#  $C\\!P$ violation and CKM studies (and first LHCb Run II results)

Nikhef and CERN
E-mail

###### Abstract:

The LHC is the new $b$-hadron factory and will be dominating flavour physics
until the start of Belle II, and beyond in many decay modes. While the $B$
factories and Tevatron experiments are still analysing their data, ATLAS, CMS
and LHCb are producing interesting new results in $C\\!P$ violation and rare
decays, that set strong constraints on models beyond that SM and exhibit some
discrepancies with the SM predictions. The LHCb collaboration used the LHC 50
ns ramp-up period of July 2015 to measure the double-differential
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$,
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$-from-$b$-hadron and charm
cross-sections at $\sqrt{s}=13\>\mathrm{\,Te\kern-1.00006ptV}$. Both
measurements were performed directly on triggered candidates using a reduced
data format that does not require offline processing.

##  1 Introduction

The first run of the Large Hadron Collider with 7 and 8
$\mathrm{\,Te\kern-1.00006ptV}$ $pp$ collisions has allowed to discover the
Higgs boson [1, *Chatrchyan:2012ufa], but not to find any hint of the
existence of other new particles. Neither supersymmetry nor any other sign of
new physics has popped out of the LHC. This situation may change during Run II
with a higher centre-of-mass energy of 13 $\mathrm{\,Te\kern-1.00006ptV}$. At
the same time it is worth investigating what the data at the lower energies
involved in the decays of $b$ hadrons can tell us about new physics.

Studies of $C\\!P$ violation in heavy flavour decays are both sensitive to the
above-mentioned high mass scales and to potential new phases beyond the phase
of the CKM matrix. Also of particular interest are rare decays that are
strongly suppressed in the Standard Model (SM), where new physics amplitudes
could be sizeable [3].

##  2 The Kobayashi-Maskawa mechanism

Flavour physics has played a prominent role in the development of the SM. As
an example, one of the most notable predictions made in this context was that
of the existence of a third quark generation, in a famous paper of 1973 by
Makoto Kobayashi and Toshihide Maskawa [4]. This work won them the Nobel Price
in Physics in 2008 “for the discovery of the origin of the broken symmetry
which predicts the existence of at least three families of quarks in nature”.
Kobayashi and Maskawa extended the Cabibbo [5] (with only $u$, $d$, and $s$
quarks) and the Glashow-Iliopoulos-Maiani [6] (GIM, including also the $c$
quark) mechanisms, pointing out that $C\\!P$ violation could be incorporated
into the emerging picture of the SM if six quarks were present. This is
commonly referred to as the Kobayashi-Maskawa (KM) mechanism. It must be
emphasised that at that time only hadrons made of the three lighter quarks had
been observed. An experimental revolution took place in 1974, when a new state
containing the $c$ quark was discovered almost simultaneously at Brookhaven
[7] and SLAC [8]. Then, the experimental observations of the $b$ [9] and $t$
[10] quarks were made at FNAL in 1977 and 1995, respectively.

The idea of Kobayashi and Maskawa, formalised in the so-called Cabibbo-
Kobayashi-Maskawa (CKM) quark mixing matrix, was then included in the SM by
the beginning of the 1980’s. The phenomenon of $C\\!P$ violation, first
revealed in 1964 using decays of neutral kaons [11], was elegantly accounted
for as an irreducible complex phase within the CKM matrix. The experimental
proof of the validity of the KM mechanism and the precise measurement of the
value of the $C\\!P$-violating phase soon became questions of paramount
importance.

###  2.1 The CKM matrix

In the SM, charged-current interactions of quarks are described by the
Lagrangian

$\mathcal{L}_{W^{\pm}}=-\frac{g}{\sqrt{2}}\overline{U}_{i}\gamma^{\mu}\frac{1-\gamma^{5}}{2}\left(V_{\rm
CKM}\right)_{ij}D_{j}W_{\mu}^{+}+h.c.,$

where $g$ is the electroweak coupling constant and $V_{\rm CKM}$ is the CKM
matrix

$V_{\rm CKM}=\left(\begin{array}[]{lcr}V_{ud}&V_{us}&V_{ub}\\\
V_{cd}&V_{cs}&V_{cb}\\\ V_{td}&V_{ts}&V_{tb}\end{array}\right),$

originating from the misalignment in flavour space of the up and down
components of the $SU(2)_{L}$ quark doublet of the SM. The $V_{ij}$ matrix
elements represent the couplings between up-type quarks $U_{i}=(u,\,c,\,t)$
and down-type quarks $D_{j}=(d,\,s,\,b)$.

###  2.2 Wolfenstein parameterisation

Experimental information leads to the evidence that transitions within the
same generation are characterised by $V_{\rm CKM}$ elements of
$\mathcal{O}(1)$. Instead, those between the first and second generations are
suppressed by a factor $\mathcal{O}(10^{-1})$; those between the second and
third generations by a factor $\mathcal{O}(10^{-2})$; and those between the
first and third generations by a factor $\mathcal{O}(10^{-3})$. The CKM matrix
can be re-written as a power expansion of the parameter $\lambda$ (which
corresponds to $\sin{\theta_{C}}$) [12]

$V_{\rm
CKM}=\left(\begin{array}[]{ccc}1-\frac{1}{2}\lambda^{2}-\frac{1}{8}\lambda^{4}&\lambda&A\lambda^{3}\left(\rho-i\eta\right)\\\
-\lambda+\frac{1}{2}A^{2}\lambda^{5}\left[1-2(\rho+i\eta)\right]&1-\frac{1}{2}\lambda^{2}-\frac{1}{8}\lambda^{4}(1+4A^{2})&A\lambda^{2}\\\
A\lambda^{3}\left[1-(\rho+i\eta)\left(1-\frac{1}{2}\lambda^{2}\right)\right]{}&~{}-A\lambda^{2}+\frac{1}{2}A\lambda^{4}\left[1-2(\rho+i\eta)\right]{}&~{}1-\frac{1}{2}A^{2}\lambda^{4}\end{array}\right),$

which is valid up to $\mathcal{O}\left(\lambda^{6}\right)$. With this
parameterisation, the CKM matrix is complex, and hence $C\\!P$ violation is
allowed for, if and only if $\eta$ differs from zero. To lowest order the
Jarlskog parameter [13] is

$J_{C\\!P}\equiv\left|\Im\left(V_{i\alpha}V_{j\beta}V_{i\beta}^{*}V_{j\alpha}^{*}\right)\right|=\lambda^{6}A^{2}\eta,\qquad\left(i\neq
j,\alpha\neq\beta\right),$

and, as expected, is directly related to the $C\\!P$-violating parameter
$\eta$.

###  2.3 The unitarity triangle

The unitarity condition of the CKM matrix, $V_{\rm CKM}V_{\rm
CKM}^{\dagger}=V_{\rm CKM}^{\dagger}V_{\rm CKM}=\mathbb{I}$, leads to a set of
12 equations: 6 for diagonal terms and 6 for off-diagonal terms. In
particular, the equations for the off-diagonal terms can be represented as
triangles in the complex plane, all characterised by the same area
$J_{C\\!P}/2$. Only two out of these six triangles have sides of the same
order of magnitude, $\mathcal{O}(\lambda^{3})$:

$\displaystyle\underbrace{V_{ud}V_{ub}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{cd}V_{cb}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{td}V_{tb}^{*}}_{\mathcal{O}(\lambda^{3})}$
$\displaystyle=$ $\displaystyle 0,$
$\displaystyle\underbrace{V_{ud}V_{td}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{us}V_{ts}^{*}}_{\mathcal{O}(\lambda^{3})}+\underbrace{V_{ub}V_{tb}^{*}}_{\mathcal{O}(\lambda^{3})}$
$\displaystyle=$ $\displaystyle 0.$

These two triangles in the complex plane are represented in Fig. 1. In
particular, the triangle defined by the former equation is commonly referred
to as _the_ unitarity triangle (UT).

Figure 1: Representation in the complex plane of the non-squashed triangles
obtained from the off-diagonal unitarity relations of the CKM matrix.

The sides of the UT are given by

$R_{u}\equiv\left|\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}}\right|=\sqrt{\bar{\rho}^{2}+\bar{\eta}^{2}},$
$R_{t}\equiv\left|\frac{V_{td}V_{tb}^{*}}{V_{cd}V_{cb}^{*}}\right|=\sqrt{\left(1-\bar{\rho}\right)^{2}+\bar{\eta}^{2}},$

where to simplify the notation the parameters $\bar{\rho}$ and $\bar{\eta}$,
namely the coordinates in the complex plane of the only non-trivial apex of
the UT, the others being (0, 0) and (1, 0), have been introduced. The angles
of the UT are related to the CKM matrix elements as

$\alpha\equiv\arg{\left(-\frac{V_{td}V_{tb}^{*}}{V_{ud}V_{ub}^{*}}\right)}=\arg{\left(-\frac{1-\bar{\rho}-i\bar{\eta}}{\bar{\rho}+i\bar{\eta}}\right)},$
$\beta\equiv\arg{\left(-\frac{V_{cd}V_{cb}^{*}}{V_{td}V_{tb}^{*}}\right)}=\arg{\left(\frac{1}{1-\bar{\rho}-i\bar{\eta}}\right)},$
$\gamma\equiv\arg{\left(-\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}}\right)}=\arg{\left(\bar{\rho}+i\bar{\eta}\right)}.$

The second non-squashed triangle has similar characteristics with respect to
the UT. The apex is placed in the point $(\rho,~{}\eta)$ and is tilted by an
angle

$\beta_{s}\equiv\arg{\left(-\frac{V_{ts}V_{tb}^{*}}{V_{cs}V_{cb}^{*}}\right)}=\lambda^{2}\eta+\mathcal{O}(\lambda^{4}).$

##  3 $C\\!P$ violation measurements

Owing to the legacy of the $B$ factories [14], we have entered the era of
precision tests of the CKM paradigm.Precise measurements of the angles of the
unitarity triangle(s) are needed to search for new sources of $C\\!P$
violation beyond the single phase of the CKM matrix.

Figure 2: CKM unitarity triangle fit status in Summer 2015. Plot from Ref.
[15].

In some cases, listed below, the same quantity—for instance the angle
$\gamma$—can be measured in different ways and the results can be compared. In
most cases though, the measurements serve as inputs to global fits of the
unitarity triangle and the overall consistency is checked. The latest fit from
the CKMFitter group is shown in Fig. 2 [15]. Similar fits with slightly
different assumptions are done by the UTFit collaboration [16]. The overall
consistency is good with the present uncertainties, though some tensions can
be seen between the intersection of the $V_{{u}{b}}$ circle and $\Delta m_{s}$
circles, and the $\sin 2\beta$ diagonal. See below for more details.

###  3.1 ${B}^{0}$ mixing

Figure 3: Feynman diagrams of (left) the dominating SM contribution to
${B}^{0}$ oscillations, and (right) the decay
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$.

The mode which allowed for the first observation of $C\\!P$ violation in $B$
decays is ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$. It allows the measurements of
$\varphi_{d}$, the relative phase between the decay of the ${B}^{0}$ meson to
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ ${K}^{0}_{\rm\scriptscriptstyle
S}$ and that of the oscillation of ${B}^{0}$ to ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ followed by the decay ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$. In the SM it is equal to $2\beta$
[17] and thus the amplitude of the oscillation is a measurement of $\sin
2\beta$. The diagrams corresponding to the dominating SM amplitudes are shown
in Fig. 3. The $B$ factories were optimised for its measurement[14, 18,
*Adachi:2012et] and determined [20]

$\sin 2\beta^{\text{Measured}}=0.682\pm 0.019,$

which defines the most precise constraint on the unitarity triangle (Fig. 2).
Recently LHCb joined the effort, publishing their first measurement of the
time dependent $C\\!P$ asymmetry in the decay
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ [21] with an uncertainty
competitive with the individual measurements from the $B$ factories. With the
upcoming LHC Run II, this will allow for further reducing the uncertainties.

The measured value is slightly lower than the expectation from all other
constraints on the UT [22]

$\sin 2\beta^{\text{Expected}}=0.771{\>}^{+{\>}0.017}_{-{\>}0.041}.$

This $2\sigma$ tension could be due to the so far neglected contribution from
penguin topologies in the decay
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ or in other
${b}\\!\rightarrow{c}{\overline{c}}{s}$ decays to $C\\!P$ eigenstates. This
penguin pollution is described in more detail in Section 3.4.

Another approach is to use decays that are less (or differently) affected by
such pollutions, like decays to open charm. Babar and Belle have recently
published their first joint paper, about the decay ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow
D_{C\\!P}^{(*)}h^{0}$ [23]. The determined value of $\sin 2\beta$ is
consistent with expectations but the uncertainty does not yet allow to
discriminate between the observed and expected values mentioned above. This
year LHCb also published a Dalitz plot analysis of the decay
${{B}^{0}}\\!\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{+}}{{\pi}^{-}}$, which
will eventually allow a measurement of $\sin 2\beta$ [24].

The frequency of ${B}^{0}$ mixing $\Delta m_{d}$ also sets strong constraints
on the Unitarity Triangle (UT) side opposite to the angle $\gamma$, especially
when combined with its ${B}^{0}_{s}$ counterpart $\Delta m_{s}$. LHCb has
recently presented a new preliminary measurement using
${{B}^{0}}\\!\rightarrow D^{(*)-}{\mu^{+}}\nu_{\mu}X$. A value of $(\Delta
m_{d})^{\text{LHCb}}=\left(503.6\pm 2.0\pm 1.3\right)\>\rm ns^{-1}$ is
obtained [25, *LHCb-PAPER-2015-031], which has a better precision than the
HFAG average [20], which including it becomes $(\Delta
m_{d})^{\text{World}}=\left(505.5\pm 2.0\right)\>\rm ns^{-1}$. This result is
not yet included in the latest UT fits.

###  3.2 ${B}^{0}_{s}$ mixing

The LHC is often considered as a ${B}^{0}_{s}$ meson factory, owing to its
large cross-section and the unprecedented capabilities of the LHC experiments
to precisely resolve oscillations.

This opens the door to precision measurements of the $C\\!P$-violating phase
$\varphi_{s}^{{c}{\overline{c}}{s}}$, which is equal to
$-2\beta_{s}\equiv-2\arg\left(-{V_{{t}{s}}}{V_{{t}{b}}^{\ast}}/{V_{{c}{s}}}{V_{{c}{b}}^{\ast}}\right)=-0.0363\pm
0.0013$ in the SM [15], neglecting sub-leading penguin contributions. It was
measured at the LHC using the flavour eigenstate
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decay with ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$ and
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$ [27, 28, 29] and
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ [30]. Recently LHCb used the decay
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{K}^{-}}$ for the first time in a polarisation-dependent way
[31]. Combined with
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$, LHCb obtains
$\varphi_{s}^{{c}{\overline{c}}{s}}=-0.010\pm 0.039$ rad. The decay mode
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ is also used by CMS [32], ATLAS [27], CDF [33] and D0 [34]. The
constraints on $\varphi_{s}^{{c}{\overline{c}}{s}}$ and the decay width
difference $\Delta\Gamma_{s}=\Gamma_{L}-\Gamma_{H}$ are shown in Fig. 4
(left).

The ${B}^{0}_{s}$ meson system has many features in common with that of the
${K}^{0}$ meson, with a heavy long-lived and a light short-lived eigenstate.
The two lifetimes are shown in Fig 4 (right). The a priori unknown admixture
of the two states contributing to a given non-flavour-specific decay causes
uncertainties in the measurement of branching fractions, for instance for the
decay ${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}\mu^{-}}$, see Ref. [35,
*DeBruyn:2012wk]. A precise determination of the decay width difference is
thus also important for the study of rare decays.

Figure 4:  Constraints on (left) $\Delta\Gamma_{s}$ and
$\varphi_{s}^{{c}{\overline{c}}{s}}$ and (right) $1/\Gamma_{L,H}$ from various
decays and experiments. Figure courtesy of HFAG [20]. The SM predictions are
from Refs. [37, *Lenz:2006hd, 15].

The same quantity was also measured with a fully hadronic final state using
the decay ${{B}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$ with
${{D}^{\pm}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{\pm}}$, yielding
$0.02\pm 0.17\pm 0.02$ rad [39]. The effective tagging power $\epsilon{D}^{2}$
in excess of 5% for this channel is unprecedented at a hadron collider.

###  3.3 Flavour Tagging at the LHC

This is just one example of analyses greatly indebted to improvements in the
flavour tagging performance. A better understanding of the underlying event
and state-of-the-art multi-variate tagging methods allowed for increases in
tagging performance up to a factor two between analyses on only 2011 data
[40], and those on the whole of Run II, see Table 1. These progresses are
likely to continue. A good example is a new tagging based on secondary charm
hadrons recently introduced by LHCb [41].

Table 1: Comparison of tagging performances $\epsilon D^{2}$ for selected time dependent $C\\!P$ violation measurements at the LHC. Experiment | Decay | 2011 | Run I | Improvement
---|---|---|---|---
LHCb | ${{B}^{0}_{s}}\\!\rightarrow\phi\phi$ | 3.29% [42] | 5.38% [43] | +64%
| ${{B}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{+}_{s}}$ |  | 5.33% [39] |
| ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}{{K}^{-}}$ | 3.13% [29] | 3.73% [31] | +19%
| ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ | 2.43% [29] | 3.89% [30] | +60%
| ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ | 2.38% [44] | 3.03% [21] | +27%
ATLAS | ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ | 1.45% [27] | 1.49% [45] |  0+3%
CMS | ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ |  | 1.31% [32] | +35%111With respect to the preliminary result [28].

###  3.4 Penguin Topologies

Figure 5: Penguin diagram contributing to
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$.

The SM predictions $\varphi_{s}=-2\beta_{s}$ and $\varphi_{d}=2\beta$ assume
tree-dominated decays, as in Fig. 3. With the precision on some CKM phases
reaching the degree level, the effects of suppressed penguin topologies (Fig.
5) cannot be neglected any more [46, *Fleischer:1999zi, *Fleischer:1999sj,
*Faller:2008zc, *DeBruyn:2010hh, 51].

Cabibbo-suppressed decay modes, where these topologies are relatively more
prominent can be used to constrain such effects. Ways of using selected
measurements enabling the sizes of penguin amplitudes to be constrained have
been described in Ref. [52, *DeBruyn:2048174, *Ligeti:2015yma, *Jung:2012mp,
*Frings:2015eva]. The LHCb collaboration is pursuing this programme, with
studies of the decays
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ [57],
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ [58] and more recently with
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ [59].

The measurement of $\sin 2\beta^{\text{eff}}$ in the latter mode allows for
constraining the shift to $\varphi_{s}^{{c}{\overline{c}}{s}}$ due to penguin
topologies to the range $[-0.018,0.021]$ rad at 68% CL. Considering the
present uncertainty of $\pm 0.039$ rad, such a shift needs to be to
constrained further.

An interesting test of the SM is provided by the measurement of the mixing
phase $\varphi_{s}^{{s}{\overline{s}}{s}}$ with a purely penguin-induced mode
as ${{B}^{0}_{s}}\\!\rightarrow\phi\phi$. In this case the measured value is
$-0.17\pm 0.15\pm 0.03$ [43], which is compatible with the SM expectation.

Similarly, the decays ${B}\\!\rightarrow hh$ with $h={\pi},{K}$ are also
sensitive to penguin topologies (as well as trees) and are sensitive to the
CKM phases $\gamma$ and $\beta_{s}$. LHCb for the first time measured time-
dependent $C\\!P$-violating observables in ${B}^{0}_{s}$ decays using the
decay ${{B}^{0}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$ [60]. Using methods
outlined in Refs. [61, *Fleischer:2007hj, 51], a combination of this and other
results from ${B}\\!\rightarrow hh$ modes allows to determine
$-2\beta_{s}=-0.12{\>}^{+{\>}0.14}_{-{\>}0.16}$ $\rm\,rad$ using as input the
angle $\gamma$ from tree decays (see below), or
$\gamma=(63.5{\>}^{+{\>}7.2}_{-{\>}6.7})^{\circ}$ constraining $-2\beta_{s}$
to the SM value [63]. These values are in principle sensitive to the amount of
U-spin breaking that is allowed in this decay and are given here for a maximum
allowed breaking of 50%.

###  3.5 The angle $\gamma$

The value of $\gamma$ obtained from penguin modes can be compared to that
obtained from tree-dominated ${B}\\!\rightarrow{D}{K}$ decays, where the
$C\\!P$-violating phase appears in the interference of the
${b}\\!\rightarrow{c}$ and ${b}\\!\rightarrow{u}$ topologies. It is the least
precisely known angle of the unitarity triangle, and its determination from
tree decays is considered free from contributions beyond the SM and unaffected
by hadronic uncertainties. Yet its precise determination is important to test
the consistency of the CKM paradigm, and to allow comparisons with
determinations from modes dominated by penguin topologies.

Figure 6: (left) Fitted values of $x$ and $y$ for ${{B}^{-}}$ and ${{B}^{+}}$
in ${{B}^{\pm}}\\!\rightarrow{D}{{K}^{\pm}}$ with
${D}\\!\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{-}$ decays [64].
(right) LHCb combination of ${B}\\!\rightarrow D{K}$ decays measuring the CKM
phase $\gamma$ [65].

The most precise determination of $\gamma$ from a single decay mode is
achieved with ${{{B}^{+}}}\\!\rightarrow D{{K}^{+}}$ followed by
$D\\!\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{-}$ with
$h={\pi},{K}$ [64]. Here the interference of the ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decay to
${{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{-}$ is exploited to measure
$C\\!P$ asymmetries [66]. The method needs external input in the form of a
measurement of the strong phase over the Dalitz plane of the $D$ decay, coming
from CLEO-c data [67]. The determined $C\\!P$-violating parameters are shown
in Fig. 6 (left), and the value of $\gamma$ is
$(62{\>}^{+{\>}15}_{-{\>}14})^{\circ}$. The same decay mode is also used in a
model-dependent measurement [68] using an amplitude model.

An experimentally very different way of determining $\gamma$ is provided by
the decay ${{B}^{0}_{s}}\\!\rightarrow{{D}^{\pm}_{s}}{K}^{\mp}$ [69,
*Aleksan:1991nh, *Fleischer:2003yb, 72]. In this case the phase is measured in
a time-dependent tagged $C\\!P$-violation analysis. Using a dataset
corresponding to 1 $\mbox{\,fb}^{-1}$, LHCb determines
$\gamma=(115{\>}^{+{\>}28}_{-{\>}43})^{\circ}$, which is not competitive with
other methods but will provide important constraints with more data.

The LHCb $\gamma$ measurements of Refs. [64, 72, 73, *LHCb-PAPER-2012-055,
*LHCb-PAPER-2013-068, *LHCb-PAPER-2014-028] have been combined into an average
value presented at the CKM Workshop [65]. Using only ${B}\\!\rightarrow D{K}$
decay modes one finds $\gamma=(73{\>}^{+{\>}9}_{-{\>}10})^{\circ}$, which is
more precise than the corresponding combination of measurements from the $B$
factories [14]. The likelihood profile is shown in Fig. 6 (right). Since then,
new measurements sensitive to $\gamma$ have been performed, notably using the
decays ${{{B}^{-}}}\\!\rightarrow{D}h^{+}h^{-}h^{-}$ with ${D}\\!\rightarrow
h^{+}h^{-}$ [77] and ${{{B}^{-}}}\\!\rightarrow{D}h^{-}$ with
${D}\\!\rightarrow h^{+}h^{-}{{\pi}^{0}}$ [78]. These and other publications
under preparation will be combined in an updated $\gamma$ determination.

###  3.6 The angle $\alpha$

A precise determination of the third angle of the unitarity triangle,
$\alpha=\arg\left(-\frac{{V_{{t}{d}}}{V_{{t}{b}}^{\ast}}}{{V_{{u}{d}}}{V_{{u}{b}}^{\ast}}}\right)$
is challenging both at the theoretical and experimental levels. It requires
the study of highly-suppressed ${b}\\!\rightarrow{u}$ transitions, which are
affected by ${b}\\!\rightarrow{d}$ or ${b}\\!\rightarrow{s}$ penguin
topologies, depending on the chosen final state. Most promising are angular
analyses of $B\\!\rightarrow VV$ decays, where $V$ is a light vector meson,
typically $\rho$ or ${K}^{*}$. At this conference the Belle collaboration
showed a preliminary angular analysis of
${{B}^{0}}\\!\rightarrow{{\rho}^{+}}{{\rho}^{-}}$ [79], and the LHCb
collaboration one of the decay
${{B}^{0}}\\!\rightarrow{{\rho}^{0}}{{\rho}^{0}}$ [80]. This latter result
solves the tension between the results for the longitudinal polarisation
fraction previously obtained by Babar and Belle [81, *Adachi:2012cz].

###  3.7 The CKM matrix elements $V_{{u}{b}}$ and $V_{{c}{b}}$

The determination of the CKM matrix elements $V_{{u}{b}}$ and $V_{{c}{b}}$ is
extremely important for closure tests of the UT. It is best measured in
semileptonic ${b}\\!\rightarrow({u},{c})\ell\nu$ decays, where there are no
hadronic uncertainties related to the decay of the emitted $W$ boson.
Unfortunately, there is a well known tension between the determinations
obtained from exclusive (${B}\\!\rightarrow\pi\ell\nu$ for instance) decays
and the inclusive mode. It is thus important to add new decay modes to the
global picture. The LHCb collaboration has done so by using ${\mathchar
28931\relax}^{0}_{b}$ baryon decays for the first time [83]. The decay rates
of ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{p}{\mu^{-}}\nu$ and
${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{\mu^{-}}\nu$ are compared to determine the ratio
$|{V_{{u}{b}}}|^{2}/|{V_{{c}{b}}}|^{2}$. It was long thought impossible to do
such an analysis at a hadron collider, due to the lack of a precise neutrino
reconstruction method. At $B$ factories, fully reconstructing the other $B$ in
the event allows to unambiguously determine the four-momentum of the missing
neutrino. At LHCb, it is the precisely determined flight path of the
$b$-hadron and the requirement that the $b$-hadron momentum must align with
its flight direction that allow for the recovery of the neutrino momentum. The
corrected mass $m_{\text{corr}}=\sqrt{m^{2}+p_{\perp}^{2}}+p_{\perp}$, the
minimal $b$-hadron mass compatible with its direction of flight, is used as
discriminating variable. See Fig. 7 (left).

Figure 7: (left) Corrected mass spectrum. (right) Experimental measurements of
$V_{{u}{b}}$ and $V_{{c}{b}}$. Figures from Ref. [83].

The two decay rates are turned into a $|{V_{{u}{b}}}|^{2}/|{V_{{c}{b}}}|^{2}$
using input from Lattice calculations [84].

At the same time came an updated Lattice calculation from the FNAL/MILC
collaboration [85] which improves the determination of $|{V_{{u}{b}}}|$ from
${{B}^{0}}\\!\rightarrow{{\pi}^{-}}\ell^{+}\nu$ by the Belle collaboration
[86]. Even with these new determinations, the puzzle still remains, as can be
seen in Fig. 7 (right).

While LHCb only uses muonic decays, the $B$ factories usually average results
from decays to muons and electrons under the assumption of lepton universality
and do not always give results separately by lepton flavour (unlike for
instance in Ref. [87, *Dungel:2010uk]). This has been discussed in Ref. [89,
*Freytsis:2015qca], in the light of signs of lepton universality violation in
${{{B}^{+}}}\\!\rightarrow{{K}^{+}}\ell^{+}\ell^{-}$ [91] and
${B}\\!\rightarrow D^{(*)}(\tau,\ell)\nu$ decays [92, *Lees:2012xj,
*Huschle:2015rga]. Incidentally, the BaBar collaboration presented an
inclusive electron spectrum and a determination of $|{V_{{u}{b}}}|$ at this
conference [95].

###  3.8 Charmed and Strange Mesons

Searches for $C\\!P$ violation in charm is a very active field of research,
especially owing to the gigantic charm yields (See Section 4) collected by the
LHCb experiment. Unfortunately, no signs have been found yet and there is
still no clear picture emerging from the measurements of the difference
between the $C\\!P$ asymmetries in ${{D}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$
and ${{D}^{0}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$, the world average being
$-0.25\pm 0.10$ [20].

New promising results have been shown by the LHCb collaboration. A search for
$C\\!P$ violation in ${{D}^{0}}\\!\rightarrow{{K}^{0}_{\rm\scriptscriptstyle
S}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ was consistent with zero, but the
improved trigger in Run II will greatly increase the sensitivity of this decay
mode [96]. Secondly, the energy test method was first applied to particle
physics to search for local asymmetries in the Dalitz plane of
${{D}^{0}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{0}}$ decays [97].

##  4 First LHCb results from Run II

The LHCb collaboration used the LHC 50 ns ramp-up period of July 2015 to
measure the double-differential ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$-from-$b$-hadron [98]
and charm cross-sections [99] at $\sqrt{s}=13\>\mathrm{\,Te\kern-1.00006ptV}$.
Both measurements were performed directly on triggered candidates using a
reduced data format that does not require offline processing.

In the Run II of the LHC, a new scheme for the LHCb software trigger has been
introduced, in which the event selection is split into two stages. This allows
for the alignment and calibration to be performed after the first stage of the
software trigger and used directly in the second stage [100]. The same
alignment and calibration are propagated offline to ensure consistent
reconstruction in the trigger and offline analysis. The larger timing budget
available in the trigger with respect to Run I also results in the convergence
of the online and offline track reconstruction, such that offline performance
is achieved in the trigger. The near identical performance of the online and
offline reconstruction offers the opportunity to perform physics analyses
directly using candidates reconstructed in the trigger [101]. The analysis
described in this paper uses the online reconstruction for the first time in
LHCb. The storage of only events containing the triggered candidates leads to
an event size that is reduced by an order of magnitude, thus permitting an
increased event rate with higher efficiency.

Essential to the measurements was a preliminary luminosity calibration using
beam gas imaging [102]. In absence of a van der Meer scan, neon gas is
injected in the LHC vacuum and beam-gas interaction vertices are reconstructed
in the vertex detector to reconstruct a three-dimensional image of the two
beams and their overlap. A preliminary calibration with an uncertainty of 3.8%
could be determined this way. With a van der Meer scan, more data and more
systematic studies, it is expected that this uncertainty will decrease to the
level of 1%, as for the 8 $\mathrm{\,Te\kern-1.00006ptV}$ data [103].

Figure 8: (left) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ pseudo-
effective lifetime and (right) $p_{\rm T}$-dependent cross-section for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from $b$-hadrons, compared to
expectations from Ref. [104]. Figures from Ref. [98].

Using $pp$ collision data corresponding to 3 $\mbox{\,pb}^{-1}$ of integrated
luminosity, LHCb measured the double differential
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ cross-section in bins of
$p_{\rm T}$ and $y$ [98]. The ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$ signal is further split into
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ produced at the primary
interaction vertex (prompt) and those produced in decays of $b$-hadrons. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ pseudo-effective lifetime
$t_{z}=\frac{(z_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}-z_{\text{PV}})M_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}{p_{z}}$ is used as a proxy for the $b$-hadron lifetime (Fig. 8,
left). While the cross-sections are found in agreement with theoretical
expectations within uncertainties, the ratio of $\sqrt{s}=13$ to 8
$\mathrm{\,Te\kern-1.00006ptV}$ ratios, where most uncertainties cancel both
in experiment and theory, are found to be slightly above the expectations
(Fig. 8, right). The cross-sections are found to be

$\displaystyle\sigma_{\text{prompt {${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$}}}(\mbox{$p_{\rm
T}$}<14\>{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$
$\displaystyle=15.30\pm 0.03\pm 0.86{\rm\,\upmu b},$
$\displaystyle\sigma_{\text{{${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$}{}-from-{$b$}}}(\mbox{$p_{\rm
T}$}<14\>{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$
$\displaystyle=\phantom{0}2.34\pm 0.01\pm 0.13{\rm\,\upmu b}.$

Naively extrapolating the latter value from the LHCb fiducial region to the
whole acceptance using PYTHIA [105, *Sjostrand:2006za], one gets a
$b$$\overline{b}$ cross-section consistent with 500 ${\rm\,\upmu b}$.
Incidentally this is the value which was used when designing the experiment.

Figure 9: ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ (left) mass and
(right) $\log\chi^{2}_{\text{IP}}$ distributions. Figures from Ref. [99].

Figure 10: (left) ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ cross-
sections. Each set of measurements and predictions in a given rapidity bin is
offset by a multiplicative factor $10^{-m}$, where the factor $m$ is shown on
the plot. (right) $c$$\overline{c}$ cross-section in LHCb acceptance from
${D}^{0}$ and ${D}^{+}$ measurements, and comparison with prediction from
Refs. [107, 104]. The scaled prediction uses the 7 TeV LHCb measurement [108]
as input.

The same dataset and procedure has been used to determine the charm cross-
section [99]. The double-differential cross-sections for ${D}^{0}$, ${D}^{+}$,
${D}^{*}$ and ${D}^{+}_{s}$ mesons are measured using data corresponding to 5
$\mbox{\,pb}^{-1}$. In this case a random trigger was used in the hardware
trigger, followed by the full selection in the software trigger. This time the
component of charm from $b$-hadrons is treated as a background and subtracted
using the $\chi^{2}_{\rm IP}$ (the quantity by which the PV $\chi^{2}$
increases when the $D$ meson is included in the fit) as discriminating
variable. The mass and $\log\chi^{2}_{\text{IP}}$ distributions are shown for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays in Fig. 9.

The cross-sections are found to be consistent with predictions from Refs.
[107, 104], but consistently on the high side. An example is shown in Fig. 10.
Using known hadronisation fractions determined at the $\Upsilon$ resonance
[109] the $c$$\overline{c}$ cross-section in the LHCb fiducial volume is
determined to be

$\displaystyle\sigma_{\text{prompt {$c$} {$\overline{c}$}}}(\mbox{$p_{\rm
T}$}<8\>{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2<y<4.5)$ $\displaystyle=2944\pm
3\pm 183\pm 156{\rm\,\upmu b},$

where the uncertainties are statistical, systematic and due to fragmentation
fractions. This value is also compatible with but on the high side of
theoretical expectations, which is very encouraging for the LHCb charm physics
programme. This number is also relevant for atmospheric neutrino measurements.
The charm production cross-section from cosmic rays in the higher atmosphere
is a dominant source of uncertainties for measurements of the IceCube
collaboration [110]. The present measurement at
$\sqrt{s}=13\mathrm{\,Te\kern-1.00006ptV}$ corresponds to a fixed-target
collision with primary cosmic ray energy of 90 PeV.

##  5 Conclusions

The LHC is the new $b$-hadron factory and will be dominating flavour physics
until the start of Belle II, and beyond in many decay modes. While the $B$
factories and Tevatron experiments are still analysing their data, ATLAS, CMS
and LHCb are producing interesting new results in $C\\!P$ violation and rare
decays, that set strong constraints on models beyond that SM and exhibit some
discrepancies with the SM predictions. The LHCb collaboration used the LHC 50
ns ramp-up period of July 2015 to measure the double-differential
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$,
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$-from-$b$-hadron and charm
cross-sections at $\sqrt{s}=13\>\mathrm{\,Te\kern-1.00006ptV}$. Both
measurements were performed directly on triggered candidates using a reduced
data format that does not require offline processing.

## Acknowledgements

The author thanks Vincenzo Vagnoni for the careful reading of the manuscript.
Some text is identical to a common previous publication [111].

## References

  * [1] ATLAS collaboration, G. Aad et al., Phys. Lett. B716 (2012) 1, arXiv:1207.7214
  * [2] CMS collaboration, S. Chatrchyan et al., Phys. Lett. B716 (2012) 30, arXiv:1207.7235
  * [3] K. Trabelsi, in these proceedings, 2015
  * [4] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49 (1973) 652
  * [5] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531
  * [6] S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2 (1970) 1285
  * [7] E598 collaboration, J. J. Aubert et al., Phys. Rev. Lett. 33 (1974) 1404
  * [8] SLAC-SP-017 collaboration, J. E. Augustin et al., Phys. Rev. Lett. 33 (1974) 1406, [Adv. Exp. Phys.5,141(1976)]
  * [9] S. W. Herb et al., Phys. Rev. Lett. 39 (1977) 252
  * [10] CDF collaboration, F. Abe et al., Phys. Rev. Lett. 74 (1995) 2626, arXiv:hep-ex/9503002
  * [11] J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett. 13 (1964) 138
  * [12] L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945
  * [13] C. Jarlskog, Phys. Rev. Lett. 55 (1985) 1039
  * [14] BaBar collaboration, Belle collaboration, A. J. Bevan et al., arXiv:1406.6311
  * [15] CKMfitter Group, J. Charles et al., Eur. Phys. J. C41 (2005) 1, arXiv:hep-ph/0406184, Updated results and plots available at: http://ckmfitter.in2p3.fr
  * [16] UTfit collaboration, M. Bona et al., JHEP 0610 (2006) 081, arXiv:hep-ph/0606167
  * [17] I. I. Y. Bigi and A. I. Sanda, Phys. Rev. D29 (1984) 1393
  * [18] BaBar collaboration, B. Aubert et al., Phys. Rev. D79 (2009) 072009, arXiv:0902.1708
  * [19] I. Adachi et al., Phys. Rev. Lett. 108 (2012) 171802, arXiv:1201.4643
  * [20] Heavy Flavor Averaging Group, Y. Amhis et al., arXiv:1412.7515, updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/
  * [21] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 115 (2015) 031601, arXiv:1503.07089
  * [22] J. Charles et al., arXiv:1501.05013
  * [23] Belle and BaBar collaborations, A. Abdesselam et al., arXiv:1505.04147
  * [24] LHCb collaboration, R. Aaij et al., Phys. Rev. D92 (2015) 032002, arXiv:1505.01710
  * [25] LHCb collaboration, LHCb-CONF-2015-003
  * [26] LHCb collaboration, R. Aaij et al., LHCb-PAPER-2015-031, in preparation
  * [27] ATLAS collaboration, G. Aad et al., Phys. Rev. D90 (2014) 052007, arXiv:1407.1796
  * [28] CMS collaboration, Tech. Rep. CMS-PAS-BPH-13-012, CERN, Geneva, 2014
  * [29] LHCb collaboration, R. Aaij et al., Phys. Rev. D87 (2013) 112010, arXiv:1304.2600
  * [30] LHCb collaboration, R. Aaij et al., Phys. Lett. B736 (2014) 186, arXiv:1405.4140
  * [31] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 114 (2015) 041801, arXiv:1411.3104
  * [32] CMS collaboration, V. Khachatryan et al., arXiv:1507.07527
  * [33] CDF collaboration, T. Aaltonen et al., Phys. Rev. Lett. 109 (2012) 171802, arXiv:1208.2967
  * [34] D0 collaboration, V. M. Abazov et al., Phys. Rev. D85 (2012) 032006, arXiv:1109.3166
  * [35] K. De Bruyn et al., Phys. Rev. D86 (2012) 014027, arXiv:1204.1735
  * [36] K. De Bruyn et al., Phys. Rev. Lett. 109 (2012) 041801, arXiv:1204.1737
  * [37] A. Lenz and U. Nierste, in CKM unitarity triangle. Proceedings, 6th International Workshop, CKM 2010, Warwick, UK, September 6-10, 2010, 2011.  arXiv:1102.4274
  * [38] A. Lenz and U. Nierste, JHEP 06 (2007) 072, arXiv:hep-ph/0612167
  * [39] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 113 (2014) 211801, arXiv:1409.4619
  * [40] LHCb collaboration, R. Aaij et al., Eur. Phys. J. C72 (2012) 2022, arXiv:1202.4979
  * [41] LHCb collaboration, R. Aaij et al., JINST 10 (2015) P10005, arXiv:1507.07892, to appear in J. Instr.
  * [42] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 110 (2013) 241802, arXiv:1303.7125
  * [43] LHCb collaboration, R. Aaij et al., Phys. Rev. D90 (2014) 052011, arXiv:1407.2222
  * [44] LHCb collaboration, R. Aaij et al., Phys. Lett. B721 (2013) 24, arXiv:1211.6093
  * [45] ATLAS collaboration, C. Alpigiani, in these proceedings, 2015
  * [46] R. Fleischer, Eur. Phys. J. C10 (1999) 299, arXiv:hep-ph/9903455
  * [47] R. Fleischer, Phys. Rev. D60 (1999) 073008, arXiv:hep-ph/9903540
  * [48] R. Fleischer, Nucl. Instrum. Meth. A446 (2000) 1, arXiv:hep-ph/9908340
  * [49] S. Faller, M. Jung, R. Fleischer, and T. Mannel, Phys. Rev. D79 (2009) 014030, arXiv:0809.0842
  * [50] K. De Bruyn, R. Fleischer, and P. Koppenburg, Eur. Phys. J. C70 (2010) 1025, arXiv:1010.0089
  * [51] M. Ciuchini, M. Pierini, and L. Silvestrini, Phys. Rev. Lett. 95 (2005) 221804, arXiv:hep-ph/0507290
  * [52] K. De Bruyn and R. Fleischer, JHEP 03 (2015) 145, arXiv:1412.6834
  * [53] K. De Bruyn, Searching for penguin footprints: Towards high precision CP violation measurements in the B meson systems, PhD thesis, Vrije U., Amsterdam, Apr, 2015, Presented 08 Oct 2015
  * [54] Z. Ligeti and D. J. Robinson, arXiv:1507.06671
  * [55] M. Jung, Phys. Rev. D86 (2012) 053008, arXiv:1206.2050
  * [56] P. Frings, U. Nierste, and M. Wiebusch, Phys. Rev. Lett. 115 (2015) 061802, arXiv:1503.00859
  * [57] LHCb collaboration, R. Aaij et al., Nucl. Phys. B873 (2013) 275, arXiv:1304.4500
  * [58] LHCb collaboration, R. Aaij et al., Phys. Lett. B742 (2015) 38, arXiv:1411.1634
  * [59] LHCb collaboration, R. Aaij et al., arXiv:1509.00400, submitted to JHEP
  * [60] LHCb collaboration, R. Aaij et al., JHEP 10 (2013) 183, arXiv:1308.1428
  * [61] R. Fleischer, Phys. Lett. B459 (1999) 306, arXiv:hep-ph/9903456
  * [62] R. Fleischer, Eur. Phys. J. C52 (2007) 267, arXiv:0705.1121
  * [63] LHCb collaboration, R. Aaij et al., Phys. Rev. D88 (2013) 072005, arXiv:1308.5916
  * [64] LHCb collaboration, R. Aaij et al., JHEP 10 (2014) 097, arXiv:1408.2748
  * [65] LHCb collaboration, LHCb-CONF-2014-004
  * [66] A. Giri, Y. Grossman, A. Soffer, and J. Zupan, Phys. Rev. D68 (2003) 054018, arXiv:hep-ph/0303187
  * [67] CLEO collaboration, J. Libby et al., Phys. Rev. D82 (2010) 112006, arXiv:1010.2817
  * [68] LHCb collaboration, R. Aaij et al., Nucl. Phys. B888 (2014) 169, arXiv:1407.6211
  * [69] I. Dunietz and R. G. Sachs, Phys. Rev. D37 (1988) 3186
  * [70] R. Aleksan, I. Dunietz, and B. Kayser, Z. Phys. C54 (1992) 653
  * [71] R. Fleischer, Nucl. Phys. B671 (2003) 459, arXiv:hep-ph/0304027
  * [72] LHCb collaboration, R. Aaij et al., JHEP 11 (2014) 060, arXiv:1407.6127
  * [73] LHCb collaboration, R. Aaij et al., Phys. Lett. B712 (2012) 203, Erratum ibid. B713 (2012) 351, arXiv:1203.3662
  * [74] LHCb collaboration, R. Aaij et al., Phys. Lett. B723 (2013) 44, arXiv:1303.4646
  * [75] LHCb collaboration, R. Aaij et al., Phys. Lett. B733 (2014) 36, arXiv:1402.2982
  * [76] LHCb collaboration, R. Aaij et al., Phys. Rev. D90 (2014) 112002, arXiv:1407.8136
  * [77] LHCb collaboration, R. Aaij et al., arXiv:1505.07044, submitted to Phys. Rev. D.
  * [78] LHCb collaboration, R. Aaij et al., Phys. Rev. D91 (2015) 112014, arXiv:1504.05442
  * [79] BaBar collaboration, P. Vanhoefer, in these proceedings, 2015
  * [80] LHCb collaboration, R. Aaij et al., Phys. Lett. B747 (2015) 468, arXiv:1503.07770
  * [81] BaBar collaboration, B. Aubert et al., Phys. Rev. D78 (2008) 071104, arXiv:0807.4977
  * [82] Belle collaboration, I. Adachi et al., arXiv:1212.4015arXiv:1212.4015, [Addendum: Phys. Rev.D89,no.11,119903(2014)]
  * [83] LHCb collaboration, R. Aaij et al., Nature Physics 11 (2015) 743, arXiv:1504.01568
  * [84] W. Detmold, C. Lehner, and S. Meinel, Phys. Rev. D92 (2015), no.~3 034503, arXiv:1503.01421
  * [85] Fermilab Lattice and MILC collaborations, J. A. Bailey et al., Phys. Rev. D92 (2015), no.~1 014024, arXiv:1503.07839
  * [86] Belle collaboration, H. Ha et al., Phys. Rev. D83 (2011) 071101, arXiv:1012.0090
  * [87] BaBar, B. Aubert et al., Phys. Rev. D79 (2009) 012002, arXiv:0809.0828
  * [88] Belle, W. Dungel et al., Phys. Rev. D82 (2010) 112007, arXiv:1010.5620
  * [89] A. Greljo, G. Isidori, and D. Marzocca, JHEP 07 (2015) 142, arXiv:1506.01705
  * [90] M. Freytsis, Z. Ligeti, and J. T. Ruderman, Phys. Rev. D92 (2015), no.~5 054018, arXiv:1506.08896
  * [91] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 113 (2014) 151601, arXiv:1406.6482
  * [92] LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 115 (2015) 111803, arXiv:1506.08614
  * [93] BaBar collaboration, J. P. Lees et al., Phys. Rev. Lett. 109 (2012) 101802, arXiv:1205.5442
  * [94] Belle collaboration, M. Huschle et al., arXiv:1507.03233
  * [95] Belle collaboration, Y. Skovpen, in these proceedings, 2015
  * [96] LHCb collaboration, R. Aaij et al., arXiv:1508.06087, to appear in JHEP
  * [97] LHCb collaboration, R. Aaij et al., Phys. Lett. B740 (2015) 158, arXiv:1410.4170
  * [98] LHCb collaboration, R. Aaij et al., arXiv:1509.00771, submitted to JHEP
  * [99] LHCb collaboration, R. Aaij et al., arXiv:1510.01707, submitted to JHEP
  * [100] G. Dujany and B. Storaci, No. LHCb-PROC-2015-011, Apr, 2015
  * [101] R. Aaij et al., JINST 8 (2013) P04022, arXiv:1211.3055
  * [102] M. Ferro-Luzzi, Nucl. Instrum. Meth. A553 (2005) 388
  * [103] LHCb collaboration, R. Aaij et al., JINST 9 (2014) P12005, arXiv:1410.0149
  * [104] M. Cacciari, M. L. Mangano, and P. Nason, arXiv:1507.06197
  * [105] I. Belyaev et al., J. Phys. Conf. Ser. 331 (2011) 032047
  * [106] T. Sjöstrand, S. Mrenna, and P. Skands, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [107] R. Gauld, J. Rojo, L. Rottoli, and J. Talbert, arXiv:1506.08025
  * [108] LHCb collaboration, R. Aaij et al., Nucl. Phys. B871 (2013) 1, arXiv:1302.2864
  * [109] Particle Data Group, C. Amsler et al., Phys. Lett. B667 (2008) 1
  * [110] IceCube collaboration, M. G. Aartsen et al., Phys. Rev. Lett. 113 (2014) 101101, arXiv:1405.5303
  * [111] P. Koppenburg and V. Vagnoni, in Precision Physics with Heavy-Flavoured Hadrons, H. Schopper and et al. , eds., pp. 31–59, World Scientific Publishing Co, July, 2015.  doi: 10.1142/9789814644150_0002