# Putting Language into Context Using Smartphone-Based Keyboard Logging

Florian Bemmann  0000-0002-5759-4976 LMU MunichFrauenlobstr.
7aMunich80337Germany<EMAIL_ADDRESS>,  Timo Koch  Institute of
Behavioral Science & Technology, University of St. GallenSt. GallenSwitzerland
0000-0001-6728-2063 ,  Maximilian Bergmann  Institute of Behavioral Science &
Technology, University of St. GallenSt. GallenSwitzerland 0000-0002-1272-0916
,  Clemens Stachl  Institute of Behavioral Science & Technology, University of
St. GallenSt. GallenSwitzerland 0000-0002-4498-3067 ,  Daniel Buschek
Department of Computer Science, University of BayreuthBayreuthGermany
0000-0002-0013-715X ,  Ramona Schoedel  Charlotte-Fresenius-Hochschule,
University of PsychologyMunichGermany 0000-0001-7275-0626 and  Sven Mayer
0000-0001-5462-8782 LMU MunichMunich80337Germany<EMAIL_ADDRESS>
(2024)

###### Abstract.

While the study of language as typed on smartphones offers valuable insights,
existing data collection methods often fall short in providing contextual
information and ensuring user privacy. We present a privacy-respectful
approach - context-enriched keyboard logging \- that allows for the extraction
of contextual information on the user’s input motive, which is meaningful for
linguistics, psychology, and behavioral sciences. In particular, with our
approach, we enable distinguishing language contents by their channel (i.e.,
comments, messaging, search inputs). Filtering by channel allows for better
pre-selection of data, which is in the interest of researchers and improves
users’ privacy. We demonstrate our approach on a large-scale six-month user
study (N=624) of language use in smartphone interactions in the wild. Finally,
we highlight the implications for research on language use in human-computer
interaction and interdisciplinary contexts.

touch keyboard, data logging, mobile sensing, data set

††copyright: acmcopyright††journalyear: 2024††doi:
XXXXXXX.XXXXXXX††conference: Make sure to enter the correct conference title
from your rights confirmation emai; September 30–October 3, 2024; Melbourne,
Australia††price: 15.00††isbn: 978-1-4503-XXXX-X/18/06††ccs: Human-centered
computing Field studies††ccs: Human-centered computing Text input††ccs: Human-
centered computing Smartphones

##  1\. Introduction

Language is one of the most effective ways to gain insights into peoples minds
(Pennebaker, 2017; Chomsky, 1992). Designing personalized interfaces with
great user experience in technical systems requires a profound understanding
of user‘s inner feelings and thoughts in relation to their interaction
behaviors in specific contexts. Digital footprints are left behind in people’s
everyday language, such as Facebook posts (Schwartz et al., 2013) or WhatsApp
instant messages (Verheijen and Stoop, 2016; Koch et al., 2021) have been
shown to provide useful information on psychologically relevant traits such as
personality traits or depression (Schwartz et al., 2013; Eichstaedt et al.,
2018). Hence, understanding the mental models, attitudes, psychological states
and dispositions of users is a core goal of research in human computer
interaction and in neighboring fields (e.g., psychology, behavioral science).
User modeling is often used in HCI to quantify individual differences for
system adaption in a technical systems.

Regarding language in context is thereby very important, as the meaning of
textual contents highly varies with the situation in that it is expressed. To
regard text inputs into context when logging smartphone typing behavior,
usually, the target app is used as a proxy, for example, by filtering for a
defined set of communication apps (i.e., WhatsApp, Signal, Telegram), or using
an app categorization mapping (cf. (Schoedel et al., 2022; Stachl et al.,
2020)). That approach has two major drawbacks: 1) Defining a list of apps that
contain the desired behavior (i.e., messaging or posting on social media) is
difficult. A wide variety of apps exist and their relevance changes rapidly.
Thus, categorization approaches require frequent adaptation. 2) An app may be
used for various purposes and thus, cannot be assigned to one category. For
example, the very popular app Instagram is used frequently to post public
content and direct messaging. However, it is regarded as a social media app
only in most app categorizations. Also, search fields that exist in nearly
every app contaminate the resulting text data.

We propose to filter for WHAT kind of content users type instead of WHERE the
content was typed. In this paper, we propose a holistic logging and
preprocessing approach for smartphone typing data. We show how input prompt UI
metadata can be used to contextualize language data and allows us to
distinguish language contents by their input motive (i.e., posts, comments,
messaging, search inputs). To enable researchers to leverage input prompt text
for language contextualization in the wild, we developed (a) a category
mapping that assigns input prompt texts to language motives, and (b) an
Android module that can retrieve mobile text inputs in-the-wild and on-device
assigns them their language motive.

We base our categorization on the dataset from a six-month representative
study (N=624) that is the first of its kind using this approach. With this
context-enriched keyboard logging and analysis method, we show the untapped
potential for research in sensing language data. We publish our input prompt
motive mapping, alongside an Android library that allows other researchers to
reuse our system in the wild. We critically discuss the threats and dangers
that are posed by such technology. While our logging approach already improves
user privacy, we point out space for further improvements and motivate future
work in that area.

##  2\. Related Work

###  2.1. Analyzing Language Data from Digital Footprints

Analyzing language use offers a window into people’s thoughts, feelings, and
motivations. Consequently, the analysis of language is a central topic in many
research fields. Initially, rather unstructured language analysis methods were
replaced step by step by automated text analysis tools in the last century
(Boyd and Schwartz, 2021). The general idea behind all methodological
approaches is to quantify raw language data.

To investigate human language use in the wild, researchers across many
disciplines have started to collect digital footprints. Many of these prior
studies relied on social media text data since it is easily accessible:
Researchers collected existing content by crawling web pages (Tausczik et al.,
2012; Yarkoni, 2010), through an Application Programming Interface (API),
(such as Twitter and previously for Facebook (Golbeck et al., 2011; Schwartz
et al., 2013)), or manual content collection (Barak and Gluck-Ofri, 2007). An
alternative source of digital footprints of text data is instant messaging
services such as WhatsApp or Telegram. Private instant messaging is growing in
popularity and increasingly moving into the focus of tech companies (Goode,
2019). Users produce immense amounts of text data using these services.
Accordingly, previous studies indicate that users engage in more self-
disclosure in private instant messages leading to more informative content
(Koch et al., 2021; Bazarova and Choi, [n.d.]).

In this context, two approaches can be distinguished: Open vocabulary
approaches derive features from the data itself (e.g., calculating frequencies
of words used in a given text in relation to all used words), while closed
vocabulary approaches use apriori defined dictionaries (Eichstaedt et al.,
2021). For example, in psychological research, one well-established dictionary
is the Linguistic Inquiry and Word Count (LIWC) (Pennebaker et al., [n.d.]).

However, text data collected from social media comes with downsides: People
might less self-disclose on social media (Koch et al., 2021; Bazarova and
Choi, [n.d.]). This could lead to systematic information gaps in the extracted
digital footprints and, thus, to various biases (e.g. (Jürgens et al., 2020)).
These users, in turn, may have certain characteristics that make them more
likely to disclose information about themselves on social media. For example,
more open individuals are more likely to be active on social media (Correa et
al., 2010). Another plausible assumption would be that people only post on
social media when they are in a certain mood, having language reflecting
momentary and situational states. However, little empirical evidence for this
assumption exists at this point.

Collecting instant messaging data is a challenging task for research purposes,
however, because there is no application programming interface (API).
Workarounds encompass manually collecting exported chat protocols separately
from each user. However, this is time-consuming and may include text data from
respective, possibly non-consenting, chat partners. Alternative approaches
currently practiced in research are, therefore, to advise participants to send
messages through the researchers’ system, which then forwards them to the chat
partner (Song et al., 2014) or adding a researcher’s bot to group
conversations (Fullwood et al., 2013). These practices have in common that
participants may be biased in their choice of donated chats and constant
awareness of being observed. Consequently, donated messages show only a
limited snapshot of participants’ language use, which is also again limited to
only one specific instant messaging application. As a consequence, there is
currently only a handful of instant messaging corpora available (Verheijen and
Stoop, 2016; Ueberwasser and Stark, 2017).

###  2.2. Methods for Collecting Language Data Using Smartphones

Another alternative to the two approaches mentioned above is using smartphones
as data collectors. Smartphones are widespread because they are relatively
inexpensive and have become our daily personal companions (Harari et al.,
2016; Miller, 2012). Sensors and APIs available in these portable devices
unobtrusively collected various types of usage data in the background (Harari
et al., 2016). Combined with self-report measures collected via surveys or
experience sampling (van Berkel et al., 2017; Buschek et al., 2018), they
provide very attractive data sets for researchers, which has led to mobile
sensing taking off in various application fields in recent years (Stachl et
al., 2020; Harari et al., 2020). Accordingly, smartphones have even been
declared as a great resource for knowledge about human behavior in recent
times (Montag et al., 2016). Mobile sensing has so far had a strong
methodological focus on extracting behavioral (e.g., app usage, calling) and
situational (e.g., GPS, ambient light) information (Harari and Gosling, 2023).
The application for collecting language data is so far a largely untapped
potential of mobile sensing. In contrast to collecting content from specific
applications, smartphones provide comprehensive behavioral data across all
applications. In general, the literature distinguishes three approaches to
collecting text data via smartphones, which will be briefly described in the
following sections.

Smartphones allow the user to install a custom
keyboard111https://developer.apple.com/documentation/uikit/keyboards_and_input/creating_a_custom_keyboard,
222https://developer.android.com/guide/topics/text/creating-input-method, and
thereby allow the developer to intercept the typed keys and log the users’
keystrokes (Rodrigues et al., 2021; Lu et al., 2016; Bemmann and Buschek,
2020). This rather low-level data is rich and detailed: Researchers can
comprehend the writing process in every detail, and the keyboard can also
listen to other kinds of events related to text input like the usage of word
suggestions and auto-completion events (Bemmann and Buschek, 2020). Device
APIs (Application Programming Interface) (Ofoeda et al., 2019) offer
application developers easily accessible functionalities or data of the device
operating system. On Android smartphones the Accessibility Service
API333https://developer.android.com/reference/android/accessibilityservice/AccessibilityService
allows to access typed language (Lee et al., 2021; Kalysch et al., 2018).
While not possible on iOS, on Android, a researcher’s app installed on the
participants’ smartphones can subscribe to text input events, and thereby
reconstruct the typed content. An alternative approach to recording
comprehensive smartphone behavior that can also be used to access typed
language is to take screenshots. (Brinberg et al., 2021) deploy an app that
takes screenshots every 5 seconds and presents a methodology using text and
image recognition to extract behavioral data. The screenshot approach allows
for the extraction of meta data, but requires additional processing through
recognition models. For example, the chat partner’s name can be extracted from
the chat app’s header in a messaging app.

The downsides of a replaced keyboard are a different look and feel than the
one the users are used to, what might, deliberately or unconsciously,
influence their behavior. Users reported a high awareness of the data logging
but no induced content change. Instead, they report an influence of the UI
differences on the interaction behavior (Bemmann and Buschek, 2020).
Screenshot approaches are in practice often accompanied by a certain
inaccuracy in the data. Machine Learning and text extraction approaches have
to be used to extract the desired contents, which do not ensure perfect
accuracy (Chiatti et al., 2017). Smartphone screenshots are heterogeneous, and
it contextualizing text contents from screenshots is not trivial (e.g.
distinguishing between typed and received messages in a chat history).
Furthermore, even a fixed-frequency screenshot approach cannot reach the level
of detail and comprehensiveness that an event-based logging approach does. All
methods have in common that they expose participants to serious privacy risks.
Raw user data is collected on a central server of the researcher and may
contain privacy-invasive content (e.g., photos, illegal activities).
Especially screenshots furthermore contain way more information than is
actually needed and thereby contradict the principle of information
minimization.

###  2.3. Privacy-friendly Mobile Language Logging in Context - Leveraging
Typing Meta Data

Figure 1. Screenshots of three text fields of the three Android apps: Google
WhatsApp (left), Google Search (middle), and Twitter (right). All three text
fields have input prompt texts, that give the user a hint about what the text
field is intended to be used for.

Besides the final text content, which is the data of interest for most
applications that leverage mobile language data, a typing user also generates
metadata. Depending on how the data is logged, this data may not be accessible
and discarded during preprocessing. Implementations that access the input
events by replacing the keyboard with a custom implementation instead allow
access to typing metadata (cf. (Bemmann and Buschek, 2020; Wampfler et al.,
2022)). However, only a few works have been conducted that make use of this
metadata, and the derivation of higher-level contextual features that are
relevant to interdisciplinary research is rare. Nowadays, when analyzing
language use, researchers mostly select and contextualize their data by
filtering by the used app, which is only a proxy for the type of content and
the user’s intention, but in practice not accurate. For example, social media
apps can be used for both crafting public content and sending private
messages.

We fill this gap and motivate further research by proposing a context-enriched
keyboard logging approach. Choosing a language logging approach that exchanges
the keyboard with a custom implementation or leverages device APIs, meta
information on where a user did type can be accessed. We specifically regard
the input target app and the input prompt text, i.e., the text that is visible
as a background or placeholder inside a text field as long as the user didn’t
type any content. We show some examples of these in Figure 1. The usage of
input prompt texts has not yet been studied as a data source for psychological
research. Studied application scenarios in HCI encompass UI automation and
privacy-enhancing tools, e.g., by (Pereira Borges Junior, 2020) to access a
specific text field for automated UI testing or by (Wanwarang et al., 2020) to
help a system understand the meaning and input concept of a UI element,
respectively the latter by (Andow et al., 2017) and (Huang et al., 2015) who
use input prompt text to estimate whether a text field is intended to contain
potentially sensitive contents. Input prompt texts can be either static or
dynamic, i.e., being hard-coded and never changing, or vary depending on the
user’s context (He et al., 2020).

We demonstrate an approach that infers a text input purpose and the user’s
intention, i.e., input motive, from metadata of the respective text input
field. We highlight which new perspectives on texting behavior it opens up,
for which patterns of research it is used, and how it makes the gained data
clearer and more focused. In doing so, we attach great importance to a
privacy-friendly implementation of such techniques. Written text and the
resulting logging data are highly privacy-sensitive. Our work supports a
privacy-friendly, on-device-processing implementation of context-enriched
keyboard logging in future user studies by proposing a set of features and
abstraction methods.

##  3\. In-the-Wild Logging of Text Input and UI Contextual Information

To tackle the aforementioned research gap, we study the potential for language
use research that lies in UI metadata. We propose to use device APIs to log
mobile typing behavior and create an approach that makes provided UI metadata
usable to create contextual variables. We develop and provide (a) logging
libraries for the Android operating systems to track language input data, and
(b) a categorization approach for UI metadata that extracts a variable on the
user motive of text input from the UI property input prompt text.

Our method puts an emphasis on:

  * •

Comprehensiveness. Being able to regard text inputs across all apps and input
methods.

  * •

Context-sensitivity. It should be possible to regard text inputs in the user’s
context.

  * •

Reducing Observer Biases. The logging method should have the least possible
observer bias on the participant.

  * •

Privacy. Text input data contains privacy-invasive information, and should
thus not simply be recorded as it is.

  * •

Replicability and Adaptability. The presented approach should be applicable to
many different kinds of research from interdisciplinary fields. Therefore we
report our full research pipeline so that it is reproducible, and can be
adapted to other research’s demands.

###  3.1. Input UI Metadata

We logged the input prompt text alongside a text input through an Android API.
This gives us access to all typing events at full granularity, and allows to
retrieve UI metadata. We abstract each typed word into psychological
categories on-device, to ensure that no raw text contents are logged. The
available text input metadata encompasses the input prompt text, also a title,
label, and styling/sizing properties. Label and input prompt texts tell users
what they are supposed to enter and which type of input the app is expecting.
Input prompt texts are visualized as placeholders, that indicate what the user
is supposed to type, e.g., ”Message” (WhatsApp) or ”Tweet your reply”
(Twitter) (see Figure 1).

###  3.2. Deriving Contextual Feature: Input Motive

In our approach, we solely rely on the input prompt texts. We create a
categorization, that maps input prompt texts into one of 7 categories, i.e.
input motives. An input motive describes the purpose and kind of content that
a user is supposed to enter into a text field, such as search inputs, direct
messaging, or public social media posts. We visualize this concept on the
example of the app Instagram in Figure 2, list the input motives in Table 1,
and describe the categorization procedure in detail in Section 5.

##  4\. Mobile Sensing Field Study

In this section, we present our field study, which to the best of our
knowledge, is the first large-scale deployment ($N=624$, 3 to 6 months) of
smartphone-typed language logging in the wild that applies privacy-respectful
on-device preprocessing. Its purpose for this paper mainly is to retrieve a
body input prompt texts from real smartphone usage to create an input prompt
categorization that maps input prompt texts to motives. This can be used as
basis for future projects, where it allows to categorize data directly on-
device. Furthermore we describe the characteristics of the obtained data, to
give researchers an overview of what data to expect from such a study.

###  4.1. Implementation

To collect a solid data basis for our categorization in the wild, we developed
an Android app that participants had to install on their smartphones. To
access typed language data, it subscribes to content change events of input
fields444Android Accessibility Event type VIEW_TEXT_CHANGED
https://developer.android.com/reference/android/view/accessibility/AccessibilityEvent#TYPE_VIEW_TEXT_CHANGED.
Thereby it is notified on each change, i.e., each typed or removed character.
For the preprocessing procedure we rely on the provided code of Bemmann and
Buschek (2020), however our logging is implemented differently, as we did not
adopt their approach of replacing the device’s keyboard with a custom
implementation. With the receiving event comes a reference to the target input
field555EditText object
https://developer.android.com/reference/android/widget/EditText from which we
retrieve additional metadata, namely the app name that the input field belongs
to, and its input prompt text.

###  4.2. Data Collection: Representative Smartphone Sensing Panel Study

The study was not conducted exclusively for and tailored toward the specific
needs of this paper. Data collection was conducted as part of a cooperation
project between the authors’ university and a research institute for large-
scale psychological studies [organization names to be added in final version].
Its purpose is to collect data to answer various research questions from
psychology, sociology, and human-computer interaction.Mobile sensing,
experience sampling, and survey data were collected during an individual study
period of up to six months (from May until November 2020). A detailed
description of data collection procedures is supplied in the pre-registration
of the study protocol [details to be provided in final version]. In the
following description, we focus on the parts of the study that are relevant
for this project. This research was ethically approved and carefully aligned
with EU GDPR guidelines.

By means of a provider for non-probability-based online panels, a starting
sample of 851 participants was recruited according to a pre-specified quota
(gender, age, education, income, confession, and relationship status)
representative of the German population in the age group 18-65. Participants
were required to own an Android smartphone, on which they were asked to
install our research app PhoneStudy: The app had access to the users’ text
inputs via the Android Accessibility
services666https://developer.android.com/guide/topics/ui/accessibility/service.The
research app ran continuously in the background of participants’ smartphones
during the study period of three to six months. Language data thereby were
preprocessed with the Language Logger abstraction module of (Bemmann and
Buschek, 2020), using the LIWC dictionary777LIWC is proprietary software. Its
usage must be cleared with the authors. (Pennebaker et al., [n.d.]) for word
categorization and a German dictionary (der, 2013) as a whitelist for word
frequency counting. The full body of measures is reported in detail in the
study preregistration (see Schoedel and Oldemeier (2020)).Participants were
compensated in stages, i.e., depending on how long and in which parts of the
study they participated. They were excluded from data collection after several
reminders if they revoked permissions for mobile sensing data collection
several times for longer than seven consecutive study days and failed to
complete two out of three monthly online surveys per study half. Participants
could withdraw their consent at any time and ask for their collected data to
be deleted. All log data was deleted from the client devices when the study
finished, i.e. immediately before prompting the participant to choose their
compensation.

###  4.3. Sample

The initial sample consisted of 851 users. We excluded participants who did
not grant all necessary permissions or experienced technical issues (42),
switched their primary smartphone during the study (44), or participated less
than two weeks (141).This leads to a final sample of $N=624$ available for
further analyses. The mean age in our sample was 42.65 years (SD = 12.60). The
age distribution follows the population in Germany, having one peak around 40
years and another between 50 and 60. Gender groups were balanced with slightly
more male participants (our sample: 55.34% male, 44.49% female, .18% other;
national statistics: 49.34% male, 50.66% female, divers is not captured by the
statistic)888Source: Federal Statistical Office of Germany
https://www.destatis.de/EN/Home/_node.html. Regarding their highest completed
education levels, our participants are rather well-educated in comparison to
national averages. We report a higher amount of participants holding a school
degree (80.00% of the participants hold a school degree as their highest
education (national statistic: 52.58%††footnotemark: ), while nearly none of
our participants does not hold any degree (0.81%, national sample: 21.27%).
19.12% hold a university degree (national statistic: 26.15%††footnotemark: ).
Only native Android users were considered as participants, i.e., people who
use an Android device as their primary phone. No devices were handed out for
the purpose of participating in this study.

###  4.4. Data Analysis and Offline Preprocessing

The data analysis was conducted on a central server with the statistics
software R999https://www.r-project.org/. No raw data was downloaded to local
computers. The data analysis was divided into two steps: In the first step, we
imported the data, did general preprocessing (e.g., parse timestamps, select
the final sample), and grouped keyboard events by their text input. Word
category occurrences were encoded in the many-hot format. The resulting data
was in a table-like format, each row representing a text input. If not
described otherwise, we analyzed events of type added and changed and
discarded removed events. The data were grouped per text input. In the second
step, we categorized apps and input prompt texts.

##  5\. Input Prompt Text Categorization: Distinguishing Language Contents by
Their Input Motive

Figure 2. Instead of categorizing collected in-the-wild text input data by the
originating app, we propose to regard the originating text field’s input
prompt text. This figure shows on the example of the app Instagram, that text
inputs into Instagram are not just social media contents such as posts and
comments, but can also have other motives such as messaging, search, and data
input.

In this section, we describe our input prompt text categorization and show the
process of how we created it. We attach our input prompt text category mapping
to this paper. However, we think it is important to enable researchers to
create their own category mapping, to meet the specific characteristics of
their dataset. We discuss the portability and validity of our yielded category
mapping in Section 7.6.

##### Prefiltering

Input prompt texts can be dynamically created by the according smartphone app,
and may thus contain private content. For example, some apps extend input
prompts such as ”Reply to message” with the corresponding user name, i.e.
”Reply to John Smith”. As it is our premise not to have names of conversation
partners in our dataset, we filtered such input prompt texts. We did this
through the assumption, that an input prompt text that contains private
information, is unlikely to occur for multiple distinct participants. Thus, we
removed all input prompt texts that only occurred with one participant. We
visualize this on the example of Instagram in Figure 2. To aggregate the input
prompt texts into input motives for further analyses, we applied a semi-
automatic, two-step categorization concept:

##### Identification of Major Motives

We identified five major motives that users follow when composing texts on
their smartphones. Those constitute our input motives: Messaging, Posting,
Commenting, Search, and Data Input. Furthermore we have the two categories
Other and Ambiguous: input prompt texts that cannot be assigned to one of
these were labeled as Other. Ambiguous was used if the meaning of an input
prompt text was unclear at all. We describe the input motives in Table 1. Our
categorization regards all smartphone text entry interactions of all
participants, regardless of app category or any other pre-selection.

Table 1. We categorize text inputs on smartphones into input motives, using a text field’s hint text.  Motive |  Description |  Example |  keywords for automatic categorization
---|---|---|---
Messaging |  A private message targeted to a defined person or group of people |  ”Type a message” (WhatsApp), ”Enter your message here” (Facebook Messenger) |  nachricht, message
Posting |  (Semi-)public posts in social media applications. They are visible to either anyone (public posts) or limited to a group of people (e.g., friends of that user) |  ”Write a caption” (Instagram), ”What are you doing?” (Facebook) |
Commenting |  Content that is attached to an existing post, usually with the same visibility as the post |  ”Comment …” (Facebook), ”Tweet your reply” (Twitter) |  komment, comment
Search |  Content that constitutes a search query. E.g. inputs into search fields |  ”Search apps, web, and more…” (Google Quicksearch), ”Search photos…” (Gallery app) |  such, search
Data Input |  Inputs that ask the user for some information, usually form fields |  ”email address” (on a login screen), ”Stop, address, …” (in a public transport service app), ”Spanish translation” (in a language learning app) |
Other |  The input prompt text cannot be assigned exactly one motive, or the purpose is clear but does not belong to one of the five main motives |  e.g. experience sampling and questionnaire items, ”write a note…” |
Ambiguous |  The input prompt text’s meaning and purpose is not understandable at all |  ”0”, ”???” |

##### Categorization Step 1: Automatic keyword stem matching:

To categorize input prompt text into input motives, we applied a semi-
automatic approach. In the first stage, we were looking for keywords that
could be used to categorize input prompts automatically. We decided to
classify all texts that contain German and respective English word snippets
”such” / ”search” as Search, ”komment” / ”comment” as Commenting, and those
containing ”nachricht” / ”message” as Messaging. With this step we could
categorize 3,671 distinct input prompt texts.

##### Categorization Step 2: Manual Coding:

For further categories, we did not find a reliable matching scheme and thus,
proceeded to categorize all remaining input prompt texts manually. We limited
our manual categorization to only those input prompt texts which occur in more
than 0.01% of all logged texts (465 input prompt texts). The categorization
was done independently by three researchers (R1 to R3), in three iterations.

R1 in the previous step created the category definitions and the first coding
iteration was done by two other researchers independently. We thereby intend
to keep the coding free of biases that arise from the motive identification
phase. R2 and R3 both coded 50 randomly selected input prompt texts
independently. They afterward compared their coding and discussed the
differences. Their notes and suggestions were given to R1, who then improved
the motive definitions. Changes included refinement of the Data Input
category, and splitting up and refining Other and Ambiguous (in R1’s initial
definition, they were joined). In the second coding iteration, R2 and R3 used
the refined motive definition to code the remaining input prompt texts. They
agreed in 89.7% cases, of 438 input prompts that were manually coded, R2 and
R3 agreed on 393 cases, and for 45 cases their coding differed. To check the
inter-coder reliability we evaluated Cohen’s Kappa (O’Connor and Joffe, 2020)
resulting in a nearly perfect agreement, according to the classification of
(Landis and Koch, 1977) ($K=0.83$, 95% CI: $[0.78;0.88]$). The remaining
discrepancies were resolved by R1 by coding the input prompts independent of
the decisions of R2 and R3. Afterward the coding of R2 and R3 were
additionally taken into account to overthink the coding of R1. The different
coding decisions were discussed where necessary, and R1 made the final
decision. This increased our final coverage to 88.4% of all text inputs, with
4,108 distinct input prompt texts being covered.

Table 2. Number of assigned motive categories, alongside disagreements and interrater agreement to each motive category of the manual coding process. | Assigned Input Prompt Texts |  |  |
---|---|---|---|---
Input Motive | Overall | Manually Coded | Disagreements | Cohen’s Kappa | 95% CI
Messaging | 568 | 31 | 4 | 0.88 | [0.79;0.97]
Posting | 20 | 20 | 4 | 0.75 | [0.6;0.9]
Commenting | 157 | 4 | 1 | 0.75 | [0.41;1]
Search | 2997 | 16 | 1 | 0.78 | [0.63;0.93]
Data Input | 248 | 248 | 12 | 0.85 | [0.81;0.9]
Other | 13 | 13 | 7 | 0.8 | [0.57;1]
Ambiguous | 105 | 105 | 16 | 0.82 | [0.75;0.88]

##  6\. Descriptive Evaluation of Input Prompt Text Categorized Data

In this section, we evaluate descriptive statistics of our input prompt text
categorization. We report the characteristics of our mobile typing language
dataset with input motive as a new independent variable. We show the
advantages that researchers gain when selecting and filtering their language
data by input motive, instead of by app category.

###  6.1. The Dataset

In total, our analysis encompasses 1,868,416 text inputs across 624 users. The
average smartphone user in our sample typed 23.40 text inputs per day
($SD=28.23$). These made up 146 words ($SD=155$) per user per day. Regarding
all text inputs, each text input consists of on average 9.44 words
($SD=30.7$). During a text input, the users added on average 8.13 words
($SD=25.6$), changed 1.31 words ($SD=6.35$), and removed 1.50 words
($SD=6.86$) words.

###  6.2. Descriptives of the Input Prompt Categorisation

Of all 1,868,416 text inputs, 1,112,317 (59.5%) obtained an input prompt text.
Our categorization labeled 983,281 (88.4%) of them, covering 52.63% of all
text inputs.

The most frequent input motives were Messaging (44.0%), Search (33.8%) and
Data Input (12.2%). The social media categories Posting (1.0%) and Commenting
(3.2%) occurred less often. The occurrence of the remainders categories
Ambiguous (4.9%) and Other (0.9%) is on a low-level, what shows that our
category mapping covers the user’s motives well in nearly 95% of all text
inputs.

###  6.3. Input Prompt Motives vs. App Categories: Changes in Data
Characteristics

####  6.3.1. Number of Words per Text Input

We compare the number of words per text input, regarding their motive
category. We found that text inputs that fulfill a functional purpose, such as
Search ($M_{Search}=2.30words$, $SD_{Search}=6.80$) and Data Input
($M_{DataInput}=2.73$, $SD_{DataInput}=9.29$), are significantly shorter than
texts of motives whose content is targeted towards other people, such as
Messaging ($M_{Messaging}=12.43$, $SD_{Messaging}=18.80$), Posting
($M_{Posting}=12.84$, $SD_{Posting}=19.00$), and Commenting
($M_{Commenting}=12.65$, $SD_{Commenting}=20.28$). Other text inputs range in
between of both clusters ($M_{Other}=5.32$, $SD_{Other}=9.42$). A Kruskal
Wallis rank sum test with a consecutive Dunn’s test (p-values adjusted with
Bonferroni method) revealed significant differences between the three groups
Search and Data Input vs. Messaging, Posting and Commenting vs. Other for all
pairwise comparisons with $\alpha<.01$.

Figure 3. Words typed per user per input motive. Search inputs are rather
short (1 to 3 words), and Messaging inputs are rather long with 5 to 50 words.
Social network contents like posts (Content Creation) and Comments range in
between.

####  6.3.2. Dictionary Matching Rates

Table 3. Comparing characteristics of text inputs filtered by input motive (yellow background) and app category (green background). We compare mean and standard deviation for the two variables  matching rate and number of words per text input. | LIWC matching rate | words per text input
---|---|---
Input Text Selection | M | SD | M | SD
App Category: Communication | 48.32% | 31.05% | 16.43 | 38.30
input motive: Messaging | 50.64% | 30.33% | 12.43 | 18.80
App Category: Social Media | 31.59% | 33.52% | 12.87 | 39.60
input motive: Posting | 38.82% | 30.34% | 12.84 | 19.00
input motive: Commenting | 41.78% | 30.35% | 12.65 | 20.28
App Category: System | 18.78% | 31.67% | 4.34 | 20.00
input motive: Search | 13.02% | 28.60% | 2.30 | 6.80

In this section, we regard how much of the logged text contents could be
matched with the applied dictionary. We analyze the different matching rates
of text input (1) selected via our motive categories derived from the input
prompt texts, and (2) filtered by the app categories of (Schoedel et al.,
2022). Therefore, we compare the matching rates of the extracted LIWC
categories for the input motive Messaging with the app category Messages, for
the input motives Posting and Comment with the app category Social Network,
and the same named input motive Search with the app category System (a
comparison with an app category is not clearly possible in this case. We have
chosen the category System, as it contains some search apps).

In general, we found matching rates for messaging content being the highest
(around 50% for both kinds of categorization), followed by social media
content between 30% and the lower 40s. Search inputs, in general, match the
dictionary rather badly (10% to 20%). This characteristic is not surprising,
as messaging consists of rather natural language, whereas hashtags and more
net-speech might enhance social media language. Search queries contain rather
specific words (names, locations, etc.) that are not contained in the
dictionary.

Filtering content by input motives instead of app categories could strengthen
these characteristics: We found higher matching rates for messaging and social
network content when selecting text input via input motives than when using
the equivalent app categories (please find the effect sizes reported in Table
3). For the category Search, the matching rate behaves oppositely, i.e., the
input motive Search shows a lower matching rate than the respective app
category System. Standard deviations when filtering by motive category instead
of app category were lower in all comparisons.

##  7\. Discussion

In this section, we discuss our context-enriched keyboard logging approach. We
interpret which implications the results of our data analysis have on research
patterns, how they can be used to foster future studies by other researchers,
and which dangers and privacy issues are revealed.

###  7.1. More Specific Data by Comparing Language Across Communication
Channels

The analysis of our study data showed that selecting text inputs via the input
prompt text yields higher matching rates in the LIWC dictionary than when
selecting via app categories for messaging and social media content. Although
we did not compare modeling scores of exemplary dependent variables and
psychological constructs (such as predictions of age and gender (Koch et al.,
2022b), affective states (Koch et al., 2022a)), this implies that the yielded
data is cleaner and of higher quality when selecting text inputs via the input
prompt text. The opposite behavior for the input motive Search is not
surprising and can be explained by the characteristics of search inputs: They
are very short, usually just a few words (see Figure 3 for comparison) and
consist of specific terms (companies, names, locations, …). They are, in
general, more ambiguous and, thus, often not covered by closed-vocabulary
approaches, such as the LIWC dictionary. Thus, lower matching rates for the
input motive Search in comparison to the equivalent app category are not a bad
sign but instead speak for a cleaner body of actual search inputs. To study
search inputs using the presented approach, we recommend designing a
dictionary specialized on the underlying research question first, such as
Remus et al. (2010) created for sentiment, or (Cheng et al., 2016) with who
collected keywords indicating depressive states.

While the results of our study indicate that selecting text inputs by input
motives instead of app categories yields higher data quality, more research is
needed to test this, empirically. We motivate future work to assert the data
quality: Language motives could be regarded as clusters and evaluated
clustering evaluation metrics such as inter-cluster and intra-cluster
distances (c.f. Ranby (2016)), or more language-specific similarity metrics as
evaluated by Krakovsky and Mokris (2013). Also, it would be interesting to
redo analyses of existing research on mobile language, with both app-
categorized data and input prompt text categorized data, to see the effect on
the results, for example, improvements in effect sizes.

###  7.2. Privacy

With great power also comes great responsibility. While the availability of
contextual information and language data yields many opportunities, it also
creates privacy risks. While people are mostly aware of the risks of language
data and have concerns about sharing them (Bemmann and Buschek, 2020),
awareness of risks about what can be inferred from passive sensing data is not
at an adequate level yet (Harari, 2020). Thus, using methods and tools like
the ones presented in this work, introduces huge responsibilities to the
applying researchers: The preprocessing features are privacy-wise only as
strong as their configuration. In the privacy-wise worst-case application, one
could configure the preprocessing with a one-to-one mapping of all words
contained in a language dictionary to the same word. The content abstraction
approach would thereby be undermined. This issue, however, is independent of
our input prompt text categorization approach.

More precise pre-filtering of text contents, that our method enables, does
support user privacy. In line with the recent calls for data minimization
(c.f. (Hatamian, 2020)), contextual information on text inputs allows for
discarding unnecessary data immediately on-device. An estimation on the
example of studying social media post language on Instagram shows that our
approach allows removing unnecessary text inputs even before they leave the
participant’s smartphone. Of 38,075 text inputs into the app Instagram, only
4693 inputs reflect posted public content (posts and comments), whereas 9992
inputs were public messages and 154 data inputs. As the latter two are not
relevant in regard to public social media language, but might contain very
privacy-sensitive content, they should be excluded for the sake of data
minimization. Our approach allows us to do so directly on the participant’s
smartphone.

###  7.3. Future Work: Derive Further Information from UI

Our work is, to the best of our knowledge, the first that investigates the
usage of the input prompt text as contextual variable about the user for
research. Building on this starting point, we see more potential in input
prompt texts that should be explored in future work:

##### Derive context from input prompt text

In our work, we used the input prompt texts to categorize text inputs by the
kind of input that developers expect. However, other kinds of categorizations
are possible as well. For example, the input prompt text can be used to infer
the language an app is configured to be in, which likely also is the input
language.

##### Take surrounding UI into account

Besides the input prompt text, surrounding UI elements could also be of
interest, such as the label of a text field or the input field’s size.

##### Automatic Categorization of Yet Unseen Input Prompts

Our approach only works for known input prompts, i.e., ones that are included
in the category mapping exactly as they are. To enhance the procedure’s
coverage, approaches that can deal with yet unseen input prompt texts would
make an improvement. That could be the matching of word stems and keywords,
word embeddings, or deep-learning-based approaches.

###  7.4. Limited Availability of Input Prompt Texts

An input prompt text is not available with all text fields. Our implementation
could access input prompt texts for 59.5% of all typing sessions. The reasons
are that input prompt texts are not always set by the app’s developer, and
that, for some cases, we cannot distinguish between input prompt text and pre-
set text, and thus have to discard the content for privacy reasons.
Furthermore, access to accessibility services might become more difficult with
future Android versions. To enhance the coverage of information, other UI
properties and elements, such as labels, could be taken into account. They
could be processed with the same procedure as input prompt text, as they
fulfill a similar purpose.

As mobile operating systems generally are a matter of change, our approach
might need adaptation for future deployments. Although our implementation
adhere’s to current Android policies, the availability of the data that we
rely on may change in the future.

###  7.5. The Long-tail Distribution of Categorization Coverage

The proposed categorization approach is not holistic. In our study, we cover
88.4% of all logged input prompt texts, covering 52.63% of all text inputs.
Input prompt texts occur in a long-tailed distribution, i.e., the top 10 most
frequently occurring input prompt texts (0.0004%) occur in 496,135 input
prompts (40.60%) of our text inputs. Thus, coding the remaining uncovered
11.6% requires a way higher coding effort than the first 88.4%. Furthermore,
input prompt texts change with apps evolving, or new apps coming up. While the
automatic coding approach might cover most of the new input prompt texts, some
others will not be covered without updating the manual coding. This issue is
already known from app categorizations, which also need to be updated
frequently as new apps proliferate at a high speed. However, due to the semi-
automatic approach, we expect our input prompt text approach to be more stable
for changes than nowadays app categorizations are. With 22,896 distinct input
prompt texts being covered already a significant proportion of the input
prompt texts of new apps might already be known, and another huge proportion
might be covered by automatic categorization. App categorizations, in
contrast, have to deal with each new app individually.

###  7.6. Portability and Reusability of our Categorization

The input prompt text categorization that we provide is fitted to our specific
study data, thus to what extend this generalizes to new data collections is
unclear. Other studies’ participants might use yet unseen apps, and input
prompt text within yet-known apps might change with app updates and thereby
the number of unclassifiable input prompt texts might increase. Due to our
large-scale and close-to-representative sample encompassing 3,325 distinct
apps with 22,895 distinct input prompt texts, we expect our categorization to
be rather stable and well-usable in the next few years. However, the issue of
a categorization becoming outdated over time, which is well known with app
categorizations (c.f. (Schoedel et al., 2022)), is well known for closed-
vocabulary approaches, and does also apply to ours. Especially when deploying
our approach in a specific context, i.e. with a specific kind of participants,
country, or regarding a specific rarely used apps, our categorization might
not yield a satisfying coverage. Therefore, not just the deployability of our
categorization but also the reproducibility of the categorization process
itself is very important to us. We recommend researchers pilot the
classification with a small subsample of participants before applying it fully
on-device. If necessary, one can then either extend the classification before
the full deployment or opt for an offline categorization approach that
initially keeps the raw data.

##  8\. Conclusion

In this paper, we motivate researchers who work with mobile language data to
take contextual data into account. Distinguishing language contents by their
input motive (i.e., comments, messaging, search inputs) creates a yet-unused
contextual variable. We show how smartphone app UI’s input prompt texts can be
preprocessed on-device, and provide an input prompt text categorization. We
base our work on a representative large-scale six-month user study (N=624) of
language use in the wild. With the analysis of our study data, we show which
data characteristics researchers have to expect from such a study and give
descriptive insights into our contextual variable input motive. We argue that
context is beneficial in many ways: It allows for better prefiltering of
mobile language data than the currently prominent approach, selecting texts by
app, does. This enables a more fine-grained selection of input texts and
improves user privacy, as unnecessary content can be discarded earlier.
Finally, we highlight implications for research on language use in psychology,
linguistics, and interdisciplinary contexts. Novel research paths are enabled
that support future work on mobile language use in the wild. Besides the
advantages and use cases, we also discuss the imposed risks on dangers that
such data have on user privacy.

###### Acknowledgements.

We would like to thank the Leibniz Institute for Psychology (ZPID) for their
great cooperation and support in the Smartphone Sensing Panel Study, from
which the dataset published here arises.

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# Violation of Geometrical Scaling in pp Collisions at NA61/SHINE

Michal Praszalowicz  M. Smoluchowski Institute of Physics, Jagellonian
University, Reymonta 4, 30-059 Krakow, Poland

###### Abstract

We analyze geometrical scaling (GS) of negative pion multiplicity $p_{\rm T}$
distributions at NA61/SHINE energies. We show that even though NA61/SHINE
energies are low, one may expect to find GS in the particle spectra. We argue
that qualitative behavior of ratios of multiplicities at different energies is
in agreement with a simple picture of GS which is violated for $p_{\rm T}$
smaller than some nonperturbative scale $\Lambda$ and when larger Bjorken $x$
of one of the scattering patrons crosses $x_{\rm max}$ above which gluonic
cloud becomes dilute and quark degrees of freedom become important.

###### pacs:

13.85.Ni,12.38.Lg

Scaling properties of physical observables have been for a long time one of
the most instructive ways to get information about the underlying physics. In
some cases this information could be fully quantified; here the most prominent
example is Bjorken scaling of Deep Inelastic Scattering (DIS) structure
functions Bjorken:1968dy . In some other cases, like the Koba -Nielsen-Olesen
scaling Koba:1972ng  for example, the underlying physics is still poorly
understood. Some theoretically conjectured scaling laws, like Feynman scaling
in high energy hadronic collisions Feynman:1969ej , have not been
experimentally confirmed. In any case both the emergence of a scaling law, and
– sometimes more importantly – its violation, test our understanding of
microscopic phenomena that are of importance in given experimental conditions.
Again Bjorken scaling is here a benchmark, since both its emergence and
violation are fully understood in terms of perturbative quantum chromodynamics
(QCD) DGLAP .

In this paper we will focus on another scaling law, called geometrical scaling
(GS), which has been introduced in the context of DIS Stasto:2000er . It has
been shown that GS scaling is present also in high energy pp collisions
McLerran:2010ex ; Praszalowicz:2011tc . An onset of GS in heavy ion collisions
at RHIC energies has been reported in Refs. Praszalowicz:2011rm .

The proton seen at low Bjorken $x<x_{\mathrm{max}}$ is dominated by a gluon
cloud characterized by a typical scale $Q_{\text{s}}(x)$ which is called
saturation scale sat1 ; sat2 ; GolecBiernat:1998js . The phenomenon of
saturation (for a review see Mueller:2001fv ; McLerran:2010ub ) appears due to
the nonlinearities of parton evolution at small $x$ given by so-called JIMWLK
hierarchy equations jimwlk  which in the large $N_{\rm c}$ limit reduce to the
Balitsky-Kovchegov equation BK . These equations admit traveling wave
solutions which explicitly exhibit GS Munier:2003vc . The appearance of GS in
the prototype of the BK equation obtained in double logarithmic approximation
by Gribov, Levin and Ryskin sat1  has been studied in Ref. Bartels:1992ix . An
effective theory describing the small $x$ regime is Color Glass Condensate
sat1 ; sat2 ; MLV . For the present study the details of saturation are not of
primary interest, it is the very existence of the saturation scale which plays
the crucial role.

Recently it has been shown Praszalowicz:2012zh  that GS in DIS works very well
up to relatively large $x_{\text{max}}\sim 0.1$ (see also Caola:2010cy ). This
should not come as a total surprise since it is known that GS scaling extends
well above the saturation scale both in the DGLAP Kwiecinski:2002ep  and BFKL
Iancu:2002tr  evolution schemes not only for the boundary conditions that
exhibit GS Caola:2008xr  to start with. For $x<x_{\mathrm{max}}$ in the first
approximation the virtual photon cross-section $\sigma_{\gamma^{\ast}p}$ in
DIS is a function of a scaling variable $\tau=-q^{2}/Q_{\text{s}}^{2}(x)$
only, where $q^{2}$ is photon virtuality Stasto:2000er ; GolecBiernat:1998js .
Similarly in hadronic collisions charged particle multiplicity in central
rapidity exhibits GS McLerran:2010ex

$\left.\frac{dN}{dyd^{2}p_{\text{T}}}\right|_{y\simeq
0}=\frac{1}{Q_{0}^{2}}F(\tau)$ (1)

where $F$ is a universal dimensionless function of the scaling variable

$\tau=p_{\text{T}}^{2}/Q_{\text{s}}^{2}(x).$ (2)

In this paper we shall address a question of applicability of Eq. (1) beyond
the central rapidity region. This is an important and interesting question for
the following reasons. First, Bjorken $x$’s of scattering gluons that produce
a particle of a given transverse momentum $p_{\mathrm{T}}$ and rapidity $y$
read

$x_{1,2}=e^{\pm y}\,p_{\text{T}}/W$ (3)

and can be quite different for large rapidities (we shall assume positive $y$,
hence $x_{2}<x_{1}$). Here $W=\sqrt{s}$ denotes pp scattering energy. If
$x_{2}$ and $x_{1}$ are different then two different saturation scales emerge:
$Q_{\text{s}1}$ and $Q_{\text{s}2}$ Kharzeev:2001gp . Whether this leads to
violation of GS depends on the form of the saturation scale (for discussion of
different forms of scaling variable see e.g. Beuf:2008mf  and references
therein). Second, and – as we shall argue below – more importantly, when the
larger Bjorken $x=x_{1}$ for some $y$ leaves the domain of GS, _i.e._
$x_{1}>x_{\text{max}}$, violation of GS should appear due to the fact that one
of the scattering gluonic clouds becomes dilute and quark degrees of freedom
become important. We are going to show in a model-independent way that this is
what indeed does happen.

The theoretical formula for the multiplicity density in pp collisions is known
since 1981 Gribov:1981kg :

$\frac{dN}{dyd^{2}p_{\text{T}}}=\frac{C}{p_{\text{T}}^{2}}{\displaystyle\int}d^{2}\vec{k}_{\text{T}}\,\alpha_{\text{s}}\,\varphi_{1}(x_{1},\vec{k}_{\text{T}}^{2})\varphi_{2}(x_{2},(\vec{k}-\vec{p}\,)_{\text{T}}^{2}).$
(4)

Here $1/p_{\text{T}}^{2}$ corresponds to the $gg\rightarrow g$ cross section,
$\varphi_{1,2}$ are unintegrated gluon densities and $\alpha_{\text{s}}$
stands for strong coupling constant. Although in principle (4) describes gluon
production, one uses parton-hadron duality Dokshitzer:1991eq  to argue that it
can be also applied to particle multiplicities where constant $C$ takes care
of the hardonization effects.

At high energies and small $x$’s unintegrated gluon densities depend on
$k_{\text{T}}$ through the ratio $k_{\text{T}}^{2}/Q_{\text{s}}^{2}(x)$
GolecBiernat:1998js  – which is an underlying mechanism behind geometrical
scaling. Throughout this paper we shall use the following form of the
saturation scale GolecBiernat:1998js :

$Q_{\text{s}}^{2}(x_{1,2})=Q_{0}^{2}(e^{\pm
y}p_{\text{T}}/(x_{0}\sqrt{s}))^{-\lambda}$ (5)

although other possibilities have been also discussed in the literature
Beuf:2008mf . Parameters $Q_{0}\sim 1$ GeV$/c$ and $x_{0}\sim 10^{-3}$ depend
on a particular model of gluon densities, whereas exponent $\lambda$ can be
extracted from the data in a model-independent way. Indeed, by analyzing
multiplicity spectra at CMS we have found that for pp collisions
$\lambda=0.27$ McLerran:2010ex . Note that for $\lambda=0$ saturation scale is
equal to $Q_{0}$ and scaling variable $\tau=p_{\text{T}}^{2}/Q_{0}^{2}$ is
essentially transverse momentum squared in units of $Q_{0}^{2}$.

There are many sources of possible violation of GS in multiplicity spectra
given by Eq.(1). First – as already discussed – one of the Bjorken $x$’s (3)
can be outside the GS domain. Second, gluons of very low $k_{\text{T}}$ will
feel nonperturbative effects of the order of $\Lambda_{\text{QCD}}$. Next,
running of the strong coupling $\alpha_{\text{s}}$ will evidently produce
logarithmic corrections to GS. Finally, gluon fragmentation into physical
particles will introduce dependence on their masses, which should induce GS
violation in spectra of identified particles.

In this paper we shall concentrate on the first two effects which can be
studied by looking at rapidity dependence of the particle multiplicities in pp
collisions. For particles produced with $y\neq 0$ Bjorken $x$’s (3) are
different and we have in fact two different saturation scales Kharzeev:2001gp
. Hence instead of $F(\tau)$ in Eq.(1) we will have some other function
$\tilde{G}(\tau_{1},\tau_{2})$. This by itself does not mean that GS is
necessarily violated since we can always rewrite
$\tilde{G}(\tau_{1},\tau_{2})=G(\tau_{1},\rho)$ with
$\rho=Q_{\text{s}1}/Q_{\text{s}2}$. For fixed rapidity $y$ ratio $\rho$ is
constant for $Q_{\text{s}}$ of the form given by Eq.(5) and universal
dependence of multiplicity distribution upon scaling variable $\tau_{1}$ is
retained. Note that $F(\tau)=G(\tau,1)$.

Figure 1: Kinematic range of NA61/SHINE experiment in the $(W,p_{\mathrm{T}})$
plane. Data points are shown as stars, squares, circles and triangles. Shaded
areas denote regions where GS is expected to be violated for $y=0.1$. For
other rapidities (marked at the r.h.s. of the plot) GS violation takes place
above the respective dashed line.

On the other hand by looking at the spectra with increasing $y$ one can
eventually reach $x_{1}>x_{\mathrm{max}}$ and GS violation should be seen.
Luckily we have at our disposal very recent pp data from the NA61/SHINE
experiment at CERN NA61  where particle spectra at different rapidities
$y=0.1\div 3.5$ and five different energies have been measured for
$p_{\text{T}}=0.025\div 1.375$ GeV$/c$. For the present analysis we shall use
negative pion spectra, which has an advantage that one avoids possible GS
violation due to particle masses. The only problem with this piece of data is
that the scattering energies are rather low:
$W_{1_{,}\ldots_{,}5}=17.28,\;12.36,\;8.77,\;7.75$, and $6.28$ GeV.
Nevertheless, as we will show below, Bjorken $x$’s involved are small enough
for GS to be present. This is mainly due to the before-mentioned fact that in
DIS $x_{\text{max}}\sim 0.1$ Praszalowicz:2012zh ; Caola:2010cy ; for the
purpose of the present analysis we shall take $x_{\text{max}}=0.09$. Then GS
should be seen if $x_{1}<x_{\text{max}}$, _i.e._ for

$p_{\text{T}}<p_{\text{Tmax}}(W,y)=x_{\text{max}}W\,e^{-y}.$ (6)

On the other hand transverse momenta of produced gluons should be larger than
some nonperturbative scale $\Lambda$:

$p_{\text{T}}>p_{\text{Tmin}}=\Lambda$ (7)

for which we take $\Lambda=250$ MeV footnote . Having fixed the kinematical
range where GS should be present, we can have a look at kinematical range of
NA61/SHINE spectra shown in Fig. 1. The shaded area below
$p_{\text{Tmin}}=\Lambda$ is excluded for all rapidities. The shaded region in
an upper part of the plot is excluded for $y=0.1$, and dashed lines represent
$p_{\text{Tmax}}(W,y)$ as functions of $W$ for different rapidities $y$.
Therefore for given rapidity only points below these lines should exhibit GS.
Experimental points for different energies are represented by stars (17.28
GeV), squares (12.36 GeV), circles (8.77 GeV), and triangles (7.75 and 6.28
GeV). One can see from Fig. 1 that for $y=0.1$ GS region extends towards the
smallest NA61/SHINE energy. This is due to the fact that $x_{\rm max}$ is as
large as 0.09. By increasing $y$ we see that some points fall outside the GS
window and finally for $y\gtrsim 1.7$ no GS should be present in NA61/SHINE
data. One may note that both $x_{\text{max}}$ and $\Lambda$ together with
exponent $\lambda$ could be determined in a self-consistent way from the
NA61/SHINE data. This is beyond the scope of the present note and will be
presented elsewhere. Therefore our analysis has to be considered mostly as a
qualitative one.

Figure 2: Ratios $R_{1k}$ as functions of $\sqrt{\tau}$ for the lowest
rapidity $y=0.1$: a) for $\lambda=0$ when $\sqrt{\tau}=p_{\mathrm{T}}$ and b)
for $\lambda=0.27$ which corresponds to GS.

Limits (6) and (7) define GS window $\tau_{\text{min}}<\tau<\tau_{\text{max}}$
in scaling variable $\tau$

$\displaystyle\tau_{\text{max}}$
$\displaystyle=e^{-2y}x_{\text{max}}^{2}W^{2}/Q_{0}^{2}\,(x_{\text{max}}/x_{0})^{\lambda},$
$\displaystyle\tau_{\text{min}}$ $\displaystyle=e^{\lambda
y}\Lambda^{2}/Q_{0}^{2}\,(\Lambda/(x_{0}W))^{\lambda}.$ (8)

We see from (8) that for fixed $W$, $\tau_{\text{max}}$ falls exponentially
with rapidity $y$ much faster than $\tau_{\text{min}}$ is rising with $y$.
When $\tau_{\text{min}}\simeq\tau_{\text{max}}$ window for GS closes, and we
get from (8) that the larger $W$ the larger $y$ when this happens. For fixed
$y$ the GS window is growing with $W$.

Now we come to the formulation of a model-independent criterion that allows
one to asses whether GS is present or not. To this end we follow Refs.
McLerran:2010ex ; Praszalowicz:2012zh  and define ratios of multiplicities

$R_{ik}(\tau;y)=\frac{dN}{dyd^{2}p_{\text{T}}}(W_{i},\tau;y)/\frac{dN}{dyd^{2}p_{\text{T}}}(W_{k},\tau;y)$
(9)

which, according to (1), should be equal to unity if GS is present. Since GS
window is the largest for $W_{1}=17.28$ GeV, we form four ratios $R_{1k}$ with
$k=2,\ldots,5$ where index $k$ refers to NA61/SHINE energies mentioned above.
In Fig. 2 we plot ratios $R_{1k}$ as functions of $\sqrt{\tau}$ for the lowest
rapidity $y=0.1$ first for $\lambda=0$, _i.e._ essentially as functions of
$p_{\text{T}}$, and second for $\lambda=0.27$. We see that for $\lambda=0$ all
ratios $R_{1k}$ are larger than $1$ and rise with $\tau$ up to $R_{1k}\sim
1.5\div 6$. In contrast, for $\lambda=0.27$ for all ratios $R_{1k}$ there
exists a domain in $\sqrt{\tau}$ where, within the errors, they are equal to
1. We see that $\tau_{\text{min}}$ for $W_{2}=12.36$ GeV is approximately 0.6
while for $W_{5}=6.28$ GeV it is 0.8 or so. On the other hand for $W_{5}$ the
GS windows closes at $\sqrt{\tau}\simeq 1.5,$ whereas for $W_{2}$ it extends
further than 2.1. This is in qualitative agreement with limits (8), and as we
will see in the following, this trend continues once we increase $y$.

Looking at Fig. 1 we see that there is no qualitative difference between
rapidities $0.1$ and $0.3$, and this is what indeed can be seen in Fig. 3.a.
However, already for $y=0.7$ the lowest energy data are no longer in the
scaling region, and we see this clearly in Fig. 3.a. Further on, for rapidity
$y=0.9$ the second lowest energy data leave the GS window, and this is again
nicely substantiated by the behavior of $R_{14}$ shown in Fig. 3.c. Finally
for $y=1.3$ none of the tested energies $W_{2}\div W_{5}$ should exhibit GS,
and this is clearly confirmed by Fig. 3.d. Note that in all these cases the
reference points at scattering energy $W_{1}$ remain in the GS window,
therefore scaling violations of ratios $R_{1k}$ should be attributed to the
points at lower energies $W_{k}<W_{1}$.

It is somewhat surprising that relatively low energy NA61/SHINE data do show
GS at all. This is due to the fact that GS scaling works up to much higher
$x$’s than originally anticipated: $x_{\text{max}}\sim 0.1$. This has been
confirmed by direct analysis of DIS in Ref. Praszalowicz:2012zh  and also
indirectly by the present study.

In this paper we have explored NA61/SHINE NA61  negative pion spectra in pp
collisions taken at different rapidities $y$. In order to study GS in
multiplicity distributions we have formed ratios (9) that should be equal to 1
for scaling variable $\tau$ within the GS window (8). We have argued that
behavior of ratios $R_{1k}$ with increasing $y$ is in qualitative agreement
with the following picture of particle production in hadronic collisions. For
low $p_{\text{T}}$’s GS is violated due to the existence of the
nonperturbative energy scale $\Lambda$. For high transverse momenta, the
larger of two Bjorken $x$’s, namely $x_{1}$, crosses the maximal $x$ for which
GS is present, $x_{1}>x_{\text{max}}$, and GS is again violated. For
rapidities larger than 1.3, the window of GS closes for all energies $W_{k}$
but $W_{1}$, and no GS is seen in ratios $R_{1k}$. This behavior of GS for
different energies with varying $y$ is strikingly in qualitative agreement
with the kinematical constraints shown in Fig.1 and more quantitatively with
the range of the GS window given by Eq.(8).

Figure 3: Ratios $R_{1k}$ as functions of $\sqrt{\tau}$ for $\lambda=0.27$ and
for different rapidities a) $y=0.3$, b) $y=0.7$, c) $y=0.9$ and d) $y=1.3$.
With increase of rapidity, gradual closure of the GS window can be seen.

Our aim here was to point out that model-independent analysis of the
multiplicity distributions at different rapidities can provide an interesting
insight into the production mechanism of low and medium $p_{\text{T}}$ pions
from the point of view of gluon saturation and geometrical scaling. One
obvious reservation is that for higher rapidities one can force ratios
$R_{1k}$ to approach unity at the expense of adjusting $\lambda$. However,
very soon $\lambda$ gets bigger than $1$ and for rapidities of the order of 2
it has to be bigger than $3.$ The quality of such ”geometrical scaling” is
very poor, and – more importantly – there is no physical picture supporting
such big values of $\lambda$. This is one of the reasons for which one should
perform a more quantitative analysis of GS in pp collisions, which will be
presented elsewhere.

Let us finish by a remark that experimental data at high LHC energies would be
best suited for an analysis outlined in this paper. For the LHC energies GS
closes for very high rapidities up to $y\sim 8$. Since one needs data at
different rapidities, perhaps the best detector for this purpose would be
LHC-b.

The author wants to thank Marek Gazdzicki and Szymon Pulawski for the access
to the NA61/SHINE data, and Andrzej Bialas and Marek Gazdzicki for careful
reading of the manuscript and remarks. This work was supported by the Polish
NCN Grant 2011/01/B/ST2/00492.

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