# An Analysis of United States Online Political Advertising Transparency

Laura Edelson  New York University ,  Shikhar Sakhuja  New York University ,
Ratan Dey  New York University and  Damon McCoy  New York University

###### Abstract.

During the summer of 2018, Facebook, Google, and Twitter created policies and
implemented transparent archives that include U.S. political advertisements
which ran on their platforms. Through our analysis of over 1.3 million ads
with political content, we show how different types of political advertisers
are disseminating U.S. political messages using Facebook, Google, and
Twitter’s advertising platforms. We find that in total, ads with political
content included in these archives have generated between 8.67 billion - 33.8
billion impressions and that sponsors have spent over $300 million USD on
advertising with U.S. political content.

We are able to improve our understanding of political advertisers on these
platforms. We have also discovered a significant amount of advertising by
quasi for-profit media companies that appeared to exist for the sole purpose
of creating deceptive online communities focused on spreading political
messaging and not for directly generating profits. Advertising by such groups
is a relatively recent phenomenon, and appears to be thriving on online
platforms due to the lower regulatory requirements compared to traditional
advertising platforms.

We have found through our attempts to collect and analyze this data that there
are many limitations and weaknesses that enable intentional or accidental
deception and bypassing of the current implementations of these transparency
archives. We provide several suggestions of how these archives could be made
more robust and useful. Overall, these efforts by Facebook, Google, and
Twitter have improved political advertising transparency of honest and, in
some cases, possibly dishonest advertisers on their platforms. We thank the
people at these companies who have built these archives and continue to
improve them.

††copyright: rightsretained††price: 15.00

##  1\. Introduction

Online advertising plays an increasingly important role in political
elections. As part of the 2016 U.S. national elections there were a number of
controversies regarding an ad-driven propaganda campaign to influence
elections (Barrett, 2018) and privacy violations (Granville, 2018). In
response to these controversies, Facebook, Google, and Twitter have all
created policies and implemented products to make transparent and archive U.S.
political advertisements that have run on their platforms. A report by Upturn
points out in their analysis of Facebook’s then-proposed political
transparency archive plans that providing effective transparency of only
political ads can be tricky in the face of a complex online ad network
(Upturn, 2018).

In this paper, we analyze Facebook (Facebook, 2018a), Google (Google, 8 15),
and Twitter’s (Twitter, 6 28a) political ad transparency implementations along
with the political ad data included in each archive. Through the lens of these
transparency efforts, we perform what is to our knowledge the first large-
scale analysis of U.S. online political advertising. Our analysis enables us
to begin to understand and describe the parts of online political advertising
in the U.S. that have been made accessible and transparent. We collected as
much data as was possible from these archives, collecting 75% of ads archived
by Facebook and 100% of ads archived by Twitter and Google from May, 2018 –
October 21st, 2018. In total, we collected and analyzed over 1.3 million
political ads from over 24 thousand sponsors. We additionally connect this
data to a public dataset published by ProPublica which was gathered by
Facebook users via a browser plugin. The ProPublica dataset provides partial
information on how Facebook ads have been targeted to the user seeing them.

Our analysis was hampered by our inability to collect all of the ads in
Facebook’s transparency archive due to limitations of their current beta API.
It was also hampered by Facebook and Google releasing ranges instead of exact
impression data. It is also unclear if spend is the best metric for measuring
the impact of an online political advertisement. Thus, there is some level of
uncertainty in much of our analysis especially that related to Facebook’s
platform. We acknowledge that all three of these political advertising
transparency archives were rapidly deployed and this has caused some of the
issues with what and how it was released. We have worked with Facebook to
improve access to the ads in their transparency archive and we hope to work
with Google and Twitter so that they can include more political advertisers in
their transparency archives.

Given these limitations and biases of our data, we perform an initial large-
scale analysis of U.S. online political advertising. As part of this study, we
provide information about the audience size of individual political ads based
on impression data for each of the platforms. We find that across all three
platforms the majority of political ads are small, costing their sponsors less
than $100 USD with 82% of all Facebook political ads costing between $0 - $99.
This confirms and quantifies the prevalence of small likely highly targeted
ads that can contain custom political messaging. We also create a taxonomy of
political ad types based on their intent (i.e., connect, donation, inform,
move) and an effective ad type classification methodology based on labeling
URLs included in political ads. Using our methodology, we are able to provide
a longitudinal analysis of political ads based on the type of ad. Finally, we
are able to identify many likely dishonest advertisers that are not correctly
disclosing or are obfuscating the real ad sponsor. We categorize these types
of advertisers into quasi for-profit media companies and corporate
astroturfers. We discuss the limitations and weaknesses that enable
intentional or accidental deception and bypassing of the current
implementations of these transparency archives. Based on our experiences
analyzing these transparency archives, we provide several suggestions of how
these archives could be made more robust and useful.

We have made as much of the data that we have collected as possible public as
well as all of our labeling, data collection, and analysis scripts public. Our
initial reports have been the basis for many journalists’ stories which have
improved online political advertising transparency.

##  2\. Background

Facebook, Google, and Twitter have all deployed political advertising
transparency archives. However, each of these transparency archives have
different criteria for the inclusion of ads and different modes of access
which we create a taxonomy of in Table 1. Each of these transparency archive
implementations has strengths and weaknesses and there is currently no “best”
archive.

| Facebook | Google | Twitter
---|---|---|---
Ads | All Candidates, | Federal | Federal
Included | Issue ads | candidate | candidate,
|  | related | Issue ads
Sponsor | Name | Name, | Name,
Info |  | FEC/EIN | billing info
Ad Contents | Ranges | Ranges | Exact
Viewed | Gender, age, | N/A | Gender, age,
Audience | geolocation |  | geolocation
Targeting | N/A | Age, gender, | Age, gender,
Info |  | geolocation | geolocation
|  | keywords |
Data | Portal, | Portal, | Portal
Availability | API (w/NDA) | Database | API
Table 1. Transparency Implementations

What is an ad? For purposes of this study, an ad is a record in an archive
with a unique id assigned by the platform. While each platform has slightly
different information associated with each record, each has 3 categories of
information associated with it: content, context, and results. The contents of
an ad consist of any text, images, and/or videos seen by an ad viewer. The
context of the ad is the information specified by the advertiser about how,
when, where, and by whom they want the ad to be seen and how much they are
willing to spend for the ad to be seen. Both the content and context of the ad
are specified by the advertiser at the time of ad creation. The results of the
ad consist of information about who ultimately interacted with the ad and when
those interactions happened, and how much was ultimately spent on the ad. Not
all of this information is made available about each record in any of the
archives, but all of this information is made available by at least one
archive.

Archive Completeness. All archives contain a unique id for each ad, impression
counts and amount spent for each advertisement, as well as the dates the ad
was active. Facebook and Google release ad impression and spend in ranges and
Twitter releasing these as exact numbers. Twitter’s implementation of
releasing exact impression and spend information from every ad enables us to
more precisely measure political advertising on their platform. It would help
remove uncertainty if Facebook and Google would also release exact ad
impressions and spend amounts instead of ranges. We also note that impressions
is an imperfect metric to measure the “reach” of an ad and it would be useful
to also include click and other interaction metrics recorded by the platforms.
Facebook and Twitter includes the ad text, image, and video content; Google’s
archive contains a link to a webpage where this content is viewable, but does
not contain the content itself. Twitter is the only platform to release
targeting information, including whether users were targeted by geography,
age, or gender. Facebook and Google have detailed information about how users
are targeting for each ad, based on advertiser produced lists of personally
identifiable information, groups they belong to, demographic or income
information that the platform has about the user, geography, or keyword search
information, however they do not currently make any of this information
available in their archives.

Ads Included. Facebook has the most inclusive policy and includes in their
archive ads that meet any of the following criteria: “(1) Is made by, on
behalf of, or about a current or former candidate for public office, a
political party, a political action committee, or advocates for the outcome of
an election to public office; (2) Relates to any election, referendum, or
ballot initiative, including ”get out the vote” or election information
campaigns; (3) Relates to any national legislative issue of public importance
in any place where the ad is being run; (Facebook, 7 03b) (4) Is regulated as
political advertising.” (Facebook, 7 03a) Facebook allows advertisers to opt
into including their ads in the archive. In order to enforce their policy,
Facebook uses a combination of user reports and machine learning algorithms to
“catch” political ads where the sponsor did not opt into making them
transparent.

Google is only including ”ads related to elections or issues that feature a
federal candidate or officeholder” (Google, 8 15). Google has stated that they
plan on expanding the set of ads included in their archive. It is unclear how
Google enforces their policy.

Twitter’s original policy was limited to only including ads sponsored directly
by federal candidates. However, Twitter has since expanded their policy to
include: “(1) Ads that refer to an election or a clearly identified candidate.
(2) Ads that advocate for legislative issues of national importance. A clearly
identified candidate refers to any candidate running for federal, state, or
local election (Twitter, 6 28b).” Based on our analysis, it appears that
Twitter is currently not enforcing their policy well.

Sponsors’ Info. Facebook only displays a text string which the sponsor
provides and is intended to identify who is paying for the ad. We went through
the vetting process of becoming a political advertiser on Facebook’s platform.
This entailed uploading a U.S. identification card which was approved
approximately five minutes later, at which time we could start posting
political ads. Facebook also validates the address of the advertiser by
sending them a post card which must be replied to within 30 days or else the
advertiser will be suspended. However, during this 30 day grace period
political advertisers can post ads without validating their address. We
disclosed to Facebook and a subsequent independent experiment by Turton, a
reporter from Vice news, showed that Facebook does not currently vet this text
string which allowed the reporter to post ads appearing to be from U.S.
Senators (Turton, 2018). This is a security issue that Facebook has
acknowledged but claims there is no effective and scalable vetting techniques
(Merrill, 2018). We will describe the issues that we found with this self-
reported text string later in this paper.

Google provides both a text string and a Federal Election Candidate (FEC) ID
or EIN (U.S. Tax ID) which is vetted for every political advertiser in their
archive. Twitter provides a text string and, when available, the billing info
of the political sponsors. Twitter initially did not vet this information but
started vetting sponsor’s EIN similar to Google on September 30th, 2018.
Providing a consistent and easy to reference identifier such as FEC or EIN for
each sponsor enables us to better study sponsors in Google and Twitter’s
archive.

Viewed Audience. Facebook and Twitter both include break downs on the
impression viewing audience by gender, age range, and state level geolocation.
Google provides this information as a heat map image that we cannot currently
extract this information from for our analysis thus we mark Google as “N/A”
for this category. Google has replied that they will work on releasing this
information in a format that we can analyze.

Targeting Info. Facebook does not include any explicit targeting information
in their archive. Google and Twitter makes transparent Age, gender, and
geolocation based targeting but do not appear to release other types of
targeting criteria, such as audience and content, which are allowed by their
advertising platforms. Google also makes transparent some aggregated keyword
targeting data. All of the platforms only release partial targeting
information, at best, which obscures a key facet of online political
advertising.

Data Availability. Facebook initially only provided a keyword based portal
that was designed for small-scale interactive user exploration of the ads in
the archive. Facebook enabled anti-scraping functionality in July 2018 that
makes it difficult to collect large-scale data by scraping this portal. In
September 2018 Facebook released an API that is currently in beta testing
which we have access to after signing an NDA stipulating that we will not
publicly release raw data collected from the API. This effectively means that
only a small set of U.S. organizations participating in the API beta test have
large-scale data collection access to ads in the Facebook archive.

Twitter has provided an open API and list of all accounts included in their
transparency archive which allows us to effectively collect all ads included
in their archive. Google implemented a portal similar to Facebook’s and also
releases a BigQuery (SQL-like) database of all the ads included in their
archive which is updated weekly. For our use case of large-scale data analysis
this database format is ideal.

##  3\. Data Collection Methodology

###  3.1. Facebook

Initially we scraped Facebook’s archive using a list of keywords that included
elected positions (i.e., governor, judge, senator), U.S. state names, and key
political issues (i.e., health care, immigration, taxes). Around the end of
July 2018, Facebook implemented anti-scraping measures which blocked our
scraper. Thus, we had no viable means of collecting large-scale ad data until
Facebook implemented their API in September 2018. We have publicly released a
report and all of the data that we collected by scraping Facebook’s archive
user portal before our scraper was blocked (Laura Edelson, 2018).

We are part of Facebook’s Political Ad Archive API beta testing program
(Facebook, 8 22) which allows us to query Facebook’s Political Ad Archive for
specific keyword terms which is matched against the page name, the disclaimer,
or ad text. Ads returned by Facebook’s API are ordered using a proprietary
ranking algorithm that was not described to us how it functions. However, most
advertisements appear to be returned in chronological order. A single query to
Facebook’s API returns at most 1,000 ads and we can page through to collect
additional ads using pagination functionality as part of the API. Currently
there is a limitation in Facebook’s Political Ad Archive API beta that
prevents us from paging past 8,000 ads. This is problematic because many
searches will return far more than 8,000 results.

Information on spend and impressions per ad is only available in broad ranges.
For impressions, the ranges presented are: 0 - 999, 1,000 - 4,999, 5,000 -
9,999, 10,000 - 49,999, 50,000 - 99,999, 100,000 - 199,999, 200,000 - 499,999,
500,000 - 999,999. For spend, the ranges presented are: 0 - 99, 100 - 499, 500
- 999, 1,000 - 4,999, 5,000 - 9,999, 10,000 - 49,999, 50,000 - 99,999, 100,000
- 199,999, 200,000 - 499,999, 500,000 - 999,999.

Additionally, the API has very low rate limits. We have found that
functionally, we could make at most 3 requests per minute on average before
hitting these rate limits. Our goal was to create as comprehensive and
representative a dataset as possible. Given the very low rate limits and
limits on the number of responses for a given search, our approach was to
search by advertising page as much as possible in order to reduce the bias in
our data. We are currently able to keep up with the rate of new advertisements
appearing in Facebook’s political ad transparency archive. We cannot publicly
release the raw data that we have collected from Facebook’s API due to the
agreement that we have signed with Facebook as a requirement for access to
their API.

We created a separate approach for discovering pages that are linked to
sponsored political ads. Our approach to discovering pages involved scraping
Facebook’s Political Ad Archive user portal interface. We chose a scraping
method for page discovery since our access to Facebook’s API is highly rate
limited and it would be logistically infeasible to perform the queries
required for both page discovery and to collect ads using our API access. Our
list was not a complete list of advertisers using Facebook’s platform since it
depends on good coverage based on our keyword searches.

Facebook started publishing a comprehensive list after the cutoff for our data
analyzed in this study. Our data collection from Facebook’s archive is our
best effort and was incomplete based on analysis of what is contained in
Facebook’s transparency report. We have changed our data collection
methodology moving forward to discover Facebook pages running political ads
using Facebook’s weekly transparency reports. This combined with improvements
we requested and Facebook implemented to their API after the data collection
period for this study will improve our coverage to a mostly complete set of
U.S. political ads Facebook has included in their transparency archive.

###  3.2. Google

Google published their archive as a public dataset in a BigQuery (SQL-like)
format and committed to keeping it public. However, we observed that ad spend
and impression values for ads, and occasionally advertiser information were
being changed after their entry into the archive. For this reason, we created
separate archives of the dataset on a weekly basis. Additionally, ad text
information was not available in the dataset itself, but was viewable at a
summary page for each ad. We scraped all of these associated pages to collect
ad text to be associated in our dataset with the underlying ad data.
Unfortunately, many of these summary pages did not render correctly, so we
were only able to collect ad text for approximately 66% of pages which
contained it. Two separate issues prevented collection. First, some ad pages
display the message:

“Advertisers are able to use approved third party vendors to serve ads on
Google. While we are able to review these ads for compliance with advertising
policies, due to technical limitations, we are currently unable to display the
content of the ad in the Transparency Report.”

Second, some ad pages displayed the message:

“Policy violation This ad violated Google’s Advertising Policy.” We recommend
that Google change their implementation so that ads served by third party
vendors or which were deleted for compliance reasons are still accessible
through their transparency archive. Google can place a click-through
disclaimer to avoid accidental exposure to policy violated content similar to
what Facebook has implemented for deleted advertisements.

Information on spend and impressions per ad are only available in broad
ranges. For impressions, the ranges presented are: ”¡= 10k”, ”10k-100k”,
”100k-1M”, ”1M-10M”, ”¿ 10M”. For spend, the ranges presented are: ”¡ 100”,
”100-1k”, ”1k-50k”, ”50k-100k”, ”¿ 100k”. The ads in this dataset are a
combination of text-only ads that are displayed alongside Google search
results and image or video-only ads that are displayed as banner or sidebar
ads on Google’s AdSense network.

In addition to per-ad data, Google also published some aggregate data on a
per-advertiser and geographic basis. One of these aggregations was exact
weekly spend per advertiser. Throughout this paper, we present minimum numbers
for impressions and spend because both Google and Facebook publish ranges for
impressions and spend for each ad, instead of exact numbers. These total
aggregations, give us a sense of how much error there is when we use these
minimum estimates for Google. According to Google, advertisers spent $45 M on
political ads but our minimum estimate of spending was only $11 M.

###  3.3. Twitter

Twitter publishes a list of all political campaigning advertisers (Twitter,
2018) which we scrape daily to discover new political campaign advertisers’
Twitter accounts. In addition to this list provided by Twitter, we have also
manually attempted to identify every federal election candidates’ personal or
campaign Twitter account. We then query each account daily using Twitter’s API
perform to collect updated information on all promoted tweets and detect
federal election candidates which are not listed on Twitter’s political
campaigning advertisers page but are sponsoring tweets. During our scraping,
we have noticed that some promoted tweets were deleted and are replaced with
the text:

“This Tweet is not available because it includes content that violated Twitter
Ads Policies.”

The information for these deleted promoted tweets is no longer accessible
through Twitter’s political transparency archive. However, if we have scraped
them before they were deleted we have retained the content and information
about these promoted tweets. We recommend that Twitter change their
implementation so that promoted tweets which were deleted are still accessible
through their transparency archive. Twitter can place a click-through
disclaimer to avoid accidental exposure to policy violated content similar to
what Facebook has implemented for deleted advertisements. We have made public
all of the data that we have collected from Twitter’s transparency archive.

Additionally, we noted that there were several accounts of federal candidates
that were not being archived according to Twitter’s policies. We would find
these ads during our regular scrapes for ads by all federal candidates, but no
billing or impression data would be available, and the ads would disappear
from Twitter’s archive after 7 days, as is typical for non-political ads. We
notified Twitter about 4 accounts which they subsequently added to their
transparency archive. However, Twitter did not retroactively include their
prior promoted tweets from these accounts and there are currently 11
additional federal candidate accounts which have promoted tweets not included
in the archive. Thus, it appears that Twitter’s process for flagging federal
election candidates’ account that should be included in their archive is not
working correctly. We will disclose this new set of 11 accounts to Twitter and
continue to work with them to improve their process for discovering and
including relevant promoted tweets in their transparency archive.

##  4\. Datasets

We have collected all of the U.S. political ad data that Google and Twitter
have made transparent and archived as of October 21st, 2018. In addition, we
have made our best effort to collect as much of the U.S. political ad data
that Facebook has made transparent and archived as of October 21st, 2018. For
Facebook, we are not able to collect all of the ad data from their
transparency archive due to the limitations in their API; this is a subset of
U.S. political ads that ran on Facebook. Note that our scraper was blocked by
Facebook in mid-July, 2018 and we were not able to collect data until the
beginning of September, 2018 when we began to use their beta API. This means
that we do not have good coverage of Facebook ads during that period since it
is difficult to retrieve older ads from Facebook’s current beta API. On
October 23rd, 2018, shortly after we froze our dataset, Facebook released
their Ad Archive Report (Facebook, 2018b). From this, we know that as of the
cutoff date for data analyzed in this study, Facebook had a total of 1.67M ads
in their archive, from a total of 256M spent across 78K pages. We have
captured over 75% of all ads in the archive, but only 49% of the pages.

On the Facebook platform, ads that run without a ’Paid for by’ label but are
later deemed to be political are removed from circulation and added to the
archive. We have been able to find 96,106 such ads in the archive, with a
total spend of at least $42.8 million and 670 million impressions. It does not
appear that Google or Twitter have any mechanism for retroactively marking an
ad as political if it is discovered after the fact, and we would encourage
them to develop this capacity.

Table 2 shows all of the data that we have collected from each of the
platforms. Most of the political ads in these archives are from late May, 2018
to October 21st, 2018 but there are several older ads from Twitter and
Facebook that have been included in their transparency archives. Facebook has
the most advertisers, ads, impressions, and spend. However, Facebook also
includes many political issue ads in their transparency archive that are not
included in Google and Twitter’s transparency archives so this is not a fair
comparison of political advertising activity across all three platforms. An
important difference between the datasets is that, while Facebook and Twitter
are publishing breakdowns of impressions on geographic and demographic lines,
Google is instead publishing geographic and demographic targetings. These
should not be considered equivalent. Below in the analysis section we will
present a more accurate comparison of political advertising activity across
all three platforms.

Additionally, we use a dataset published by ProPublica of political ads that
have been viewed by their users who have installed browser extensions that
automatically collected advertisements on their Facebook pages and sent them
to ProPublica’s servers (ProPublica, 0 21). Table 3 provides an overview of
this dataset. We were able to connect ads in the ProPublica dataset to ads in
our dataset of archived political ads by mapping the ad IDs used in the
ProPublica dataset to the ad archive IDs used in the archive. To do this, we
scraped the Facebook’s web-based political ad archive, as both the ad IDs and
ad archive ids were available. Each record in this dataset contains, among
other things, the text of the data, the various targetings received by the
different users who saw the ad, the page associated with the ad, and the ’Paid
by’ ad sponsor string associated with the ad. Of the 33,308 ads in the
ProPublica dataset with a creation date after May 7th, 2018, the official
start of the Facebook dataset, we were able to find 18,010. Because the users
who contribute data to this dataset are self-selecting, these ads should not
be considered a representative sample of ads in the larger Facebook Ad
Archive. Among other things, the average ad spend on ads in this dataset was
$644, compared to $107 for the larger dataset.

As part of our analysis, we manually categorized the top advertisers on all
three platforms. We categorized these advertisers by organization type
(political candidate, Political Action Committee (PAC), Union, For Profit,
etc). For Facebook, we were able to classify the organizations of the
advertisers who were responsible for at least 75% of the total number of ads
in the Facebook archive. For Google, we labeled the organization of top
advertisers who were responsible for 80% of the total number of ads, and for
Twitter we we were able to label all 88 advertisers with their organization
type. We were able to categorize 12,833 of the top ad sponsors. If we were not
able to categorize an advertiser, it is marked as ’Unknown’.

We also classified the ads themselves into 5 categories: Inform, Connect,
Donate, Move, or Commercial. Inform ads seek to persuade the viewer, but do
not make an explicit ask. Connect ads seek the user’s contact information.
Donate ads seek the user’s money. Move ads attempt to motivate the user to
take some action in the physical world, such as attending a rally or voting.
Commercial ads seek to sell the user goods or services. We classified the ads
based on the outgoing links from the ads. Ads that had no outgoing links were
always classified as Inform ads, as they could not have any further ask from
the user. Ads that linked directly third-party sites for event management
(eventbrite.com), contact management(Google Docs), or payments management
(actblue.com) were solely classified as Move, Connect, or Donate ads
respectively. Ads that linked to general campaign sites were usually multiple-
classed as some combination of the three, as these ads and pages typically
made multiple asks. Ads by For Profit Media organizations were classified as
Inform ads, as these advertisers do not sell goods or services to users. Ads
by For Profit organizations that linked to store sites or sites selling
services were classified as Commercial. We were able to categorize 907,840 ads
with these methods. Heavy use of third-party service providers by advertisers
was extremely helpful in making these classifications. If we were not able to
categorize an ad, it was marked as ’Unknown’. We validated this method of ad
categorization by taking a random sample of 300 categorized ads from each
platform and manually verifying them. The error rate for Facebook was 4%, for
Google was 3.7%, and for Twitter was 3.7%

A limitation that applies to all our datasets is that we do not know when the
spend and impressions for each ad occurred during the lifetime of the ad. Some
ads run for several weeks and some for only a day, but in either case, we
attribute their entire spend and total impressions to the creation date of the
ad.

Platform | Total Ads | Total Sponsors | Total Pages | Impressions | Spend | First Ad Date | Last Ad Date
---|---|---|---|---|---|---|---
Facebook | 1.26 M | 24 K | 38 k | 7.35 B - 21.12 B | $135 M - $567 M | July 14th, 2014 | October 21st, 2018
Google | 41 K | 616 | NA | 1.3 B - 11.6 B | $45 M | May 31st, 2018 | October 21st, 2018
Twitter | 1808 | 88 | NA | 118 M | $1.6 M | December 21st, 2016 | October 21st, 2018
Table 2. Overall Datasets Total Ads | 81,052
---|---
Total Pages | 2,363
Total Ad Sponsors | 2395
Earliest Ad Date | July 31st, 2017
Latest Ad Date | October 18th, 2018
Table 3. ProPublica Political Advertisements From Facebook

##  5\. Results

We calculate total spend and impression minimum and maximum for Facebook ads
by summing respectively the smallest and largest value for the range given for
each ad. For Google, advertiser weekly spend data was aggregated for all
advertisers, so we did not have to estimate that number. For Twitter, exact
numbers for impressions and spend were available, so no estimation was needed.
We also note that we are only able to collect a subset of political
advertisements from Facebook’s transparency archive due to accessibility
issues with their beta API. We stress that because the criteria for inclusion
in these archives differed on the different platforms, the figures on relative
proportions of ad types and advertiser types should be seen as a reflection of
what the platforms chose to make transparent in addition to what is
organically present on these platforms.

With that in mind, we can see clear differences between the platforms. Of
particular note is the difference in ad size visible in Figure 1, with
Facebook having a much larger sized share of the smallest size of ad. Also of
note is the differing prevalence of types of advertisers in Figure 3, with
PACs making up a much larger percentage of spend on Google compared with the
other platforms.

Figure 1. Distribution of ads by size Figure 2. Distribution of ads by type
Figure 3. Distribution of spend by advertiser type

###  5.1. Data Over Time

The time period during which we were collecting data coincided with the 2018
midterm elections in the United States. Thus, we were able to observe changing
patterns in spend leading up to a major election. Figure 4 shows spend by week
for the 5 month period leading up to the election and Figure 5 shows raw ad
count for the same period. We note that our data, particularly for Facebook
spend, is right-censored for the final two weeks. This is caused by Facebook’s
API limitations which only enable us to be able to recheck ad spends weekly.
Thus, newly create ads have likely not spent much of their budget when we
initially discover them. This right censor effect also likely effects Google
and Twitter to a lesser degree due to ads with larger budgets that take
several days to spend down completely. This can be corrected by periodically
rechecking the ads until they have all spent their budgets which is normally
within a week. If the paper is accepted, we will update the data to include
ads up to the U.S. midterm elections.

We can see the expected increases in the number of ads on all three platforms
as the U.S. midterm elections approach. On Facebook’s platform there is an
increase in connect ads and on Twitter there is an increase in move ads. Both
of these are related to sophisticated “get out the vote” efforts that many
groups have deployed. These move ads include images which include specific
polling place addresses and websites that provide polling place directions and
information. The connect ads often provide users with instructions on how they
can volunteer to help with early and day-of voter turnout efforts. The cause
of the spending spikes for Facebook’s platform can be attributed to a few
unknown sponsors that we could not link to a legally registered entity but
that were likely quasi for-profit advertisers which we will discuss further
later in the paper. The spending spikes on Twitter’s platform can be
attributed to candidates who ran a few ads with larger budgets.

Figure 4. Platform Ad Count By Ad Type By Week  Figure 5. Platform Spend By
Advertiser Type By Week

###  5.2. Federal Candidate Comparison

In order to understand how political advertising across these platforms
differ, we attempted to create a comparable subset of advertisers and ads.
This is difficult because each platform has slightly different criteria for
inclusion. To do this, we present results for advertising only paid for by
candidates for federal office, which was the broadest set that was reliably
included in all three archives. Note, this does not include ads by current
officeholders who are not seeking re-election or ads that merely mention a
federal candidate but are paid for by another party. Results for these
advertisers are presented in Table 4.

Figure 6. Federal Candidate ads by Size  Figure 7. Federal Candidate Spend by Ad Type  Figure 8. CDF of Regions by Ad Type for Federal Candidates Results | Facebook | Google | Twitter
---|---|---|---
Total Advertisers | 1 K | 534 | 54
Total Ads | 161 K | 15 K | 1 K
Total Impressions | 800 M - 2.4 B | 280 M- 3 B | 100 M
Total USD Spend | $12 M - $60 M | $13.5 M | $1.4 M
Ave Impressions/Ad | 5 K - 15 K | 32 K - 283 K | 65 K
Ave USD Spend/Ad | $74 - $373 | $1 K | $885
Table 4. Federal Candidate Only Results

Table 4 shows that Facebook is the platform with the broadest appeal to
federal candidate advertisers, with far more advertisers and ads than Google.
However, political advertising by this group on Google appears to generate
more spend and possibly more impressions than ads on Facebook. The average ad
size on Facebook in terms of impressions and spend are the smallest based on
our minimum estimates indicating that advertisers are running smaller, likely
more targeted ads on Facebook. These small ads on Facebook are what are called
micro targeted, which we define as less than 1,000 impressions or a spend of
less than $100. For Facebook, microtargeted ads make up 81% of the overall
number of ads for federal candidates in our dataset. For Twitter, this number
is 62%, and for Google it is 54%. Figure 6 shows the share of ads by size of
spend, and here we can begin to see how federal candidates use these platforms
in different ways. We note that the distribution of ads by size for federal
candidates in Figure 6 is very similar to the overall distribution of ads by
size seen in Figure 1.

Figure 7 shows the relative spend on different ad platforms, where we see very
different percentages for types of ads. Commercial ads are not shown in this
figure because there were too few commercial ads to be visible. Particularly
of note is the fact that ads seeking donations were far more common on the
Google platform, and ads seeking to spread a message (’Inform’) were much more
common on Facebook.

Seeing these differences in both ad size and the types of ads that were run,
we wanted to understand if advertisers were trying to reach different
geographic audiences with different types of ads. To do this, we compared the
number of regions in which various ads had impressions on Facebook and
Twitter, and the number of regions targeted for Google. Figure 8 shows that a
variation in targeting strategy is visible on Facebook and Twitter. On
Facebook, ’Move’ ads that encouraged people to attend a rally, volunteer for a
candidate, or some other in-person activity were viewed, on average, in 4
regions, while ’Donate’ ads were viewed in 24 regions on average. This makes a
certain amount of intuitive sense; people are willing to travel only so far to
attend a rally, but can donate to candidates anywhere in the United States.

###  5.3. Ad Targeting

One of the deficiencies with the Facebook political ad archive is that while
it does share geographic and demographic information about who saw a
particular ad, we have no way of knowing how that ad was targeted. However we
were able to connect our dataset containing information about who consumed ads
with one published by ProPublica, which contains some data about how ads were
targeted. The ProPublica data was collected by a browser plugin operated by
ProPublica which anyone can install. ProPublica’s browser plugin (ProPublica,
9 07) uses a supervised Natural Language Processing (NLP) classifier to detect
political ads in addition to allowing users to manually classify ads they see
as political. The browser plugin then collects the partial ad targeting
explanations Facebook provides by automatically clicking on the “Why am I
seeing this?” button for political ads and sends it to ProPublica for them to
make public.

We first provide a brief background on Facebook targeting audience options
(Venkatadri et al., 2018b). Facebook exposes prospective advertisers to a
plethora of options. First, advertisers can target users based on age, gender,
location and languages they speak. Second, advertisers can choose to send
their ads to users in a custom audience or lookalike audience. Custom
audiences contain a list of identifiers of specific users. Advertisers can use
various types of data to create a custom audience list, ranging from
specifying the emails, phone numbers or physical addresses of people they want
to reach, to users that have visited their website, installed their mobile
application, or liked their Facebook Page. Lookalike audiences allow
advertisers to let Facebook choose to whom to sends their ads based on
previous campaigns. Finally, advertisers can choose from a long list of
targeting attributes the characteristics they want users who receive their ads
to have (e.g., users interested in Catholic Church). Targeting attributes are
categorized in types such as demographics, behaviors and interests.
Advertisers can choose multiple attributes, to target.

A prior study by Athanasioshas, et al. (Andreou et al., 2018) reverse
engineered what Facebook chooses to show and the limitations of the ad
targeting explanation Facebook provides. This study showed that ad
explanations are incomplete; each explanation, shows at most one targeting
attribute (plus age/gender/location information), regardless of how many
attributes the advertisers use. This means that explanations reveal only part
of the targeting attributes that were used, providing us – and the users –
with an incomplete picture of the attributes that advertisers were using.
However, in the same study, authors performed a number of controlled
experiments that suggest – but not conclusively prove – that there is a logic
behind which attributes appear in an explanation and which do not. Given a
targeting audience A obtained from two attributes $a1$ and $a2$, if $a1$ and
$a2$ come from different attribute categories (e.g. Demographic, Behavior,
Interest, etc.), the attribute shown follows a specific precedence
(Demographics and Age/Gender/Location ¿ Interests ¿ PII based lists ¿
Behaviors). If $a1$ and $a2$ come from the same attribute category, the one
that appears in the explanation is the one with the highest estimated audience
size. This will result in a systematic under-counting of lower priority
targeting types.

There are two main sources of biases and limitations in ProPublica’s dataset.
One comes from users that installed ProPublica’s plugin and which political
ads they were shown. Another is from the way Facebook provides ad
explanations. The ProPublica dataset is the only publicly available source of
targeting information for Facebook political ads. Thus, we present these
results to provide an initial insight into how Facebook political advertisers
are targeting their ads with the understanding of likely biases and
limitations.

Figure 9. ProPublica Spend by Ad Type

With these caveats in mind, we proceed to an analysis of the 18,010 ads which
we were able to connect between the ProPublica dataset and ours. In Figure 9,
we see that different types of ads do indeed rely on different targeting
strategies. Of particular note is the the divergence of ’Commercial’ ads, of
which 74% rely on targeting by interest groups, and of ’Donate’ ads, of which
only 24% do. The average ad size did not differ significantly between
targeting types, but was significantly larger than the average for the
Facebook archive as a whole. We believe this to be an artifact of the
collection mechanism, which is biased toward finding larger ads. 91% of ads in
the overall ProPublica dataset had some kind of geographic targeting, and 92%
had age or gender targeting. On average, ads in this dataset had on average
4.1 different targeting parameters, so for Facebook these should be thought of
as a minimum criteria. By contrast, 58% of ads in the Google archive had no
geographic targeting whatsoever and 70% had neither age nor gender targeting.

In Figure 10, we also see diverging strategies between advertisers, with
Political Candidates and PACs making heavy use of custom lists of users and
For Profit and For Profit Media companies relying far more on targeting users
by their interests. Campaigns have numerous potential sources from which to
compile lists of users. In addition to their own lists of donors and voter
rolls, campaigns can rent lists from other candidates (Kenneth P. Vogel, 0
13).

Both Google and Twitter offer advertisers similar targeting criteria to what
we have described for Facebook, including custom audiences and lookalike
audiences. Both even allow targeting of users based on interests, although
they infer these interests in different ways. Both have made transparent
demographic and geographic targeting information for ads in their archive, but
without other targeting information, this is an incomplete picture at best. We
encourage Google and Twitter to at minimum follow Facebook’s example and make
transparent to users information about why they have been targetted for ads
that they are seeing.

Figure 10. ProPublica Targeting by Advertiser Type

###  5.4. New Types of Political Advertisers

####  5.4.1. For-Profit Media

One advertiser type in particular proved to be an interesting outlier. The
category ’For Profit Media’ contains advertisers whose ads are not considered
traditional news by Facebook (those ads are in a separate part of the archive
that we did not include) but have content intended solely to entertain or sway
the opinion of the viewer. Over the Facebook dataset as a whole, the average
ad sponsor ran ads on 1.6 pages. Advertisers in the for-profit media category
however, ran ads on 3.2 pages on average. We have examined many of these for-
profit media companies to understand why they are running across many Facebook
pages. What we have found in numerous instances is unknown for-profit media
companies that appear to be creating disingenuous communities that appear to
be “grassroots movements” to target different demographics and interests with
a combination of paid and organic political messaging.

A good example of this type of advertiser is ”New American Media Group LLC”.
This ad sponsor ran left leaning ads on 10 different pages. These pages were
designed to appeal to different demographics (”Melanin” for people of color,
”The Soldier Network” for Veterans, ”Raising Tomorrow” for parents, etc.) but
often run the same content on multiple pages. While this LLC has an extremely
similar name to a now-defunct genuine left-leaning media outlet (New America
Media), it appears to have no connection to that prior group, and also appears
to have no activity off of Facebook.

While some advertisers in this category were fairly traditional entertainment
websites (i.e., Comedy Central), some were “for-profit” companies in name only
that appeared to exist for no other purpose other than to spread a particular
political message and had no way of generating an actual profit. We also
discovered “News for Democracy” is an LLC that ran left leaning ads on 14
different Facebook pages most of which were designed to be appealing to groups
with traditionally conservative view points, such as “The Holy Tribune.”
Journalists investigated this LLC and linked it to MotiveAI which is a liberal
political advertising company.

####  5.4.2. Corporate Astroturfing

Corporations paying for political advertising is not an entirely new
phenomenon and has traditionally been funded through industry trade groups and
PACs. However, the reporting requirements by the FCC for U.S. political
advertising on television often made this political messaging traceable to the
real sponsor. These stricter reporting requirements do not apply to online
political advertising and the ad-hoc reporting requirements that online
platforms have enacted are being abused by corporations and industry trade
groups to undo transparency efforts.

We discovered in our analysis 355 ads sponsored by “Citizens for Tobacco
Rights” which is not a registered company in the U.S. but does disclose on
their website and Facebook page that it is operated by cigarette company
Philip Morris. However, someone who only saw the Facebook ad disclaimer would
not be able to connect the ads to Philip Morris without further investigation.
Other journalists have found instances of oil and insurance lobbying groups
that also provided sponsor names that did not match the legally incorporated
entity sponsoring the ads (Merrill, 2018). These organizations are seemingly
taking advantage of Facebook’s policy of not vetting sponsor names since some
of these entities also ran political ads on Google’s ad platform but provided
Google with their EIN (tax ID) and correct legally incorporated names of their
organizations (Merrill, 2018).

###  5.5. Discussion

The different policies, bugs, idiosyncrasies, and security weaknesses of each
transparency archive implementation present challenges to our analysis
efforts. We find many of the issues with these archives likely stem from a
combination of their hasty creation and the fact that the platforms are still
working out how to improve security of these archives such they are difficult
to deceive or evade. We will first discuss issues related to accidentally or
intentionally deceiving these transparency efforts and how they might be
improved by implementing more robust sponsor attribution techniques. The
second part of our discussion will focus on issues related to bypassing
inclusion into the different platforms’ archives and what can be done to
improve these issues.

####  5.5.1. Sponsor Attribution

The for-profit political advertisers appear to be the ones that are accidental
or intentionally skirting and violating the spirit of online transparency
sponsorship disclosure policies. As we discussed in the Ad Targeting section,
it’s extremely easy for groups such as ’New American Media’ to obscure who
they actually are from users and researchers.

It is worth noting that such advertising by for-profit corporations was not
legal until the Citizens United Supreme Court decision in 2010 (Cit, 3 24)
that struck down restrictions on election spending by for-profit corporations.
However, political messaging advertisers who run ads on television or radio
stations governed by the FCC must still report the name and contact
information of the business which paid for the ad, including the company’s
officers and directors. Such data is published by the FCC in a public
database. Political advertisers who send direct mail through the U.S. Postal
Service (USPS) must also report their activities through the FEC with similar
public disclosure of the name and contact information of the business. The
regulations that require such disclosure for ads that mention candidates do
not apply to online advertising, largely because the laws that mandate such
public disclosures were drafted before these platforms were as ubiquitous as
they have become.

What this means in practice though, is that people who want to publicize a
political message can form a for-profit company for doing so with no intent of
making an profit. As a private company, they do not need to publicly disclose
their investors in the way that PACs are required to disclose their donors.
Then, the for-profit company can advertise on social media, also without
disclosing the legal entity providing the funds to pay for the ad.

On Facebook’s platform, advertisers can easily mislead when providing the ’ad
sponsor’ string associated with their ads, either intentionally or
accidentally. Thus, it is effectively free to circumvent Facebook’s
transparency implementation. We see numerous instances on Facebook’s platforms
of this occurring. Sometimes, the unreliability of the ad sponsor label
appeared to be caused purely by human error, such as typos or variation during
data entry. For example, Donald J. Trump For President, Inc. sponsored ads on
both the Donald J. Trump page and the Mike Pence page. However, when
sponsoring ads on the Donald J. Trump page, the organization is known as
’Donald J. Trump For President, Inc’ and when sponsoring ads on the Mike Pence
page, is known as ’Donald J. Trump For President, Inc.’. Facebook has not
publicly stated plans to implement additional vetting of political sponsors.
Facebook’s argument is that anything they might implement for additional
vetting would not be scalable because of their broader inclusion policy which
extends to political issue ads (Merrill, 2018). However, this has created a
weakness in Facebook’s transparency implementation that greatly diminishes its
effectiveness for studying dishonest political advertisers.

Google and Twitter both vet sponsors so companies must either reveal their
legally incorporated name, pay existing third-parties to create ads on their
behalf, or create shell organizations (i.e., LLC, PACs). We should note that
we see instances of political ads on Facebook and Twitter where the sponsor is
a third-party advertising agency instead of the actual entity that paid for
the ads. This is an example of the complexities of correctly attributing
political ads to the real sponsors. It is clear from analysis that we need
more discussion about how to implement sponsorship disclosure and vetting in a
way that makes it practical to deploy at scale and more difficult to
circumvent.

####  5.5.2. Transparency Infrastructure

As we have noted, we appreciate the speed with which these transparency
archives were created. However, the lack of full integration of these archives
into the broader ad platforms of these companies is currently hurting the
efficacy of these transparency efforts.

We believe that there are ads on the Google and Twitter platforms that would
be considered political content that are not included in their transparency
archives because their criteria for inclusion are too narrow or their
mechanisms for finding this content are insufficient. More research needs to
be done into exactly what the general population considers to be political
advertising. We would encourage these platforms to create policies and
enforcement mechanisms that will make transparent advertising content that the
general population would consider political.

We also encountered several technical and policy issues with the archives as
they currently exist. Many ads, particularly in the Google archive, were
missing content information. Information on spend and impressions were only
available in broad ranges from Facebook and Google. No targeting information
or very little targeting information was available from any of the platforms.
Facebook required us to sign an NDA that prohibited us from sharing our raw
data even with other researchers or even discussing our findings directly with
non- U.S. Persons.

We call on these organizations to re-architect their platforms and policies to
support full transparency of all political ads. We realize that making the
changes we recommend will require investment of time and money both in the
technology of these platforms and the corporate culture of the organizations
that own them.

##  6\. Related Work

###  6.1. Online Advertising

Korolova (Korolova, 2010) was the first to point out privacy attacks based on
micro-targeted online ads. Followup work has reverse-engineered the targeting
options provided by major online ad networks (Venkatadri et al., 2018a) and
explored privacy (Andreou et al., 2018) and bias (Speicher et al., 2018)
issues of these online ad networks. There has also been work on designing
improved ad transparency mechanisms (Liu et al., 2013). For our study, we
leverage this prior work on reverse-engineering online advertising networks’
targeting options and how Facebook’s ad targeting explanation likely is
implemented.

To the best of our knowledge, there has been no systematic analysis of online
advertisers to this point likely due to the difficulty of collecting large-
scale data from online ad networks (Guha et al., 2010). One of the only prior
large-scale quantitative studies of online advertisers focused on how their
strategies effected conversion rates based on aggregate analysis of
advertisers on Microsoft’s ad network (Vattikonda et al., 2015). XRay (Lecuyer
et al., 2014) and Sunshine (Lecuyer et al., 2015) are two techniques that were
created to detect and infer online ad targeting methods. However, these were
proof of concept systems and not deployed at large-scale. An initial analysis
of Facebook’s proposed ad transparency archive implementations pointed out the
issue of only including political ads and not revealing targeting information
(Upturn, 2018). This report was released before Facebook implemented their
transparency archive and therefor did not analyze the ad data archived by
Facebook or issues with the actual implementation. We have conducted the first
large-scale analysis of online political advertising based on the data
recently made transparent by Facebook, Google, and Twitter.

###  6.2. Political Advertising

Analysis of political television ads has been the focus of most prior
political advertising studies likely due to this data being publicly published
by the FCC and easy to access (Kaid and Postelnicu, 2005; West, 2018). There
is at least one prior study that explored the influence of political
television ads on online discussion (Shah et al., [n. d.]). There have also
been studies of investigating the polarization of online political discourse
(Flynn et al., [n. d.]; Barberá et al., 2015). The closest related to our
study is a prior study which showed that uploading political video
advertisements to YouTube generated unpaid organic-views and improved their
effectiveness (Ridout et al., 2010). However, to the best of our knowledge
ours is the first large-scale study of online political advertising.

##  7\. Conclusions

We have performed an analysis of the ads that we were able to collect from
Facebook, Google, and Twitter’s transparency archives related to U.S.
politics. Based on the data we collected, we provide an initial understanding
and taxonomies of online political advertising strategies for both honest and
possibly dishonest U.S. political advertisers. We also point out limitations
and weaknesses of the policies and current implementations of these archives.
As part of our analysis, we demonstrate how advertisers are intentionally or
accidentally deceiving and bypassing these political transparency archives. We
provide a concrete list of suggestions that would likely make them more robust
and useful for enabling a better understanding of political advertising. We
are actively working with each archive product teams to improve their
implementations.

We commend Facebook, Google and Twitter for their efforts so far in improving
transparency into political advertising on their platforms. We note the speed
with which these archives were made available after public concern about this
issue was raised, and that these transparency efforts have improved a great
deal in the short time that these tools have been available. We encourage the
platforms to continue to improve.

## References

  * (1)
  * Cit (3 24) 2009-03-24.  _Citizens United v. Federal Election Commission_.
  * Andreou et al. (2018) Athanasios Andreou, Giridhari Venkatadri, Oana Goga, Krishna P. Gummadi, Patrick Loiseau, and Alan Mislove. 2018\.  Investigating ad transparency mechanisms in social media: A case study of Facebook’s explanations. In _NDSS 2018, Network and Distributed Systems Security Symposium_. San Diego, UNITED STATES, 18 – 21.
  * Barberá et al. (2015) Pablo Barberá, John T. Jost, Jonathan Nagler, Joshua A. Tucker, and Richard Bonneau. 2015.  Tweeting From Left to Right: Is Online Political Communication More Than an Echo Chamber?  _Psychological Science_ 26, 10 (2015), 1531–1542.
  * Barrett (2018) Brian Barrett. 2018\.  For Russia, Unraveling US Democracy Was Just Another Day Job.  https://www.wired.com/story/mueller-indictment-internet-research-agency/.
  * Facebook (2018a) Facebook. 2018a.  Ad Archive.  https://www.facebook.com/ads/archive/.
  * Facebook (2018b) Facebook. 2018b.  Facebook Ad Archive Report.  Retrieved October 25th, 2018 from https://www.facebook.com/ads/archive/report
  * Facebook (7 03a) Facebook. 2018-07-03a.  About ads that include political content.  "https://www.facebook.com/business/help/167836590566506".
  * Facebook (7 03b) Facebook. 2018-07-03b.  National issues of public importance.  "https://www.facebook.com/business/help/214754279118974".
  * Facebook (8 22) Facebook. 2018-08-22.  Introducing the Ad Archive API.  https://newsroom.fb.com/news/2018/08/introducing-the-ad-archive-api/.
  * Flynn et al. ([n. d.]) D.J. Flynn, Brendan Nyhan, and Jason Reifler. [n. d.].  The Nature and Origins of Misperceptions: Understanding False and Unsupported Beliefs About Politics.  _Political Psychology_ 38, S1 ([n. d.]), 127–150.
  * Google (8 15) Google. 2018-08-15.  Transparency Report - Political Ads.  https://transparencyreport.google.com/political-ads/library.
  * Granville (2018) Kevin Granville. 2018\.  Facebook and Cambridge Analytica: What You Need to Know as Fallout Widens.  https://www.nytimes.com/2018/03/19/technology/facebook-cambridge-analytica-explained.html.
  * Guha et al. (2010) Saikat Guha, Bin Cheng, and Paul Francis. 2010.  Challenges in Measuring Online Advertising Systems. In _Proceedings of the 10th ACM SIGCOMM Conference on Internet Measurement_ _(IMC ’10)_. ACM, 81–87.
  * Kaid and Postelnicu (2005) Lynda Lee Kaid and Monica Postelnicu. 2005.  Political Advertising in the 2004 Election: Comparison of Traditional Television and Internet Messages.  _American Behavioral Scientist_ 49, 2 (2005), 265–278.
  * Kenneth P. Vogel (0 13) Maggie Haberman Kenneth P. Vogel. 2018-10-13.  https://www.nytimes.com/2018/10/13/us/politics/trump-political-data.html.  https://www.propublica.org/article/help-us-monitor-political-ads-online.
  * Korolova (2010) A. Korolova. 2010\.  Privacy Violations Using Microtargeted Ads: A Case Study. In _2010 IEEE International Conference on Data Mining Workshops_. 474–482.
  * Laura Edelson (2018) Shikhar Sakhuja Laura Edelson. 2018\.  An Analysis of United States Online Political Advertising.  https://online-pol-ads.github.io/Online-Political-Ads-Analysis/.
  * Lecuyer et al. (2014) Mathias Lecuyer, Guillaume Ducoffe, Francis Lan, Andrei Papancea, Theofilos Petsios, Riley Spahn, Augustin Chaintreau, and Roxana Geambasu. 2014.  XRay: Enhancing the Web’s Transparency with Differential Correlation. In _USENIX Security Symposium_. San Diego, United States.
  * Lecuyer et al. (2015) Mathias Lecuyer, Riley Spahn, Yannis Spiliopolous, Augustin Chaintreau, Roxana Geambasu, and Daniel Hsu. 2015.  Sunlight: Fine-grained Targeting Detection at Scale with Statistical Confidence. In _Proceedings of the 22Nd ACM SIGSAC Conference on Computer and Communications Security_ _(CCS ’15)_. ACM, New York, NY, USA, 554–566.  https://doi.org/10.1145/2810103.2813614
  * Liu et al. (2013) Bin Liu, Anmol Sheth, Udi Weinsberg, Jaideep Chandrashekar, and Ramesh Govindan. 2013.  AdReveal: Improving Transparency into Online Targeted Advertising. In _Proceedings of the Twelfth ACM Workshop on Hot Topics in Networks_ _(HotNets-XII)_. ACM, New York, NY, USA, Article 12, 7 pages.  https://doi.org/10.1145/2535771.2535783
  * Merrill (2018) Jeremy B. Merrill. 2018\.  How Big Oil Dodges Facebook’s New Ad Transparency Rules.  https://www.propublica.org/article/how-big-oil-dodges-facebooks-new-ad-transparency-rules.
  * ProPublica (9 07) ProPublica. 2017-09-07.  Political Advertisements from Facebook.  https://www.propublica.org/article/help-us-monitor-political-ads-online.
  * ProPublica (0 21) ProPublica. 2018-10-21.  Political Advertisements from Facebook.  https://www.propublica.org/datastore/dataset/political-advertisements-from-facebook.
  * Ridout et al. (2010) Travis N. Ridout, Erika Franklin Fowler, and John Branstetter. 2010\.  Political Advertising in the 21st Century: The Rise of the YouTube Ad. In _APSA 2010 Annual Meeting_.
  * Shah et al. ([n. d.]) Dhavan V. Shah, Jaeho Cho, Seungahn Nah, Melissa R. Gotlieb, Hyunseo Hwang, Nam-Jin Lee, Rosanne M. Scholl, and Douglas M. McLeod. [n. d.].  Campaign Ads, Online Messaging, and Participation: Extending the Communication Mediation Model.  _Journal of Communication_ 57, 4 ([n. d.]), 676–703.
  * Speicher et al. (2018) Till Speicher, Muhammad Ali, Giridhari Venkatadri, Filipe Nunes Ribeiro, George Arvanitakis, Fabrício Benevenuto, Krishna P. Gummadi, Patrick Loiseau, and Alan Mislove. 2018\.  Potential for Discrimination in Online Targeted Advertising. In _Proceedings of the 1st Conference on Fairness, Accountability and Transparency_ _(Proceedings of Machine Learning Research)_ , Sorelle A. Friedler and Christo Wilson (Eds.), Vol. 81. PMLR, New York, NY, USA, 5–19.
  * Turton (2018) William Turton. 2018\.  We posed as 100 Senators to run ads on Facebook. Facebook approved all of them.  https://news.vice.com/en_us/article/xw9n3q/we-posed-as-100-senators-to-run-ads-on-facebook-facebook-approved-all-of-them.
  * Twitter (2018) Twitter. 2018.  Political campaigning advertisers.  https://ads.twitter.com/transparency/i/political_advertisers.
  * Twitter (6 28a) Twitter. 2018-06-28a.  Ad Transparency Center.  https://ads.twitter.com/transparency.
  * Twitter (6 28b) Twitter. 2018-06-28b.  Political Content in the United States.  https://business.twitter.com/en/help/ads-policies/restricted-content-policies/political-campaigning/US-political-content.html.
  * Upturn (2018) Upturn. 2018.  Leveling the Platform: Real Transparency for Paid Messages on Facebook.  https://www.teamupturn.org/reports/2018/facebook-ads/.
  * Vattikonda et al. (2015) Bhanu C. Vattikonda, Vacha Dave, Saikat Guha, and Alex C. Snoeren. 2015.  Empirical Analysis of Search Advertising Strategies. In _Proceedings of the 2015 Internet Measurement Conference_ _(IMC ’15)_. ACM, New York, NY, USA, 79–91.  https://doi.org/10.1145/2815675.2815694
  * Venkatadri et al. (2018a) G. Venkatadri, A. Andreou, Y. Liu, A. Mislove, K. P. Gummadi, P. Loiseau, and O. Goga. 2018a.  Privacy Risks with Facebook’s PII-Based Targeting: Auditing a Data Broker’s Advertising Interface. In _2018 IEEE Symposium on Security and Privacy (SP)_. 89–107.
  * Venkatadri et al. (2018b) Giridhari Venkatadri, Yabing Liu, Athanasios Andreou, Oana Goga, Patrick Loiseau, Alan Mislove, and Krishna P. Gummadi. 2018b.  Privacy Risks with Facebook’s PII-based Targeting: Auditing a Data Broker’s Advertising Interface. In _Proceedings of the IEEE Symposium on Security and Privacy (IEEE S &P’18)_. San Francisco, CA, USA.
  * West (2018) David West. 2018\.  _Air wars : television advertising and social media in election campaigns, 1952-2016_.  SAGE/CQ Press.


# On the non-universality of heavy quark hadronization in elementary high-
energy collisions

Yuxuan Dai  Department of Applied Physics, Nanjing University of Science and
Technology, Nanjing 210094, China  Shouxing Zhao  Department of Applied
Physics, Nanjing University of Science and Technology, Nanjing 210094, China
Min He  Department of Applied Physics, Nanjing University of Science and
Technology, Nanjing 210094, China  Shanghai Research Center for Theoretical
Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China

###### Abstract

It has been traditionally hypothesized that the heavy quark (charm, $c$ and
bottom, $b$) fragmentation is universal across different collision systems,
based on the notion that hadronization as a soft process should occur at the
characteristic non-perturbative QCD scale, $\Lambda_{QCD}$. However, this
universality hypothesis has recently been challenged by the observation that
the $c$\- and $b$-baryon production relative to their meson counterparts in
minimum bias proton-proton ($pp$) collisions at the LHC energies is
significantly enhanced as compared to the electron-positron ($e^{+}e^{-}$)
collisions. The conception of non-universality is unambiguously reinforced by
the latest measurement of the charged-particle multiplicity dependence of the
$b$-baryon-to-meson yield ratio, $\Lambda_{b}/B$, by the LHCb experiment in
$\sqrt{s}=13$ TeV $pp$ collisions at the LHC, evolving continuously from the
saturation value in minimum bias $pp$ collisions toward the small value in
$e^{+}e^{-}$ collisions as the system size gradually reduces. We address the
multiplicity dependence of $b$-baryon production in the canonical statistical
hadronization model with input $b$-hadron spectrum augmented with many
hitherto unobserved states from quark model predictions. We demonstrate that
the decreasing trend of the $\Lambda_{b}/B$ toward low multiplicities can be
quantitatively understood from the canonical suppression on the yield of
$\Lambda_{b}$, as caused by the requirement of strict conservation of baryon
number in sufficiently small systems. We have therefore proposed a plausible
scenario for understanding the origin of the non-universality of heavy quark
fragmentation in elementary collisions.

##  I Introduction

Owing to their large masses, the production of heavy quarks (charm, $c$, and
bottom, $b$) are arguably separated from their hadronization, as implied in
the QCD factorization theorem describing the production cross sections of
heavy hadrons at collider energies Collins:1989gx . While the heavy quark
partonic cross section can be computed as perturbative series in powers of the
coupling constant, the hadronization, usually termed fragmentation in
elementary collisions, is an intrinsically soft process and thus relies on
phenomenological modelling Norrbin:2000zc . Fragmentation fractions of heavy
quarks into weakly decaying heavy hadrons (including feeddown contributions
from excited states via strong or electromagnetic decays) and ratios between
their production yields provide critical probes of the pertinent hadronization
mechanisms. Traditionally these fractions (and thus ratios) are thought to be
universal across different colliding systems and energies Lisovyi:2015uqa .

However, recent measurements of the charm baryon-to-meson production ratios
($\Lambda_{c}/D$, $\Sigma_{c}/D$ and $\Xi_{c}/D$) by ALICE experiment in
minimum bias $pp$ collisions at the LHC energies have revealed a significant
enhancement at low transverse momentum ($p_{T}$) relative to the corresponding
values in $e^{+}e^{-}$ collisions ALICE:2020wfu ; ALICE:2021rzj ;
ALICE:2021bli , therefore challenging the universality hypothesis. A
significantly larger $b$ baryon-to-meson yield ratio ($\Lambda_{b}/B$) at low
$p_{T}$ compared to $e^{+}e^{-}$ collisions has also been observed by the LHCb
experiment LHCb:2019fns ; LHCb:2023wbo  in $pp$ collisions and earlier in
$p\bar{p}$ collisions at the Tevatron HFLAV:2019otj . To account for the
enhancement of these ratios in hadronic collisions, a statistical
hadronization model (SHM) was put forward by assuming relative chemical
equilibrium between the production yields of different heavy hadron species
and augmenting the $c$ or $b$-baryon mass spectrum with many hitherto
unobserved but theoretically predicted excited states He:2019tik ; He:2022tod
; the observed enhancement of the $\Lambda_{c}$ and $\Lambda_{b}$ production
was attributed to the feeddown from these “missing” states. The measured
$\Lambda_{c}/D$ in $pp$ collisions was also explained by PYTHIA8 calculations
that include new color-reconnection “junctions” fragmenting into baryons
Christiansen:2015yqa  and by a coalescence model in the presence of a
deconfined partonic droplet Minissale:2020bif .

The charged-particle-multiplicity dependent measurements provide a natural
means to quantify the evolution of these ratios from $e^{+}e^{-}$ to minimum
bias $pp$ collisions, and thus characterize how the fragmentation of heavy
quarks depends on the density of partons involved. This has been undertaken by
ALICE experiment in $pp$ collisions at $\sqrt{s}=13$ GeV, where
$\Lambda_{c}^{+}/D^{0}$ was measured as a function of charged-particle
pseudorapidity density $\langle dN_{\rm ch}/d\eta\rangle$ at mid-rapidity and
shown to exhibit a significant increase from the lowest to highest
multiplicity intervals for $1<p_{T}<12$ GeV ALICE:2021npz . The same endeavor
has been recently also pursued by the LHCb experiment in the $b$ sector in
$\sqrt{s}=13$ GeV $pp$ collisions at forward rapidity; both $B_{s}^{0}/B^{0}$
LHCb:2022syj  and $\Lambda_{b}^{0}/B^{0}$ LHCb:2023wbo  were measured and
demonstrated to increase with multiplicity when limited to relatively low
$p_{T}$. In particular, the high-quality data of $p_{T}$-integrated
$\Lambda_{b}^{0}/B^{0}$ converges to the value measured in $e^{+}e^{-}$
collisions at the lowest multiplicity and increases by a factor of $\sim$2
toward the saturation value at high multiplicities LHCb:2023wbo , providing an
ideal chance of looking into the evolution of heavy quark fragmentation versus
the density of the hadronic environment.

To account for the system size dependence of the $\Lambda_{c}^{+}/D^{0}$, it
was noted that strict conservation of quantum charges, e.g., baryon number, is
important when the multiplicity becomes sufficiently low; therefore, one
should turn to the version of canonical ensemble of statistical hadronization
model Chen:2020drg . Indeed, the strict baryon number conservation would
require the simultaneous production of an antibaryon when creating a baryon,
which is very expensive in term of energy, given that the lightest baryon
(proton) already has a large mass $\sim 1$ GeV (compared to the typical
hadronization temperature $T_{H}\sim 160$-170 MeV). Consequently, the
production of the heavy baryons suffers from a canonical suppression,
resulting in a decreasing baryon-to-meson ratio toward low multiplicities.

In the present work, we generalize the canonical treatment of the statistical
hadornization to the $b$ sector, utilizing the augmented $b$-hadron spectrum
that proved indispensable for the statistical interpretation of the
enhancement of $\Lambda_{b}/B$ in minimum bias $pp$ collisions relative to the
$e^{+}e^{-}$ case He:2022tod . We compute the chemical factors and thermal
densities of $b$ hadrons from the canonical partition function and demonstrate
the system size dependence of the production of $B_{s}$ mesons and
$\Lambda_{b}$ and $\Xi_{b}$ baryons relative to that of $B$ mesons, for both
the integrated and $p_{T}$ differential yields. We show that, with the
$b$-hadron input spectrum augmented with many more excited states (in
particular excited baryons) beyond the current measured listings, LHCb data of
the multiplicity dependence of $\Lambda_{b}/B$ can be quantitatively
understood from the canonical suppression on $\Lambda_{b}$ production as
caused by the strict conservation of baryon number toward small
multiplicities, thereby unveiling a plausible origin of the non-universality
of heavy quark hadronization in elementary collisions that is currently under
hot debates ALICE:2022wpn ; Rossi:2023xqa ; Altmann:2024icx .

$CF$ |  $V_{C}$=5 ${\rm fm}^{3}$ | 10 | 20 | 30 | 50 | 100 | 200
---|---|---|---|---|---|---|---
$\bar{B}^{0}$ | 0.0097194 | 0.023927 | 0.058660 | 0.094845 | 0.16493 | 0.32591 | 0.56988
$B^{-}$ | 0.0078259 | 0.021863 | 0.056893 | 0.093168 | 0.16331 | 0.32438 | 0.56858
$\bar{B}_{s}^{0}$ | 0.0039920 | 0.013624 | 0.045935 | 0.082725 | 0.15364 | 0.31546 | 0.56101
$\Lambda_{b}^{0}$ | 0.0049325 | 0.014844 | 0.047305 | 0.084415 | 0.15574 | 0.31768 | 0.56300
$\Xi_{b}^{0-}$ | 0.0021863 | 0.0089128 | 0.037336 | 0.073498 | 0.14477 | 0.30720 | 0.55402
$\Omega_{b}^{-}$ | 0.0004649 | 0.0030092 | 0.019475 | 0.047296 | 0.11221 | 0.27231 | 0.52265
$\bar{B}_{s}^{0}/\bar{B}^{0}$ | 0.41072 | 0.56939 | 0.78307 | 0.87221 | 0.93155 | 0.96793 | 0.98443
$\Lambda_{b}^{0}/\bar{B}^{0}$ | 0.50749 | 0.62039 | 0.80643 | 0.89003 | 0.94427 | 0.97474 | 0.98793
$\Xi_{b}^{0-}/\bar{B}^{0}$ | 0.22494 | 0.37250 | 0.63648 | 0.77493 | 0.87776 | 0.94259 | 0.97217
Table 1: Chemical factors (CF) of the direct ground-state $b$-hadrons at
$T_{H}=170$ MeV, $\gamma_{s}=0.6$, $\gamma_{c}=15$ and $\gamma_{b}=10^{9}$ for
varying correlation volumes, with $b$-hadron input spectrum taken from the RQM
scenario. The ratios of the CF’s of $B_{s}^{0}$, $\Lambda_{b}^{0}$ and
$\Xi_{b}^{0-}$ to $\bar{B}^{0}$ are also summarized in the last three rows.

##  II Canonical partition function and input bottom-hadron spectrum

When applied to large systems where the fluctuations of quantum charges are
relatively small, SHM is formulated in a grand-canonical ensemble (GCE) of an
ideal hadron resonance gas Andronic:2017pug . The Abelian quantum charges,
such as electric charge $Q$, baryon number $N$, strangeness $S$, charm number
$C$ and bottom number $B$ are thus conserved on average and regulated by the
corresponding chemical potentials
$\vec{\mu}=(\mu_{Q},\mu_{N},\mu_{S},\mu_{C},\mu_{B})$. The primary mean yield
for the $j$-th hadron produced from GCE-SHM is given by

$\displaystyle\langle
N_{j}\rangle^{GCE}=\gamma_{s}^{N_{sj}}\gamma_{c}^{N_{cj}}\gamma_{b}^{N_{bj}}z_{j}e^{\vec{\mu}\cdot\vec{q}_{j}/T_{H}},$
(1)

where $\vec{q}_{j}=(Q_{j},N_{j},S_{j},C_{j},B_{j})$ denote the quantum charges
for the hadron and $z_{j}$ is the one-particle partition function

$\displaystyle
z_{j}=(2J_{j}+1)\frac{VT_{H}}{2\pi^{2}}m_{j}^{2}K_{2}(\frac{m_{j}}{T_{H}}),$
(2)

which specifies the chemical equilibrium multiplicity of the $j$-th hadron of
mass $m_{j}$ and spin $J_{j}$ in a fireball of volume $V$ under the Boltzmann
approximation at hadronization temperature $T_{H}$, with $K_{2}$ being the
modified Bessel function of the second order. In Eq. (1), $\gamma_{s}$,
$\gamma_{c}$ and $\gamma_{b}$ denote fugacities that account for the deviation
from chemical equilibrium for hadrons containing $N_{sj}$, $N_{cj}$ and
$N_{bj}$ strange, charm and bottom quarks or antiquarks, respectively.

In contrast, for sufficiently small systems where relative fluctuations of
quantum charges become significant, one has to turn to the canonical ensemble
(CE) SHM, in order to strictly conserve the quantum charges Rafelski:1980gk ;
Hagedorn:1984uy ; Vovchenko:2019kes ; Cleymans:2020fsc ; Chen:2020drg . For a
system having conserved quantum charges $\vec{Q}=(Q,N,S,C,B)$ with associated
phase angles $\vec{\phi}=(\phi_{Q},\phi_{N},\phi_{S},\phi_{C},\phi_{B}$), the
CE-SHM partition function reads

$\displaystyle
Z(\vec{Q})=\int_{0}^{2\pi}\frac{d^{5}\phi}{(2\pi)^{5}}e^{i\vec{Q}\cdot\vec{\phi}}{\rm
exp}[\sum_{j}\gamma_{s}^{N_{sj}}\gamma_{c}^{N_{cj}}\gamma_{b}^{N_{bj}}e^{-i\vec{q}_{j}\cdot\vec{\phi}}z_{j}],$
(3)

where the volume in $z_{j}$ should now be understood as the correlation volume
$V_{C}$ that characterizes the range of the strict conservation of quantum
charges. In Eq. (3), the summation $\sum_{j}$ should be taken over all hadrons
up to the most massive $b$-mesons and -baryons, for the present aim of
investigating the statistical hadronization of $b$ quarks. More specifically,
all light hadrons in the particle data group (PDG) listings
ParticleDataGroup:2022pth  are included. For $c$ hadrons, in particular $c$
baryons, excited states from relativistic quark model (RQM) predictions
Ebert:2009ua ; Ebert:2011kk  beyond the current PDG listings are included,
which have proved essential for interpreting the observed enhancement of
$\Lambda_{c}/D$ in minimum bias $pp$ collisions in the GCE-SHM He:2019tik .
All charmonium states listed in PDG are also included. For $b$-hadron spectrum
serving as the direct input for the present study, we compare two sets of $b$
hadrons in the same spirit as in the GCE-SHM study for minimum bias collisions
He:2022tod : (a) PDG-only states ParticleDataGroup:2022pth  and (b) RQM states
Ebert:2009ua ; Ebert:2011kk  that additionally include 18 $B$’s, 16 $B_{s}$’s,
27 $\Lambda_{b}$’s, 45 $\Sigma_{b}$’s, 71 $\Xi_{b}$’s and 41 $\Omega_{b}$’s,
up to meson (baryon) masses of 6.5 (7.0) GeV.

The primary mean yield of the $j$-th hadron produced from the CE-SHM then
reads Chen:2020drg ; Becattini:2009sc

$\displaystyle\langle
N_{j}\rangle^{CE}=\gamma_{s}^{N_{sj}}\gamma_{c}^{N_{cj}}\gamma_{b}^{N_{bj}}z_{j}\frac{Z(\vec{Q}-\vec{q}_{j})}{Z(\vec{Q})}.$
(4)

The chemical factor $Z(\vec{Q}-\vec{q}_{j})/Z(\vec{Q})$ in favor of the
chemical potential term in Eq. (1) arises from the requirement of exact
conservation of quantum charges. As will be shown in the following, for a
completely neutral system (i.e., $\vec{Q}=0$ and thus $\vec{\mu}=0$), this
factor for charged hadrons with $\vec{q}_{j}\neq 0$ is always less than unity
but only tends to unity at asymptotically large volumes, therefore
characterizing the canonical suppression of the production of charged hadrons
at small system size.

##  III System size dependence of $b$-hadron yields

The measurements of charged particle multiplicity dependence of $B_{s}/B$
LHCb:2022syj  and $\Lambda_{b}/B$ LHCb:2023wbo  by the LHCb experiment in
$\sqrt{s}=13$ TeV $pp$ collisions were performed at forward rapidity
($2<y<4.5$), where particle and anti-particle production is not totally
symmetric. However, the measured asymmetry between $\Lambda_{b}^{0}$ and
$\bar{\Lambda}_{b}^{0}$ is at the level of $\sim$1-2$\%$ in $\sqrt{s}=7$ TeV
$pp$ collisions at $2<y<4.5$, and becomes even smaller in $\sqrt{s}=8$ TeV
collisions LHCb:2021xyh . Therefore, as a good approximation, we focus on a
completely neutral system with vanishing quantum charges
($\vec{Q}=(Q,N,S,C,B)=(0,0,0,0,0)$) in the following CE-SHM studies, with RQM
being the default scenario for $b$-hadron spectrum input.

###  III.1 Chemical factors of direct $b$ hadrons

$n_{\alpha}(\cdot 10^{-5}~{}{\rm fm^{-3}})$ |  $V_{C}$=5 ${\rm fm}^{3}$ | 10 | 20 | 30 | 50 | 100 | 200 | GCE
---|---|---|---|---|---|---|---|---
$\bar{B}^{0}$ | 1.1220 | 2.7920 | 6.9508 | 11.313 | 19.759 | 39.148 | 68.534 | 120.41
$B^{-}$ | 0.96934 | 2.6261 | 6.8105 | 11.181 | 19.635 | 39.038 | 68.452 | 120.45
$\bar{B}_{s}^{0}$ | 0.14641 | 0.47267 | 1.5299 | 2.7242 | 5.0273 | 10.285 | 18.263 | 32.513
$\Lambda_{b}^{0}$ | 0.29886 | 0.90201 | 2.8845 | 5.1551 | 9.5210 | 19.435 | 34.453 | 61.702
$\Xi_{b}^{0-}$ | 0.043883 | 0.17479 | 0.72393 | 1.4247 | 2.8132 | 5.9882 | 10.818 | 19.548
$\Omega_{b}^{-}$ | 0.00028060 | 0.0018164 | 0.011755 | 0.028549 | 0.067730 | 0.16437 | 0.31548 | 0.63204
$\bar{B}_{s}^{0}/\bar{B}^{0}$ | 0.13049 | 0.16929 | 0.22010 | 0.24080 | 0.25443 | 0.26273 | 0.26648 | 0.27002
$\Lambda_{b}^{0}/\bar{B}^{0}$ | 0.26635 | 0.32307 | 0.41499 | 0.45568 | 0.48186 | 0.49644 | 0.50271 | 0.51243
$\Xi_{b}^{0-}/\bar{B}^{0}$ | 0.039110 | 0.062602 | 0.10415 | 0.12594 | 0.14238 | 0.15296 | 0.15785 | 0.16235
Table 2: Total (i.e., with feeddowns) thermal densities of ground-state
$b$-hadrons at $T_{H}=170$ MeV, $\gamma_{s}=0.6$, $\gamma_{c}=15$ and
$\gamma_{b}=10^{9}$ for varying correlation volumes, with $b$-hadron input
spectrum taken from the RQM scenario. The ratios of the thermal densities of
$B_{s}^{0}$, $\Lambda_{b}^{0}$ and $\Xi_{b}^{0-}$ to $\bar{B}^{0}$ are also
summarized in the last three rows. The last column denotes the values in the
grand canonical limit.

To evaluate the canonical partition function, hadrons to be summed over in the
exponential of Eq. (3) are divided into three categories Chen:2020drg : the
completely neutral mesons with
$\vec{q}_{j}=(Q_{j},N_{j},S_{j},C_{j},B_{j})=(0,0,0,0,0)$, e.g., $\pi^{0}$,
$\rho^{0}$, $\phi$ and $J/\psi$; the charged mesons, including positively
charged mesons with at least one of $Q_{j}=+1,S_{j}=+1,C_{j}=+1,B_{j}=+1$ but
$N_{j}=0$, e.g., $\pi^{+}$, $K^{+}$, $D^{+}$, $D_{s}^{+}$, $B^{+}$,
$B_{s}^{0}$ and their antimesons; the baryons with $N_{j}=+1$ and antibaryons
with $N_{j}=-1$. The hadronization temperature is taken to be $T_{H}=170$ MeV
He:2022tod ; as we’ve checked for the GCE-SHM study He:2022tod , using a lower
$T_{H}\sim 160$ MeV leads to similar results for the $b$-hadron fragmentation
fractions. To proceed, the strangeness under-saturation parameter (fugacity)
is fixed to be the typical value $\gamma_{s}=0.6$ in elementary collisions
He:2019tik ; He:2022tod , which has been shown to be insensitive to the system
size for charged particle multiplicity $dN_{ch}/d\eta\leq 50$
Vovchenko:2019kes . For the $c$ and $b$ fugacity, $\gamma_{c}$ and
$\gamma_{b}$ respectively, that measure their initial hard production in
excess of the chemical equilibrium limit, we take the typical value of
$\gamma_{c}\sim 15$ Chen:2020drg  and $\gamma_{b}\sim 10^{9}$ determined in
the canonical SHM study of semi-central heavy-ion collisions at the LHC energy
Andronic:2021erx ; Andronic:2022ucg . We’ve checked that our final result of
the $b$-baryon relative to -meson production is rather robust against a
significant variation of $\gamma_{b}$ within four orders of magnitude around
the default value used here, since anyway the rather massive $b$ hadrons only
account for a tiny contribution to the canonical partition function (through
summation in the exponential of Eq. (3)).

In Table 1, chemical factors (CF) of the direct ground state $b$ hadrons are
displayed for varying correlation volumes ($V_{C}$). At small $V_{C}$,
$\bar{B}_{s}^{0}$ and $\Lambda_{b}^{0}$ exhibit significantly smaller CF’s
than $\bar{B}^{0}$ and $B^{-}$ (we focus on mesons and baryons both containing
a $b$ quark, instead of the antiquark $\bar{b}$), owing to the canonical
suppression brought about by the exact strangeness and baryon number
conservation, respectively. Despite all being $b$-baryon, the CF’s of
$\Xi_{b}^{0-}$ and $\Omega_{b}^{-}$ are further progressively smaller compared
to that of $\Lambda_{b}^{0}$, as a result of their increasing strangeness
content leading to stronger canonical strangeness suppression. As the
correlation volume increases, the canonical suppression effects induced by the
exact strangeness and baryon-number conservation attenuate, and hence at
asymptotically large volume, the CF’s of all $b$ hadrons end up with almost
the same residual value $\sim 0.56$ that arises solely from their common
canonical bottom-number suppression. This is also seen from the gradual
increase of the relative canonical suppression (i.e., the ratios of CF’s
listed in the last three rows of Table 1) $\bar{B}_{s}^{0}/\bar{B}^{0}$,
$\Lambda_{b}^{0}/\bar{B}^{0}$ and $\Xi_{b}^{0-}/\bar{B}^{0}$ toward unity from
small to large volumes.

###  III.2 Total thermal densities of ground-state $b$ hadrons

With the primary mean yields of $b$ hadrons computed from Eq. (4), the total
thermal densities of ground state $b$ hadrons are obtained from the sum of the
direct one and the feeddown contributions from excited states

$n_{\alpha}=\frac{\langle N_{\alpha}\rangle^{CE}}{V_{C}}+\sum_{j}\frac{\langle
N_{j}\rangle^{CE}}{V_{C}}\cdot{\rm BR}(j\rightarrow\alpha),$ (5)

where the branching ratios (BR) for excited $b$ hadrons decaying to the ground
states were given from a ${}^{3}P_{0}$ quark model estimate He:2022tod . These
densities are shown in Table 2 for varying correlations volumes, together with
the GCE-SHM results. An immediate observation is that as the volume increases,
the thermal density for each $b$-hadron also grows. While these thermal
densities at the largest volume ($V_{C}=200~{}{\rm fm}^{3}$) computed here are
still far from the GCE-SHM values, the corresponding ratios between them are
already almost the same as the grand-canonical limiting values, simply because
the effects of canonical strangeness and baryon-number suppression already
become vanishing and the residual canonical bottom-number suppression is
common for all $b$ hadrons. As the most important finding of the present work,
the thermal density ratios $\bar{B}_{s}^{0}/\bar{B}^{0}$,
$\Lambda_{b}^{0}/\bar{B}^{0}$ and $\Xi_{b}^{0-}/\bar{B}^{0}$, as summarized in
the last three rows of Table 2 and also plotted in Fig. 1, demonstrate a
marked system-size dependence, amounting to a factor of 2-4 reduction from the
saturation value in the grand-canonical limit to the smallest volume and
serving as a direct signal of the canonical suppression effects due to strict
conservation of strangeness and baryon number.

Figure 1: The correlation volume dependence of the ratios of the thermal
densities of $\bar{B}_{s}^{0}$, $\Lambda_{b}^{0}$, and $\Xi_{b}^{0-}$ to that
of $\bar{B}^{0}$ from CE-SHM with $b$-hadron input spectrum taken from the RQM
scenario.

###  III.3 Confronting LHCb data

Figure 2: The system size dependence of the yield ratios of (a)
$\bar{B}_{s}^{0}/\bar{B}^{0}$ and (b) $\Lambda_{b}^{0}/\bar{B}^{0}$ as
predicted from CE-SHM with $b$-hadron input spectrum taken from the RQM (solid
lines) versus PDG (dashed lines) scenario, in comparison with LHCb data
LHCb:2022syj ; LHCb:2023wbo . The filled box at the right vertical axis of the
upper panel indicate a separate measurement of
$\bar{B}_{s}^{0}/\bar{B}^{0}=0.2539\pm 0.0079$ in minimum bias $pp$ collisions
at the same $\sqrt{s}=13$ TeV by the LHCb experiment LHCb:2021qbv , and the
filled box at the left vertical axis of the lower panel indicates the
$\Lambda_{b}^{0}/\bar{B}^{0}$ measured in $e^{+}e^{-}$ collisions
HFLAV:2019otj ; LHCb:2023wbo .

In order to compare the system size dependence of the
$\bar{B}_{s}^{0}/\bar{B}^{0}$, $\Lambda_{b}^{0}/\bar{B}^{0}$ as uncovered from
the present GC-SHM study with the LHCb measurements LHCb:2022syj ;
LHCb:2023wbo , where the system size was quantified by the total number of
charged tracks, we follow a previous canonical thermal study of the light
hadrons that suggests a linear dependence between the correlation volume and
the measured charged particle multiplicity Vovchenko:2019kes . We find that
assuming a mean correlation volume $\langle V_{C}\rangle=22.6~{}{\rm fm}^{3}$
corresponding to the mean number of tracks $\langle N_{\rm tracks}^{\rm
VELO}\rangle_{\rm NB}$, one could establish a simple relation $V_{C}/\langle
V_{C}\rangle=N_{\rm tracks}^{\rm VELO}/\langle N_{\rm tracks}^{\rm
VELO}\rangle_{\rm NB}$ that translates the predicted volume dependence of
$\Lambda_{b}^{0}/\bar{B}^{0}$ into a best fit of the LHCb data, as shown in
Fig. 2(b) together with $\bar{B}_{s}^{0}/\bar{B}^{0}$ (Fig. 2(a)), where we
also compare the RQM versus PDG scenario as the $b$-hadron spectrum input.
While the current LHCb data of the system size dependence of
$\bar{B}_{s}^{0}/\bar{B}^{0}$ do not allow for a discrimination between the
PDG and RQM scenario (however the minimum bias datum indicated by the filled
box at the right vertical axis in panel (a) prefers the RQM scenario), data of
$\Lambda_{b}^{0}/\bar{B}^{0}$ show an unambiguous preference for the RQM
scenario. In particular, the decreasing behavior of the
$\Lambda_{b}^{0}/\bar{B}^{0}$ data from the saturation value in minimum bias
collisions toward the $e^{+}e^{-}$ value at the smallest system size is
quantitatively described by our CE-SHM prediction within the RQM scenario.
This provides another strong evidence for the existence of many not-yet-
observed excited states of $b$ hadrons (particularly baryons) He:2022tod , and
suggests a plausible mechanism for the non-universality of heavy quark
fragmentation in elementary collisions, namely the canonical suppression of
baryon production at sufficiently small system size as caused by the
requirement of exact baryon-number conservation.

##  IV Fragmentation simulation: $p_{T}$ differential ratios

Figure 3: The $p_{T}$ differential $\Lambda_{b}^{0}/\bar{B}^{0}$ in two
multiplicity intervals in comparison with LHCb data LHCb:2023wbo .

To compute the $p_{T}$ differential spectrum and ratios of ground-state $b$
hadrons, we sample the perturbative $b$ quark $p_{t}$ spectrum computed from
FONLL Frixione:2007nw ; Cacciari:2012ny  in $\sqrt{s}=13$ TeV collisions and
perform the fragmentation simulation with the fragmentation function

$D_{b\rightarrow H_{b}}(z)\propto z^{\alpha}(1-z)\ ,$ (6)

where $z=p_{T}/p_{t}$ is the fraction of the $b$-hadron’s ($H_{b}$) transverse
momentum, $p_{T}$, over the $b$-quark one, $p_{t}$. The fragmentation weight
of $H_{b}$ is assumed to be proportional to its primary thermal density,
$\langle N_{H_{b}}\rangle^{CE}/V_{C}$ (Eq. (4)), in the spirit of relative
chemical equilibrium. Each $H_{b}$ produced from fragmentation is then decayed
into the ground-state particles with a constant matrix element (i.e., decay
kinematics solely determined by phase space) and ${\rm BR}$’s used in Eq. (5)
He:2022tod . The parameter $\alpha$ in Eq. (6) is tuned to fit the slope of
the $p_{T}$ spectrum of ground-state $b$ hadrons. For simplicity, we take
$\alpha=45,25,8$ for all $B$ mesons, all $B_{s}$ mesons and all $b$-baryons,
respectively, following Ref.He:2022tod  for minimum bias collisions. The
$p_{T}$ spectra of $\bar{B}^{0}$ and $\Lambda_{b}^{0}$ thus obtained are
divided each other to get the $p_{T}$ differential ratio of
$\Lambda_{b}^{0}/\bar{B}^{0}$, as shown in Fig. 3 for two correlation volumes
in comparison with LHCb data for the low and high multiplicity intervals. The
separation of $\Lambda_{b}^{0}/\bar{B}^{0}$ between these two intervals and
its trend of $p_{T}$ dependence can be qualitatively described.

##  V Summary

We have addressed the system size dependence of the production of $b$ baryons
relative to that of mesons in high-energy $pp$ collisions. By introducing many
hitherto unobserved but theoretically predicted $b$ hadrons (in particular
excited baryons) into the canonical ensemble SHM, we’ve demonstrated that the
charged-particle-multiplicity dependence of $\Lambda_{b}/B$ measured by the
LHCb experiment can be quantitatively described, attributed to the canonical
suppression on $\Lambda_{b}$ production toward low multiplicities as a result
of exact conservation of baryon number as required by the canonical treatment
of SHM. The $\Lambda_{b}/B$ as explored bridges continuously the gap between
the saturation value in minimum bias $pp$ collisions and the small value in
$e^{+}e^{-}$ collisions, reinforcing the conception that the heavy quark
hadronization depends on the hadronic environment involved in the collision
systems. We have therefore proposed a possible origin of the non-universality
of heavy quark hadronization in terms of canonical baryon suppression at
sufficiently small system size in the presence of many “missing” baryons
awaiting discovery.

###### Acknowledgements.

M. H. thanks Profs. Y.-G. Ma, G.-L. Ma and J.-H. Chen for the hospitality
during his stay as a visiting scholar at Shanghai Research Center for
Theoretical Nuclear Physics of Fudan University where the work was finalized.
This work was supported by the National Natural Science Foundation of China
(NSFC) under Grants No.12075122 (M. H.) and No.12147101 (via Shanghai Research
Center for Theoretical Nuclear Physics).

## References

  * (1) J. C. Collins, D. E. Soper and G. F. Sterman, Adv. Ser. Direct. High Energy Phys. 5, 1-91 (1989).
  * (2) E. Norrbin and T. Sjostrand, Eur. Phys. J. C 17, 137-161 (2000).
  * (3) M. Lisovyi, A. Verbytskyi and O. Zenaiev, Eur. Phys. J. C 76, no.7, 397 (2016).
  * (4) S. Acharya et al. [ALICE], Phys. Rev. Lett. 127, no.20, 202301 (2021).
  * (5) S. Acharya et al. [ALICE], Phys. Rev. Lett. 128, no.1, 012001 (2022).
  * (6) S. Acharya et al. [ALICE], Phys. Rev. Lett. 127, no.27, 272001 (2021).
  * (7) R. Aaij et al. [LHCb], Phys. Rev. D 100, no.3, 031102 (2019).
  * (8) R. Aaij et al. [LHCb], [arXiv:2310.12278 [hep-ex]].
  * (9) Y. S. Amhis et al. [HFLAV], Eur. Phys. J. C 81, no.3, 226 (2021).
  * (10) M. He and R. Rapp, Phys. Lett. B 795, 117-121 (2019).
  * (11) M. He and R. Rapp, Phys. Rev. Lett. 131, no.1, 1 (2023).
  * (12) J. R. Christiansen and P. Z. Skands, JHEP 08, 003 (2015).
  * (13) V. Minissale, S. Plumari and V. Greco, Phys. Lett. B 821, 136622 (2021).
  * (14) S. Acharya et al. [ALICE], Phys. Lett. B 829, 137065 (2022).
  * (15) R. Aaij et al. [LHCb], Phys. Rev. Lett. 131, 061901 (2023).
  * (16) Y. Chen and M. He, Phys. Lett. B 815, 136144 (2021).
  * (17) [ALICE], [arXiv:2211.04384 [nucl-ex]].
  * (18) A. Rossi, [arXiv:2308.10202 [hep-ex]].
  * (19) J. Altmann, C. Andres, A. Andronic, F. Antinori, P. Antonioli, A. Beraudo, E. Berti, L. Bianchi, T. Boettcher and L. Capriotti, et al. [arXiv:2401.09930 [hep-ex]].
  * (20) A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, Nature 561, no.7723, 321-330 (2018).
  * (21) J. Rafelski and M. Danos, Phys. Lett. B 97, 279-282 (1980).
  * (22) R. Hagedorn and K. Redlich, Z. Phys. C 27, 541 (1985).
  * (23) V. Vovchenko, B. Dönigus and H. Stoecker, Phys. Rev. C 100, no.5, 054906 (2019).
  * (24) J. Cleymans, P. M. Lo, K. Redlich and N. Sharma, Phys. Rev. C 103, no.1, 014904 (2021).
  * (25) R. L. Workman et al. [Particle Data Group], PTEP 2022, 083C01 (2022).
  * (26) D. Ebert, R. N. Faustov and V. O. Galkin, Eur. Phys. J. C 66, 197-206 (2010).
  * (27) D. Ebert, R. N. Faustov and V. O. Galkin, Phys. Rev. D 84, 014025 (2011).
  * (28) F. Becattini, [arXiv:0901.3643 [hep-ph]].
  * (29) R. Aaij et al. [LHCb], JHEP 10, 060 (2021).
  * (30) A. Andronic, P. Braun-Munzinger, M. K. Köhler, A. Mazeliauskas, K. Redlich, J. Stachel and V. Vislavicius, JHEP 07, 035 (2021).
  * (31) A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, Acta Phys. Polon. Supp. 16, no.1, 1-A107 (2023).
  * (32) R. Aaij et al. [LHCb], Phys. Rev. D 104, no.3, 032005 (2021).
  * (33) S. Frixione, P. Nason and G. Ridolfi, JHEP 09, 126 (2007).
  * (34) M. Cacciari, S. Frixione, N. Houdeau, M. L. Mangano, P. Nason and G. Ridolfi, JHEP 10, 137 (2012).