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# VALID: A perceptually validated Virtual Avatar Library for Inclusion and
Diversity

Tiffany D. Do<EMAIL_ADDRESS>University of Central
FloridaOrlandoFloridaUSA ,  Steve Zelenty<EMAIL_ADDRESS>University of Central FloridaOrlandoFloridaUSA ,  Mar Gonzalez-Franco
<EMAIL_ADDRESS>Google LabsSeattleWashingtonUSA and  Ryan P. McMahan
<EMAIL_ADDRESS>University of Central FloridaOrlandoFloridaUSA

###### Abstract.

As consumer adoption of immersive technologies grows, virtual avatars will
play a prominent role in the future of social computing. However, as people
begin to interact more frequently through virtual avatars, it is important to
ensure that the research community has validated tools to evaluate the effects
and consequences of such technologies. We present the first iteration of a
new, freely available 3D avatar library called the Virtual Avatar Library for
Inclusion and Diversity (VALID), which includes 210 fully rigged avatars with
a focus on advancing racial diversity and inclusion. We present a detailed
process for creating, iterating, and validating avatars of diversity. Through
a large online study ($n=132$) with participants from 33 countries, we provide
statistically validated labels for each avatar’s perceived race and gender.
Through our validation study, we also advance knowledge pertaining to the
perception of an avatar’s race. In particular, we found that avatars of some
races were more accurately identified by participants of the same race.

††copyright: none

##  1\. Introduction

The study of human behavior in virtual worlds is becoming increasingly
important as more and more people spend time in these digital spaces. In
particular, understanding how behaviors in virtual environments compare to
behaviors in real life can provide insight into the ways in which humans
interact with technology and each other. Furthermore, it can also help inform
the design of virtual environments, making them more realistic and socially
acceptable.

One area of significant interest is virtual avatars, which are 3D
representations of virtual humans often used in virtual worlds and simulations
(Pelachaud, 2009). Virtual avatars have a prominent role in social computing
and immersive environments (Yee and Bailenson, 2007; Heidicker et al., 2017;
Fox et al., 2015). For example, previous studies have utilized virtual avatars
to express emotions (Butler et al., 2017), recreate social psychology
phenomena (Gonzalez-Franco et al., 2018; Do et al., 2022), and influence
feelings of presence or embodiment (Peck and Gonzalez-Franco, 2021; Nowak and
Biocca, 2003). Moreover, virtual avatars are expected to play evermore
important roles in the future. For instance, virtual avatars are at the center
of every social virtual reality (VR) and augmented reality (AR) interaction,
as they are key to representing remote participants (Piumsomboon et al., 2018)
and facilitating collaboration (Sra and Schmandt, 2015).

Open virtual avatar libraries facilitate research by providing freely
available resources to the community. For instance, Microsoft’s Rocketbox
avatar library (Gonzalez-Franco et al., 2020b) has been extensively used in
multiple studies (e.g., (Cheng et al., 2022; Jeong et al., 2020; Huang et al.,
2022)), with over 400 stars and 100 forks on GitHub since its release in 2020.
However, the representation of races in currently available avatar libraries
are limited and have not been validated through user perception studies. As
examples, over 40% of the Rocketbox avatars are white males, and
MakeHuman111http://www.makehumancommunity.org/, another popular resource for
3D avatars, only includes options for African, Asian, and Caucasian avatars.
Due to such limitations, many researchers are unable to properly investigate
the effects of diversity for virtual avatars. Furthermore, existing libraries
not only have limited diversity but are also biased in their lack of
inclusivity with regard to professions for minority avatars. For instance,
Rocketbox lacks Asian avatars dressed for medical scenarios.

The limited representation of currently available resources may have an
inherently detrimental impact by introducing biases into research
investigations from the outset, such as restricting the development of
scenarios with Asian medical professionals. Furthermore, as immersive
technologies grow in popularity worldwide, Taylor et al. (Taylor et al., 2020)
have called for improved racial/ethnic representations in VR to mitigate
potential negative effects of racial bias. This can be especially important
since virtual avatar race222We use the term race to refer to a “visually
distinct social group with a common ethnicity” (Rhodes et al., 2010). can have
a strong influence on human behavior. For example, research has found that
embodying a virtual avatar of a different race can affect implicit racial
bias, as demonstrated by several prior studies (Peck et al., 2013; Groom et
al., 2009; Maister et al., 2015; Salmanowitz, 2018). As such, it is critical
to provide more inclusive avatar resources.

The goal of this work was dual purpose. First, we sought to develop an open
library of validated virtual avatars, which we refer to as the Virtual Avatar
Library for Inclusion and Diversity (VALID). This library has been designed to
inclusively represent a range of races across various professions. Secondly,
we wanted to better understand how humans perceive avatars, particular with
regard to race. In this first iteration of VALID, we followed the
recommendations of the 2015 National Content Test Race and Ethnicity Analysis
Report from the U.S. Census Bureau (Matthews et al., 2017) to ensure that a
wide range of people was represented in our library. For example, this report
found that members of Middle Eastern and North African (MENA) communities use
the MENA category when it is available, but have trouble identifying their
race when it is not available. Similarly, it also found that Hispanics can
better identify their ethnicity by combining the conventional race and
Hispanic origin questions into one. Therefore, to overcome those traditional
problems on racial and ethnic categorization, VALID includes seven races as
recommended by the U.S. Census Bureau report (Matthews et al., 2017) (which
differs from the 2020 U.S. Census): American Indian or Native Alaskan
(AIAN)333We use racial abbreviations as defined in the U.S. Census Bureau
report., Asian, Black or African American (Black), Hispanic, Latino, or
Spanish (Hispanic), Middle Eastern or North African (MENA), Native Hawaiian or
Pacific Islander (NHPI), and White.

VALID includes 210 fully rigged virtual avatars designed to advance diversity
and inclusion. We iteratively created 42 base avatars(7 target races $\times$
2 genders $\times$ 3 individuals) using a process that combined data-driven
average facial features with extensive collaboration with representative
stakeholders from each racial group. To address the longstanding issue of the
lack of diversity in virtual designers and to empower diverse voices (Boberg
et al., 2008), we adopted a participatory design method. This approach
involved actively involving individuals ($n=22$) from diverse backgrounds,
particularly different racial and ethnic identities, in the design process. By
including these individuals as active participants, we aimed to ensure that
their perspectives, experiences, and needs were considered and incorporated
into the design of the avatars.

Once the avatars were created, we sought to evaluate their perception on a
global scale. We then conducted a large online study ($n=132$) with
participants from 33 countries, self-identifying as one of the seven
represented races, to determine whether the race and gender of each avatar are
recognizable, and therefore validated. We found that all Asian, Black, and
White avatars were universally identified as their modeled race by all
participants, while our AIAN, Hispanic, and MENA avatars were typically only
identified by participants of the same race, indicating that participant race
can bias perceptions of a virtual avatar’s race. We have since modeled the 42
base avatars in five different outfits (casual, business, medical, military,
and utility), yielding a total of 210 fully rigged avatars.

To foster diversity and inclusivity in virtual avatar research, we are making
all of the avatars in our library freely available to the community as open
source models. In addition to the avatars, we are also providing statistically
validated labels for the race and gender of all 42 base avatars. Our models
are available in FBX format, are compatible with previous libraries like
Rocketbox (Gonzalez-Franco et al., 2020b), and can be easily integrated into
most game engines such as Unity and Unreal. Additionally, the avatars come
equipped with facial blend shapes to enable researchers and developers to
easily create dynamic facial expressions and lip-sync animations. All avatars,
labels, and metadata can be found at our GitHub repository:
https://github.com/xrtlab/Validated-Avatar-Library-for-Inclusion-and-Diversity
---VALID.

This paper makes three primary contributions:

  1. (1)

We provide 210 openly available, fully rigged, and perceptually validated
avatars for the research community, with a focus on advancing diversity and
inclusion.

  2. (2)

Our diversity-represented user study sheds new light on the ways in which
people’s own racial identity can affect their perceptions of a virtual
avatar’s race. In our repository, we also include the agreement rates of all
avatars, disaggregated by every participant race, which offers valuable
insights into how individuals from different racial backgrounds perceive our
avatars.

  3. (3)

We describe a comprehensive process for creating, iterating, and validating a
library of diverse virtual avatars. Our approach involved close collaboration
with stakeholders and a commitment to transparency and rigor. This could serve
as a model for other researchers seeking to create more inclusive and
representative virtual experiences.

##  2\. Related Work

In this section, we describe how virtual avatars are used within current
research in order to highlight the need for diverse avatars. We conclude the
section with a discussion on currently available resources used for virtual
avatars and virtual agents.

###  2.1. Effect of Avatar Race

Virtual avatars are widely used in research simulations such as training,
education, and social psychology. The race of a virtual avatar is a crucial
factor that can affect the outcomes of these studies. For example, research
has shown that underrepresented students often prefer virtual instructors who
share their ethnicity (Baylor, 2003; Moreno and Flowerday, 2006). Similarly,
studies have suggested that designing a virtual teacher of the same race as
inner-city youth can have a positive influence on them (Baylor, 2009), while a
culturally relevant virtual instructor, such as an African-American instructor
for African-American children, can improve academic achievement (Gilbert et
al., 2008).

The design of virtual avatars is especially important for minority or
marginalized participants. Kim and Lim (Kim and Lim, 2013) reported that
minority students who feel unsupported in traditional classrooms develop more
positive attitudes towards avatar-based learning. In addition, children with
autism spectrum disorder treat virtual avatars as real social partners (Li et
al., 2021; Ali et al., 2020). Therefore, to better meet the needs of all
individuals participating in such studies, it is important for researchers to
have access to diverse avatars that participants can comfortably interact
with. Diversity in virtual avatars is important not only for improving
representation, but also for enhancing the effectiveness of simulations. Halan
et al. (Halan et al., 2015) found that medical students who trained with
virtual patients of a particular race demonstrated increased empathy towards
real patients of that race. Similarly, Bickmore et al. (Bickmore et al., 2021)
showed that interacting with a minority virtual avatar reduced racial biases
in job hiring simulations.

These findings highlight the importance of diverse and inclusive virtual
avatars in research simulations and emphasize the need for more comprehensive
representation of different races. Access to a wide range of validated avatars
through VALID will help to create more inclusive and representative
simulations, and enable researchers to investigate the impact of avatar race
or gender on participants’ experiences. This will help improve the inclusivity
of simulations and contribute towards addressing issues of bias.

###  2.2. Implicit Racial Bias and Virtual Avatars

Avatars are becoming increasingly important in immersive applications,
particularly in the realm of VR, where they are becoming ubiquitous (Dewez et
al., 2021). Research suggests that the degree of similarity between a user’s
real body and their virtual avatar can influence embodiment, presence, and
cognition (Jo et al., 2017; Jung et al., 2018; McIntosh et al., 2020; Ogawa et
al., 2020). Maister et al. (Maister et al., 2015) proposed that non-matching
self-avatars can affect a user’s self-association and influence social
cognition. Moreover, studies have demonstrated that embodying a darker-skinned
avatar in front of a virtual mirror can reduce implicit racial biases (Peck et
al., 2013; Groom et al., 2009; Maister et al., 2015; Salmanowitz, 2018), which
are unconscious biases that can lead to discriminatory behavior (Chapman et
al., 2013). For instance, Salmanowitz et al. (Salmanowitz, 2018) found that a
VR participant’s implicit racial bias affects their willingness to convict a
darker-skinned suspect based on inconclusive evidence. Similarly, Peck et al.
(Peck et al., 2021) found that each participant’s implicit racial bias was
related to their nuanced head and hand motions in a firearm simulation. These
foundational studies provide compelling evidence that embodying an avatar of a
different race can affect implicit biases and further emphasize the need for
diverse avatar resources.

Our study examines how participants perceive the race of diverse virtual
avatars. While some studies have explored how a virtual avatar’s race affects
user interactions (e.g., (Baylor, 2003; Gamberini et al., 2015; Zipp and
Craig, 2019)), little research has been conducted on how individuals actively
perceive the race of virtual avatars. Setoh et al. (Setoh et al., 2019) note
that racial identification can predict implicit racial bias, making it crucial
to understand how people perceive the race of virtual avatars to further
investigate these effects.

###  2.3. Own-Race Bias

Own-race bias, also known as the ”other-race effect,” refers to the phenomenon
in which individuals process the faces of their own race differently from
those of other races (Rhodes et al., 2009; Civile and Mclaren, 2022; Meissner
and Brigham, 2001; Ge et al., 2009). Studies have suggested that this bias can
influence the way individuals categorize race. For example, MacLin and Malpass
(MacLin and Malpass, 2001) found that Hispanic participants were more likely
to categorize Hispanic faces as fitting their racial category than Black
faces, and Blascovich et al. (Blascovich et al., 1997) observed that
participants who strongly identify with their in-group are more accurate in
identifying in-group members.

Although own-race bias has not yet been studied in the context of 3D virtual
avatars, Saneyoshi et al. (Saneyoshi et al., 2022) recently discovered that it
extends to the uncanny valley effect (Mori et al., 2012) for 2D computer-
generated faces. Specifically, they found that Asian and European participants
rated distorted faces of their own race as more unpleasant than those of other
races. Building on this research, we extended the study of own-race bias to 3D
virtual avatars and focused on race categorization rather than perceived
pleasantness. Our study included avatars and participants from seven different
races, providing insights into how a diverse user population may interact
within equally diverse virtual worlds.

###  2.4. Virtual Avatar Resources

There are numerous resources for creating virtual avatars. Artists can use 3D
modeling tools, such as Autodesk 3ds
Max444https://www.autodesk.com/products/3ds-max/overview, Autodesk
Maya555https://www.autodesk.com/products/maya/overview,
Blender666https://www.blender.org, or ZBrush777https://www.maxon.net/en/zbrush
to manually model, texture, and rig virtual avatars. However, such work
requires expertise in 3D modeling and character design, and is often a tedious
process (Gonzalez-Franco et al., 2020b). On the other hand, parametric models,
including freely available tools like
MakeHuman888http://www.makehumancommunity.org/ and Autodesk Character
Generator999https://charactergenerator.autodesk.com/, as well as commercially
available ones such as Daz3D101010https://www.daz3d.com,
Poser111111https://www.posersoftware.com, and Reallusion Character
Creator121212https://www.reallusion.com/character-creator/, enable users to
generate virtual avatars from predefined parameters, thereby significantly
expediting the avatar generation process. Nonetheless, using these tools still
requires learning a new program and time to customize each model, despite the
absence of the artistic expertise needed for manual tools.

Another alternative to traditional modeling is to use scanning technologies,
which can capture 3D models of real people. For instance, Shapiro et al.
(Shapiro et al., 2014) and Waltemate et al. (Waltemate et al., 2018) used 3D
cameras and photogrammetry, respectively, to capture 3D models of their users.
Singular Inversions FaceGen Modeller131313https://facegen.com/modeller.htm has
also been employed to generate 3D faces from user photos and then apply them
to a general 3D avatar body (Blom et al., 2014; Gonzalez-Franco et al., 2016).
However, scanning approaches require the ability to physically scan the user,
limiting their use for certain applications, particularly remote ones.

Most closely related to our goal of providing a free and open library of
ready-to-use avatars is the Microsoft Rocketbox library (Gonzalez-Franco et
al., 2020b) and its accompanying HeadBox (Volonte et al., 2022) and MoveBox
(Gonzalez-Franco et al., 2020a) toolkits. Rocketbox provides a free set of 111
fully rigged adult avatars of various races and outfits. However, it falls
short in terms of representation by not including any avatars of AIAN or NHPI
descent. Additionally, the library offers only a limited number of Asian,
Hispanic, and MENA avatars, excluding minority representations for some
professions (e.g., Rocketbox does not include any Asian medical avatars).
Furthermore, none of the available avatar libraries have been validated by
user perception studies to ensure their efficacy and inclusivity. Therefore,
our VALID project aims to fill this gap by providing a free and validated
library of diverse avatars.

##  3\. Avatar Creation Procedure

Figure 1. An example of the creation of a 3D avatar using our methodology. 1)
We select 4-7 faces from a database (Bainbridge et al., 2013) or stock photos.
2) We calculate the average face using WebMorph (DeBruine, 2018). 3) A 3D
artist recreates the average face using modeling software. 4) The models are
improved iteratively through recurrent consultation with representative
volunteers.

This section outlines our iterative process for developing the VALID library,
which includes 42 base avatars. We began by using data-driven averaged facial
features to create our initial models. We then conducted interviews with
representative volunteers to iteratively refine and modify the avatars based
on their feedback.

###  3.1. Initial Modeling

To ensure a broad diversity of people were represented in our library, we
initially created 42 base avatars (7 target races $\times$ 2 genders $\times$
3 individuals ) modeled after the seven racial groups recommended by the 2015
National Content Test Race and Ethnicity Analysis Report (Matthews et al.,
2017): AIAN, Asian, Black, Hispanic, MENA, NHPI, and White. We created 3 male
and 3 female individuals for each race, resulting in a total of 6 individuals
per race.

Preliminary models were based on averaged facial features of multiple photos
selected from the 10k US Adult Faces Database (Bainbridge et al., 2013) and
stock photos from Google for races missing from the database (e.g., AIAN,
MENA, and NHPI). These photos were used as input to a face-averaging algorithm
(DeBruine, 2018), which extracted average facial features for each race and
gender pair. Using these averages as a reference, a 3D artist recreated the
average faces for each race and gender pair using Autodesk Character Generator
(due to its generous licensing and right to freely edit and distribute
generated models141414https://knowledge.autodesk.com/support/character-
generator/learn-explore/caas/sfdcarticles/sfdcarticles/Character-Generator-
Legal-Restrictions-and-Allowances-when-using-Character-Generator.html) and
Blender to make modifications not supported by Autodesk Character Generator
(see Figure 1).

###  3.2. Iterative Improvements through Representative Interviews

After the preliminary avatars were created based on the facial averages, we
worked closely with 2 to 4 volunteers of each represented race (see Table 1)
to adjust the avatars through a series of Zoom meetings. This process ensured
that all avatars were respectful and reduced the likelihood of harmful or
stereotypical representations. Volunteers self identified their race and were
recruited from university cultural clubs (e.g., Asian Student Association,
Latinx Student Association), community organizations (e.g., Pacific Islanders
Center), and email lists. We iteratively asked these volunteers for feedback
on all avatars representing their race, showing them the model from three
perspectives (see Figure 2). Volunteers were specifically asked to identify
accurate features and suggest changes to be made. Once the changes were
completed based on the feedback, we presented the updated avatars to the
volunteers. This process was repeated until they approved the appearance of
the avatars. For example, volunteers requested changes to facial features,
such as:

  * •

“Many Native women I know have a softer face and jawline [than this avatar].”
–AIAN Volunteer 3

  * •

“The nose bridge is too high and looks too European. Asians mostly have low
nose bridges.” –Asian Volunteer 2

  * •

“Middle Eastern women usually have wider, almond-shaped eyes.” –MENA Volunteer
2

  * •

“The nose [for this avatar] should be a little bit thicker, less pointy, and
more round.” –NHPI Volunteer 1

Additionally, we modified hairstyles according to feedback:

  * •

“[These hairstyles] look straighter and more Eurocentric. So I would choose
[these facial features] and then do a natural [hair] texture.” –Black
Volunteer 1

  * •

“Usually the men have curly hair or their hair is cut short on the sides with
the top showing.” –NHPI Volunteer 1

Once the avatars were approved by their corresponding volunteer
representatives, we conducted an online study to validate the race and gender
of each avatar based on user perceptions.

Table 1. Breakdown of our volunteer representatives by race, gender (male, female, or non-binary), and country. Race | Gender | Country
---|---|---
AIAN | 2M, 1F | USA (Native American) (3)
Asian | 2M, 2F |  | China (1), USA (Chinese-American) (1),
---
USA (Vietnamese-American) (2)
Black | 1M, 2F | USA (African-American) (3)
Hispanic | 2M, 1F | Mexico (1), USA (Mexican-American) (2)
MENA | 1M, 2F | Iran (2), Saudi Arabia (1)
NHPI | 1M, 2F | Samoa (2), USA (Native Haiwaiian) (1)
White | 2M, 1F | USA (3)

##  4\. Avatar Validation Study

We conducted an online, worldwide user study to determine whether the target
race and gender of each avatar is recognizable and, therefore, validated.
Participants were recruited from the online Prolific
marketplace151515https://www.prolific.co, which is similar to Amazon
Mechanical Turk. Prior research shows that Prolific has a pool of more diverse
and honest participants (Peer et al., 2017) and has more transparency than
Mechanical Turk (Palan and Schitter, 2018). Since diversity was a core theme
of our research, we chose Prolific to ensure that our participants would be
diverse.

###  4.1. Procedure

The following procedure was reviewed and approved by our university
Institutional Review Board (IRB). The study consisted of one online Qualtrics
survey that lasted an average of 14 minutes. Each participant first completed
a background survey that captured their self-identified demographics,
including race, gender, and education. Afterwards, they were asked to
familiarize themselves with the racial terms as defined by the U.S. Census
Bureau research (Matthews et al., 2017). Participants were then asked to
categorize the 42 avatars by their perceived race and gender. Participants
were shown only one avatar at a time and the order was randomized.

For each of the avatars, participants were shown three perspectives: a
$45^{\circ}$ left headshot, a direct or $0^{\circ}$ headshot, and a
$45^{\circ}$ right headshot (see Figure 2). Avatars were shown from the
shoulders up and were dressed in a plain gray shirt. The images were rendered
in Unity using the standard diffuse shader and renderer. The avatars were
illuminated by a soft white (#FFFEF5) directional light with an intensity of
1.0, and light gray (#7F7F7F) was used for the background. Participants were
asked to select all races that each avatar could represent: “American Indian
or Alaskan Native”, “Asian”, “Black or African American”, “Hispanic, Latino,
or Spanish”, “Middle Eastern or North African”, “Native Hawaiian or Pacific
Islander”, “White”, or “Other”. “Other” included an optional textbox if a
participant wanted to be specific. We allowed participants to select multiple
categories according to the U.S. Census Bureau’s recommendations for surveying
race (Matthews et al., 2017). For gender, participants were able to select
“Male”, “Female”, or “Non-binary”. Participants were paid $5.00 via Prolific
for completing the study.

Figure 2. An example of how each avatar was presented to participants during
our validation study.

###  4.2. Participants

A total of 132 participants (65 male, 63 female, 4 non-binary) from 33
different countries were recruited to take part in the study. We aimed to
ensure a diverse representation of perspectives by balancing participants by
race and gender. Table 2 provides a breakdown of our participants by race,
gender, and country. Despite multiple recruitment attempts, including targeted
solicitations via Prolific, we had difficulty recruiting NHPI participants. It
is important to note that we excluded volunteers who had previously assisted
with modeling the avatars from participating in the validation study to avoid
potentially overfitting their own biases.

Table 2. Breakdown of our validation study’s participants by race, gender (male, female, or non-binary), and country. Race | Gender | Country
---|---|---
AIAN | 9M, 10F, 1NB |  | U.S. (14), Canada (3), Chile (1), Mexico (1),
---
Cambodia (1)
Asian | 10M, 10F |  | U.K. (5), Canada (3), South Africa (3),
---
India (2), Indonesia (2), China (1), France (1),
Germany (1), Italy (1), Malaysia (1)
Black | 10M, 9F, 1NB |  | South Africa (16), Nigeria (2),
---
Swaziland (1), U.K. (1)
Hispanic | 10M, 9F, 1NB | Mexico (15), Chile (3), Portugal (2)
MENA | 10M, 10F |  | Israel (9), Lebanon (3), Jordan (2),
---
Bahrain (1), Egypt (1), Iran (1), Iraq (1),
Saudi Arabia (1), Syria (1)
NHPI | 7M, 5F |  | New Zealand (Maori) (8), Samoa (2),
---
Fiji (1), U.S. (1)
White | 9M, 10F, 1NB |  | Portugal (5), Italy (5), Poland (3),
---
Mexico (2), Belgium (1), Greece (1),
Ireland (1), U.K. (1), U.S. (1)

###  4.3. Data Analysis and Labeling Approach

To validate the racial identification of our virtual avatars, we used
Cochran’s Q test (Sheskin, 2011), which allowed us to analyze any significant
differences among the selected race categories. This approach was necessary
since our survey format allowed participants to select more than one race
category for each avatar, following the U.S. Census Bureau’s research
recommendations (Matthews et al., 2017). Since the Chi-squared goodness of fit
test requires mutually exclusive categories, we were unable to use it in our
analysis. Furthermore, since our data was dichotomous, a repeated-measures
analysis of variance (ANOVA) was not appropriate. Therefore, Cochran’s Q test
was the most appropriate statistical analysis method for our survey data.

We used a rigorous statistical approach to assign race and gender labels to
each avatar. First, we conducted the Cochran’s Q test across all participants
($n=132$) at a 95% confidence level to identify significant differences in the
participants’ responses. If the test indicated significant differences, we
performed pairwise comparisons between each race using Dunn’s test to
determine which races were significantly different.

For each avatar, we assigned a race label if the race was selected by the
majority of participants (i.e., over 50% of participants selected it) and if
the race was selected significantly more than other race choices and not
significantly less than any other race. This approach resulted in a single
race label for most avatars, but some avatars were assigned multiple race
labels due to multiple races being selected significantly more than all other
races. If no race was selected significantly more than the majority, then we
categorized the avatar as “Ambiguous”. We followed a similar procedure for
assigning gender labels.

To account for the possibility that the race of the participant might
influence their perception of virtual race, we also assigned labels based on
same-race participants. This involved using the same procedure for assigning
labels as described above, except based only on the selections of participants
who identified as the same race as the avatar. This also allows future
researchers to have the flexibility to use the labels from all study
participants for studies focused on individuals from diverse racial
backgrounds or to use the labels from participants of the same race for
studies targeting specific racial groups.

##  5\. Results

Table 3. Assigned labels for all 42 base avatars. “All” indicates that the label was identified by all 132 participants, while “Same-Race” only includes the data of participants who identify as the race that the avatar was modeled for. Agreement labels were calculated as the percentage of participants who perceived an avatar to represent a race or gender. Avatar | Race (All) | Agreement | Race (Same-Race) | Agreement | Gender (All) | Agreement
---|---|---|---|---|---|---
AIAN_M_1 | AIAN | 0.67 | AIAN | 0.90 | Male | 0.89
AIAN_M_2 | AIAN | 0.65 | AIAN | 0.75 | Male | 0.89
AIAN_F_1 | AIAN | 0.55 | AIAN | 0.60 | Female | 0.64
AIAN_F_2 | AIAN | 0.55 | AIAN | 0.75 | Female | 0.75
Asian_M_1 | Asian | 0.86 | Asian | 0.90 | Male | 0.95
Asian_M_2 | Asian | 0.98 | Asian | 1.00 | Male | 0.91
Asian_M_3 | Asian | 0.98 | Asian | 1.00 | Male | 0.91
Asian_F_1 | Asian | 0.98 | Asian | 1.00 | Female | 0.98
Asian_F_2 | Asian | 0.93 | Asian | 0.90 | Female | 0.96
Asian_F_3 | Asian | 0.95 | Asian | 1.00 | Female | 0.97
Black_M_1 | Black | 0.98 | Black | 1.00 | Male | 0.98
Black_M_2 | Black | 0.97 | Black | 1.00 | Male | 0.98
Black_M_3 | Black | 0.98 | Black | 1.00 | Male | 0.73
Black_F_1 | Black | 0.98 | Black | 1.00 | Female | 0.98
Black_F_2 | Black | 0.98 | Black | 1.00 | Female | 0.94
Black_F_3 | Black | 0.95 | Black | 1.00 | Female | 0.97
Hispanic_M_1 | Hispanic/White | 0.65/0.55 | Hispanic | 0.85 | Male | 0.98
Hispanic_M_2 | White | 0.64 | Hispanic | 0.80 | Male | 0.98
Hispanic_M_3 | Hispanic/White | 0.55/0.51 | Hispanic | 0.75 | Male | 0.97
Hispanic_F_1 | Hispanic | 0.64 | Hispanic | 0.80 | Female | 0.95
Hispanic_F_2 | White | 0.70 | Hispanic/White | 0.55/0.60 | Female | 0.95
Hispanic_F_3 | Hispanic/White | 0.59/0.52 | Hispanic | 0.75 | Female | 0.93
MENA_M_1 | White | 0.56 | MENA | 0.70 | Male | 0.99
MENA_M_2 | White | 0.64 | MENA/White | 0.65/0.60 | Male | 1.00
MENA_M_3 | MENA/White | 0.55/0.65 | MENA/White | 0.75/0.55 | Male | 0.98
MENA_F_1 | White | 0.58 | MENA/White | 0.70/0.60 | Female | 0.98
MENA_F_2 | White | 0.60 | MENA | 0.60 | Female | 0.98
NHPI_M_1 | NHPI | 0.52 | NHPI | 0.58 | Male | 0.98
NHPI_M_2 | Hispanic | 0.65 | NHPI | 0.67 | Male | 1.00
White_M_1 | White | 0.96 | White | 0.95 | Male | 0.99
White_M_2 | White | 0.98 | White | 0.95 | Male | 1.00
White_M_3 | White | 0.93 | White | 0.90 | Male | 0.99
White_F_1 | White | 0.94 | White | 0.95 | Female | 0.97
White_F_2 | White | 0.96 | White | 0.95 | Female | 0.98
White_F_3 | White | 0.94 | White | 0.95 | Female | 0.99
X_AIAN_M_1 | Hispanic | 0.64 | Hispanic | 0.75 | Male | 0.99
X_AIAN_F_1 | Hispanic | 0.54 | Hispanic | 0.45 | Female | 0.86
X_MENA_F_1 | Ambiguous | N/A | Ambiguous | N/A | Female | 0.98
X_NHPI_M_1 | Hispanic | 0.55 | Asian | 0.58 | Male | 0.98
X_NHPI_F_1 | Hispanic | 0.55 | Ambiguous | N/A | Female | 0.92
X_NHPI_F_2 | Hispanic | 0.58 | Ambiguous | N/A | Female | 0.95
X_NHPI_F_3 | NHPI | 0.52 | Ambiguous | N/A | Female | 0.92

###  5.1. Validated Avatar Labels

Table 3 summarizes our results and labels for all 42 base avatars across all
participants and for same-race participants.

####  5.1.1. Race and Gender Labels

Asian, Black, and White avatars were correctly identified as their intended
race across all participants, while most of the remaining avatars were
accurately identified by same-race participants (see Table 3 for all and same-
race agreement rates). Therefore, we observed some differences in
identification rates based on the race of the participants, highlighting the
potential impact of own-race bias on the perception of virtual avatars.
Notably, there were no significant differences in gender identification rates
based on participant race, indicating that all avatars were correctly
perceived as their intended gender by all participants, regardless of their
racial background.

####  5.1.2. Naming Convention

If an avatar was identified as its intended race by corresponding same-race
participants, we named it after that race. For instance, the avatar
`Hispanic_M_2` was labeled as White by all participants. However, our Hispanic
participants perceived it as solely Hispanic. Hence, we left the original
name. However, if an avatar was labeled as “Ambiguous” or as a different race
by same-race participants, we added an `X` at the beginning of its name to
indicate that it was not validated. Avatars were also labeled by their
identified gender (“M” or “F”).

Figure 3. Confusion matrix heatmap of agreement rates for the 42 base avatars
by separated by other-race participants and same-race participants (i.e.,
participants of a different or same race as the avatar). Agreement rates were
calculated as the percentage of participants who perceived an avatar to
represent a race or gender.

###  5.2. Other-Race vs. Same-Race Perception

To further examine how participant race affected perception of virtual avatar
race, we additionally analyzed the data by separating same-race and other-race
agreement rates. In effect, we separated the selections of the participants
who were the same race as the avatar modeled and those who were not.

####  5.2.1. Difference in Agreement Rates

Figure 3 displays the difference in agreement rates between same-race and
other-race. Figure 3 shows that several avatars were strongly identified by
both other-race and same-race participants. In particular, all Asian, Black,
and White avatars were perceived as their intended race with high agreement
rates by both same-race and other-race participants (over 90% agreement for
all but one). However, some avatars were only identified by participants of
the same race as the avatar. For example, our analysis of the agreement rates
for different racial groups revealed interesting trends. For instance, non-
Hispanic participants had an average agreement rate of 54.5% for Hispanic
avatars, while Hispanic participants had a much higher average agreement of
75.0%. Similar patterns were observed for AIAN (57.8% other-race, 75.0% same-
race) and MENA (40.4% other-race, 68.0% same-race) avatars.

(a) Other-race clustering

(b) Same-race clustering

Figure 4. Clustered scatterplots of each avatar’s relation to one another
based on Principle Component Analysis and K-means clustering for other-race
and same-race participant identifications. The Voronoi analysis shows the
borders of the clusters where each category was assigned. Each avatar is color
coded by its validated label.

####  5.2.2. Perceived Race Clusters

To gain deeper insights into how participants perceived the avatars’ races, we
employed Principle Component Analysis (PCA) to reduce the agreement rates of
each of the 42 base avatars down to two dimensions. Next, we performed K-means
clustering (Likas et al., 2003) on the resulting two-dimensional data to group
the avatars based on their perceived race. We optimized the number of clusters
using the elbow method and distortion scores (Bengfort et al., 2018). We
applied this technique to both other-race and same-race agreement rates to
determine whether there were any differences in the clustering based on
participant race. By visualizing the clusters, we aimed to better understand
the differences in how participants perceived the avatars’ races.

Figure 4 shows that Asian, Black, and White avatars were perceived
consistently by all participants, with clearly defined clusters. However,
there was more confusion in perceiving AIAN, Hispanic, MENA, and NHPI avatars,
which clustered closer together. Same-race participants had less overlap and
more-accurately perceived these avatars, with more separation between them.
For example, the Hispanic and MENA avatars were in separate clusters for same-
race participants, except for one avatar (`Hispanic_F_2`). On the other hand,
the Hispanic and MENA avatars were entirely clustered together for other-race
participants.

##  6\. Discussion

In this section, we discuss the validation of our avatars. Specifically, we
examine the extent to which each avatar was correctly identified as its
intended race and the variability in identification across different
participant groups. Additionally, we discuss the implications of our results
for virtual avatar research, highlighting the importance of considering the
potential impact of own-race bias on avatar race perception. Finally, we
describe the potential future impact of our avatar library in the community,
including how it can be used to promote diversity and inclusion.

Figure 5. Images of the skeleton and facial blend shapes included with our
avatars.

###  6.1. Race Identification

####  6.1.1. Universally Identified Avatars

We found that our Asian, Black, and White avatars were recognized by all
participants with high agreement rates. This suggests that these avatars can
be a valuable tool for researchers seeking to create virtual humans that can
be easily identified by individuals from different racial backgrounds.

Our results may be due to perceptual expertise or familiarity with other-race
faces, as proposed by Civile et al. (Civile and Mclaren, 2022). We hypothesize
that this familiarity could be explained by the prevalence of these racial
groups in global media and pop culture. For example, White cast members were
the most represented in popular Hollywood movies over the last decade,
followed by Black cast members (Malik et al., 2022). Since Hollywood movies
have a dominant share in the global film industry (Maisuwong, 2012), people
may be more familiar with characters that are prevalent in these films.
Additionally, East Asian media culture has become widely popular worldwide
over the past few decades (Jin et al., 2021; Iwabuchi, 2010). Phenomena like
”The Hallyu Wave” and ”Cool Japan” (Lux, 2021) have enabled East Asian films,
dramas, and pop music to gain a global following. As people may often
encounter these racial groups in media, this familiarity may have facilitated
their recognition of these avatars.

####  6.1.2. Same-Race Identified Avatars

As expected, some avatars were only identified by participants of the same
race as the avatar, consistent with the own-race bias effect. For example, as
seen in Table 3, the Hispanic avatars received mixed ratings of White and
Hispanic across all participants, but most were perceived as solely Hispanic
by Hispanic-only participants. Similarly, only one MENA avatar was perceived
as MENA by all participants, while five were perceived as MENA by MENA-only
participants. These results suggest that participants’ own-race bias, a well-
known phenomenon in psychology, may also affect their perception of virtual
avatars. The findings point to the importance of considering participants’
race when using virtual avatars in research or applications that require
accurate representation of different racial groups.

####  6.1.3. Ambiguous Avatars

Several avatars in our library were perceived ambiguously by all participants
and only same-race participants, and therefore labeled as such (see Table 3
for details). Identifying the reason for these avatars’ lack of clear
identification is not straightforward, and multiple factors could be at play.
For instance, the two ambiguous AIAN avatars were the only ones with short
hairstyles, which may have impacted their identification as AIAN. Long hair
carries cultural and spiritual significance in many AIAN tribes (Thanikachalam
et al., 2019), and some participants may have perceived the avatars as non-
AIAN as a result, even among AIAN participants.

The validation of our NHPI avatars was limited, possibly due to the low number
of NHPI participants ($n=12$) in our study, despite our targeted recruitment
efforts. As a consequence, most of the NHPI avatars were not validated by NHPI
participants, including the lack of validation for any female NHPI avatars.
Another potential reason for this lack of validation is that the majority of
our NHPI participants identified themselves as New Zealand Maori, whereas our
avatars were developed with the help of Samoan and Native Hawaiian volunteer
representatives. Therefore, it is possible that our NHPI avatars are
representative of some NHPI cultures, but not New Zealand Maori. In future
studies, expanding recruitment efforts for both interview volunteers and study
participants will be crucial, despite the challenges involved in doing so. For
example, future studies may need to compensate NHPI participants more than
participants of other races.

###  6.2. Implications for Virtual Avatars

Our study provides valuable insights for virtual avatar applications and
research. Our findings indicate that human behavior in race categorization can
apply to virtual avatars, which has notable implications for interactions in
virtual experiences. Kawakami et al. (Kawakami et al., 2017) suggest that in-
group and out-group categorization can lead to stereotyping, social judgments,
and group-based evaluations. Therefore, designers and developers should be
aware of this and take necessary steps to mitigate unintended consequences in
virtual experiences. For example, regulating codes of conduct (Taylor et al.,
2020) can help to improve interracial interactions in VR.

Interestingly, our study also replicated a nuanced finding from more recent
psychology research on the perception of ambiguous avatars (Nicolas et al.,
2019). As seen in Table 3, most of the misidentified avatars were identified
as Hispanic by all participants. Similarly, Nicolas et al. (Nicolas et al.,
2019) recently found that participants classify racially ambiguous photos as
Hispanic or MENA, regardless of their parent ethnicities. We believe that this
effect extended to our virtual avatars.

###  6.3. An Open Library of Validated Avatars

As a contribution to the research community, we are providing open access to
our virtual avatar library, which includes all 210 fully rigged avatars, along
with validated labels for each avatar’s race and gender. Our library features
avatars of seven different races, providing a diverse selection for
researchers to use in their studies. The validated labels can facilitate
research on the impact of avatar race, and researchers can choose to use the
labels for studies aimed at individuals from different racial backgrounds or
same-race labels for specific study populations.

The Virtual Avatar Library for Inclusion and Diversity (VALID) provides
researchers and developers with a diverse set of fully rigged avatars suitable
for various scenarios such as casual, business, medical, military, and
utility. Each avatar comes with 65 facial blend shapes, enabling dynamic
facial expressions (see Figure 5). The library is readily available for
download and can be used in popular game engines like Unity or Unreal.
Although this is the first iteration of the library, we plan to update it by
adding more professions and outfits soon. In addition, the library can be used
for a wide range of research purposes, including social psychology simulations
and educational applications.

###  6.4. Limitations and Future Work

We recognize that our VALID avatar library is only a small step towards
achieving greater diversity and inclusion in avatar resources. We acknowledge
that the representation of each demographic is limited and plan to expand the
diversity within each group by creating new avatars. For example, our Asian
avatars are modeled after East Asians, but we plan to expand VALID to include
South Asian and Southeast Asian avatars as well. Our Hispanic representatives
have pointed out the need for more diverse Hispanic avatars, including varying
skin tones to represent different South American populations, such as Mexican
and Cuban. Additionally, our NHPI representatives have suggested the inclusion
of tattoos, which hold cultural significance for some NHPI communities, could
improve the identifiability of our NHPI avatars, in addition to improving our
NHPI recruitment methods. Any future updates to the library will undergo the
same rigorous creation, iteration, and validation process as the current
avatars.

While our first iteration of the library focused on diversity in terms of
race, we realize that the avatars mostly represent young and fit adults, which
does not reflect all types of people. In the future, we plan to update the
library with a diversity of body types that include different body mass index
(BMI) representations and ages. Including avatars with different BMI
representations is not only more inclusive, but can also be useful for studies
targeting physical activity, food regulation, and therapy (Scarpina et al.,
2019). Likewise, we plan to include shaders and bump maps (Hughes, 2011) that
can age any given avatar by creating realistic wrinkles and skin folds,
further improving the diversity and inclusivity of VALID

Another limitation of the current work is that our library includes only male
and female representations. In future updates, we plan to include non-binary
and androgynous avatars. Currently, there are not many androgynous models that
are freely available. However, they can be an area of important study. For
example, previous studies found that androgynous avatars reduce gender bias
and stereotypical assumptions in virtual agents (Nag and Yalçln, 2020) and
improve student attitudes (Booth et al., 2010). Thus, we plan to include these
avatars in a future update by following Nag et al.’s (Nag and Yalçln, 2020)
guidelines for creating androgynous virtual humans.

Our study, while diverse in terms of race and country, is not representative
of everyone. We recruited participants through the online platform Prolific,
which is known for its increased diversity compared to other crowdsourcing
platforms such as Mechanical Turk. However, due to the online nature of the
platform, we primarily recruited younger adults. It is possible that
perceptions of our avatars may differ among other age groups, such as children
or older adults. Therefore, it is important to broaden recruitment efforts by
exploring alternative platforms and recruitment strategies that may be more
effective in reaching a wider range of participants. Future studies could also
consider conducting in-person studies or focus groups to gather additional
insights into avatar perception.

##  7\. Conclusion

We have introduced a new virtual avatar library comprised of 210 fully rigged
avatars with diverse professions and outfits, available for free. Our library
aims to promote diversity and inclusion by creating equitable representation
of seven races across various professions. We designed 42 base avatars using
data-driven facial averages and collaborated with volunteer representatives of
each ethnicity. A large validation study involving participants from around
the world was conducted to obtain validated labels and metadata for the
perceived race and gender of each avatar. Additionally, we offer a
comprehensive process for creating, iterating, and validating diverse avatars
to aid other researchers in creating similarly validated avatars.

Our validation study revealed that the majority of avatars were accurately
perceived as the race they were modeled for. However, we observed that some
avatars, such as the Hispanic and MENA avatars, were only validated as such by
participants who identified as Hispanic or MENA, respectively. This finding
suggests that the perception of virtual avatars may be influenced by own-race
bias or the other-race effect, as described in the psychology literature.
Moving forward, we plan to expand the library to include additional races,
professions, body types, age ranges, and gender representations to further
improve diversity and inclusion.

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FERMILAB-Pub-08-051-T

# Accumulating evidence for nonstandard leptonic decays of $D_{s}$ mesons

Bogdan A. Dobrescu and Andreas S. Kronfeld  Theoretical Physics Department,
Fermi National Accelerator Laboratory, Batavia, Illinois, USA

(March 4, 2008; revised April 28, 2008)

###### Abstract

The measured rate for $D_{s}^{+}\\!\to\\!\ell^{+}\nu$ decays, where $\ell$ is
a muon or tau, is larger than the standard model prediction, which relies on
lattice QCD, at the 3.8$\sigma$ level. We discuss how robust the theoretical
prediction is, and we show that the discrepancy with experiment may be
explained by a charged Higgs boson or a leptoquark.

###### pacs:

13.20.Fc,12.60-i,14.80.-j

Introduction.—The pattern of flavor and $CP$ violation of the standard model
has been established by a wide range of experiments. This agreement, however,
leaves room for new flavor effects to show up as calculations and measurements
improve. Intriguingly, decays of the $D_{s}$ meson (the lightest $c\bar{s}$
state) could be more sensitive to new physics than any other process explored
so far. It suffices that a new particle couples predominantly to leptons and
up-type quarks, but not to the first generation.

In this Letter we examine the leptonic decays of the $D_{s}$. Recently, the
calculation of the relevant QCD matrix element has improved significantly, and
more accurate measurements of the rate have been made. The average of the
experimental results disagrees with the standard model by almost four standard
deviations. We discuss the evidence, and propose that a nonstandard amplitude
interferes with the standard $W$-mediated amplitude. We show that the tree-
level exchange of a spin-0 particle with mass of order 1 TeV may account for
the discrepancy.

Leptonic $D_{s}$ decays.—The $D_{s}\\!\to\\!\ell\nu$ branching fraction, where
$\ell$ is a charged lepton of mass $m_{\ell}$, is given in the standard model
by

$B(D_{s}\\!\to\\!\ell\nu)=\frac{m_{D_{s}}}{8\pi}\tau_{D_{s}}f_{D_{s}}^{2}\left|G_{F}V^{*}_{cs}m_{\ell}\right|^{2}\left(1\\!-\frac{m_{\ell}^{2}}{m_{D_{s}}^{2}}\right)^{\\!\\!2}.$
(1)

Here $m_{D_{s}}$ and $\tau_{D_{s}}$ are the mass and lifetime of the $D_{s}$,
$G_{F}$ is the Fermi constant, and $V_{cs}$ is a Cabibbo-Kobayashi-Maskawa
(CKM) element. The decay constant $f_{D_{s}}$ is defined by

$\langle
0|\,\bar{s}\gamma_{\mu}\gamma_{5}c\,|D_{s}(p)\rangle=if_{D_{s}}p_{\mu},$ (2)

where $p_{\mu}$ is the 4-momentum of the $D_{s}$ meson. Although the
electroweak transition proceeds at the tree level,
$D_{s}^{+}\\!\to\\!W^{+}\\!\to\\!\ell^{+}\nu_{\ell}$, its rate is suppressed.
The helicity of the lepton must flip, leading to the factor $m_{\ell}$ in the
amplitude. For the muon, this helicity suppression $(m_{\ell}/m_{D_{s}})^{2}$
is $2.8\times 10^{-3}$. The $\tau$ mass is only 10% smaller than the $D_{s}$
mass (1.969 GeV), so there is no significant helicity suppression, but the
phase space suppression [the last factor in Eq. (1)] is $3.4\times 10^{-2}$.

Table 1: Experimental values of $f_{D_{s}}$. Our averages treat systematic uncertainties as uncorrelated and omit the PDG entry Yao:2006px , which is an average of earlier experiments. final state | reference |  $f_{D_{s}}$ (MeV)
---|---|---
$\ell\nu$ | PDG Yao:2006px  | $294\pm 27$
$\mu\nu$ | BaBar Aubert:2006sd  | $283\pm 17\pm 16$
$\mu\nu$ | CLEO Pedlar:2007za  | $264\pm 15\pm\;7$
$\mu\nu$ | Belle Widhalm:2007mi  | $275\pm 16\pm 12$
$\tau\nu$ ($\tau\\!\to\\!\pi\nu$) | CLEO Pedlar:2007za  | $310\pm 25\pm~{}8$
$\tau\nu$ ($\tau\\!\to\\!e\nu\bar{\nu}$) | CLEO Ecklund:2007zm  | $273\pm 16\pm\;8$
$\mu\nu$ | our average | $273\pm 11$
$\tau\nu$ | our average | $285\pm 15$

We have collected in Table 1 all precise experimental measurements of
$B(D_{s}\\!\to\\!\ell\nu)$, which are usually quoted in terms of $f_{D_{s}}$
Yao:2006px ; Rosner:2008yu . Combining the error bars in quadrature, our
average of $\tau\nu$ and $\mu\nu$ final states is

$\left(f_{D_{s}}\right)_{\rm expt}=277\pm 9\;\textrm{MeV}.$ (3)

The most accurate calculation from lattice QCD is Follana:2007uv

$\left(f_{D_{s}}\right)_{\rm QCD}=241\pm 3\;\textrm{MeV},$ (4)

where statistical and systematic uncertainties are combined in the fitting
methods. The only other modern lattice-QCD calculation agrees, $249\pm 3\pm
16$ MeV Aubin:2005ar , but its quoted error is five times larger and would not
influence a weighted average with Eq. (4). The discrepancy between Eqs. (3)
and (4) is 15% and 3.8$\sigma$. Table 1 also shows averages for each mode
separately: for $\tau\nu$ ($\mu\nu$) alone, the discrepancy is 18% and
2.9$\sigma$ (13% and 2.7$\sigma$).

If the BaBar result is omitted from the average, as in Ref. Rosner:2008yu ,
then the discrepancy is 3.4$\sigma$. On the other hand, if the earlier
measurements Yao:2006px  as well as the BaBar result are included, we find a
4.1$\sigma$ discrepancy.

Experiments.—CLEO Pedlar:2007za ; Ecklund:2007zm  produces $D_{s}$ pairs near
threshold, where the multiplicity is low. Their method reconstructs one
$D_{s}^{(*)}$ and then counts how often the opposite-side $D_{s}$ decays
leptonically. When the charged lepton is a muon, the neutrino is “detected” by
requiring the missing mass-squared to peak at zero. When the charged lepton is
a $\tau$, the identification is made through the subsequent decays
$\tau\\!\to\\!e\nu\bar{\nu}$ and $\tau\\!\to\\!\pi\bar{\nu}$. BaBar
Aubert:2006sd  observes $D_{s}$ coming from the decay
$D_{s}^{*}\\!\to\\!D_{s}\gamma$, produced well above threshold. They compare
the relative number of subsequent $D_{s}\\!\to\\!\mu^{+}\nu$ and
$D_{s}\\!\to\\!\phi\pi$, and then use their own measurement of
$B(D_{s}\\!\to\\!\phi\pi)$ to determine $B(D_{s}\\!\to\\!\ell\nu)$. Belle
Widhalm:2007mi  also observes $D_{s}$ via $D_{s}^{*}\\!\to\\!D_{s}\gamma$, but
the whole event is reconstructed, using a Monte Carlo technique. In summary,
all these measurements have central values and error bars that are
straightforward to interpret, and to combine to obtain Eq. (3).

The measured branching fraction and Eq. (1) yield $|V_{cs}|f_{D_{s}}$. Three-
generation CKM unitarity is assumed, either taking $|V_{cs}|$ from a global
fit to flavor physics Yao:2006px , or setting $|V_{cs}|=|V_{ud}|$. The
difference is numerically irrelevant. Relaxing the assumption cannot lead to
agreement between theory and experiment because unitarity, even for more than
three generations, requires $|V_{cs}|<1$, whereas the discrepancy would
require $|V_{cs}|\approx 1.1$.

Radiative corrections.—The measurements are not, strictly speaking, for
$D_{s}\\!\to\\!\ell\nu$ alone, because some photons are always radiated. The
radiative corrections have been studied, focusing on effects that could
overcome the helicity suppression Burdman:1994ip ; Hwang:2005uk .

For $D_{s}\\!\to\\!\tau^{+}\nu$ there is no sizable helicity suppression. In
the rest frame of the $D_{s}$, the $\tau$ acquires only 9.3 MeV of kinetic
energy, so it cannot radiate much. Explicit calculation Burdman:1994ip  shows
that the radiative corrections are too small to account for the discrepancy
Wang:2001mm .

For $D_{s}\\!\to\\!\mu^{+}\nu$ radiative corrections could play a role due to
processes of the form $D_{s}\\!\to\\!\gamma
D_{s}^{*}\\!\to\\!\gamma\mu^{+}\nu$, where $D_{s}^{*}$ is a (virtual) vector
or axial-vector meson. The transition $D_{s}^{*}\\!\to\\!\mu^{+}\nu$ is not
helicity-suppressed, so the factor $\alpha$ for radiation is compensated by a
relative factor $m_{D_{s}}^{2}/m_{\mu}^{2}$ for omitting helicity suppression.
Using Eq. (12) of Ref. Burdman:1994ip  and imposing the CLEO Pedlar:2007za
cut $E_{\gamma}>300$ MeV, we find that the radiative rate is around 1% and,
hence, insufficient to explain the discrepancy.

Lattice QCD—There are many lattice-QCD calculations for $f_{D_{s}}$ in the
literature, but only Refs. Follana:2007uv ; Aubin:2005ar  include 2+1 flavors
of sea quarks, which is necessary to find agreement for many “gold-plated”
quantities, namely those for which errors are easiest to control Davies:2003ik
. Both calculations start with lattice gauge fields generated by the MILC
Collaboration Bernard:2001av , which employ “rooted staggered fermions” for
the sea quarks. At finite lattice spacing this approach has small violations
of unitarity and locality. Theoretical and numerical evidence suggests that
these vanish in the continuum limit, such that QCD is obtained, with the
undesirable features controlled with chiral perturbation theory. The strengths
and weaknesses of this approach have been reviewed in detail Sharpe:2006re .

Reference Follana:2007uv  reports an error five times smaller than that of
Ref. Aubin:2005ar  for several reasons. The largest uncertainties in Ref.
Aubin:2005ar  come from a power-counting estimate of the discretization error
for the charm quark, and from uncertainties in the chiral extrapolation.
Reference Follana:2007uv  employs a different discretization for the charm
quark, which allows a controlled extrapolation to the continuum limit. Thus,
the discretization error here is driven by the underlying numerical data.

The action for the charm quark in Ref. Follana:2007uv , called HISQ
Follana:2006rc , is the same as that used for the light valence quarks. As a
result the statistical errors are smaller than those of the heavy-quark method
used in Ref. Aubin:2005ar , and the axial current automatically has the
physical normalization. The suitability of HISQ for charm is one of its design
features, it has been tested via the charmonium spectrum Follana:2006rc , and
the computed $D$ and $D_{s}$ masses agree with experiment. The $D^{+}$ decay
constant $f_{D^{+}}$ also agrees with experiment, at $1\sigma$.

Another feature of Ref. Follana:2007uv  is the way the lattice-spacing and
sea-quark mass dependence is fitted. Full details are not yet published, but
it is noteworthy that the same analysis yields $f_{\pi}$ and $f_{K}$ in
agreement with experiment Yao:2006px  and earlier, equally precise, lattice-
QCD calculations Aubin:2004fs . The $D_{s}$ meson is simpler than the pion or
kaon for lattice QCD, because none of the valence quarks is light, so
$f_{D_{s}}$ is easier to determine than $f_{\pi}$. We find that simple
extrapolations lead to the same central values for both $m_{D_{s}}$ and
$f_{D_{s}}$.

The error bar in Eq. (4) is smaller than that in Eq. (3). Therefore, it is the
combined experimental error that provides the yardstick for the deviation. To
illustrate, if the lattice-QCD error bar were doubled, the discrepancy becomes
2.7$\sigma$, 2.5$\sigma$, and 3.3$\sigma$ for $\tau$, $\mu$, and combined.
Hence, even if additional sources of uncertainty are uncovered, evidence for a
deviation may well remain.

Nonstandard effective interactions.—Although the experiments quote the final
states as $\mu^{+}\nu_{\mu}$ and $\tau^{+}\nu_{\tau}$ (and their charge
conjugates), the flavor of the neutrino is not detected. Nonstandard physics
could lead to any neutrino flavor, even a sterile neutrino. However, given the
large effect that needs to be explained, we shall restrict our attention to
amplitudes that could interfere with the standard model, which fixes the
neutrino flavor. Lorentz-invariant new physics may contribute to
$D_{s}\\!\to\\!\ell\nu_{\ell}$ only through the following effective
Lagrangian:

$\frac{C_{A}^{\ell}}{M^{2}}\left(\bar{s}\gamma_{\mu}\gamma_{5}c\right)\left(\bar{\nu}_{L}\gamma^{\mu}\ell_{L}\right)+\frac{C_{P}^{\ell}}{M^{2}}\left(\bar{s}\gamma_{5}c\right)\left(\bar{\nu}_{L}\ell_{R}\right)+{\rm
H.c.},$ (5)

where $C_{A}^{\ell}$ and $C_{P}^{\ell}$ are complex dimensionless parameters,
$M$ is the mass of some particle whose exchange induces the 4-fermion
operators (5), and the $c,s,\ell$ fields are taken in the mass-eigenstate
basis. The hadronic matrix element required for the decay induced by
$(\bar{s}\gamma_{5}c)(\bar{\nu}_{L}\ell_{R})$ is related to the one of Eq. (2)
by partial conservation of the axial current: $(m_{c}+m_{s})\langle
0|\,\bar{s}i\gamma_{5}c\,|D_{s}\rangle=f_{D_{s}}m^{2}_{D_{s}}$. The branching
fraction in the presence of the operators (5) is given by Eq. (1) with
$G_{F}V^{*}_{cs}m_{\ell}$ replaced by

$G_{F}V^{*}_{cs}m_{\ell}+\frac{1}{\sqrt{2}M^{2}}\left(C_{A}^{\ell}m_{\ell}+\frac{C_{P}^{\ell}\,m_{D_{s}}^{2}}{m_{c}+m_{s}}\right)~{},$
(6)

with no helicity suppression in the last term.

The imaginary part of $V_{cs}$ is negligible (in the standard CKM
parametrization Yao:2006px ), so constructive interference, which would
increase $B(D_{s}\\!\to\\!\ell\nu)$, requires the real part of $C_{A}^{\ell}$
or $C_{P}^{\ell}$ to be nonzero and positive. Assuming only one nonzero
coefficient, the amplitude for $\tau^{+}\nu_{\tau}$ ($\mu^{+}\nu_{\mu}$) could
be increased by 12% (8.4%) only if

$\displaystyle\frac{M}{(\mathop{\rm Re}C_{A}^{\ell})^{1/2}}$
$\displaystyle\lesssim$
$\displaystyle\left\\{\begin{array}[]{rl}710~{}\textrm{GeV}&\textrm{for}~{}\ell=\tau\\\\[2.84526pt]
\hphantom{3}850~{}\textrm{GeV}&\textrm{for}~{}\ell=\mu\end{array}\right.\;,$
(9) $\displaystyle\frac{M}{(\mathop{\rm Re}C_{P}^{\ell})^{1/2}}$
$\displaystyle\lesssim$
$\displaystyle\left\\{\begin{array}[]{rl}920~{}\textrm{GeV}&\textrm{for}~{}\ell=\tau\\\\[2.84526pt]
4500~{}\textrm{GeV}&\textrm{for}~{}\ell=\mu\end{array}\right.\;,$ (12)

thereby reducing the discrepancy to $1\sigma$ in each case. These bounds are a
key new result of this Letter, because they constrain any model of new
physics.

The effective interaction (5) also contributes to the semileptonic decays
$D\\!\to\\!K\mu^{+}\nu$. This proceeds through two amplitudes, corresponding
to angular momentum $J=1$ or $0$ for the lepton pair. For $J=1$, the standard-
model amplitude and that from $C_{A}^{\mu}$ are not helicity suppressed, while
that from $C_{P}^{\mu}$ is. For $J=0$, the pattern of helicity suppression is
as for the leptonic decay. Hence, only the $J=1$ part of the rate will be
visible, and as the accuracy of the lattice-QCD calculations improves, the
comparison with experiment will help decide which interactions are responsible
for the effect in $D_{s}\\!\to\\!\ell\nu$. The current status favors
$C_{P}^{\mu}\neq 0$ rather than $C_{A}^{\mu}\neq 0$, because the lattice-QCD
prediction for $D\\!\to\\!K\mu\nu$ Aubin:2004ej  agrees with experiment
Widhalm:2006wz , albeit at the $\sim 7\%$ level.

New particles.—There are three choices for the electric charge of a boson that
can mediate the four-fermion operators (5): $+1,+2/3,-1/3$, corresponding to
the three diagrams shown in Fig. 1. The exchanged boson (taken to be emitted
from the vertex where $c$ is absorbed) is a color singlet if the electric
charge is +1, and a color triplet if the electric charge is $+2/3$ or $-1/3$.
We shall consider only the cases where the new boson has spin 0 or 1, and its
interactions are renormalizable.

11  1 (20,20)(0,0)(0,40)(20,20) (90,40)(70,20)(70,20)(90,0) (20,20)(70,20)4
(-9,37)[c]$c$(-9,5)[c]$\bar{s}$(103,37)[c]$\ell^{+}$(99,5)[c]$\nu$(45,30)[c]$(+1)$(20,20)(0,0)(40,0)(20,20)
(20,60)(40,80)(0,80)(20,60) (20,60)(20,20)3
(-5,70)[c]$c$(-5,10)[c]$\bar{s}$(44,70)[c]$\nu$(49,10)[c]$\ell^{+}$(44,40)[c]$(+2/3)$(20,20)(0,0)(20,20)(40,0)
(40,80)(20,60)(0,80)(20,60) (20,60)(20,20)3
(-5,70)[c]$c$(-5,10)[c]$\bar{s}$(46,70)[c]$\ell^{+}$(45,10)[c]$\nu$(44,40)[c]$(-1/3)$

Figure 1: Four-fermion operators induced by boson exchange.

A new vector boson, $W^{\prime}$, of electric charge $+1$ would contribute
only to $C_{A}^{\ell}$. Such a boson must be associated with a new gauge
symmetry, which makes it difficult to allow large couplings to left-handed
leptons. One possibility is that $W$ and $W^{\prime}$ mix, but the constraint
from electroweak data on mixing ($\lesssim 10^{-2}$) is too strong to allow
noticeable deviations in $D_{s}$ decays. Another possibility is that some new
vector-like fermions transform under the new gauge symmetry and mix with the
left-handed leptons. Such mixing is also tightly constrained, especially by
the nonobservation of vector-like fermions at LEP and the Tevatron. Overall, a
$W^{\prime}$ is inconsistent with Eq. (9), barring perhaps some finely-tuned
elaborate model (e.g., with large $W$-$W^{\prime}$ mixing whose electroweak
effects are cancelled by other particles).

A spin-0 particle of charge +1, $H^{+}$, appears in models with two or more
Higgs doublets. Its interactions, in the mass eigenstate basis for charged
fermions, include

$H^{+}\left(y_{c}\bar{c}_{R}s_{L}+y_{s}\bar{c}_{L}s_{R}+y_{\ell}\bar{\nu}_{\ell}\ell\right)+{\rm
H.c.},$ (13)

where $y_{c},y_{s},y_{\ell}$ are complex Yukawa couplings. The exchange of
$H^{+}$ induces $C_{A}^{\ell}=0$ and

$C_{P}^{\ell}=\frac{1}{2}\left(y_{c}^{*}-y_{s}^{*}\right)y_{\ell}~{},$ (14)

taking $M$ equal to the $H^{+}$ mass. If $H^{+}$ is the charged Higgs boson
present in the Type-II two-Higgs-doublet model, then
$y_{c}/y_{s}=m_{c}/(m_{s}\tan^{2}\\!\beta)$ so that $C_{P}^{\ell}$ can have
either sign Hewett:1995aw , but the Yukawa couplings are too small to be
compatible with Eq. (12). Other models lead to large constructive
interference. For example, a two-Higgs-doublet model where one doublet gives
the $c$, $u$ (but not $d$, $s$, $b$, or $t$) and lepton masses, and has a
vacuum expectation value of $\sim 2$ GeV, yields $|y_{s}|\ll
y_{\tau},y_{c}^{*}\sim O(1)$. Thus, $C_{P}^{\ell}>0$ and the limits (12) are
satisfied for $M\lesssim 500$ GeV. Furthermore, such a model explains why the
deviations in $\tau\nu$ and $\mu\nu$ are comparable. It is encouraging that
this two-Higgs-doublet model does not induce tree-level flavor-changing
neutral currents, and the off-diagonal couplings of $H^{+}$ are CKM
suppressed. Given that this model has not been previously studied, its 1-loop
contributions to flavor-changing processes (such as $b\\!\to\\!s\gamma$) need
to be computed before deciding whether some fine tuning is required to evade
experimental bounds.

The charge $-1/3$ and $+2/3$ exchanges correspond to leptoquarks. A scalar
charge $+2/3$ exchange arises for the $(3,2,+7/6)$ set of
$SU(3)_{c}\\!\times\\!SU(2)_{W}\\!\times\\!U(1)_{Y}$ charges. This leptoquark
appears, for example, in a new theory of quark and lepton masses Dobrescu:2008
. Let $r=(r_{u},r_{d})$ be the doublet leptoquark, where $r_{d}$ is its charge
$+2/3$ component. The interaction terms relevant here, written in the same
basis as (5), are
$\lambda_{c\ell}r_{d}\bar{c}_{R}\nu_{L}^{\ell}+\lambda^{\prime}_{s\ell}r_{d}\bar{s}_{L}\ell_{R}$.
The $r_{d}$ exchange gives $C_{A}^{\ell}=0$ and
$C_{P}^{\ell}=-\lambda_{c\ell}^{*}\lambda^{\prime}_{s\ell}/4$. Since the
leptoquark couplings can have any phase, the new amplitude can interfere
constructively. Still, various flavor processes constrain the couplings of
$r$. Even if its couplings to first-generation fermions were negligible, the
lepton-flavor violating decays $\tau\\!\to\\!\mu\bar{s}s$, where $\bar{s}s$
hadronizes to $\eta$, $\eta^{\prime}$, $\phi$ or $K\bar{K}$, set a lower limit
on $M^{2}\\!/|\lambda^{\prime}_{s\tau}\lambda^{\prime}_{s\mu}|$, which is hard
to reconcile with Eq. (12). One way out would be a model with two $r$
leptoquarks, with one coupling to $\tau$ and the other one to $\mu$. The
constraint from $\tau\\!\to\\!\mu\bar{s}s$ similarly disfavors spin-1
leptoquarks of charge $+2/3$.

A scalar leptoquark of charge $-1/3$ (also discussed in Dobrescu:2008 ) arises
in the case of two sets of $SU(3)_{c}\times SU(2)_{W}\times U(1)_{Y}$ charges:
$(3,1,-1/3)$ or $(3,3,-1/3)$. Let us denote the former by $\tilde{d}$. Its
Yukawa couplings are given by

$\tilde{d}\left[\kappa_{\ell}\left(\bar{c}_{L}\ell_{L}^{c}-\bar{s}_{L}\nu_{L}^{\ell
c}\right)+\kappa^{\prime}_{\ell}\,\bar{c}_{R}\ell_{R}^{c}\right]+{\rm H.c.},$
(15)

where $\kappa_{\ell}$ and $\kappa^{\prime}_{\ell}$ are complex parameters.
These interactions are present, for example, in $R$-parity violating
supersymmetric models (their effect on $D_{s}\\!\to\\!e^{+}\nu$ has been
analyzed in Ref. Akeroyd:2002pi ). The $\tilde{d}$ exchange, as in the last
diagram of Fig. 1, gives (for $M$ equal to the $\tilde{d}$ mass)

$C_{A}^{\ell}=\frac{1}{4}\,|\kappa_{\ell}|^{2}\;\;\;,\;\;\;C_{P}^{\ell}=\frac{1}{4}\,\kappa_{\ell}\kappa^{\prime*}_{\ell}~{}~{}.$
(16)

For $|\kappa_{\ell}^{\prime}/\kappa_{\ell}|\ll m_{\ell}m_{c}/m_{D_{s}}^{2}$,
the interference is automatically constructive [see Eq. (6)], and the
resulting deviations in $\tau\nu$ and $\mu\nu$ are approximately equal if
$|\kappa_{\mu}|\approx|\kappa_{\tau}|$. Moreover, there are no severe
constraints from other processes on the couplings $\kappa_{\ell}$ and
$\kappa^{\prime}_{\ell}$ with $\ell=\tau$ or $\mu$. The $\tilde{d}$ couplings
to the electron can be forbidden by a symmetry, and the ones to first-
generation quarks could be small.

The $(3,3,-1/3)$ scalar leptoquark includes an $SU(2)_{W}$ component of charge
$-4/3$ which mediates $\tau\\!\to\\!\mu\bar{s}s$. The vector leptoquark of
charge $-1/3$ has the same problem.

Conclusions.—We have argued that the $3.8\sigma$ discrepancy between the
standard model and the combined experimental measurements of
$D_{s}\\!\to\\!\ell\nu$ appears so far to be robust, and thus it is worth
interpreting it in terms of new physics. The upper bounds (9) and (12) on the
scale of four-fermion operators are low enough to allow exploration of the
underlying physics at the LHC.

A $\tilde{d}$ scalar leptoquark of charge $-1/3$ may solve the $D_{s}$ puzzle
without running into conflict with any other measurements. At the LHC, the
$\tilde{d}$ can be strongly produced in pairs, and the final states would be
$\ell^{+}\ell^{-}jj$, where $\ell$ is a $\tau$ or a $\mu$, and $j$ is a
$c$-jet. Given that there are two $\ell j$ pairs, each of them forming a
resonance at the $\tilde{d}$ mass, the backgrounds can be kept under control.
The current limits on the $\tilde{d}$ mass from similar searches at the
Tevatron are around 200 GeV Abulencia:2005ua .

An alternative explanation is provided by an $H^{+}$ exchange in a (new) model
where a Higgs doublet gives masses to the charged leptons and $c$ and $u$
quarks, and a second Higgs doublet gives masses to the down-type and top
quarks. Both the leptoquark and charged Higgs solutions lead naturally to
comparable increases in the branching fractions for
$D_{s}\\!\to\\!\tau^{+}\nu$ and $D_{s}\\!\to\\!\mu^{+}\nu$, as suggested by
the data.

Acknowledgments.—We thank P. Fox, E. Lunghi, S. Stone and R. Van de Water for
helpful discussions. Fermilab is operated by Fermi Research Alliance, LLC,
under US DoE Contract DE-AC02-07CH11359.

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