the final decision and raises concerns on the
transparency.

Figure 1. PhishTank inconsistent examples

We propose PhishChain, a transparent and decentralized system to blacklist
phishing URLs in a crowd-sourced manner while addressing the limitations
mentioned above. We envision a blacklisting system where a consortium of
mostly targeted organizations such as Paypal, Apple, Microsoft and Facebook
form an alliance to put our proposal to use. Our key design goals are as
follows: (1) System should be decentralized where anyone can participate and
no single authority should be controlling it, (2) All operations should be
immutable and recorded, (3) URLs should be assigned a final phish score based
on the participants’ assessment, (4) Participants should be incentivized by
assigning skill points instead of a cryptocurrency in order to encourage
voluntary participation 111Phishtank and APWG work through voluntary
participation, but we observe that only a handful of participants contribute
to the lists maintained., and (5) The system and data should be publicly
available for anyone to consume.

There are a few notable efforts to build blockchain based decentralized
solutions for phishing blacklisting or crowd sourcing in general. However,
they suffer from one or two drawbacks. PhishLedger (Liu et al., 2019) is a
private blockchain solution for blacklisting phishing URLs, and they do not
support crowd sourcing. Further, the system is not available for public
consumption and is managed in a closed environment. Hence, the verifications
performed in this system are questionable. CrowdBC (Li et al., 2019) and
ZebraLancer (Lu et al., 2018) are blockchain based crowd sourcing systems, but
they rely on a cryptocurrency to maintain the functionality.

Demonstration Scenarios: PhishChain is designed as the next generation
decentralized phishing blacklisting system. We show the following three use
cases. (1) URL verification, (2) URL detailed dashobard and transaction, and
(3) URL verification graph and timeline along with the phish score and
verifier skill points.

##  2\. System Architecture

###  2.1. Overall System Design

Figure 2 shows the overall system architecture. The key components in the
system are blockchain network, smart contracts, truth discovery algorithm, and
API services modules. The system supports three main functions in addition to
user and system management functionality: (1) URL submission, (2) URL
verification and (3) URL lookup.

Figure 2. High Level System Design

Blockchain Network Module: Blockchain network is the backbone of the
decentralized infrastructure. Each node in our blockchain network is either a
validator or a normal node. A validator node validates each and every
transaction whereas a normal node is a read-only participant. Note that the
validation node only participate in the blockchain block verification process
similar to committing data to the blockchain ledger, whereas the verifier
participates in the URL verification process itself. Istanbul Byzantine Fault
Tolerance is utilized as the consensus algorithm since our threat model
assumes that there can be malicious participants. In order to meet our system
goals, a consortium type blockchain system called, Quorum (ConsenSys, 2021a),
is employed as the blockchain network. Tessera (ConsenSys, 2021b) is used to
manage transactions of the Quorum network.

Smart Contract Module: The crowd source functionality is implemented using
smart contracts (Solidity version 0.5.0). We categorize the smart contracts
into three main groups: (1) user management, (2) URL management and (3) URL
verification.

Truth Discovery Module: In our crowd sourcing environment, URL verifiers are
the workers and the task is to assess if a URL is phishing or non phishing.
Due to the varying degree of expertise and experience of verifiers, one cannot
simply take, for example, the majority answer as the final phish score of a
URL. Instead, a truth discovery algorithm which takes potentially conflicting
status for a URL and verifier information, and arrives at the final phish
score, should be employed. We observe that existing truth discovery algorithms
developed by the database community (Li et al., 2016) are performing poorly on
our problem as these algorithms assume that the majority of the verifiers
respond to each URL verification task, which is not true for verifying URLs.
Our retrospective analysis of PhishTank URLs show that only a handful of
verifiers verify a given URL even though there are thousands of them
altogether. Hence, we design a new truth discovery algorithm by leveraging
page ranking (PR) algorithm on _verifier-verifier graph_. We construct the
verifier-verifier graph by using the “ _follower_ ” relationship. We define
verifier $v_{1}$ follows $v_{2}$ for a given URL if $v_{1}$ verifies the URL
before $v_{2}$. A directed edge from $v_{1}$ to $v_{2}$ is created in this
case. The generated graph represent real world relationships among users which
captures how users are following others and how they are being followed.
Applying the page rank algorithm on top of this graph computes a rank, a real
value number between 0 and 1, for each node (i.e. user), indicating how
important it is with respect to the whole user population. It follows the
intuition that, the more the number of followers are, the more recognition a
user receive from its peers. We utilize the computed ranks to calculate the
weighted voting score for each URL and assess if it is phishing or not.

Table 1 shows how our algorithm outperforms in comparison to popular truth
discovery algorithms on a real-world dataset obtained from PhishTank. We
collect URLs submitted and verified in PhishTank from January 1st 2020 to
December 23rd 2020\. The cleaned dataset contains 17,000 phishing URLs and
6,000 non phishing URLs. We scrape the additional information of each of these
URLs to identify the verifiers and their order of verification. We use a
balanced dataset of 6,000 URLs from each class for the evaluation.

We use our PR based algorithm to assign skill points to verifiers as well as
final phish score to URLs. The skill points of verifiers are computed based on
the verifier reputation score returned by the truth discovery algorithm and
the proportion of correctly labeled URLs. The phish score of a URL is computed
with the weighted score of phishing and non phishing verifiers.

Note that in PhishChain system, we enforce transparency and consistency on the
data by following the consensus algorithm. In other words, all the data
related to URLs (URLs themselves, votes, status) on the blockchain is
consistent and hardened from unauthorized modifications. While our system has
a separate truth discovery server for URL verification due to the practical
limitations in the Solidity framework utilized, as the algorithm and the data
are publicly available and verifiable, any user can verify the the results
produced by the URL verification proces is indeed correct.

Table 1. Truth Discovery Algorithm Comparison Algorithm |  Acc. |  Prec. |  Rec.
---|---|---|---
Our Approach |  95.45% |  96.74% |  94.31%
EM |  93.71% |  91.01% |  97.75%
GLAD |  93.98% |  91.72% |  97.39%

API Services Module: This module facilitates the communication with the
blockchain network. The demo web application we build is a consumer of this
API.

##  3\. Demonstration

In this section, we describe the main use cases of our system. As shown in
Figure 3, we setup a consortium blockchain consisting of 7 validation nodes
each possessing a copy of the blockchain ledger and participating in
validating each transaction. In a real-world setup, these validation nodes are
to be hosted by organizations mostly targeted by phishers (e.g. Paypal,
Facebook, Microsoft) as such a system is in their best interest to defend
against phishing attacks and a collective effort is likely to yield a
significantly better blocklist compared to having individual systems.

Figure 3. Cakeshop blockchain explorer showing the Quorum

###  3.1. URL Verification

Any user can sign up and participate in the process of submission and
verification of URLs. Figure 4 shows the UI for the verification of a given
URL as phishing or not phishing. Once user submits their verdict, the
validation nodes validate the transaction adhering to the consensus algorithm
resulting the transaction shown in Figure 5. Once verified, if there are at
least 3 votes for the URL, truth discovery model is invoked and assigns the
ULR’s calculated score where a positive score indicates that the URL is a
phishing URL. Note that the users in here are real-world users with varying
degree of domain expertise who may either submit URLs or verify whether the
URL is phishing or not. Further, in order to limit the abuse of the system,
PhishChain enforces that each URL submitted to the system should be
accompanied with a valid email referring to the the URL 222Similar to existing
blocklists, the goal of PhishChain to assess suspicious URLs found in likely
phishing emails..

Figure 4. UI for URL Verification

Figure 5. UI for URL Verification Transaction Details

###  3.2. URL Detailed Dashboard

Figure 6 shows the details of the URL submitted by user 1, and it is verified
by users 3 and 4 as phishing and users 2 and 5 as non phishing. The system
assigns an overall final phishing score of 0.3452 based on PR based truth
discovery algorithm. Since it is a positive value, the system concludes that
the URL is a phishing URL at that point in time.

Figure 6. UI for URL Detailed Dashboard

###  3.3. URL Verification Graph and Timeline

Figure 7 and Figure 8 show the verification graph and the timeline of
verification respectively. Based on the participation in the system and the
proportion of accurately labeled URLs, each user is assigned skill points. For
example, user 1 has the highest skill points of 153. Notice that after the 3rd
vote, the URL is marked as phishing with a score of 0.64, but after the 4th
vote, URL is still marked as phishing but with a lower phishing score of 0.35.
The phishing score changes with every additional vote as truth discovery
algorithm is invoked on affected URLs. Such a detailed timeline easily allows
an analyst to not only assess the latest status but also understand how our
system arrived at the decision.

Figure 7. UI for URL Verification Graph

Figure 8. UI for URL Verification Timeline

##  4\. Discussion

The motivation for introducing skill points is inspired from the question
answering systems such as StackOverflow and StackExchange. Such systems show
that even though participants do not receive any monetary benefits by
contributing, these participants attain various “expertise” levels that have
far more significance in their respective domains. We believe a similar system
for malicious URL verification could assist solve the problem of the limited
participation in the volunteer based blacklisting systems currently available.

In this work, we assume that users do not maliciously try to manipulate the
truth discovery based system. However, one may extend PhishChain to defend
against such manipulations by introducing additional mechanisms that the
reputation/recommender system community has already made available (Friedman
et al., 2007).

##  5\. Conclusions

We propose, PhishChain, a truly transparent and decentralized phishing URL
blacklisting system that is managed by a consortium instead of a centralized
entity. Based on the proposed page rank based truth discovery algorithm, we
compute a phish score for each URL as well as verifier skill points. Smart
contracts are employed to implement the proposed functionality over the Quorum
blockchain. We demonstrate three use cases: (1) URL verification, (2) URL
dashboard and its transaction, and (3) URL verification graph and timeline. We
believe our approach is generally applicable to any crowd sourced blacklisting
system.

## References

  * (1)
  * ConsenSys (2021a) ConsenSys. 2021a.  Quorum.  Available at https://consensys.net/quorum.
  * ConsenSys (2021b) ConsenSys. 2021b.  Tessera.  Available at https://github.com/ConsenSys/tessera.
  * Friedman et al. (2007) Eric Friedman, Paul Resnick, and Rahul Sami. 2007\.  Manipulation-resistant reputation systems.  _Algorithmic Game Theory_ 677 (2007).
  * Li et al. (2019) M. Li, J. Weng, A. Yang, W. Lu, Y. Zhang, L. Hou, J. Liu, Y. Xiang, and R. Deng. 2019\.  CrowdBC: A blockchain-based decentralized framework for crowdsourcing.  _IEEE Trans. on Para. and Dist. Sys._ 30, 6 (2019), 1251–1266.
  * Li et al. (2016) Yaliang Li, Jing Gao, Chuishi Meng, Qi Li, Lu Su, Bo Zhao, Wei Fan, and Jiawei Han. 2016.  A Survey on Truth Discovery.  _ACM SIGKDD Explorations Newsletter_ 17, 2 (2016), 1–16.  https://doi.org/10.1145/2897350.2897352 arXiv:1505.02463
  * Liu et al. (2019) D. Liu, W. Wang, Y. Wang, and Y. Tan. 2019\.  PhishLedger: A decentralized phishing data sharing mechanism.  _ACM International Conference Proceeding Series_ (2019), 84–89.
  * Lu et al. (2018) Y. Lu, Q. Tang, and G. Wang. 2018.  ZebraLancer: Crowdsource Knowledge atop Open Blockchain, Privately and Anonymously.  July (2018), 1–17.  arXiv:1803.01256 http://arxiv.org/abs/1803.01256