# Exploring Text Selection in Augmented Reality Systems

Xinyi Liu<EMAIL_ADDRESS>Xi’an Jiaotong-Liverpool
UniversitySuzhouChina ,  Xuanru Meng<EMAIL_ADDRESS>Xi’an
Jiaotong-Liverpool UniversitySuzhouChina ,  Becky Spittle
<EMAIL_ADDRESS>Birmingham City UniversityBirminghamUK ,  Wenge Xu
<EMAIL_ADDRESS>Birmingham City UniversityBirminghamUK ,  BoYu Gao
<EMAIL_ADDRESS>Jinan UniversityGuangzhouChina and  Hai-Ning Liang
<EMAIL_ADDRESS>Xi’an Jiaotong-Liverpool UniversitySuzhouChina

(2022)

###### Abstract.

Text selection is a common and essential activity during text interaction in
all interactive systems. As Augmented Reality (AR) head-mounted displays
(HMDs) become more widespread, they will need to provide effective interaction
techniques for text selection that ensure users can complete a range of text
manipulation tasks (e.g., to highlight, copy, and paste text, send instant
messages, and browse the web). As a relatively new platform, text selection in
AR is largely unexplored and the suitability of interaction techniques
supported by current AR HMDs for text selection tasks is unclear. This
research aims to fill this gap and reports on an experiment with 12
participants, which compares the performance and usability (user experience
and workload) of four possible techniques (Hand+Pinch, Hand+Dwell, Head+Pinch,
and Head+Dwell). Our results suggest that Head+Dwell should be the default
selection technique, as it is relatively fast, has the lowest error rate and
workload, and has the highest-rated user experience and social acceptance.

Text Selection, Augmented Reality, Pointing Methods, Selection Mechanisms,
User Study

††journalyear: 2022††copyright: acmcopyright††conference: The 18th ACM
SIGGRAPH International Conference on Virtual-Reality Continuum and its
Applications in Industry; December 27–29, 2022; Guangzhou, China††booktitle:
The 18th ACM SIGGRAPH International Conference on Virtual-Reality Continuum
and its Applications in Industry (VRCAI ’22), December 27–29, 2022, Guangzhou,
China††price: 15.00††doi: 10.1145/3574131.3574459††isbn:
979-8-4007-0031-6/22/12††ccs: Human-centered computing Mixed / augmented
reality††ccs: Human-centered computing Gestural input††ccs: Human-centered
computing Text input††ccs: Human-centered computing User studies

Figure 1. The four text selection techniques explored in this research: (a)
Hand-based: Hand+Pinch and Hand+Dwell, (b) Head-based: Head+Pinch and
Head+Dwell. The experimental interface used in this research: (1) an
‘interaction panel’, (2) an ‘instruction panel’, (3) the ‘start’ button, and
(4) the ‘check’ button.

The four text selection techniques explored in this research: (a) Hand-based:
Hand+Pinch and Hand+Dwell, (b) Head-based: Head+Pinch and Head+Dwell.
Experimental interface setup: (1) an ‘interaction panel’, (2) an ‘instruction
panel’, (3) the ‘start’ button, and (4) the ‘check’ button.

##  1\. Introduction

Augmented reality (AR) head-mounted displays (HMDs) represent the next
generation of mobile computing devices that can transform how people engage
with digital information. Currently, AR users can read academic papers, make
personal notes111https://www.microsoft.com/en-
us/p/airnotes/9phsgp1kt88c?activetab=pivot:overviewtab, have live meetings
with colleagues222https://docs.microsoft.com/en-us/dynamics365/mixed-
reality/remote-assist/overview-hololens), and send instant messages. There has
been some prior work exploring the use of AR to support tasks surrounding text
manipulation (Xu et al., 2019). However, fundamental to any text manipulation
task, including highlighting, modifying, and creating documents, is text
selection, which is still largely unexplored on AR HMDs.

This work investigates a basic but essential and common task related to text
manipulation, i.e., text selection. Text selection is the first stage involved
in text editing tasks (Xu et al., 2019), and is the process of selecting text
fragments that need further manipulation (e.g., copying, cutting, or deleting)
or making notes on a document. As a foundational activity, text selection can
be used in a wide range of scenarios, such as (1) copying and pasting text
between different applications (e.g., instant messaging apps), (2)
highlighting text fragments for later reference while reading articles, and
(3) editing text in text boxes and fields in online forms. Darbar et al.
(Darbar et al., 2021) have explored using an external handheld device (a
smartphone) as an input medium for text selection, which has several
limitations: (1) the current positional tracking of the smartphone is not
practical (because of this, Darbar et al. had to use external optical-based
tracking devices), and (2) it is dependent on having a handheld device at all
times, which is not always convenient and practical.

To overcome these limitations, this paper explores existing interaction
techniques (hands-free or handheld-device-free—having no need for users to
hold a device in their hands; see examples provided in Figure 1) that can be
captured by the sensors that are built into commercial AR HMDs. Specifically,
we focus on the combination of pointing methods and selection mechanisms (Xu
et al., 2019), where the pointing method is used for identifying a text
fragment to be selected, and the selection mechanism is used to initiate and
finalize a selection (Meng et al., 2022; Xu et al., 2022). Although there have
been studies on interaction techniques for tasks like text entry in VR (Xu et
al., 2019) and object acquisition in AR (Brasier et al., 2020), these results
cannot be applied directly to text selection. This is because (1) text
selection tasks require users to hold the selection mechanism from the start
of selection to the end, a process that requires effective precision, control,
and focus over a period of time; (2) the density of text information is
usually high because letters and sentences tend to be close to one another;
and (3) given the limited field of view of AR HMDs, the letters are displayed
in an even smaller area, which makes selections more difficult.

We conducted a user study with twelve participants to evaluate the performance
and usability of four interaction techniques (Hand+Dwell, Hand+Pinch,
Head+Dwell, Head+Pinch) for AR HMDs (see Figure 1 for an illustration of the
techniques). The two most prominent pointing methods used for AR HMDs are
explored (head-based and hand-based), as well as two feasible selection
mechanisms (Dwell and Pinch), which were chosen based on findings from prior
work and results from our pilot tests. Our results suggest that Head+Dwell is
the leading candidate for text selection with AR HMDs since it is relatively
fast, has the lowest error rate and workload rating, has the highest user
experience rating, and is socially acceptable.

The main contribution of this work is a foundational empirical study of four
possible techniques for text selection on AR HMDs, regarding their
performance, user experience, and workload. Our work provides insights and
suggestions for AR HMDs to support text manipulation tasks for such devices.

##  2\. Related Work

###  2.1. Text Selection for AR/VR HMDs

There has been some recent work on text selection for VR HMDs (Meng et al.,
2022; Xu et al., 2022). However, text selection in AR is more problematic and
complex and differs from VR in several areas: (1) layer interference (Kruijff
et al., 2010); (2) low visibility, due to screen brightness and contrast, or
color and texture patterns that can interfere with the captured environment
(Kruijff et al., 2010); and (3) layout foreground-background issues (Xu et
al., 2019). In addition, AR HMDs require smooth, efficient tracking that is
capable of maintaining robustness under diverse environmental conditions, such
as changing light levels (Peddie, 2017). These factors affect text readability
and visibility and can introduce scene distortion, hence making it more
difficult to complete text selections (Kruijff et al., 2010).

There have been some studies exploring the use of other external devices for
text selection with AR HMDs. For instance, EYEditor (Ghosh et al., 2020) uses
a ring mouse for cursor navigation and text selection, where a button is used
for placing the cursor before and after a text fragment to be selected, while
the selection is made via a touchpad. Researchers have also investigated using
a smartphone for input on AR HMDs. For example, Lee et al. (LEE et al., 2020)
have used a force-sensitive smartphone as their input device, and users exert
a force on a thumb-sized circular button to select a desired text fragment.
Similarly, Darbar et al. (Darbar et al., 2021) have explored several methods
(continuous touch, discrete touch, spatial movement, and ray casting) that
rely on a smartphone for text selection with AR HMDs and found that continuous
touch is more efficient than the other three methods. However, just like
controller-based input, these proposed external input devices are not that
convenient, need extra external hardware, and are often not efficient and
usable (Ghosh et al., 2020). In general, because there has been limited
research, there is still a lack of understanding of what techniques are
supportive regarding text selection tasks with AR HMDs, especially those that
do not require any additional input device but rely solely on the hardware
features available on the HMDs themselves.

###  2.2. Handheld-device-free Pointing-based Interaction with AR HMDs

####  2.2.1. Head-based

Head-based pointing has been widely adopted as a standard method for pointing
at virtual objects in HMDs since it is accurate, comfortable, and convenient,
especially when handheld pointing devices are not available (Kytö et al.,
2018) but lacks an intrinsic mechanism for users to confirm an identified
target (Esteves et al., 2020). One selection method that has been widely
coupled with Head-based pointing is the Dwell technique. It has been
recommended as the first option in both handheld-device free and hands-free
scenarios for text selection for VR HMDs (Xu et al., 2022). Although it is
less error-prone (Xu et al., 2022), it is comparably slow and the predefined
dwell time might be perceived to be stressful for users during interaction, as
they often feel that they are continually being pushed towards making the next
selection quickly.

Performing bare hand gestures, such as a Pinch (i.e., closing the thumb and
index finger together), is another handheld-device-free method for indicating
a selection and can be used with Head-based pointing during interaction (Xu et
al., 2022). Prior work suggests that using a Pinch gesture is as effective as
clicking a button on a handheld controller and is faster than Dwell for object
acquisition tasks with eye-gaze pointing (Mutasim et al., 2021). The negative
aspect of Pinch is that users tend to leave their hand posture to a ”comfort
grip”, which can unintentionally activate selections, leading to high errors,
whereas Dwell has no such issues and error types (Pfeuffer et al., 2017). In
addition, using a hand gesture to indicate a selection has been found to cause
higher fatigue than Dwell (Yan et al., 2020).

####  2.2.2. Hand-based

Hand-based pointing is now possible on several AR and VR HMDs and is perceived
to be a natural and intuitive interaction method. Users can use hand-based
pointing to point at distant objects and then perform a hand gesture to
indicate a selection (typically a Pinch gesture). This method has a short
learning curve, but users tend to leave their hand posture in a ”comfort grip”
(Pfeuffer et al., 2017), as described previously, which can lead to more
errors. In this case, users can use Dwell to prevent the types of errors
caused by the ”comfort grip” tendency. In addition, it has been observed that
due to the relatively small hand tracking field of view and users’
unfamiliarity with new technology, novice users may inadvertently move their
hands outside the hand tracking area captured by an AR HMD’s tracking sensors,
which can lead to mistakes during interaction (Xu et al., 2020).

####  2.2.3. Eye Gaze-based

Eye tracking is becoming a standard feature of AR HMDs (e.g., HoloLens 2 and
Magic Leap series). It is a fast and effortless contextual input and it is
most powerful when combined with other selection methods such as Voice or
Pinch to confirm the user’s intent 333https://docs.microsoft.com/en-
us/windows/mixed-reality/design/eye-gaze-interaction. However, we did not
consider gaze because of its inaccuracy in selecting small targets (text
letters are smaller than the recommended 2∘ in reading angle)33footnotemark: 3
in dense areas (as texts are also usually placed very close to each other). We
tested the accuracy of the HoloLens 2’s eye tracking sensors for text
selection with five pilot users and confirmed that, as described on the
official website, it was not that stable for fixations when reading texts
within the small AR display.

####  2.2.4. Other Handheld-device-free Selection Methods

Eye blinking has been recently used for confirming selections (Lu et al.,
2020, 2021) and has been found to be a viable solution for confirming a text
selection for VR HMDs (Meng et al., 2022). To determine whether it is also
feasible for AR HMDs, we implemented eye blinks (Lu et al., 2020, 2021) and
asked our five pilot users to test the technique. Results revealed that it is
hard for users to stop their eyes from blinking while trying to look at the AR
screen carefully, especially for long text fragments. Users could adequately
indicate the starting selection point, but arriving at the end selection point
was challenging, as they would often blink their eyes unconsciously prior to
reaching the endpoint, thereby causing a large number of false positive
activations. Given these results, we did not consider eye blinks further.

Voice activation has been widely used as an input modality. Nevertheless, we
did not include it because: (1) speech interaction is not very robust as the
system may struggle to adapt to the range of inconsistencies present in
natural language (which includes people’s accents, dialects, and other
pronunciation patterns) (Spittle et al., 2022); (2) the recognition can be
affected by background noise when it is used in a public venue; and (3) using
voice input may affect nearby users in the work environment (e.g., co-workers)
and users found it to be not socially acceptable as a text confirming method
(Meng et al., 2022); our pilot study also confirmed it.

Neck Motions such as forward and backward movements along the depth dimension
(or z dimension from the users’ perspective) have been explored for
object/information activation tasks (Lu et al., 2020). However, we did not
include this method as prior work suggests that (1) these types of motions are
not precise enough when dealing with text content, (2) users dislike them as
they found them tiring and uncomfortable to perform, and (3) users found it is
not socially acceptable to perform in public (Meng et al., 2022). Our pilot
study with 5 users confirmed these findings.

###  2.3. Inclusion Criteria for the Techniques

We identified four usability criteria for the methods that can be used for
confirming a selection (that can work well with both Head-based and Hand-based
pointing).

  * •

C1: Simple, easy, and efficient to use. Text selection is a two-step process,
where selection confirmation needs to be well coordinated with the pointer
movement. With users controlling the pointer with their heads or hands while
paying attention to the highlighted text, selection should be simple, easy to
use, and fast/efficient, so that it is possible to perform the two tasks
almost simultaneously.

  * •

C2: Minimal error rate and workload. Both Head-based and Hand-based
interaction should be accurate, comfortable, and convenient to perform. As
such, the ideal situation is that the selection mechanism minimizes any
additional workload during text selection and has some degree of precision
while allowing fast interaction and minimizing false activations, as
recovering from errors during text selection can be difficult and frustrating.

  * •

C3: Accessible and mobility enabling. AR HMDs are projected to become
ubiquitous smart devices that people will use to interact on the go.
Consequently, they should be as portable as possible. Even when they are not
used outdoors, people often employ them for mobile applications and scenarios
(Spittle et al., 2022). As such, given that Head-based and Hand-based pointing
can now be achieved without using external tracking devices, the selection
mechanism should also be handheld-device-free and support users’ mobility.

  * •

C4: Socially acceptable. AR HMDs are meant to be highly portable and enable
interaction with multiple users in one physical space. Therefore, as prior
research has shown (Alallah et al., 2018; Pandey et al., 2021; Vergari et al.,
2021), the social acceptability of interactions used for AR HMDs can be an
important factor in determining their widespread adoption and usability. As
such, the interactions should also be socially acceptable and transferable to
a range of situations and use cases.

Table 1. Ratings for each criterion regarding the five possible selection mechanisms identified from the literature (0-3 ticks indicate ratings from worst to the best). (C1) Simple, easy, and efficient to use; (C2) Minimal error rate and workload; (C3) Accessible and mobility enabling; and (C4) Socially acceptable. Mechanism |  C1 |  C2 |  C3 |  C4
---|---|---|---|---
Dwell |  ✓✓✓ |  ✓✓✓ |  ✓✓✓ |  ✓✓✓
Pinch |  ✓✓✓ |  ✓✓ |  ✓✓✓ |  ✓✓
Eye blinks |  ✓✓✓ |  - |  ✓✓✓ |  ✓✓✓
Voice |  ✓✓ |  ✓✓ |  ✓✓✓ |  -
Neck |  - |  ✓ |  ✓✓✓ |  -

The criteria and the decision as to whether they should be chosen were based
on the literature review and pilot tests (see above sections). Table 1 shows
the ratings of the five possible selection methods found in the literature
against the four usability criteria. The ratings are based also on the results
of prior work together with results from our tests with 5 pilot users. To
qualify as a suitable candidate, a mechanism should have at least one tick for
each of the four criteria. While they meet C3 (mobility) well, only Dwell and
Pinch passed the overall evaluation. Both Voice and Neck did poorly in C4
(social acceptability) and because of this, as well as other weaknesses, they
were not considered in our experiment. Eye blinks were considered to be a good
candidate based on findings from prior work, especially in text entry.
However, we found that they were not suitable for text selection due to poor
ratings in C2 (error rate and workload).

##  3\. Experiment

###  3.1. AR Testbed Environment

The testbed environment was developed using Unity3D (v2019.4.30). Figure 1
shows the environment used in this experiment. An ‘interaction panel’ is
located in the center, from where the participant could use an interaction
technique to select a text fragment. Above the ‘interaction panel’, there is
an ‘instruction panel’ showing the target text that needs to be selected.
There are two buttons on the right-hand side, where clicking the ‘start’
button would start the timer, and clicking the ‘check’ button would check if
the selection is correct and record the time. Participants would only move on
to the next trial when a correct selection was made.

The parameters of the environment were defined according to recommendations
found in AR and VR literature and were determined through a pilot study with
five pilot testers. The length of the material was kept between 35 and 40
characters per line (including symbols and spaces) (Wei et al., 2020). A dark
color was used as the background for the panels (Kim et al., 2019), and
contrasting colored text was overlaid using the Arial typeface with 1.8∘
angular size to maximize legibility (Dingler et al., 2018). The main
interaction panel was located 2 meters in front of the user. The pilot users
confirmed that they were able to read the text clearly without any
difficulties. Also, the interface elements were clear and easy to understand,
and thus we ensured there were no issues with environmental lighting and
contrast conditions.

###  3.2. Evaluated Interaction Techniques

All of the following techniques were developed using the default input
functions provided by the MRTK Unity Plugin (v2.7).

####  3.2.1. Head-based Pointing

A cursor was attached to the end of an invisible ray, which extended from the
HMD towards the viewing direction (see Figure 1.b).

Head-based pointing + Dwell (Head+D). The user started the selection of the
desired text fragment by dwelling (maintaining cursor position for one second)
directly before the first letter and completed the selection by dwelling (one
second) again at the end of the text fragment. The dwell duration was
determined through our pilot study, which tested a range of thresholds from
400ms to 1s.

Head-based pointing + Pinch (Head+P). The user started the selection by
positioning the head cursor at the beginning of the text fragment and
performing the “Pinch” gesture. They then held the gesture until the head
pointer moved to the end of the target text fragment, and released the Pinch
gesture to end the selection.

####  3.2.2. Hand-based Pointing

Figure 1.a shows the two hand-based techniques implemented in our study. A
cursor was attached to the end of a ray rendered from the palm. We controlled
the lighting of the physical environment, based on the recommendations of the
HoloLens 2 official website 444https://docs.microsoft.com/en-
us/hololens/hololens-environment-considerations, to ensure the hand tracking
was reliable and consistent throughout the study.

Hand-based pointing + Dwell (Hand+D). Hand+D was analogous to Head+D, but
employed Hand-based pointing with a Dwell time.

Hand-based pointing + Pinch (Hand+P). Hand+P was analogous to Head+P, but used
Hand-based pointing in combination with Pinch.

To deliver a good interaction experience, we retained the default support and
feedback provided by the MRTK plugin. Specifically, we employed the following
implementation: (1) the hand ray visualization was enabled whereas the head
ray was invisible; (2) the end of the ray was akin to a donut-shaped cursor to
indicate the location where the ray intersected with a target object. The
cursor would change from being hollow to being filled to indicate a selection
had been made, with both Dwell and Pinch. In addition, we implemented the
following support and feedback for each selection: (1) the selected text was
highlighted in yellow; (2) the dwell time was displayed as a loading circle;
and (3) voice prompts were provided “Your selection was incorrect, please re-
select” if the text was selected incorrectly.

###  3.3. Design and Task

The experiment followed a within-subjects design with Interaction Techniques
(Head+D, Head+P, Hand+D, Hand+P) as the independent variable. For each
condition, participants completed a series of selection tasks, where they were
required to make text selections for different Sentence Lengths: (1) short (1
word) and (2) long (5-6 lines) fragments. Overall, participants completed 8
training trials (4 short, 4 long text fragments) and 20 experimental trials
(10 short, 10 long text fragments). Text fragments were randomly selected from
a corpus of standardized English reading assessments (Quinn et al., 2007). To
avoid learning effects, each text fragment appeared only once in a given
condition. The order of the Sentence Length was random, and the order of the
Interaction Technique was counterbalanced across participants. A total of 960
experimental trials were collected (12 participants × 4 interaction techniques
× 20 selections).

###  3.4. Participants and Apparatus

A total of 12 university students (6 males; 6 females), aged between 19 and 23
years were recruited for this experiment (M=21.4, SD=1.00). They were all
right-handed, had normal or corrected-to-normal vision, and had no
difficulties with arm and head movements (which we checked prior to the
experiment). Ten participants had previous experience with VR HMDs, and four
of them were regular users (daily or weekly). Nine participants had previous
experience with AR HMDs (they had used them in the last 3-6 months), but none
were frequent users. During the experiment, participants were seated in an
office chair and were allowed to utilize the armrests. The HoloLens 2 HMD was
used to conduct our study.

####  3.4.1. Measurements

To assess the text selection performance and experience, we collected the
following measurements:

  * •

Objective. (a) Task completion time: Time from when the participant clicked
the start button to the time the participant clicked the check button (when
the correct selection was made); (b) Error rate: the number of incorrect
selections (recorded by the Check button) compared to the total number of
selections.

  * •

Subjective. (a) Workload: NASA-TLX questionnaire (Hart and Staveland, 1988),
and (b) User Experience: User Experience Questionnaire (UEQ) (Laugwitz et al.,
2008). Qualitative feedback, regarding the advantages and disadvantages of
each interaction method, was also captured, together with user rankings of the
text selection techniques.

###  3.5. Procedure

Prior to the experiment, participants were informed of the purpose of the
research and filled out a demographics questionnaire to collect personal
anonymized information (i.e., age, experience with AR/VR, etc.). Before the
start of each condition, the corresponding text selection technique was
explained to the participants, and they were required to undergo training
where they completed 8 trials for each technique (4 short texts and 4 long
texts). For the formal trials, participants needed to complete 20 text
selections for each condition (as described in section 3.3). Participants were
allowed to rest for as long as they wanted between conditions. At the end of
each condition, participants completed the NASA-TLX and UEQ. At the end of the
experiment, they participated in a structured interview that collected their
preferences and rankings of the four techniques, plus any other feedback they
had.

###  3.6. Results

We used Shapiro-Wilks tests and Q-Q plots to check if the data was normally
distributed.

##### Performance analysis

For normally distributed data, two-way repeated measures ANOVAs were used with
Interaction Techniques (Head+D, Head+P, Hand+D, Hand+P) and Sentence Lengths
(short, long) as within-subjects variables. For non-normally distributed data,
we processed the data through an Aligned Rank Transform (ART) (Wobbrock et
al., 2011) before using repeated-measures ANOVAs with the transformed data.
Experience analysis. For normally distributed data, we used one-way repeated
measures ANOVAs with Interaction Techniques as the within-subjects variable.
Otherwise, we first processed the data through ART and then used repeated
measures ANOVAs with the transformed data.

For both analyses, we used Bonferroni correction for pairwise comparisons and
Greenhouse-Geisser adjustment for degrees of freedom where the assumption of
sphericity was violated. All tests were conducted with two-tailed p-values.

####  3.6.1. Performance

##### Task completion time

There was a statistically significant difference in the completion time for
each Sentence Length ($F_{1,77}=286.251,p<.001$). Post-hoc analysis with
Bonferroni correction suggested that, for all the techniques (all $p<.0001$),
the completion time for long-text tasks was longer than for short-text tasks.
There was no significant main effect of Interaction Techniques
($F_{3,77}=1.69,p=.175$) on task completion time, or an effect of Interaction
Techniques $\times$ Sentence Lengths ($F_{3,77}=0.79,p=.504$).

##### Error rate

A two-way repeated measures ANOVA yielded a significant main effect of
Interaction Techniques ($F_{3,77}=4.49,p<.01$) on error rate. Post-hoc
analysis with Bonferroni correction suggested that Head+D outperformed Hand+D
($p<0.05$). We could not find a significant main effect of Sentence Lengths
($F_{1,77}=0.68,p=.412$) or any effect of Interaction Techniques $\times$
Sentence Lengths ($F_{3,77}=1.10,p=.352$). Details of error rate results can
be found in Table 2.

Table 2. Performance data for each Interaction Technique for two Sentence Lengths, mean (SD). The top 3 techniques of each condition are presented with Roman numerals (I: yellow; II: purple; and III: green). Performance Metrics |  Sentence Length |  Head+D |  Head+P |  Hand+D |  Hand+P
---|---|---|---|---|---
Task completion time |  Short |  III: 4.56 (1.98) |  I: 3.86 (1.57) |  5.06 (2.50) |  II: 4.47 (1.82)
|  Long |  I: 7.59 (2.78) |  II: 7.93 (2.72) |  8.43 (3.33) |  III: 8.23 (2.70)
Error rate |  Short |  I: 6.34% (7.41%) |  III: 16.96% (10.68%) |  23.79% (15.32%) |  II: 11.67% (10.58%)
|  Long |  I: 10.00% (6.23%) |  III: 14.06% (8.51%) |  15.6% (13.08%) |  II: 11.40% (9.18%)

####  3.6.2. Experience

##### UEQ

The average UEQ scores for each Interaction Technique are Hand+D (M=-0.06,
SD=0.31), Hand+P (M=-0.01, SD=0.14), Head+D (M=0.27, SD=0.33), Head+P (M=0.10,
SD=0.26). ANOVA tests revealed a significant difference between Interaction
Techniques on the average UEQ scores ($F_{2.638,187.270}=14.818,p<.001$), with
post-hoc pairwise comparison tests suggesting that: (1) Head+D outperformed
Hand+D ($p<.001$) and Hand+P ($p<.01$); (2) Head+P performed better than
Hand+D ($p<.001$); and (3) Hand+P outperformed Hand+D ($p<.05$).

Regarding the UEQ subscales, there was a significant effect of Interaction
Techniques on Efficiency ($F_{3,33}=9.007,p<.005$). Post-hoc tests indicated
that Head+D had a higher Efficiency than Hand+D ($p<.005$) and Hand+P
($p<.005$). ANOVA tests also suggested a significant effect of Interaction
Techniques on Stimulation ($F_{3,33}=3.056,p<0.05$). However, we could not
find any significant difference between Interaction Techniques based on the
results from the post-hoc pairwise comparisons. No other significant effect
were found on Attractiveness ($F_{3,33}=2.154,p=0.112$), Perspicuity
($F_{3,33}=0.90,p=0.965$), Dependability ($F_{3,33}=0.391,p=0.760$), and
Novelty ($F_{3,33}=2.855,p=0.052$). Details of each UEQ subscale score can be
found in Figure 2.

Figure 2. UEQ subscale ratings of the evaluated techniques with respect to the
relative benchmark values.

##### Workload

ANOVA tests revealed a significant effect of Interaction Techniques
($F_{3,33}=7.098,p<.005$) on the overall workload. Pairwise post-hoc
comparisons suggested that Head+D required less workload than Hand+D
($p<.01$). The overall workload for each Interaction Technique is: Hand+D
(M=48.42, SD=17.68), Hand+P (M=37.61, SD=13.76), Head+D (M=24.17, SD=13.94),
Head+P (M=34.69, SD=23.45).

For NASA-TLX workload subscales, we observed a significant effect of
Interaction Techniques on Temporal Demand ($F_{3,33}=5.717,p<.01$) and Effort
($F_{3,33}=9.072,p<.001$). Post-hoc pairwise comparisons revealed that Head+D
had lower Temporal Demand and Effort than Hand+D (both $p<.01$). ANOVA tests
also indicated that there were significant effects of Interaction Techniques
on Performance ($F_{3,33}=5.298,p<.01$) and Frustration
($F_{3,33}=3.303,p<.05$). Post-hoc tests showed that Head+D had a
significantly better performance than Hand+P ($p<.05$). However, we could not
find any significant difference between techniques on Frustration. In
addition, ANOVA tests yielded no significant effect of Interaction Techniques
on Mental ($F_{3,33}=1.492,p=0.235$) and Physical Demand
($F_{3,33}=2.787,p=0.056$). Figure 3 shows the detailed results of the NASA-
TLX subscales.

Figure 3. The mean responses for the 6 subscales of the NASA TLX
questionnaire. Error bars indicate a 95% confidence interval.

##### Ranking

Head+D was the most popular technique, with ten participants ranking it first
and one ranking it second. This was followed by Head+P; one participant ranked
it first and seven ranked it second. The rankings of the Hand-based techniques
were generally worse, with the majority of participants ranking them third
(four voted for Hand+D and five for Hand+P) or fourth (five voted for Hand+D
and another five for Hand+P).

####  3.6.3. Qualitative Feedback

Feedback for Head-based techniques was mostly positive. For instance, Head+D
was perceived to be “easy and simple” (N=7), “fast” (N=5), and “stable” (N=2).
For Head+P, participants considered it as “novel” (N=7). However, there was
also some negative feedback. For Head+D, participants mentioned that “head
shaking” could lead to re-dwell (N=4) and that the technique could cause “sore
eyes” or “tiring eyes” from prolonged use (N=2). As for Head+P, participants
complained about “poor gesture recognition” (N=6) and the danger of becoming
“easily distracted” (N=1).

Hand-based techniques were generally perceived to be “novice and/or
interesting” (Hand+D: N=5; Hand+P: N=4), Hand+P was perceived to be
“convenient and easy to understand” (N=3). However, like Head+P, participants
complained about the gesture having “poor recognition accuracy” (N=6) and
being “difficult to perform” (N=2). Hand+D was largely perceived to be
“tiring” (N=6).

##  4\. Discussion

###  4.1. Performance

Our results suggest that the four evaluated interaction techniques (Head+D,
Head+P, Hand+D, Hand+P) have comparable task completion time. Head+D was found
to be a better option than Hand+D regarding error rate. Prior work found that
Dwell would outperform Pinch if using the same pointing technique (Mutasim et
al., 2021); however, this is not supported by our findings. Our results
suggest that Head+D did not outperform Head+P, nor did Hand+D outperform
Hand+P. As expected, we observe that the Sentence Length could affect the task
completion time, as participants needed to move further distances across the
paragraphs when selecting longer text fragments.

###  4.2. User Experience and Workload

We found Head+D to be the best technique among the 4 evaluated techniques. It
outperformed both Hand+D and Hand+P on the average UEQ score and efficiency
subscale, due to its good performance in task completion speed and accuracy.
This was followed by Head+P, which outperformed Hand+D in the average UEQ
rating. The poor ratings for Hand-based techniques could be due to hand/arm
fatigue (Jang et al., 2017) and tracking/recognition issues inherent in
HoloLens 2 (supported by participants’ comments), although it is one of the
best AR HMDs in the market. Although we recommend Head+D among these 4
techniques, it is worth noting that none of these techniques, including
Head+D, have any subscale reaching the “Above Average” to “Excellent” score
compared to the benchmark scores provided by the UEQ tool (Schrepp et al.,
2017). This suggests that users felt the overall interaction was “Bad” or
“Below Average” based on their prior experience with text selection on other
platforms. Consequently, a better text selection technique is desirable.

We asked participants how comfortable they would feel about performing the
techniques in public places and in front of others (e.g. co-workers, friends,
and strangers). In general, participants said that they would be comfortable
doing Head+D in front of others, as the technique is discreet. They said they
would not mind involving Hand-based interaction in public places, but if they
had a choice, they would choose not to. In terms of Selection Mechanism alone,
participants said that they would be more comfortable using Dwell, especially
with Head-based pointing. They stated that they would use Pinch when no other
less conspicuous choices were available.

Like user experience measurements, Head+D is generally the best technique for
workload, having a lower mean workload and requiring less Temporal Demand and
Effort than Hand+D. Head+D was also found to deliver better performance than
Hand+P, which is in line with previous work (Maier et al., 2011).

###  4.3. Usability Criteria (Revisited)

We revisited the Usability Criteria scores based on our results. Instead of
re-evaluating the selection mechanisms and pointing methods separately, we
considered the four combined techniques that were evaluated in the user study.
Of the two techniques using Dwell as their selection mechanism, Head+D
received the highest ratings. For the most part, Dwell complemented Head-based
pointing well, which resulted in the combined technique having the highest
ratings across the four criteria. These findings were similar to the ratings
for Dwell as a selection mechanism in standalone (see Table 1). On the other
hand, Hand+D did not attain the same positive results, as participants found
that, in general, Hand-based interaction was not as usable—that is, the
disadvantages of Hand-based pointing had a negative impact on the overall
usability and performance of the combined technique. As shown in Table 3, both
techniques that use pinch as their selection mechanism received a low rating
for C1 and C4. However, Head+P received a low rating for C2, but not Hand+P.
This is because users’ hands would often move outside the active hand tracking
area when used as a secondary input modality (i.e., for solely performing the
gesture). This would occur as users tended to keep their hands in a more
comfortable position (Xu et al., 2020; Chiu et al., 2019).

Table 3. Ratings for each usability criterion for all techniques based on the results of our experiment (0-3 ticks indicate ratings from worst to the best). (C1) Simple, easy, and efficient to use; (C2) Minimal error rate and workload; (C3) Accessible and mobility enabling; and (C4) Socially acceptable. Mechanism |  C1 |  C2 |  C3 |  C4
---|---|---|---|---
Head+Dwell |  ✓✓✓ |  ✓✓✓ |  ✓✓✓ |  ✓✓✓
Head+Pinch |  ✓ |  ✓ |  ✓✓✓ |  ✓
Hand+Dwell |  - |  - |  ✓✓✓ |  ✓
Hand+Pinch |  ✓ |  ✓✓ |  ✓✓✓ |  ✓

###  4.4. Key Takeaways and Lessons

  * •

Head+D should be provided as the default interaction technique for text
selection due to its relatively fast speed, lowest error rate, highest user
experience, and lowest workload among the four evaluated techniques.

  * •

Hand+P is recommended as an alternative option, as opposed to Head+P, since
participants mentioned that Hand+P was less distracting as their hands always
remained within the hand tracking volume.

  * •

Head+P and Hand+D should only be used when no better options are available due
to their poor ratings in all measures.

###  4.5. Limitations and Future Work

One limitation is that we only considered distant interaction (i.e., out of
users’ arms’ reach). However, there are cases where users need to interact
within arm’s reach (e.g., hold an instruction handbook). Future work will
investigate suitable text selection techniques for different close-range text
manipulation tasks. In addition, we did not consider eye gaze as a pointing
mechanism as it was not that stable for fixations when reading small texts. As
eye tracking and AR display technology advance further, we want to revisit
this approach and explore it as part of our future work.

AR HMDs have been used as an external tool to support text manipulation tasks
(i.e., reading, taking notes) (Li et al., 2019). In the future, building upon
the findings obtained from this study, we plan to explore the integration of
Head+D into the next steps of text manipulation, e.g., copy/cutting, deleting,
and transferring selected texts to other platforms. As suggested by Microsoft,
regarding the fundamentals of interaction in AR
555https://docs.microsoft.com/en-us/windows/mixed-reality/design/interaction-
fundamentals, “it’s best to follow the guidance for a single model from
beginning to end”.

##  5\. Conclusion

This work has evaluated four text selection techniques, which were defined by
combining different permutations of pointing methods (head-based, hand-based)
and selection mechanisms (Dwell, Pinch), by conducting a study with 12
participants completing text selection tasks with a commercial Augmented
Reality Head-Mounted Display. The experimental results show that Head+Dwell
should be considered the first choice for text selection in such devices since
it has a good performance (relatively fast speed and lowest error rate),
provides the best user experience, is perceived to have the lowest workload,
and is socially acceptable to use. Of the remaining techniques, Hand+Pinch can
be provided as an alternative solution, while the results suggest the other
two methods (Head+Pinch, Hand+Dwell) should be avoided.

###### Acknowledgements.

This work was supported in part by Xi’an Jiaotong-Liverpool University Key
Special Fund (#KSF-A-03), Natural Science Foundation of Guangdong Province
(#2021A1515012629), and Guangzhou Basic and Applied Basic Foundation
(#202102021131).

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#  Peccei-Quinn symmetry with residual symmetries

Pei-Hong Gu<EMAIL_ADDRESS>School of Physics, Jiulonghu Campus, Southeast
University, Nanjing 211189, China

###### Abstract

So far the null results from axion searches have enforced a huge hierarchy
between the Peccei-Quinn and electroweak symmetry breaking scales. Then the
inevitable Higgs portal poses a large fine tuning on the standard model Higgs
scalar. Now we find if the Peccei-Quinn global symmetry has a set of
residually discrete symmetries, these global and discrete symmetries can
achieve a chain breaking at low scales such as the accessible TeV scale. This
novel mechanism can accommodate some new phenomena including a sizable
coupling of the standard model Higgs boson to the axion.

##  I  Introduction

The most popular solution to the so-called strong CP problem is to introduce a
global Peccei-Quinn (PQ) symmetry pq1977 , which is traditionally called the
$U(1)_{\textrm{PQ}}$ symmetry. Through the color anomaly adler1969 ; bj1969 ;
ab1969 , the Nambu-Goldstone (NG) boson from the spontaneous PQ symmetry
breaking picks up a mass and hence becomes a pseudo NG boson, the axion
weinberg1978 ; wilczek1978 . However, the axion has not been observed in any
experiments. This stringently constrains the strength of the interactions
between the axion and the standard model (SM) particles kg2010 ; pdg2020 . In
fact the original PQ model with two Higgs doublets was shortly ruled out.
Currently the Kim-Shifman-Vainstein-Zakharov (KSVZ) model kim1979 ; svz1980
and the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model dfs1981 ;
zhitnitsky1980  are widely adopted for decreasing the coupling of the axion to
the SM.

In the KSVZ and DFSZ invisible axion models, the spontaneous PQ symmetry
breaking should take place far far above the weak scale to evade all
experimental limits from the mixing of the axion to the $\pi$ and $\eta$
mesons kg2010 ; pdg2020 . Accordingly, the accompanying new particles in these
models will be very heavy, i.e. of the order of the PQ symmetry breaking
scale, unless the related couplings are artificially chosen to be very small.
Hence they will be completely isolated from experimental verification. On the
theoretical point of view, it is also difficult to naturally explain the huge
hierarchy between the PQ and electroweak symmetry breaking scales. With such
hierarchy, unless the inevitable Higgs portal has an extremely small coupling,
its contribution should have a large cancellation with the rarely quadratic
term of the SM Higgs scalar. This problem plagues all of the invisible axion
models. In this sense, we probably should say the high-scale PQ symmetry
breaking provides a solution to the strong CP problem by paying a price of
additionally fine tuning on the SM Higgs scalar.

In an early work mrs2001 , the authors tried to realize a theory with low-
scale PQ symmetry breaking by introducing a large extra dimension and an
anomalous $U(1)_{A}$ gauge symmetry. In this model, two Higgs scalars in our
brane could obtain their hierarchical vacuum expectation values (VEVs) after
another Higgs scalar developed its VEV in a distant brane. The $U(1)_{A}$
gauge field then could eat the most fraction of the NG boson coupling to a
pair of new colored fermions. This could give a suppressed coupling of the
axion to the new colored fermions and hence could allow an invisible axion
from a low-scale PQ symmetry breaking. This model would be more attractive if
it had no gauge anomalies.

In the present work, we shall propose a novel mechanism to lower the PQ
symmetry breaking scale without any anomalous gauge symmetries. The key in our
mechanism is to make the PQ global symmetry have a set of residually discrete
symmetries by assigning proper PQ charges to the related Higgs scalars. Then
the axion can appear if and only if the PQ symmetry and its residual
symmetries are all broken spontaneously. In this chain breaking of the PQ and
residual symmetries, the Higgs scalar(s) coupling to the colored fermions can
only contribute a tiny fraction to the axion. As a result, the low breaking
scales of these global and discrete symmetries can still allow a highly
suppressed coupling of the axion to the colored fermions. In particular, when
the PQ symmetry breaking scale is near the electroweak one, the SM Higgs boson
can sizably couple to the axion through the Higgs portal, meanwhile, the new
fermions in the KSVZ model or the new scalars in the DFSZ model can occur at
the TeV scale to be verified experimentally.

##  II The chain breaking of a global symmetry and its residual symmetries

For demonstration we first consider a simple system with two singlet scalars,

$\displaystyle\sigma_{1}(1)\,,~{}~{}\sigma_{n}(q_{n})\,.$ (1)

Here and thereafter the numbers in the brackets following the fields are the
charges under a $U(1)_{G}$ global symmetry. In order to realize this global
symmetry, we do not constrain the model at renormalizable level. Instead, we
give the scalar potential up to dimension-$(1+q_{n})$, i.e.

$\displaystyle V$ $\displaystyle=$
$\displaystyle\mu_{1}^{2}\sigma^{\dagger}_{1}\sigma_{1}+\lambda_{11}(\sigma^{\dagger}_{1}\sigma_{1})^{2}+\mu_{n}^{2}\sigma^{\dagger}_{n}\sigma_{n}+\lambda_{nn}(\sigma^{\dagger}_{n}\sigma_{n})^{2}$
(2)
$\displaystyle+2\lambda_{1n}\sigma^{\dagger}_{1}\sigma_{1}\sigma^{\dagger}_{n}\sigma_{n}+\frac{1}{\Lambda^{q_{n}-3}}(\sigma^{\dagger}_{n}\sigma^{q_{n}}_{1}+\textrm{H.c.})$
$\displaystyle+\sum_{x+y=3}^{\textrm{min}\\{\frac{1}{2}q_{n},\frac{1}{2}(q_{n}+1)\\}}\frac{c_{xy}}{\Lambda^{2x+2y-4}}(\sigma_{1}^{\dagger}\sigma_{1})^{x}(\sigma_{n}^{\dagger}\sigma_{n})^{y}\,,$

where the last but one term actually defines the global symmetry (1).

For a proper parameter choice, we can require the scalar $\sigma_{n}$ to
develop the VEV before the other scalar $\sigma_{1}$. In this case, the
initially global symmetry $U(1)_{G}$ can have a residually discrete symmetry
$Z_{q_{n}}$ due to the last but one term in Eq. (2). The symmetry breaking
pattern is nothing but

$\displaystyle
U(1)_{G}\stackrel{{\scriptstyle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle\langle\sigma_{n}\rangle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle}}{{\rightarrow}}Z_{q_{n}}\stackrel{{\scriptstyle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle\langle\sigma_{1}\rangle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle}}{{\rightarrow}}I\,.$
(3)

After the scalars $\sigma_{1,n}$ acquire their VEVs $v_{1,n}$, they can be
expressed by

$\displaystyle\sigma_{1}=\frac{1}{\sqrt{2}}(v_{1}+S_{1}+iP_{1})\,,~{}~{}\sigma_{n}=\frac{1}{\sqrt{2}}(v_{n}+S_{n}+iP_{n})\,,$
(4)

with $S_{1,n}$ being the Higgs bosons while $P_{1,n}$ being the pseudo
scalars.

Since the symmetry breaking (3) only involves one global symmetry, the two
pseudo scalars $P_{1,n}$ should give one massless NG boson and one massive
pseudo scalar. In fact, by taking the extreme condition into account,

$\displaystyle\frac{\partial V}{\partial v_{1}}=0\,,~{}~{}\frac{\partial
V}{\partial v_{n}}=0\,,$ (5)

we can deduce the mass terms of the two pseudo scalars $P_{1,n}$ to be

$\displaystyle V$ $\displaystyle\supset$
$\displaystyle-\frac{v_{1}^{q_{n}-2}}{4(\sqrt{2}\Lambda)^{q_{n}-3}v_{n}}\left(q_{n}v_{n}P_{1}-v_{1}P_{n}\right)^{2}\,.$
(6)

Therefore, the mass eigenstates should be

$\displaystyle\hat{P}_{1}=\frac{q_{n}v_{n}P_{1}-v_{1}P_{n}}{\sqrt{v_{1}^{2}+q^{2}_{n}v_{n}^{2}}}\,,~{}~{}a=\frac{v_{1}P_{1}+q_{n}v_{n}P_{n}}{\sqrt{v_{1}^{2}+q^{2}_{n}v_{n}^{2}}}\,,$
(7)

with the mass eigenvalues,

$\displaystyle
m_{\hat{P}_{1}}^{2}=-\frac{v_{1}^{q_{n}-2}(v_{1}^{2}+q^{2}_{n}v_{n}^{2})}{2(\sqrt{2}\Lambda)^{q_{n}-3}v_{n}}\,,~{}~{}m_{a}=0\,.$
(8)

Remarkably, $P_{1}$ rather than $P_{n}$ can contribute a dominant fraction to
$\hat{P}_{1}$ but a tiny fraction to $a$ if $v_{1,n}$ and $q_{n}$ match the
condition $v_{1}\ll q_{n}v_{n}$. In this case, we can still have the
flexibility to assign $q_{n}\gg 1$ even if we take $v_{1}\sim v_{n}$.

In the above effective theory, the $U(1)_{G}$ charge $q_{n}$ is expected to be
a very big number. If such number requires an explanation, it can be induced
in some renormalizable models. For example, we can replace the scalar
potential (2) by the following one,

$\displaystyle V$ $\displaystyle=$
$\displaystyle\sum_{i,j=1}^{n}\left(\mu_{i}^{2}\sigma_{i}^{\dagger}\sigma_{i}+\lambda_{ij}\sigma_{i}^{\dagger}\sigma_{i}\sigma_{j}^{\dagger}\sigma_{j}\right)$
(9)
$\displaystyle+\sum_{i=2}^{n}\rho_{i}\left(\sigma_{i}^{\dagger}\sigma_{i-1}^{z_{i}}+\textrm{H.c.}\right),~{}~{}(z_{i}=2~{}\textrm{or}~{}3)\,.$

Here the singlet scalars $\sigma_{1,...,n}$ carry the $U(1)_{G}$ charges as
below,

$\displaystyle\sigma_{1}(1)\,,~{}~{}\sigma_{i}(q_{i})~{}~{}\textrm{with}~{}~{}q_{i}=\prod_{j=2}^{i\geq
2}z_{j}\,.$ (10)

Then we can require the symmetry breaking pattern to be

$\displaystyle
U(1)_{G}\stackrel{{\scriptstyle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle\langle\sigma_{n}\rangle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle}}{{\rightarrow}}Z_{q_{n}}\stackrel{{\scriptstyle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle\langle\sigma_{n-1}\rangle}}{{-\\!\\!\\!-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle}}{{\rightarrow}}Z_{q_{n-1}}\,...\,Z_{q_{2}}\stackrel{{\scriptstyle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle\langle\sigma_{1}\rangle}}{{-\\!\\!\\!-}}\\!\\!\\!\stackrel{{\scriptstyle}}{{\rightarrow}}I\,.$
(11)

By inserting the expressions

$\displaystyle\sigma_{i}=\frac{1}{\sqrt{2}}(v_{i}+S_{i}+iP_{i})\,,~{}~{}(i=1,...,n)\,,$
(12)

into the scalar potential (9), we in principle can solve the VEVs
$v_{1,...,n}$ by minimising the potential, i.e. $\partial V/\partial v_{i}=0$,
and then can obtain the mass terms of the Higgs bosons $S_{1,...,n}$ and the
pseudo scalars $P_{1,...,n}$. According to the $U(1)_{G}$ global symmetry
breaking, the $n$ pseudo scalars $P_{1,...,n}$ should leave $n-1$ massive
pseudo scalars $\hat{P}_{1,...,n-1}$ and one massless NG boson $a$. For
simplicity we do not try to give the complicated expressions of
$\hat{P}_{1,...,n-1}$. Instead we only give the elegant expression of $a$,
i.e.

$\displaystyle
a=\frac{v_{1}P_{1}+\sum_{i=2}^{n}q_{i}v_{i}P_{i}}{\sqrt{v_{1}^{2}+\sum_{i=2}^{n}(q_{i}v_{i})^{2}}}~{}~{}\textrm{with}~{}~{}m_{a}=0\,.$
(13)

Clearly, $P_{1}$ can only give a tiny contribution to $a$ if $q_{n}\gg 1$ and
$v_{1}\sim v_{2}\sim...\sim v_{n-1}\sim v_{n}$.

We emphasize that the large $U(1)_{G}$ charges in the above demonstrations
will not plague any problems because the $U(1)_{G}$ global symmetry has no
perturbation requirement.

##  III The invisible axion from chain symmetry breaking

In order to identify the above $U(1)_{G}$ symmetry with a PQ symmetry, we
introduce a pair of new color-triplet fermions $Q_{L,R}$ with a hypercharge
$-1/3$ or $+2/3$. These new fermions $Q_{L,R}$ then can have a Yukawa coupling
with the previously singlet scalar $\sigma_{1}$, i.e.

$\displaystyle\mathcal{L}\supset-
y_{Q}\left(\sigma_{1}\bar{Q}_{L}Q_{R}+\textrm{H.c.}\right)~{}~{}\textrm{for}~{}~{}Q_{L}(0)\,,~{}~{}Q_{R}(-1)\,.$
(14)

After the singlet scalar $\sigma_{1}$ acquires its VEV $v_{1}$, the chiral
fermions $Q_{L,R}$ can form a mass eigenstate, i.e.

$\displaystyle\mathcal{L}$ $\displaystyle\supset$ $\displaystyle-
M_{Q}\left(\bar{Q}_{L}Q_{R}+\textrm{H.c.}\right)=-M_{Q}\bar{Q}Q$ (15)
$\displaystyle\textrm{with}~{}~{}M_{Q}=\frac{1}{\sqrt{2}}y_{Q}v_{1}\,.$

At the same time, the pseudo scalar $P_{1}$ from the singlet scalar
$\sigma_{1}$, see Eq. (4) or (12), can couple to the axial-vector current of
new quark $Q$, i.e.

$\displaystyle\mathcal{L}$ $\displaystyle\supset$
$\displaystyle-i\frac{y_{Q}}{\sqrt{2}}P_{1}\bar{Q}\gamma_{5}Q=-\frac{P_{1}}{2v_{1}}\partial_{\mu}\left(\bar{Q}\gamma_{5}\gamma^{\mu}Q\right)\,.$
(16)

Here we have made use of the Dirac equation.

Clearly, if there were no chain breaking (3) or (11), this $U(1)_{G}$ global
symmetry would be the usual PQ symmetry and this model would be just a KSVZ
invisible axion model, where the pseudo scalar $P_{1}$ fully gives the axion
$a$, while the VEV $v_{1}$ fully determines the axion decay constant $f_{a}$.
Now as shown in Eq. (7) or (13), the fraction of the axion $a$ in the pseudo
scalar $P_{1}$ is just

$\displaystyle
P_{1}=\frac{v_{1}}{f_{\sigma}}a+...~{}~{}\textrm{with}~{}~{}f_{\sigma}=\left\\{\begin{array}[]{ll}\sqrt{v_{1}^{2}+q^{2}_{n}v_{n}^{2}}\\\\[2.84526pt]
\textrm{or}\\\\[2.84526pt]
\sqrt{v_{1}^{2}+\sum_{i=2}^{n}(q_{i}v_{i})^{2}}\,.\end{array}\right.$ (20)

Thus the true coupling between the axion $a$ and the new quark $Q$ should be

$\displaystyle\mathcal{L}\supset-\frac{a}{f_{a}}\partial_{\mu}\left(\bar{Q}\gamma_{5}\gamma^{\mu}Q\right)~{}~{}\textrm{with}~{}~{}f_{a}=2f_{\sigma}\,.$
(21)

We now apply the chain breaking (3) or (11) to the DFSZ model with two Higgs
doublets, i.e.

$\displaystyle\mathcal{L}\supset-
y_{d}\bar{q}_{L}\phi_{d}d_{R}-y_{u}\bar{q}_{L}\tilde{\phi}_{u}u_{R}-\rho\sigma_{1}\phi_{u}^{\dagger}\phi_{d}+\textrm{H.c.}\,.$
(22)

Here the SM quarks and the two Higgs doublets carry the $U(1)_{G}$ charges as
below,

$\displaystyle q_{L}(0)=\left[\begin{array}[]{c}u_{L}\\\\[5.69054pt]
d_{L}\end{array}\right],~{}~{}d_{R}(-1/2),~{}~{}u_{R}(-1/2),$ (25)
$\displaystyle\phi_{d}(-1/2)=\left[\begin{array}[]{c}\phi_{d}^{+}\\\\[5.69054pt]
\phi_{d}^{0}\end{array}\right],~{}~{}\phi_{u}(+1/2)=\left[\begin{array}[]{c}\phi_{u}^{+}\\\\[5.69054pt]
\phi_{u}^{0}\end{array}\right].$ (30)

When these Higgs doublets develop their VEVs to drive the $SU(2)_{L}\times
U(1)_{Y}\rightarrow U(1)_{em}$ electroweak symmetry breaking, they can be
rewritten by

$\displaystyle\phi_{d}$ $\displaystyle=$
$\displaystyle\left[\begin{array}[]{c}\phi_{d}^{+}\\\\[5.69054pt]
(v_{d}+h_{d}+iP_{d})/\sqrt{2}\end{array}\right],$ (33) $\displaystyle\phi_{u}$
$\displaystyle=$
$\displaystyle\left[\begin{array}[]{c}\phi_{u}^{+}\\\\[5.69054pt]
(v_{u}+h_{u}+iP_{u})/\sqrt{2}\end{array}\right],$ (36)

with $v_{d,u}$ being the VEVs, $h_{d,u}$ being the Higgs bosons and $P_{d,u}$
being the pseudo scalars.

The doublets $\phi_{d,u}$ and the singlets $\sigma_{1,n}$ or
$\sigma_{1,...,n}$ should totally leave four NG bosons according to the
electroweak gauge symmetry breaking and the PQ global symmetry breaking. As
usual, the three NG bosons,

$\displaystyle
G^{\pm}=\frac{v_{u}}{v_{\phi}}\phi^{\pm}_{u}+\frac{v_{d}}{v_{\phi}}\phi^{\pm}_{d}\,,~{}~{}G^{0}=\frac{v_{u}}{v_{\phi}}P_{u}+\frac{v_{d}}{v_{\phi}}P_{d}$
$\displaystyle\textrm{with}~{}~{}v_{\phi}=\sqrt{v_{d}^{2}+v_{u}^{2}}=246\,\textrm{GeV}\,,$
(37)

should be eaten by the three SM gauge bosons $W^{\pm}$ and $Z^{0}$. As for the
forth one, the axion $a$, it should be

$\displaystyle a$ $\displaystyle=$
$\displaystyle\frac{(v_{d}P_{u}-v_{u}P_{d})v_{d}v_{u}/v^{2}_{\phi}+v_{1}P_{1}+q_{n}v_{n}P_{n}}{\sqrt{v_{d}^{2}v_{u}^{2}/v^{2}_{\phi}+f_{\sigma}^{2}}}$
$\displaystyle\textrm{with}~{}~{}f_{\sigma}=\sqrt{v_{1}^{2}+(q_{n}v_{n})^{2}}\,,$
or $\displaystyle a$ $\displaystyle=$
$\displaystyle\frac{(v_{d}P_{u}-v_{u}P_{d})v_{d}v_{u}/v^{2}_{\phi}+v_{1}P_{1}+\sum_{i=2}^{n}q_{i}v_{i}P_{i}}{\sqrt{v_{d}^{2}v_{u}^{2}/v^{2}_{\phi}+f_{\sigma}^{2}}}$
(38)
$\displaystyle\textrm{with}~{}~{}f_{\sigma}=\sqrt{v_{1}^{2}+\sum_{i=2}^{n}(q_{i}v_{i})^{2}}\,.$

Then the couplings of the axion to the SM quarks can be given by

$\displaystyle\mathcal{L}$ $\displaystyle\supset$
$\displaystyle-i\frac{y_{d}}{\sqrt{2}}P_{d}\bar{d}\gamma_{5}d+i\frac{y_{u}}{\sqrt{2}}P_{u}\bar{u}\gamma_{5}u$
(39) $\displaystyle=$
$\displaystyle-\frac{P_{d}}{2v_{d}}\partial_{\mu}\left(\bar{d}\gamma_{5}\gamma^{\mu}d\right)+\frac{P_{u}}{2v_{u}}\partial_{\mu}\left(\bar{u}\gamma_{5}\gamma^{\mu}u\right)$
$\displaystyle=$
$\displaystyle-\frac{a}{f_{a}}\left(\frac{v_{d}^{2}}{v_{\phi}^{2}}\partial_{\mu}\bar{d}\gamma_{5}\gamma^{\mu}d+\frac{v_{u}^{2}}{v_{\phi}^{2}}\partial_{\mu}\bar{u}\gamma_{5}\gamma^{\mu}u\right)$
$\displaystyle\textrm{with}~{}~{}f_{a}=2\sqrt{v_{d}^{2}v_{u}^{2}/v_{\phi}^{2}+f_{\sigma}^{2}}\simeq
2f_{\sigma}\gg v_{\phi}\,.$

Currently, the null results from axion searches have put a low limit on the
axion decay constant, i.e. $f_{a}\gtrsim 10^{9}\,\textrm{GeV}$. This
constraint can be satisfied in our mechanism even if the PQ symmetry and its
residual symmetries are all broken at the TeV scale. For example, in the
renormalizable models (9), we can simplify

$\displaystyle v_{1,...,n}\equiv v_{\sigma}\,,~{}~{}z_{1,...,n}\equiv 3\,,$
(40)

to produce

$\displaystyle f_{a}$ $\displaystyle\simeq$ $\displaystyle
2v_{\sigma}\sqrt{\frac{9^{n}-1}{8}}=3\times 10^{9}\,\textrm{GeV}$ (41)
$\displaystyle\textrm{for}~{}~{}v_{\sigma}=10\,v_{\phi}~{}~{}\textrm{and}~{}~{}n=14\,.$

##  IV  Other phenomena

In the usual KSVZ and DFSZ invisible axion models, the new particles should be
of the order of the PQ symmetry breaking scale and hence they could not leave
any signals to be verified experimentally, unless we do some fine tuning on
the related couplings. However, our models can allow the PQ symmetry and its
residual symmetries to be spontaneously broken at some low scales such as the
TeV scale. These low-scale symmetry breaking could naturally lead to some
observable phenomena at colliders.

The SM Higgs doublet $\phi$, which is one of the linear combinations of the
two Higgs doublets $\phi_{d,u}$ in the DFSZ model,

$\displaystyle\phi=\frac{v_{d}}{v_{\phi}}\phi_{d}+\frac{v_{u}}{v_{\phi}}\phi_{u}\,,~{}~{}\eta=\frac{v_{u}}{v_{\phi}}\phi_{d}-\frac{v_{d}}{v_{\phi}}\phi_{u}\,,$
(42)

can have the quartic couplings with the singlet scalars $\sigma_{1,n}$ or
$\sigma_{1,...,n}$, besides its rarely quadratic term, i.e.

$\displaystyle V$ $\displaystyle\supset$
$\displaystyle\mu_{\phi}^{2}\phi^{\dagger}\phi+\lambda_{\sigma_{1}\phi}\sigma_{1}^{\dagger}\sigma_{1}\phi^{\dagger}\phi+\lambda_{\sigma_{n}\phi}\sigma_{n}^{\dagger}\sigma_{n}\phi^{\dagger}\phi\,,$
or $\displaystyle V$ $\displaystyle\supset$
$\displaystyle\mu_{\phi}^{2}\phi^{\dagger}\phi+\sum_{i=1}^{n}\lambda_{\sigma_{i}\phi}\sigma_{i}^{\dagger}\sigma_{i}\phi^{\dagger}\phi\,.$
(43)

With these Higgs portal, the full quadratic term of the SM Higgs doublet
should be

$\displaystyle V$ $\displaystyle\supset$
$\displaystyle\left(\mu_{\phi}^{2}+\frac{1}{2}\lambda_{\sigma_{1}\phi}v_{1}^{2}+\frac{1}{2}\lambda_{\sigma_{n}\phi}v_{n}^{2}\right)\phi^{\dagger}\phi\,,$
or $\displaystyle V$ $\displaystyle\supset$
$\displaystyle\left(\mu_{\phi}^{2}+\frac{1}{2}\sum_{i=1}^{n}\lambda_{\sigma_{i}\phi}v_{i}^{2}\right)\phi^{\dagger}\phi\,.$
(44)

Obviously, for a high-scale PQ symmetry breaking, the Higgs portal should be
extremely weak in order to give the SM Higgs doublet, otherwise, there should
be a large cancellation among the terms in the brackets. In fact, we should
take $\lambda_{\sigma_{i}\phi}\lesssim 10^{-14}$ for $v_{i}\gtrsim
10^{9}\,\textrm{GeV}$ and
$\mu_{\phi}^{2}=\mathcal{O}((100\,\textrm{GeV})^{2})$. Now the Higgs portal
couplings need not be too small because the PQ symmetry and its residual
symmetries are allowed to be broken near the weak scale. Then the Higgs boson
$h$ from $\phi$ can have a sufficient mixing with the Higgs bosons $S_{1,n}$
from $\sigma_{1,n}$ or $S_{1,...,n}$ from $\sigma_{1,...,n}$. This mixing of
order $\lambda_{\sigma_{i}\phi}v_{\phi}/v_{i}$ is small enough so that $h$ can
behave almost exactly like the SM Higgs boson. However, the effective coupling
of the SM Higgs boson to the axion,

$\displaystyle V\supset\frac{1}{2}\lambda_{ah}v_{\phi}ha^{2}\,,$ (45)

can be expected to significantly affect the invisible decay width of the SM
Higgs boson as well as the scattering of axion off electron. Note the
annihilating and scattering processes by this effective coupling can safely
decouple above the QCD scale and hence will not change the other phenomena of
the invisible axion.

The new quark $Q$ in the KSVZ model now is naturally allowed at the TeV scale
and also mixes with the down-type quarks $d$ or the up-type quarks $u$.
Through its single or pair production, the TeV-scale $Q$ can be verified at
the LHC atlas2012 ; cms2018 . For example, the search is sensitive to both
charged current and neutral current processes, $pp\rightarrow Qq\rightarrow
Wqq^{\prime}$ and $pp\rightarrow Qq\rightarrow Zqq^{\prime}$ with a leptonic
decay of the vector gauge boson. Note the new quark $Q$ can always have a TeV-
scale mass in the usual KSVZ model as long as the Yukawa coupling in Eq. (14)
is small enough dmt2014 . However, the TeV-scale $Q$ in our mechanism can
contribute to the $h\rightarrow\gamma\gamma$ and $h\rightarrow gg$ channels
through the unsuppressed Yukawa and Higgs portal interactions.

As for the DFSZ model in our mechanism, it can become a typical two Higgs
doublet model with rich phenomena bhp1990  after the PQ symmetry and its
residual symmetries are all broken at the TeV scale. Actually the non-SM Higgs
doublet $\eta$ in Eq. (42) could be at the TeV scale without fine tuning the
Higgs portal. Such Higgs doublet has been studied in a lot of literatures.

##  V  Conclusion

In this work, we have proposed a low-scale PQ symmetry breaking without
introducing any anomalous gauge symmetries. Specifically, the PQ global
symmetry should have a set of residually discrete symmetries. In order to
generate the axion, the PQ symmetry and its residual symmetries should be all
broken spontaneously. In this chain breaking of the PQ and residual
symmetries, the Higgs scalar(s) coupling to the colored fermions can only have
a negligible contribution to the axion. So, the low breaking scales of these
global and discrete symmetries can be consistent with a highly suppressed
coupling of the axion to the colored fermions. For such PQ symmetry with
residual symmetries, the SM Higgs boson can sufficiently couple to the axion
through the Higgs portal, meanwhile, the new fermions in the KSVZ model or the
new scalars in the DFSZ model can have the masses at the TeV scale.

Acknowledgement: The author would like to thank Yu Gao, Xiao-Gang He, Tianjun
Li, Ernest Ma, Rabi N. Mohapatra, Utpal Sarkar and Qiaoli Yang for useful
communications. This work was supported in part by the Fundamental Research
Funds for the Central Universities.

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