# MobileCodec: Neural Inter-frame Video Compression
on Mobile Devices

Hoang Le, Liang Zhang, Amir Said, Guillaume Sautiere,
Yang Yang‡, Pranav Shrestha, Fei Yin‡, Reza Pourreza, Auke Wiggers  Qualcomm
AI Research*

(copyrightyear)

###### Abstract.

Realizing the potential of neural video codecs on mobile devices is a big
technological challenge due to the computational complexity of deep networks
and the power-constrained mobile hardware. We demonstrate practical
feasibility by leveraging Qualcomm’s technology and innovation, bridging the
gap from neural network-based codec simulations running on wall-powered
workstations, to real-time operation on a mobile device powered by Snapdragon®
technology. We show the first-ever inter-frame neural video decoder running on
a commercial mobile phone, decoding high-definition videos in real-time while
maintaining a low bitrate and high visual quality.

††journalyear: acmyear††copyright: rightsretained††conference: acmconference;
acmbooktitle††booktitle: ;††doi: acmdoi††isbn: acmisbn††ccs: Computer systems
organization Real-time system architecture†† Snapdragon and Qualcomm AI Engine
are products of Qualcomm Technologies, Inc. and/or its subsidiaries. Qualcomm
AI Research is an initiative of Qualcomm Technologies, Inc.†† $\ddagger$: This
work was completed during employment at Qualcomm Technologies, Inc.

##  1\. Introduction

Video compression technologies have been actively researched and engineered
over the past decades to obtain broad video adoption across a wide range of
devices, distribution media, and services. As neural network (NN) technologies
have been revolutionizing the world, NN-based video coding methods, especially
deep generative model-based approaches, have a strong potential to further
extend the capabilities and efficiency of video compression. Instead of
manually designing a sophisticated pipeline with multiple stages and
optimizing each stage separately, a NN-based codec can learn to directly
extract and code a low-dimensional feature representation of the input data in
an end-to-end process, offering a better rate-distortion tradeoff. Moreover,
it is easy to upgrade and deploy new NN-based codecs, as their models are
trained in a relatively short amount of time in comparison to the development
of conventional video codecs. Equally important is that neural codecs can
leverage general-purpose AI hardware accelerators, which are already
ubiquitous in many different computing platforms.

Recent advances in deep learning have revolutionized the way lossy data
compression algorithms are designed. Specifically, we have seen remarkable
success in image and video compression, achieved by employing a convolutional
autoencoder as a flexible learned non-linear transform (Ballé et al., 2017,
2020), deep generative models as powerful entropy models (Ballé et al., 2018;
Minnen et al., 2018), and various neural motion estimation and compensation
algorithms for high-quality frame interpolation and extrapolation (Yang and
Ramanan, 2019; Zhang et al., 2020). After a few years of development, neural
video codecs (Lu et al., 2019; Agustsson et al., 2020; Pourreza and Cohen,
2021; Hu et al., 2021; Rippel et al., 2021; Hu et al., 2022) are now on par
with or even outperform handcrafted solutions such as HEVC (Sullivan et al.,
2012), and have become a vibrant research area with consistent year-over-year
improvements in rate-distortion performance.

Besides competitive rate-distortion performance, learnable codecs also open
new opportunities such as easy adaptation to different data distributions
(Rozendaal et al., 2021; Strümpler et al., 2021). Their flexibility allows
optimization of subjective quality of reconstructed video as well, for example
using learned region-of-interest coding to allocate more bits to semantically
interesting regions (Perugachi-Diaz et al., 2022), or the use of
differentiable perceptual metrics (Mentzer et al., 2020, 2021; Yang et al.,
2021).

However, most of the studies use wall-powered high-end GPUs with floating-
point computation, and the used neural network models are often not optimized
for fast inference. As a result, most neural video codecs are unable to run in
real-time on power-constrained devices such as mobile phones. This is a hurdle
for adoption of neural codecs, as a large part of video communication today
takes place on mobile.

In this paper, we therefore demonstrate that neural video decoding on a mobile
phone is feasible. Leveraging the Qualcomm® AI Engine, we achieve the first
real-time neural inter-frame decoder running on a commercial mobile device.
The main contributions of this work are:

  * •

A demonstration of the first real-time neural inter-frame video decoder on a
mobile device.

  * •

An efficient neural inter-frame codec architecture, specifically designed for
deployment on a mobile platform.

  * •

A parallel entropy coding algorithm tailored for neural entropy models.

Figure 1. MobileCodec network architecture

##  2\. Related Work

##### Neural image compression

There has been significant progress in the development of neural image
compression solutions in recent years. While earlier works proposed different
types of generative models (Toderici et al., 2015, 2017; Rippel and Bourdev,
2017; Mentzer et al., 2018), many recent works are based on the hierarchical
hyperprior architecture (Ballé et al., 2016, 2016, 2018; Lu et al., 2021; Zhu
et al., 2021). Its variants equipped with autoregressive models (Minnen et
al., 2018; Minnen and Singh, 2020) and attention mechanisms (Chen et al.,
2021) are currently the most widely adopted architectures.

##### Neural video compression

Neural video compression has seen advances for both low-latency video (Liu et
al., 2020a; Lu et al., 2019, 2020) and video streaming applications (Wu et
al., 2018; Cheng et al., 2019; Habibian et al., 2019; Djelouah et al., 2019;
Pourreza and Cohen, 2021). The low-latency solutions often include
unidirectional motion estimation/compensation followed by a residual
correction (Chen et al., 2020; Agustsson et al., 2020). Recent works have
introduced recurrency (Golinski et al., 2020; Rippel et al., 2019) or longer
range dependencies (Lin et al., 2020; Rippel et al., 2021; Hu et al., 2021,
2022) to improve performance. In the settings where it is acceptable to incur
latency by using reference frames from future timepoints, the existing
solutions include bidirectional motion estimation and compensation (Djelouah
et al., 2019; Pourreza and Cohen, 2021), frame interpolation (Wu et al., 2018;
Cheng et al., 2019) followed by residual correction, or implicit multi-frame
coding approaches based on 3D convolutions (Habibian et al., 2019).

Figure 2. Asymmetric efficient network architecture . A network used in the
receiver uses smaller number of filters than a network used in the
transmitter. We use fewer filters at high resolution to reduce computation as
well.

##### Efficient neural codecs

Despite the progress in developing neural image and video compression
solutions, literature that explicitly aims to improve their efficiency and
practical usefulness is limited. Efficient architectures are explored in (Liu
et al., 2020b; Rippel and Bourdev, 2017; Rippel et al., 2021; Johnston et al.,
2019). Overfitting to a video or segments of a video is another means to
reduce model complexity while improving rate-distortion performance (van
Rozendaal et al., 2021; Strümpler et al., 2021; Zhang et al., 2021). Yet, in
their current form, these methods are unable to run in real-time on resource-
constrained mobile devices. To the best of our knowledge, these exists only a
single public neural video codec deployed to a mobile device (research, 2021)
that runs in all-intra mode, i.e., all frames are coded as images.

##  3\. Approach

We enable real-time neural inter-frame decoding using three main steps. First,
we design a mobile-friendly neural network architecture, MobileCodec,
optimized for efficient inference on a mobile device. Second, we use
quantization-aware training (Nagel et al., 2021) to quantize network
parameters and activations to fixed point, retaining the networks original
floating-point performance. Finally, we develop a parallel entropy coding
algorithm that leverages the parallel inference property of neural network-
based codecs. We describe these steps in more details in the following
sections.

###  3.1. Mobile friendly network architecture

To optimize MobileCodec for performance on a mobile device, we use a network
consisting of mostly convolutional layers and ReLU activations, as both
operations are extremely efficient. Figure 1 shows the overall design of our
network architecture. The system consists of two codecs: an intra-frame codec
that compresses each video frame independently (as an image), and an inter-
frame codec that compresses a frame conditioned on a previously decoded frame.
The intra-frame codec is used to compress the first frame of each video
segment, and the inter-frame codec is used to compress the rest of the frames
of that segment. Such a segment is typically referred to as a Group of
Pictures (GoP).

###  3.2. Intra-frame MobileCodec

The design of our Intra-frame codec is derived from the image compression
method by Balle et al. (Ballé et al., 2018). Please refer to the original
paper for a detailed description of the method. Summarizing, as shown in
Figure 1, the encoder (or analysis transform) $I_{a}$ transforms each frame
$x_{0}$ into a latent variable $y^{I}=I_{a}(x_{0})$. This latent $y^{I}$ is
then quantized by a rounding operator $Q$, and entropy coded by an arithmetic
encoder ($AE$). The resulting bitstream is sent to the receiver, where it will
be decoded by an arithmetic decoder ($AD$) and reconstructed back to obtain a
reconstruction $\hat{x}_{0}$ via the synthesis decoder $I_{s}$:
$\hat{x}_{0}=I_{s}(y^{I})$. Following (Ballé et al., 2018), we also use a
hypercodec network to model the probability distribution of the encoded
latents $y^{I}$. Specifically, the hyper-encoder $H^{I}_{a}$ transforms the
latent $y^{I}$ into a latent variable $z^{I}=H^{I}_{a}(y^{I})$, referred to as
a hyper-latent. Hyper-latent $z^{I}$ is also quantized, entropy coded, and
sent to the receiver where it will be decoded and fed into a hyper-decoder
network $H_{s}^{I}$ to predict the scale $\sigma^{I}$ of the distribution over
latents $\hat{y}^{I}$: $\sigma^{I}=H^{I}_{s}(\hat{z}^{I})$. The predicted
scale $\sigma^{I}$ characterizes a distribution $p(\hat{y}^{I})$, which is
used for arithmetic encoding $AC$ only in the transmitter side, and for
arithmetic decoding $AD$ in both transmitter and receiver side. Note that, in
contrast to (Ballé et al., 2018), we as use ReLU as the nonlinearity after
each layer of the network instead of a GDN block. We empirically observed that
ReLU non-linearities are more quantization friendly than GDN blocks, and that
they can be used without a drop in rate-distortion performance.

####  3.2.1. Inter-frame MobileCodec

For our inter-frame codec, we follow the recent design of neural inter-frame
codec methods (Agustsson et al., 2020; Lu et al., 2019) and include two
consecutive sub-networks: a motion network and a residual network. First, the
motion network takes a previously decoded frame $\hat{x}_{t-1}$ and the
current frame $x_{t}$, and encodes the motion between them. The decoded motion
is used to obtain an initial reconstruction $\tilde{x}_{t}$ at the receiver
end. The residual network encodes the difference $r_{t}$ between the
reconstructed frame $\tilde{x}_{t}$ and the current frame $x_{t}$. This
reconstructed residual $\hat{r}_{t}$ is then used to refine the reconstructed
frame $\tilde{x}_{t}$ to obtain the final reconstructed frame $\hat{x}_{t}$.

####  3.2.2. Flow-Agnostic Motion Compensation

Motion compensation is an important component that contributes significantly
in saving bitrate for an inter-frame codec. Inter-frame codecs typically
exploit redundancies between consecutive frames by transmitting the motion
between them, as described earlier. Most existing neural video coding
approaches implement motion compensation either by pixel warping (Agustsson et
al., 2020; Lu et al., 2019) or feature-space warping (Hu et al., 2021). These
methods require large memory buffers to enable memory access to the arbitrary
location of a video frame or the corresponding features. As a result, these
operations may not be efficient on a mobile device. Moreover, these operations
do not scale well with image resolution, as they allow arbitrary warping of
pixels from anywhere in the frame. In contrast, convolutional operations
operate on each image block and are highly efficient on mobile devices. For
this reason, we design a flow-agnostic motion compensation network that uses
only convolutional operations, thereby avoiding less efficient warping
operations. As illustrated in Figure 1, our motion compensation method
includes two feature extractors $F_{prev}$ and $F_{curr}$ to extract
representative features $f_{t-1}$ and $f_{t}$ of the previously decoded frame
$\hat{x}_{t-1}$ and the current frame $x_{t}$ respectively:

(1) $f_{t-1}=F_{prev}(\hat{x}_{t-1})\\\ $ (2) $f_{t}=F_{curr}(x_{t})$

The extracted features $f_{t-1}$ and $f_{t}$ are concatenated as input into
the feature correlation module $M_{c}$ to extract the motion features between
the two frames:

(3) $y^{M}=M_{c}(concat(f_{t-1},f_{t}))$

These motion features are quantized via the quantizer $Q$, then coded via
arithmetic coding $AE$, and sent to the receiver.

At the receiver end, the decoded motion features $\hat{y}^{M}$ are
concatenated with the feature $f_{t-1}$ extracted from the previous frame
$\hat{x}_{t-1}$, which is available for both transmitter and receiver. These
features are then fed into an image synthesis network $M_{s}$ to reconstruct
the current frame $\tilde{x}_{t}$.

(4) $\tilde{x}_{t}=M_{s}(concat(f_{t-1},\hat{y}^{M}))$

Next, the residual error $r_{t}=x_{t}-\tilde{x}_{t}$ of the reconstructed
image $\tilde{x}_{t}$ is fed into a residual analysis encoder $R_{a}$ to
extract the latent feature $y^{R}$.

(5) $y^{R}=R_{a}(r_{t})$

This latent feature $y^{R}$ is then also quantized via the quantizer $Q$ and
entropy coded via $AE$, and sent to the receiver. On the receiver side, the
decoded latent $\hat{y}^{R}$ is input into the residual decoder $R_{s}$ to
reconstruct the residual $\hat{r}_{t}$.

(6) $\hat{r}_{t}=R_{s}(\hat{y}^{R})$

The final reconstructed frame is generated by adding the reconstructed
residual $\hat{r}_{t}$ to the motion compensated image $\tilde{x}_{t}$:

(7) $\hat{x}_{t}=\tilde{x}_{t}+\hat{r}_{t}$

We follow (Ballé et al., 2018) and use a hyperprior network to predict the
scale $\sigma^{M}$ and $\sigma^{R}$ for each latent feature in $y^{M}$ and
$y^{R}$ to be entropy coded respectively. Specifically, the hyperprior
analysis encoder $H_{a}^{M}$ transforms the motion latent $y^{M}$ into motion
hyperlatent $z^{M}$

(8) $z^{M}=H^{M}_{a}(y^{M})$

This motion hyperlatent $z^{M}$ is quantized, then entropy coded and sent to
the receiver. At the receiver end, the decoded latent $\hat{z}^{M}$ is input
into a hyperdecoder network $H_{s}^{M}$ to predict the scale $\sigma_{M}$
which is then used for entropy encoding and decoding for the latent
$\hat{y}^{M}$. The same process is also employed for the entropy coding of the
residual latent $\hat{y}^{R}$.

####  3.2.3. Asymmetric neural network architecture

We use an asymmetric encoder-decoder architecture in order to enable real-time
decoding. This design is consistent with a recent video coding approach
proposed in (Rippel et al., 2021), which showed that reducing decoder compute
is possible without a reduction in rate-distortion performance. Figure 2 shows
the details of our asymmetric architecture, and lists the number of channels
and kernel size for each layer.

###  3.3. Channel-wise Quantization Aware Training

ALthough using 32 bit floating-point operations is a default operating mode on
wall-powered computing devices like workstations or training servers, it is
often more efficient to run in lower bitwidths or fixed point, especially on
power-constrained devices. To increase runtime and improve power efficiency,
we need to quantize the network parameters and activations to low-precision
integers. However, naive post-training quantization of neural network to 8 bit
integers would significantly reduce the rate-distortion performance. To
alleviate this issue, we finetune our MobileCodec using the quantization-aware
training (QAT) pipeline described in Nagel et al. (2021). This allows learning
the quantization binwidth for each layer weight and activations by introducing
simulated straight-through gradient estimation.

We quantize the entire model to 8-bit fixed point. For the convolutional
weights, we use separate quantization parameters for each output channel (also
known as per-channel quantization) (Nagel et al., 2019), as we observe the
range of both weights and activations varies widely between channels. This
observation is in line with recent work (Minnen and Singh, 2020) which shows
that different channels of the latent impact the compression quality
differently.

In addition, we pay particular attention to the variables that are important
for entropy coding. The scale $\sigma$ in the hyperprior must cover several
orders of magnitude, and would require very high precision if directly
quantized. A better approach is to have the hyperprior networks learn an
entropy coding parametrization suitable for low-precision representations.
This enhanced entropy coding approach is described in more detail in (Said et
al., 2022). For this video coding demo, a simplified version of that approach
was used, where the hyperencoder and hyperdecoder learn a logarithmic scale
(i.e., they learn $\ln(\sigma)$ instead of $\sigma$), which is then quantized
to a single 8-bit integer in order to match pre-computed lookup tables (see
Section 3.4). The value of this 8-bit integer $n$ that is fed to the entropy
encoder and decoder is computed using:

(9)
$n=\max\left[0,\min\left[255,\lfloor\gamma\ln({\sigma})\rfloor+\theta\right]\right]$

We set $\sigma=32$ and $\theta=70$ to cover the range of $\sigma$ needed for
the demo. Reference (Said et al., 2022) presents more examples of alternative
parametrizations.

Figure 3. Parallel entropy coding for our neural video codec (excluding data
stream with hyperprior latents).

###  3.4. Parallel Entropy Coding

Entropy coding is employed to losslessly compress the quantized latents and
hyperlatents, and further reduce the bit rate. This is the stage where the
bitstream representing the video is created (at the transmitter) or parsed (at
the receiver). For high resolution and quality levels, entropy coding must
support very high throughputs, which can be difficult and computationally
expensive without parallelization, even with custom hardware.

As the probability models in our MobileCodec are designed to be
(conditionally) independent , the probability of each element in $y$ and $z$
is (conditionally) independent as well. We can therefore code all variables in
a latent tensor in parallel. This was implemented by partitioning and indexing
the bitstream, providing entry points for parallel decoding (Said et al.,
2015). Figure 3 shows an illustration of this process. Concurrent encoders
save data to temporary memory buffers, and after frame encoding is completed,
those bitstreams are concatenated to create the combined bitstream for that
frame. Note that this bitstream must include a header indicating starting
positions for each independent part, which are used as entry points for
parallel decoding.

The coding method is an implementation of static (instead of adaptive)
arithmetic coding using 32-bit registers, with 16-bit values for probabilities
and range, and byte-based renormalization (Said, 2003). Since it uses only
simple arithmetic and logic operations, it can be executed with multiple
threads, without specialized hardware.

The integer cumulative distribution arrays needed for arithmetic coding (Said,
2003) are pre-computed, according to the quantized entropy coding parameter
defined by eq. (9), assuming that the latent variables to be encoded have
normal probability distributions, and are converted to integers using unit-
step uniform quantization (i.e., simple rounding). These arrays need to be
stored at the transmitter and receiver side.

Another important factor for entropy coding on a mobile device is therefore
the amount of memory needed for storing code tables. Throughput is maximized
when coding tables stay loaded on small caches with the fastest memory.
Fortunately, for NN-based codecs these tables are read-only (conventional
codecs use adaptive coding requiring reading and writing), and the techniques
and analysis developed for low-precision quantization in (Said et al., 2022)
could also be employed to further reduce table memory to a few kilobytes.

Figure 4. Configuration of our demo, showing sender (left) and receiver
(right).

##  4\. Experiments

The goal of our experiments is to assess the ability of our neural codec to
run in real-time on a mobile device while outputting high visual quality
videos. To showcase our codec, we collected 13 off-the-shelf videos of various
categories at 4k resolution from www.pexels.com. Figure 5 shows snapshots of
the sample videos. These videos were then downsampled to a HD 720p resolution
to reduce artifacts from compression. As the codec and hyper-codec use six
convolutions with stride two, the input resolution must be a multiple of 64.
We therefore pad the input to $768\times 1280$ before encoding, and the
reconstructions are cropped back to $720\times 1280$ before they are shown.

Following the training scheme for the existing Scale-Space Flow video codec
(Agustsson et al., 2020), our MobileCodec was first trained on $256\times 256$
crops on the Vimeo-90k dataset (Xue et al., 2019) for one million iterations.
The resulting floating-point model was subsequently finetuned using
quantization-aware training for another 100 thousands iterations, before
quantizing to 8 bits. The end result is an efficient 8-bit quantized neural
video codec.

Figure 5. Off-the-shelf videos collected from www.pexels.com . The video set
contains video of various categories of content, lighting, motion.

###  4.1. Real-time HD video decoding

We evaluated the performance of MobileCodec on the Pexels videos in a real-
time decoding configuration. Figure 4 shows the setup of our experiments.
Specifically, the input videos were encoded offline, stored as a bitstream,
and then sent to a receiver, which is a mobile phone powered by a Snapdragon 8
chip. The receiver then decodes the bitstream into video frames at real-time
speed. Although our demo was configured as an offline setup, the videos were
encoded in low-delay mode, which could also enable live streaming in future
work.

Figure 6. Performance of MobileCodec on the video compression dataset UVG.
(Mercat et al., 2020)

In Table 1, we show the quantitative measurement of our MobileCodec on each
demo video. The results show that our Mobile codec can consistently run at
faster than real-time speeds while obtaining satisfactory visual quality
results. Specifically, our MobileCodec took 32ms to decode each frame, which
is equivalent to 31 frames per second (FPS), while obtaining an average PSNR
of 40.18dB.

###  4.2. Quantitative Evaluation

To further access the quality of our MobileCodec we also test its performance
on the video compression dataset UVG (Mercat et al., 2020), which is widely
used for benchmarking video codecs. To the best of our knowledge, our
MobileCodec is the first neural inter-frame video codec that can run real-time
decoding on a mobile device. Therefore, we do not compare to neural video
codecs here, but do compare to fast implementations of H.264 and H.265, both
among the most popular video codecs used in both regular and mobile platforms.
Figure 6 shows the performance of our MobileCodec in comparison with the
commonly used conventional codecs H264 and H265 in ffmpeg ultrafast and medium
preset, tuned for fast encoding (zerolatency mode). This indicates that
MobileCodec can obtain competitive results in comparison to the ffmpeg
baselines. Of course, stronger video codecs already exist today, both in the
standards setting and in the neural codec literature. We believe that when
these are implemented on mobile phones, we can include other codecs that are
able to perform realtime decoding. As hardware and neural inference ecosystem
for mobile continues to improve, it will become increasingly easy to run
neural codecs on mobile devices.

###  4.3. Computational complexity

We report the complexity of the used components in terms of network parameters
and Multiply-and-Accumulate operations (MACs) in Table 2. We compute MAC count
on an artificial sequence of 2 timesteps, and normalize i t with respect to
number of input pixels to facilitate comparisons across input resolutions. On
the side of the sender, all modules need to be run in their entirety. On the
side of the receiver, we only have to run the decoder and hyper-decoder of
each component, as well as the analysis transform that processes the previous
frame for motion compensation purposes. This means that the MAC count on the
receiver end is up to two times lower than on the sender side.

Note that the I-frame net only has to be run once per Group of Pictures, after
which only the P-frame components are used. This means that the total cost of
decoding one P-frame, which involves running the motion receiver and residual
receiver, is the sum of the P-frame components only: 257.1 KMACs per pixel. We
emphasize that the operators used in MobileCodec are highly optimized in
neural accelerators, and that inference is highly parallelizable as well.

Video | MSSSIM | PSNR | BPP | Frames |  | Time
---
(ms)
Sports | 0.9886 | 42.31 | 0.18 | 300 | 30
Animal | 0.9891 | 39.55 | 0.35 | 265 | 33
Ocean | 0.9842 | 40.21 | 0.35 | 300 | 33
Driving | 0.9907 | 41.4 | 0.20 | 173 | 30
Driving | 0.9904 | 40.56 | 0.31 | 274 | 33
Sports | 0.9905 | 41.78 | 0.22 | 189 | 31
Horsebackriding | 0.9921 | 41.55 | 0.28 | 300 | 31
Barbequing | 0.9872 | 38.08 | 0.36 | 300 | 33
Welding | 0.9859 | 37.56 | 0.48 | 300 | 33
Bartending | 0.9901 | 37.89 | 0.37 | 300 | 32
Food_Restaurant | 0.9915 | 39.16 | 0.35 | 300 | 33
Cutting | 0.9910 | 42.62 | 0.13 | 300 | 29
Food_Restaurant | 0.9857 | 39.67 | 0.28 | 300 | 33
Average | 0.9890 | 40.18 | 0.30 | 277 | 32
Table 1. Performance and decoding time of MobileCodec on off-the-shelf HD videos from Pexels.  Module | Parameters | KMACs / pixel
---|---|---
I-frame net | 6.678M | 26.8% | 211.6 | 37.0%
Motion net | 11.630M | 46.7% | 175.6 | 30.8%
Residual net | 6.573M | 26.5% | 183.6 | 32.2%
Total | 24.881M | 100.0% | 570.8 | 100.0%
I-frame receiver | 2.857M | 24.7% | 130.9 | 33.6%
Motion receiver | 5.980M | 51.6% | 156.2 | 40.0%
Residual receiver | 2.752M | 23.7% | 102.9 | 26.4%
Total receiver | 11.589M | 100.0% | 390.1 | 100.0%
Table 2. Parameter count and MACs of MobileCodec for the sender (top) and
receiver side (bottom).

##  5\. Conclusion

This paper presents MobileCodec, an efficient neural video codec designed for
deployment on a mobile platform. Specifically, we design an inter-frame video
compression architecture that performs motion compensation and transmission
jointly and in feature space. We describe our approach to prepare this video
codec for deployment, which includes a quantization-aware training step to
quantize the model to 8-bit fixed point, and a parallel entropy coding
algorithm that efficiently encodes neural network outputs to bitstream. The
result is the first public demo of real-time ($\geq 30$ FPS) decoding of HD
720p videos using a neural inter-frame video codec on a mobile device.

## References

  * (1)
  * Agustsson et al. (2020) Eirikur Agustsson, David Minnen, Nick Johnston, Johannes Balle, Sung Jin Hwang, and George Toderici. 2020\.  Scale-Space Flow for End-to-End Optimized Video Compression. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 8503–8512.
  * Ballé et al. (2020) Johannes Ballé, Philip A Chou, David Minnen, Saurabh Singh, Nick Johnston, Eirikur Agustsson, Sung Jin Hwang, and George Toderici. 2020.  Nonlinear transform coding.  _IEEE Journal of Selected Topics in Signal Processing_ (2020).
  * Ballé et al. (2016) Johannes Ballé, Valero Laparra, and Eero P. Simoncelli. 2016\.  Density modeling of images using a generalized normalization transformation.  4th International Conference on Learning Representations, ICLR 2016.
  * Ballé et al. (2017) Johannes Ballé, Valero Laparra, and Eero P Simoncelli. 2017\.  End-to-end optimized image compression. In _International Conference on Learning Representations_.
  * Ballé et al. (2018) Johannes Ballé, David Minnen, Saurabh Singh, Sung Jin Hwang, and Nick Johnston. 2018.  Variational image compression with a scale hyperprior. In _International Conference on Learning Representations_.
  * Ballé et al. (2016) J. Ballé, V. Laparra, and E. P. Simoncelli. 2016\.  End-to-end optimization of nonlinear transform codes for perceptual quality. In _2016 Picture Coding Symposium (PCS)_. 1–5.  https://doi.org/10.1109/PCS.2016.7906310
  * Chen et al. (2020) Meixu Chen, Todd Goodall, Anjul Patney, and Alan C. Bovik. 2020\.  Learning to Compress Videos without Computing Motion.  arXiv:2009.14110 [eess.IV]
  * Chen et al. (2021) T. Chen, H. Liu, Z. Ma, Q. Shen, X. Cao, and Y. Wang. 2021.  End-to-End Learnt Image Compression via Non-Local Attention Optimization and Improved Context Modeling.  _IEEE Transactions on Image Processing_ 30 (2021), 3179–3191.  https://doi.org/10.1109/TIP.2021.3058615
  * Cheng et al. (2019) Zhengxue Cheng, Heming Sun, Masaru Takeuchi, and Jiro Katto. 2019\.  Learning Image and Video Compression Through Spatial-Temporal Energy Compaction. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_.
  * Djelouah et al. (2019) Abdelaziz Djelouah, Joaquim Campos, Simone Schaub-Meyer, and Christopher Schroers. 2019\.  Neural Inter-Frame Compression for Video Coding. In _Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)_.
  * Golinski et al. (2020) Adam Golinski, Reza Pourreza, Yang Yang, Guillaume Sautiere, and Taco S. Cohen. 2020.  Feedback Recurrent Autoencoder for Video Compression. In _Proceedings of the Asian Conference on Computer Vision (ACCV)_.
  * Habibian et al. (2019) Amirhossein Habibian, Ties van Rozendaal, Jakub M. Tomczak, and Taco S. Cohen. 2019.  Video Compression With Rate-Distortion Autoencoders. In _Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)_.
  * Hu et al. (2022) Zhihao Hu, Guo Lu, Jinyang Guo, Shan Liu, Wei Jiang, and Dong Xu. 2022\.  Coarse-To-Fine Deep Video Coding With Hyperprior-Guided Mode Prediction. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 5921–5930.
  * Hu et al. (2021) Zhihao Hu, Guo Lu, and Dong Xu. 2021.  FVC: A New Framework towards Deep Video Compression in Feature Space.  (May 2021).  arXiv:2105.09600 [eess.IV]
  * Johnston et al. (2019) Nick Johnston, Elad Eban, Ariel Gordon, and Johannes Ballé. 2019\.  Computationally Efficient Neural Image Compression.  (Dec. 2019).  arXiv:1912.08771 [eess.IV]
  * Lin et al. (2020) Jianping Lin, Dong Liu, Houqiang Li, and Feng Wu. 2020\.  M-LVC: Multiple Frames Prediction for Learned Video Compression. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_.
  * Liu et al. (2020a) Haojie Liu, Han Shen, Lichao Huang, Ming Lu, Tong Chen, and Zhan Ma. 2020a.  Learned Video Compression via Joint Spatial-Temporal Correlation Exploration.  _Proceedings of the AAAI Conference on Artificial Intelligence_ 34, 07 (Apr. 2020), 11580–11587.  https://doi.org/10.1609/aaai.v34i07.6825
  * Liu et al. (2020b) Jerry Liu, Shenlong Wang, W. Ma, Meet Shah, Rui Hu, Pranaab Dhawan, and R. Urtasun. 2020b.  Conditional entropy coding for efficient video compression. In _European Conference on Computer Vision (ECCV)_.
  * Lu et al. (2019) Guo Lu, Wanli Ouyang, Dong Xu, Xiaoyun Zhang, Chunlei Cai, and Zhiyong Gao. 2019\.  Dvc: An end-to-end deep video compression framework. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_.
  * Lu et al. (2020) G. Lu, X. Zhang, W. Ouyang, L. Chen, Z. Gao, and D. Xu. 2020\.  An End-to-End Learning Framework for Video Compression.  _IEEE Transactions on Pattern Analysis and Machine Intelligence_ (2020).
  * Lu et al. (2021) Yadong Lu, Yinhao Zhu, Yang Yang, Amir Said, and Taco S Cohen. 2021.  Progressive Neural Image Compression with Nested Quantization and Latent Ordering.  arXiv:2102.02913 [cs.LG]
  * Mentzer et al. (2021) Fabian Mentzer, Eirikur Agustsson, Johannes Ballé, David Minnen, Nick Johnston, and George Toderici. 2021.  Towards Generative Video Compression.  _arXiv preprint arXiv:2107.12038_ (2021).
  * Mentzer et al. (2018) Fabian Mentzer, Eirikur Agustsson, Michael Tschannen, Radu Timofte, and Luc Van Gool. 2018\.  Conditional Probability Models for Deep Image Compression. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_.
  * Mentzer et al. (2020) Fabian Mentzer, George D Toderici, Michael Tschannen, and Eirikur Agustsson. 2020.  High-Fidelity Generative Image Compression. In _Advances in Neural Information Processing Systems_.
  * Mercat et al. (2020) Alexandre Mercat, Marko Viitanen, and Jarno Vanne. 2020\.  UVG dataset: 50/120fps 4K sequences for video codec analysis and development. In _Proceedings of the 11th ACM Multimedia Systems Conference_ (Istanbul, Turkey) _(MMSys ’20)_. Association for Computing Machinery, New York, NY, USA, 297–302.
  * Minnen et al. (2018) David Minnen, Johannes Ballé, and George D Toderici. 2018\.  Joint Autoregressive and Hierarchical Priors for Learned Image Compression. In _Advances in Neural Information Processing Systems_.
  * Minnen and Singh (2020) David Minnen and Saurabh Singh. 2020.  Channel-wise Autoregressive Entropy Models for Learned Image Compression. In _IEEE International Conference on Image Processing (ICIP)_.
  * Nagel et al. (2021) Markus Nagel, Marios Fournarakis, Rana Ali Amjad, Yelysei Bondarenko, Mart van Baalen, and Tijmen Blankevoort. 2021.  A White Paper on Neural Network Quantization.  (June 2021).  arXiv:2106.08295 [cs.LG]
  * Nagel et al. (2019) Markus Nagel, Mart van Baalen, Tijmen Blankevoort, and Max Welling. 2019.  Data-Free Quantization Through Weight Equalization and Bias Correction.  (2019).  arXiv:1906.04721 [cs.LG]
  * Perugachi-Diaz et al. (2022) Yura Perugachi-Diaz, Guillaume Sautière, Davide Abati, Yang Yang, Amirhossein Habibian, and Taco S Cohen. 2022.  Region-of-Interest Based Neural Video Compression.  _arXiv preprint arXiv:2203.01978_ (2022).
  * Pourreza and Cohen (2021) Reza Pourreza and Taco Cohen. 2021.  Extending Neural P-Frame Codecs for B-Frame Coding. In _Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)_. 6680–6689.
  * research (2021) Qualcomm AI research. 2021\.  World’s first software-based neural video decoder running HD formatin real-time on a commercial smartphone.  https://www.qualcomm.com/news/onq/2021/06/17/worlds-first-software-based-neural-video-decoder-running-hd-format-real-time
  * Rippel et al. (2021) Oren Rippel, Alexander G Anderson, Kedar Tatwawadi, Sanjay Nair, Craig Lytle, and Lubomir Bourdev. 2021\.  ELF-VC: Efficient Learned Flexible-Rate Video Coding. In _Proceedings of the IEEE/CVF International Conference on Computer Vision_. 14479–14488.
  * Rippel and Bourdev (2017) Oren Rippel and Lubomir Bourdev. 2017.  Real-Time Adaptive Image Compression. In _Proceedings of the 34th International Conference on Machine Learning_ , Vol. 70. 2922–2930.
  * Rippel et al. (2019) Oren Rippel, Sanjay Nair, Carissa Lew, Steve Branson, Alexander G. Anderson, and Lubomir Bourdev. 2019.  Learned Video Compression. In _Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)_.
  * Rozendaal et al. (2021) Van Ties Rozendaal, Iris AM Huijben, and Taco S Cohen. 2021\.  Overfitting for Fun and Profit: Instance-Adaptive Data Compression. In _International Conference on Learning Representations_.
  * Said (2003) Amir Said. 2003\.  Arithmetic coding.  In _Lossless Compression Handbook_ , Khalid Sayood (Ed.). Academic Press, San Diego, CA, Chapter 5, 101–152.  http://www.hpl.hp.com/techreports/2004/HPL-2004-76.pdf.
  * Said et al. (2015) Amir Said, Abo-Talib Mahfoodh, and Sehoon Yea. 2015\.  Compressed data organization for high throughput parallel entropy coding. In _Proc. SPIE Vol. 9599: Applicat. Digital Image Process._ San Diego, CA, USA.
  * Said et al. (2022) Amir Said, Reza Pourreza, and Hoang Le. 2022.  Optimized learned entropy coding parameters for practical neural-based image and video compression. In _IEEE Int. Conf. Image Proc._
  * Strümpler et al. (2021) Yannick Strümpler, Janis Postels, Ren Yang, Luc Van Gool, and Federico Tombari. 2021\.  Implicit neural representations for image compression.  _arXiv preprint arXiv:2112.04267_ (2021).
  * Sullivan et al. (2012) Gary J. Sullivan, Jens-Rainer Ohm, Woo-Jin Han, and Thomas Wiegand. 2012.  Overview of the High Efficiency Video Coding (HEVC) Standard.  _IEEE Transactions on Circuits and Systems for Video Technology_ (2012).
  * Toderici et al. (2015) George Toderici, Sean M. O’Malley, Sung Jin Hwang, Damien Vincent, David Minnen, Shumeet Baluja, Michele Covell, and Rahul Sukthankar. 2015\.  Variable Rate Image Compression with Recurrent Neural Networks.  _CoRR_ abs/1511.06085 (2015).  http://dblp.uni-trier.de/db/journals/corr/corr1511.html#TodericiOHVMBCS15
  * Toderici et al. (2017) George Toderici, Damien Vincent, Nick Johnston, Sung Jin Hwang, David Minnen, Joel Shor, and Michele Covell. 2017.  Full Resolution Image Compression With Recurrent Neural Networks. In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_.
  * van Rozendaal et al. (2021) Ties van Rozendaal, Iris A. M. Huijben, and Taco Cohen. 2021\.  Overfitting for Fun and Profit: Instance-Adaptive Data Compression. In _ICLR_.  https://openreview.net/forum?id=oFp8Mx_V5FL
  * Wu et al. (2018) Chao-Yuan Wu, Nayan Singhal, and Philipp Krahenbuhl. 2018\.  Video Compression through Image Interpolation. In _Proceedings of the European Conference on Computer Vision (ECCV)_.
  * Xue et al. (2019) Tianfan Xue, Baian Chen, Jiajun Wu, Donglai Wei, and William T Freeman. 2019.  Video Enhancement with Task-Oriented Flow.  _International Journal of Computer Vision (IJCV)_ 127, 8 (2019), 1106–1125.
  * Yang and Ramanan (2019) Gengshan Yang and Deva Ramanan. 2019.  Volumetric Correspondence Networks for Optical Flow. In _Advances in Neural Information Processing Systems_.
  * Yang et al. (2021) Ren Yang, Luc Van Gool, and Radu Timofte. 2021.  Perceptual Learned Video Compression with Recurrent Conditional GAN.  _arXiv preprint arXiv:2109.03082_ (2021).
  * Zhang et al. (2021) Yunfan Zhang, Ties van Rozendaal, Johann Brehmer, Markus Nagel, and Taco Cohen. 2021.  Implicit neural video compression.  _arXiv preprint arXiv:2112.11312_ (2021).
  * Zhang et al. (2020) Youjian Zhang, Chaoyue Wang, and Dacheng Tao. 2020.  Video Frame Interpolation without Temporal Priors. In _Advances in Neural Information Processing Systems_.
  * Zhu et al. (2021) Yinhao Zhu, Yang Yang, and Taco Cohen. 2021.  Transformer-based Transform Coding. In _International Conference on Learning Representations_.


EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-090 LHCb-PAPER-2011-044 31 March 2012

First observation of the decay $B_{c}^{+}\rightarrow
J/\psi\pi^{+}\pi^{-}\pi^{+}$

The LHCb collaboration †††Authors are listed on the following pages.

The decay $B_{c}^{+}\rightarrow J/\psi\pi^{+}\pi^{-}\pi^{+}$ is observed for
the first time, using 0.8 fb-1 of $pp$ collisions at $\sqrt{s}=7$ TeV
collected by the LHCb experiment. The ratio of branching fractions ${\cal
B}(B_{c}^{+}\rightarrow J/\psi\pi^{+}\pi^{-}\pi^{+})/{\cal
B}(B_{c}^{+}\rightarrow J/\psi\pi^{+})$ is measured to be $2.41\pm 0.30\pm
0.33$, where the first uncertainty is statistical and the second systematic.
The result is in agreement with theoretical predictions.

Submitted to Physical Review Letters

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, B. Adeva34, M. Adinolfi43, C. Adrover6, A.
Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M. Alexander48, S.
Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22, S. Amato2, Y.
Amhis36, J. Anderson37, R.B. Appleby51, O. Aquines Gutierrez10, F.
Archilli18,35, A. Artamonov 32, M. Artuso53,35, E. Aslanides6, G.
Auriemma22,m, S. Bachmann11, J.J. Back45, V. Balagura28,35, W. Baldini16, R.J.
Barlow51, C. Barschel35, S. Barsuk7, W. Barter44, A. Bates48, C. Bauer10, Th.
Bauer38, A. Bay36, I. Bediaga1, S. Belogurov28, K. Belous32, I. Belyaev28, E.
Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, R.
Bernet37, M.-O. Bettler17, M. van Beuzekom38, A. Bien11, S. Bifani12, T.
Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50,
J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W.
Bonivento15, S. Borghi48,51, A. Borgia53, T.J.V. Bowcock49, C. Bozzi16, T.
Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10, T.
Britton53, N.H. Brook43, H. Brown49, A. Büchler-Germann37, I. Burducea26, A.
Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo
Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14, G. Carboni21,k, R.
Cardinale19,i,35, A. Cardini15, L. Carson50, K. Carvalho Akiba2, G. Casse49,
M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph. Charpentier35, N. Chiapolini37,
K. Ciba35, X. Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47, M. Clemencic35,
H.V. Cliff44, J. Closier35, C. Coca26, V. Coco38, J. Cogan6, P. Collins35, A.
Comerma-Montells33, A. Contu52, A. Cook43, M. Coombes43, G. Corti35, B.
Couturier35, G.A. Cowan36, R. Currie47, C. D’Ambrosio35, P. David8, P.N.Y.
David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, M. De Cian37, J.M. De
Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H.
Degaudenzi36,35, L. Del Buono8, C. Deplano15, D. Derkach14,35, O. Deschamps5,
F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1, F. Domingo
Bonal33,n, S. Donleavy49, F. Dordei11, A. Dosil Suárez34, D. Dossett45, A.
Dovbnya40, F. Dupertuis36, R. Dzhelyadin32, A. Dziurda23, S. Easo46, U.
Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38, F. Eisele11, S.
Eisenhardt47, R. Ekelhof9, L. Eklund48, Ch. Elsasser37, D. Elsby42, D.
Esperante Pereira34, A. Falabella16,e,14, C. Färber11, G. Fardell47, C.
Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, M. Ferro-Luzzi35, S.
Filippov30, C. Fitzpatrick47, M. Fontana10, F. Fontanelli19,i, R. Forty35, O.
Francisco2, M. Frank35, C. Frei35, M. Frosini17,f, S. Furcas20, A. Gallas
Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J-C.
Garnier35, J. Garofoli53, J. Garra Tico44, L. Garrido33, D. Gascon33, C.
Gaspar35, R. Gauld52, N. Gauvin36, M. Gersabeck35, T. Gershon45,35, Ph. Ghez4,
V. Gibson44, V.V. Gligorov35, C. Göbel54, D. Golubkov28, A. Golutvin50,28,35,
A. Gomes2, H. Gordon52, M. Grabalosa Gándara33, R. Graciani Diaz33, L.A.
Granado Cardoso35, E. Graugés33, G. Graziani17, A. Grecu26, E. Greening52, S.
Gregson44, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35, C. Hadjivasiliou53,
G. Haefeli36, C. Haen35, S.C. Haines44, T. Hampson43, S. Hansmann-Menzemer11,
R. Harji50, N. Harnew52, J. Harrison51, P.F. Harrison45, T. Hartmann55, J.
He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando Morata34, E. van
Herwijnen35, E. Hicks49, K. Holubyev11, P. Hopchev4, W. Hulsbergen38, P.
Hunt52, T. Huse49, R.S. Huston12, D. Hutchcroft49, D. Hynds48, V. Iakovenko41,
P. Ilten12, J. Imong43, R. Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E.
Jans38, F. Jansen38, P. Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D.
Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35,
T.M. Karbach9, J. Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A.
Keune36, B. Khanji6, Y.M. Kim47, M. Knecht36, R.F. Koopman39, P. Koppenburg38,
M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M. Kreps45, G.
Krocker11, P. Krokovny31, F. Kruse9, K. Kruzelecki35, M. Kucharczyk20,23,35,j,
V. Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G.
Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G.
Lanfranchi18, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J.
van Leerdam38, J.-P. Lees4, R. Lefèvre5, A. Leflat29,35, J. Lefrançois7, O.
Leroy6, T. Lesiak23, L. Li3, L. Li Gioi5, M. Lieng9, M. Liles49, R. Lindner35,
C. Linn11, B. Liu3, G. Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33,
N. Lopez-March36, H. Lu3, J. Luisier36, A. Mac Raighne48, F. Machefert7, I.V.
Machikhiliyan4,28, F. Maciuc10, O. Maev27,35, J. Magnin1, S. Malde52, R.M.D.
Mamunur35, G. Manca15,d, G. Mancinelli6, N. Mangiafave44, U. Marconi14, R.
Märki36, J. Marks11, G. Martellotti22, A. Martens8, L. Martin52, A. Martín
Sánchez7, M. Martinelli38, D. Martinez Santos35, A. Massafferri1, Z. Mathe12,
C. Matteuzzi20, M. Matveev27, E. Maurice6, B. Maynard53, A. Mazurov16,30,35,
G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9, S.
Miglioranzi35, D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S.
Monteil5, D. Moran12, P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K.
Müller37, R. Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P.
Naik43, T. Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35,
A.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29, T.
Nikodem11, A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V.
Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M.
Orlandea26, J.M. Otalora Goicochea2, P. Owen50, B.K. Pal53, J. Palacios37, A.
Palano13,b, M. Palutan18, J. Panman35, A. Papanestis46, M. Pappagallo48, C.
Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M. Patel50, S.K.
Paterson50, G.N. Patrick46, C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos
Alvarez34, A. Pellegrino38, G. Penso22,l, M. Pepe Altarelli35, S.
Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. Pérez-Calero Yzquierdo33,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrolini19,i, A. Phan53, E.
Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilař45, D. Pinci22, R.
Plackett48, S. Playfer47, M. Plo Casasus34, G. Polok23, A. Poluektov45,31, E.
Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A. Powell52, J.
Prisciandaro36, V. Pugatch41, A. Puig Navarro33, W. Qian53, J.H. Rademacker43,
B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, G. Raven39, S. Redford52,
M.M. Reid45, A.C. dos Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, D.A.
Roa Romero5, P. Robbe7, E. Rodrigues48,51, F. Rodrigues2, P. Rodriguez
Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32, M. Rosello33,n, J.
Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34, N.
Sagidova27, P. Sail48, B. Saitta15,d, C. Salzmann37, M. Sannino19,i, R.
Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M.
Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D.
Savrina28, P. Schaack50, M. Schiller39, H. Schindler35, S. Schleich9, M.
Schlupp9, M. Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H.
Schune7, R. Schwemmer35, B. Sciascia18, A. Sciubba18,l, M. Seco34, A.
Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P.
Seyfert11, M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T.
Shears49, L. Shekhtman31, O. Shevchenko40, V. Shevchenko28, A. Shires50, R.
Silva Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, K. Sobczak5,
F.J.P. Soler48, A. Solomin43, F. Soomro18,35, B. Souza De Paula2, B. Spaan9,
A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37, S.
Stoica26, S. Stone53,35, B. Storaci38, M. Straticiuc26, U. Straumann37, V.K.
Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36, T. Szumlak24, S.
T’Jampens4, E. Teodorescu26, F. Teubert35, C. Thomas52, E. Thomas35, J. van
Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39, S. Topp-Joergensen52, N.
Torr52, E. Tournefier4,50, S. Tourneur36, M.T. Tran36, A. Tsaregorodtsev6, N.
Tuning38, M. Ubeda Garcia35, A. Ukleja25, U. Uwer11, V. Vagnoni14, G.
Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J.
Velthuis43, M. Veltri17,g, B. Viaud7, I. Videau7, D. Vieira2, X. Vilasis-
Cardona33,n, J. Visniakov34, A. Vollhardt37, D. Volyanskyy10, D. Voong43, A.
Vorobyev27, V. Vorobyev31, H. Voss10, R. Waldi55, S. Wandernoth11, J. Wang53,
D.R. Ward44, N.K. Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, D.
Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50,
F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A. Wotton44, K.
Wyllie35, Y. Xie47, F. Xing52, Z. Xing53, Z. Yang3, R. Young47, O.
Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A. Zvyagin35.

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 Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
24AGH University of Science and Technology, Kraków, Poland
25Soltan Institute for Nuclear Studies, Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35European Organization for Nuclear Research (CERN), Geneva, Switzerland
36Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
37Physik-Institut, Universität Zürich, Zürich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45Department of Physics, University of Warwick, Coventry, United Kingdom
46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
48School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam

The $B_{c}^{+}$ meson is the ground state of the $\bar{b}c$ quark pair
system111Charge-conjugate states are implied in this Letter.. Studies of its
properties are important, since it is the only meson consisting of two
different heavy quarks. It is also the only meson in which decays of both
constituents compete with each other. Numerous predictions for $B_{c}^{+}$
branching fractions have been published (for a review see e.g. Ref. [1]). To
date, no measurements exist which would allow to test these predictions, even
in ratios. $B_{c}^{+}$ production rates are about three orders of magnitude
smaller at high energy colliders than for the other $B$ mesons composed of a
$b$ quark and a light quark ($B^{+}$, $B^{0}$ and $B_{s}^{0}$). On the
experimental side, whatever is known about the $B_{c}^{+}$ meson was measured
at the Tevatron. It was discovered by the CDF experiment in the semileptonic
decay, $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}l^{+}\nu X$ [2]. This decay mode was later used to measure the
$B_{c}^{+}$ lifetime [3, 4], which is a factor of three shorter than for the
other $B$ mesons as both $b$ and $c$ quark may decay. Only one hadronic decay
mode of $B_{c}^{+}$ has been observed so far,
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$. It
was utilized by CDF [5] and DØ [6] to measure the $B_{c}^{+}$ mass222We use
mass and momentum units in which $c=1$., $6277\pm 6$ MeV [7].

In this Letter, the first observation of the decay mode
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ is presented using a data sample corresponding to
an integrated luminosity of $0.8$ fb-1 collected in 2011 by the LHCb detector
[8], in $pp$ collisions at the LHC at $\sqrt{s}=7$ TeV. The branching fraction
for this decay is expected to be $1.5-2.3$ times higher than for
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$ [9,
10]. However, the larger number of pions in the final state results in a
smaller total detection efficiency due to the limited detector acceptance. We
measure the $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ branching fraction relative to that for the
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$
decay and test the above theoretical predictions.

The LHCb detector [8] is a single-arm forward spectrometer covering the
pseudo-rapidity 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. The
combined tracking system has a momentum resolution $\Delta p/p$ that varies
from 0.4% at 5 GeV to 0.6% at 100 GeV, and an impact parameter (IP) resolution
of 20$\,\upmu\rm m$ for tracks with high transverse momentum. Charged hadrons
are identified using two ring-imaging Cherenkov detectors. Photon, electron
and hadron candidates are identified by a calorimeter system consisting of
scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and
a hadronic calorimeter. Muons are identified by a muon system composed of
alternating layers of iron and multiwire proportional chambers. The muon
system, electromagnetic and hadron calorimeters provide the capability of
first-level hardware triggering. The single and dimuon hardware triggers
provide good efficiency for
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\rightarrow\mu^{+}\mu^{-}$ events. Here, $\pi^{+}[\pi^{-}\pi^{+}]$
stands for either $\pi^{+}$ or $\pi^{+}\pi^{-}\pi^{+}$ depending on the
$B_{c}^{+}$ decay mode. Events passing the hardware trigger are read out and
sent to an event-filter farm for further processing. Here, a software-based
two-stage trigger reduces the rate from 1 MHz to about 3 kHz. The most
efficient software triggers [11] for this analysis require a charged track
with transverse momentum ($p_{\rm T}$) of more than $1.7$ GeV ($p_{\rm T}>1.0$
GeV if identified as muon) and with an IP to any primary $pp$-interaction
vertex (PV) larger than $100$ $\mu$m. A dimuon trigger requiring $p_{\rm
T}(\mu)>0.5$ GeV, large dimuon mass, $M(\mu^{+}\mu^{-})>2.7$ GeV, and with no
IP requirement complements the single track triggers. At the final stage, we
either require a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\rightarrow\mu^{+}\mu^{-}$ candidate with $p_{\rm T}>2.7$ GeV ($>1.5$
GeV in the first 42% of data) or a muon-track pair with significant IP.

In the subsequent offline analysis of the data,
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$
candidates are selected with the following criteria: $p_{\rm T}(\mu)>0.9$ GeV,
$p_{\rm T}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})>3.0$ GeV ($>1.5$ GeV
in the first 42% of data), $\chi^{2}$ per degree of freedom of the two muons
forming a common vertex, $\chi^{2}_{\rm vtx}(\mu^{+}\mu^{-})/\hbox{\rm
ndf}<9$, and a mass window $3.04<M(\mu^{+}\mu^{-})<3.14$ GeV. We then find
$\pi^{+}\pi^{-}\pi^{+}$ combinations consistent with originating from a common
vertex with $\chi^{2}_{\rm vtx}(\pi^{+}\pi^{-}\pi^{+})/\hbox{\rm ndf}<9$, with
each pion separated from all PVs by at least three standard deviations
($\chi^{2}_{\rm IP}(\pi)>9$), and having $p_{\rm T}(\pi)>0.25$ GeV. A loose
kaon veto is applied using the particle identification system. A five-track
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}$ vertex is
formed ($\chi^{2}_{\rm vtx}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+})/\hbox{\rm ndf}<9$). To look for candidates in the
normalization mode, $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}$, the criteria $p_{\rm T}(\pi)>1.5$ GeV and $\chi^{2}_{\rm
vtx}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+})/\hbox{\rm ndf}<16$
are used. All $B_{c}^{+}$ candidates are required to have $p_{\rm T}>4.0$ GeV
and a decay time of at least $0.25$ ps. When more than one PV is
reconstructed, that which gives the smallest IP significance for the
$B_{c}^{+}$ candidate is chosen. The invariant mass of a
$\mu^{+}\mu^{-}\pi^{+}[\pi^{-}\pi^{+}]$ combination is evaluated after the
muon pair is constrained to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mass and all final state particles are constrained to form a common vertex.

Further background suppression is provided by an event selection based on a
likelihood ratio. In the case of uncorrelated input variables this provides
the most efficient discrimination between signal and background. The overall
likelihood is a product of the probability density functions (PDFs), ${\cal
P}(x_{i})$, for the four sensitive variables ($x_{i}$): smallest
$\chi^{2}_{\rm IP}(\pi)$ among the pion candidates, $\chi^{2}_{\rm
vtx}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}])/\hbox{\rm ndf}$, $B_{c}^{+}$ candidate IP
significance, $\chi^{2}_{\rm IP}(B_{c})$, and cosine of the largest opening
angle between the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and pion
candidates in the plane transverse to the beam. The latter peaks at positive
values for the signal as the $B_{c}^{+}$ meson has a high transverse momentum.
Background events that combine particles from two different $B$ mesons peak at
negative values, whilst background events that include random combinations of
tracks are uniformly distributed. The signal PDFs, ${\cal P}_{\rm
sig}(x_{i})$, are obtained from a Monte Carlo simulation of
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$ decays. The background PDFs, ${\cal P}_{\rm
bkg}(x_{i})$, are obtained from the data with a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$
invariant mass in the range $5.35-5.80$ GeV or $6.80-8.50$ GeV (far-
sidebands). A logarithm of the ratio of the signal and background PDFs is
formed: ${\rm DLL}_{\rm sig/bkg}=-2\sum_{i=1}^{4}\ln({\cal P}_{\rm
sig}(x_{i})/{\cal P}_{\rm bkg}(x_{i}))$. Requirements on the log-likelihood
ratio, ${\rm DLL}_{\rm sig/bkg}<-5$ for
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ and ${\rm DLL}_{\rm sig/bkg}<-1$ for
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$,
have been chosen to maximize $N_{\rm sig}/\sqrt{N_{\rm sig}+N_{\rm bkg}}$,
where $N_{\rm sig}$ is the expected
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$ signal yield and the $N_{\rm bkg}$ is the
background yield in the $B_{c}^{+}$ peak region ($\pm 2.5\,\sigma$). The
absolute normalization of $N_{\rm sig}$ and $N_{\rm bkg}$ is obtained from a
fit to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$ invariant mass distribution with ${\rm
DLL}_{\rm sig/bkg}<0$, while their dependence on the ${\rm DLL}_{\rm sig/bkg}$
requirement comes from the signal simulation and the far-sidebands,
respectively. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}[\pi^{-}\pi^{+}]$ mass distributions after applying all
requirements are shown in Fig. 1. To determine the signal yields, a Gaussian
signal shape with position and width as free parameters is fitted to these
distributions on top of a background assumed to be an exponential function
with a second order polynomial as argument. We observe $135\pm 14$
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ and $414\pm 25$
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$
signal events. Using different signal and background parameterizations in the
fits, the ratio of the signal yields changes by up to 3%.

Figure 1: Invariant mass distribution of
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ (top) and
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$
(bottom) candidates. The maximum likelihood fits of $B_{c}^{+}$ signals are
superimposed. Figure 2: Invariant mass distribution of the
$\pi^{+}\pi^{-}\pi^{+}$ combinations for the sideband-subtracted
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ data (points) and signal simulation (lines). The
solid blue line corresponds to the BLL simulations, the PH model is shown as a
green dashed line and the PHPOL model is shown as a red dotted line. All error
bars are statistical.

The ratio of event yields is converted into a measurement of the ratio of
branching fractions ${\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+})/{\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+})$,
where we rely on the simulation for the determination of the ratio of event
selection efficiencies. The production of $B_{c}^{+}$ mesons is simulated
using the BCVEGPY generator [12, 13] which gives a good description of the
observed transverse momentum and pseudorapidity distributions in our data. The
simulation of the two-body
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$
decay takes into account the spins of the particles and contains no
ambiguities. The phenomenological model by Berezhnoy, Likhoded and Luchinsky
[10, 14] (BLL) is used to simulate
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ decays. This model, which is based on amplitude
factorisation into hadronic and weak currents, implements
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}W^{+*}$
axial-vector form-factors and a $W^{+*}\rightarrow\pi^{+}\pi^{-}\pi^{+}$ decay
via the exchange of the virtual $a_{1}^{+}(1260)$ and $\rho^{0}(770)$
resonances. Since it is not possible to identify which of the same-sign pions
originates from the $\rho^{0}$ decay, the two $\rho^{0}$ paths interfere. To
explore the model dependence of the efficiency we also use two phase-space
models, implementing the same decay chain with no interference and with either
no polarization in the decay (PH) or helicity amplitudes of 0.46, 0.87 and
0.20 for $+1$, $0$ and $-1$ ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
helicities (PHPOL), respectively. For the helicity structure in the PHPOL
model, we use the expectation for the $B^{+}\rightarrow D^{*0}a_{1}^{+}(1260)$
decay based on QCD factorisation [15]. The background-subtracted
distribution333For comparisons between the data and simulation we use the data
within $\pm 2.5\,\sigma$ of the observed peak position in the $B_{c}^{+}$ mass
(signal region). We subtract the background distributions as estimated from
the $\pm(5-30)\,\sigma$ near-sidebands. of the $M(\pi^{+}\pi^{-}\pi^{+})$ mass
for the $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ data shown in Fig. 2 exhibits an
$a_{1}^{+}(1260)$ peak and favours the BLL model. The $\rho^{0}(770)$ peak in
the $M(\pi^{+}\pi^{-})$ mass distribution shown in Fig. 3 is smaller than in
the two phase-space models, but more pronounced than in the BLL model, with
the tail favouring the BLL model. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ helicity angle distribution shown in Fig. 4 disfavours the model with
no polarization. Since the BLL model gives the best overall description of the
data, we choose it to evaluate the central value of the ratio of
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ to
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$
efficiencies, $0.135\pm 0.004$, and use the phase-space models to quantify the
systematic uncertainty. The phase-space models produce relative efficiencies
different by $-9\%$ (PHPOL) and $+5\%$ (PH). We assign a 9% systematic
uncertainty to the model dependence of
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ efficiency.

Figure 3: Invariant mass distribution of the $\pi^{+}\pi^{-}$ combinations
(two entries per $B_{c}^{+}$ candidate) for the sideband-subtracted
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ data (points) and signal simulation (lines). The
solid blue line corresponds to the BLL simulations, the PH model is shown as a
green dashed line and the PHPOL model is shown as a red dotted line. All error
bars are statistical.  Figure 4: Distributions of the cosine of the angle
between the $\mu^{+}$ and $B_{c}^{+}$ boosted to the rest frame of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson for the sideband-
subtracted $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}$ (top) and
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ (bottom) data (points) and signal simulation
(lines). In the bottom plot, the solid blue line corresponds to the BLL
simulations, the PH model is shown as a green dashed line and the PHPOL model
is shown as a red dotted line. All error bars are statistical.

The distribution of the $M({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-})$ mass has an isolated peak of four events at the
$\psi(2S)$ mass. From the $B_{c}^{+}$ sidebands we expect $0.50\pm 0.25$
background events in this peak. This is consistent with $3.6\pm 0.6$ expected
$B_{c}^{+}\rightarrow\psi(2S)\pi^{+}$ events, assuming ${\cal
B}(B_{c}^{+}\rightarrow\psi(2S)\pi^{+})/{\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+})$
equals to ${\cal B}(B^{+}\rightarrow\psi(2S)\pi^{+})/{\cal
B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+})=0.52\pm 0.07$ [7] after subtracting 10% to account for the
phase-space difference. Since this contribution is only $(2.6\pm 1.5)\%$ of
the $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}$ signal yield, we do not subtract it and assign a
$2\%$ systematic uncertainty to the ratio of the branching fractions due to
the efficiency difference between the
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}a_{1}(1260)$
and $B_{c}^{+}\rightarrow\psi(2S)\pi^{+}$,
$\psi(2S)\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ decays, as obtained from the simulation.

Other systematic uncertainties are due to limited knowledge of the $B_{c}^{+}$
lifetime [7] ($4\%$), uncertainty in the simulation of charged tracking
efficiency ($5\%$), trigger ($4\%$) and the kaon veto ($5\%$). Summing all
contributions in quadrature, the total systematic error on the branching
fractions ratio amounts to 14%. As a result, we measure the branching fraction
ratio

$\frac{{\cal B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+})}{{\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+})}=2.41\pm 0.30\pm 0.33,$

where the first uncertainty is statistical and the second systematic.

The obtained result can be compared to theoretical predictions; these assume
factorisation into $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}W^{+*}$ and $W^{+*}\rightarrow\pi^{+}[\pi^{-}\pi^{+}]$. The
contributions of strong interactions to
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}W^{+*}$ are
included in form-factors which can be calculated in various approaches such as
a non-relativistic quark model or sum rules. The coupling of a single pion to
a $W^{+*}$ is described by the pion decay constant. The coupling of three
pions to a $W^{+*}$ is measured in
$\tau^{-}\rightarrow\nu_{\tau}\pi^{-}\pi^{+}\pi^{-}$ decays, which are
dominated by the $a_{1}(1260)$ resonance. The prediction by Rakitin and
Koshkarev, using the no-recoil approximation in
$B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}W^{+*}$, is
${\cal B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+})/{\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+})=1.5$ [9]. Likhoded and Luchinsky used three different
approaches to predict the form factors and obtained ${\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+})/{\cal
B}(B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+})=1.9,2.0$ and $2.3$, respectively [10]. Our result prefers the
latter predictions. It is also consistent with ${\cal
B}(B^{+}\rightarrow\bar{D}^{*0}\pi^{+}\pi^{-}\pi^{+})/{\cal
B}(B^{+}\rightarrow\bar{D}^{*0}\pi^{+})=2.00\pm 0.25$ [7], which is mediated
by similar decay mechanisms, and with a similiar ratio of phase-space factors.
Our result constitutes the first test of theoretical predictions for branching
fractions of $B_{c}^{+}$ 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 CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, XuntaGal and GENCAT
(Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United
Kingdom); NSF (USA). We also acknowledge the support received from the ERC
under FP7 and the Region Auvergne.

## References

  * [1] Quarkonium Working Group, N. Brambilla et al., Heavy quarkonium physics, arXiv:hep-ph/0412158, published as CERN Yellow Report CERN-2005-005
  * [2] CDF collaboration, F. Abe et al., Observation of the $B_{c}$ meson in $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV, Phys. Rev. Lett. 81 (1998) 2432, arXiv:hep-ex/9805034
  * [3] CDF collaboration, A. Abulencia et al., Measurement of the $B_{c}^{+}$ meson lifetime using $B_{c}^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}e^{+}\nu_{e}$, Phys. Rev. Lett. 97 (2006) 012002, arXiv:hep-ex/0603027
  * [4] DØ collaboration, V. M. Abazov et al., Measurement of the lifetime of the $B_{c}^{\pm}$ meson in the semileptonic decay channel, Phys. Rev. Lett. 102 (2009) 092001, arXiv:0805.2614
  * [5] CDF collaboration, T. Aaltonen et al., Observation of the decay $B_{c}^{\pm}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{\pm}$ and measurement of the $B_{c}^{\pm}$ mass, Phys. Rev. Lett. 100 (2008) 182002, arXiv:0712.1506
  * [6] DØ collaboration, V. M. Abazov et al., Observation of the $B_{c}$ meson in the exclusive decay $B_{c}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi$, Phys. Rev. Lett. 101 (2008) 012001, arXiv:0802.4258
  * [7] Particle Data Group, K. Nakamura et al., Review of particle physics, J. Phys. G37 (2010) 075021
  * [8] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [9] A. Rakitin and S. Koshkarev, Hadronic $B_{c}$ decays as a test of $B_{c}$ cross section, Phys. Rev. D81 (2010) 014005, arXiv:0911.3287
  * [10] A. K. Likhoded and A. V. Luchinsky, Light hadron production in $B_{c}\rightarrow J/\psi+X$ decays, Phys. Rev. D81 (2010) 014015, arXiv:0910.3089
  * [11] V. Gligorov, C. Thomas, and M. Williams, The HLT inclusive $B$ triggers, LHCb-PUB-2011-016
  * [12] C.-H. Chang, C. Driouichi, P. Eerola, and X. G. Wu, BCVEGPY: an event generator for hadronic production of the $B_{c}$ meson, Comput. Phys. Commun. 159 (2004) 192, arXiv:hep-ph/0309120
  * [13] C.-H. Chang, J.-X. Wang, and X.-G. Wu, An upgraded version of the generator BCVEGPY2.0 for hadronic production of $B_{c}$ meson and its excited states, Comput. Phys. Commun. 175 (2006) 624, arXiv:hep-ph/0604238
  * [14] A. Berezhnoy, A. Likhoded, and A. Luchinsky, BC_NPI module for the analysis of $B_{c}\rightarrow J/\psi+n\pi$ and $B_{c}\rightarrow B_{s}+n\pi$ decays within the EvtGen package, arXiv:1104.0808
  * [15] J. L. Rosner, Determination of pseudoscalar-charmed-meson decay constants from B-meson decays, Phys. Rev. D42 (1990) 3732