# Roles for Computing in Social Change

Rediet Abebe  Harvard University<EMAIL_ADDRESS>,  Solon Barocas
Microsoft Research and Cornell University<EMAIL_ADDRESS>,  Jon
Kleinberg  Cornell University<EMAIL_ADDRESS>,  Karen Levy  Cornell
University<EMAIL_ADDRESS>,  Manish Raghavan  Cornell University
<EMAIL_ADDRESS>and  David G. Robinson  Cornell University
<EMAIL_ADDRESS>
(2020)

###### Abstract.

A recent normative turn in computer science has brought concerns about
fairness, bias, and accountability to the core of the field. Yet recent
scholarship has warned that much of this technical work treats problematic
features of the status quo as fixed, and fails to address deeper patterns of
injustice and inequality. While acknowledging these critiques, we posit that
computational research has valuable roles to play in addressing social
problems — roles whose value can be recognized even from a perspective that
aspires toward fundamental social change. In this paper, we articulate four
such roles, through an analysis that considers the opportunities as well as
the significant risks inherent in such work. Computing research can serve as a
diagnostic, helping us to understand and measure social problems with
precision and clarity. As a formalizer, computing shapes how social problems
are explicitly defined — changing how those problems, and possible responses
to them, are understood. Computing serves as rebuttal when it illuminates the
boundaries of what is possible through technical means. And computing acts as
synecdoche when it makes long-standing social problems newly salient in the
public eye. We offer these paths forward as modalities that leverage the
particular strengths of computational work in the service of social change,
without overclaiming computing’s capacity to solve social problems on its own.

social change, inequality, discrimination, societal implications of AI

††journalyear: 2020††copyright: rightsretained††conference: Conference on
Fairness, Accountability, and Transparency; January 27–30, 2020; Barcelona,
Spain††booktitle: Conference on Fairness, Accountability, and Transparency
(FAT* ’20), January 27–30, 2020, Barcelona, Spain††doi:
10.1145/3351095.3372871††isbn: 978-1-4503-6936-7/20/01††ccs: Social and
professional topics Computing / technology policy††ccs: Applied computing
Computers in other domains

##  1\. Introduction

In high-stakes decision-making, algorithmic systems have the potential to
predict outcomes more accurately and to allocate scarce societal resources
more efficiently — but also the potential to introduce, perpetuate, and worsen
inequality. Algorithmic accountability, fairness, and bias have quickly become
watchwords of mainstream technical research and practice, gaining currency
both in computer science scholarship and in technology companies. And these
concerns are having a public moment, with policymakers and practitioners newly
attuned to their import.

Recently, these concerns have sparked debate about the relationship between
computing and social change — in particular, about the degree to which
technical interventions can address fundamental problems of justice and
equity. Scholars have recently raised concerns about taking a computational
lens to certain social problems, questioning whether modifications to
automated decision-making can ever address the structural conditions that
relegate certain social groups to the margins of society (Eubanks, 2018;
Crawford, [n. d.]; Gebru, 2019; Broussard et al., 2019; Green, 2018; D’Ignazio
and Klein, 2019). On these accounts, realizing principles of justice and
equity requires addressing the root social, economic, and political origins of
these problems — not optimizing around them (Barabas et al., 2018; Costanza-
Chock, 2018; Whittaker et al., 2018; Pasquale, 2018; Powles, 2018; Selbst et
al., 2019; Overdorf et al., 2018; Greene et al., 2019; Dencik et al., 2018;
Hoffmann, 2019; Gangadharan and Niklas, 2019; Bennett and Keyes, 2019).

This debate has happened against the backdrop of a long history of critical
reflection on the values embodied in technical artifacts, and the need to
design with such values in mind. Scholars have spent decades working to draw
attention to the normative commitments expressed in and through technology.
This call for recognition of values has been a core project of science and
technology studies (Winner, 1980; Agre, 1997; Jasanoff, 2006), Values-in-
Design (Introna and Nissenbaum, 2000; Friedman and Hendry, 2019), legal
scholarship (Reidenberg, 1997; Lessig, 2009; Citron, 2018), and allied
disciplines for years, and remains an active area of research. Algorithms have
become objects of particular scrutiny over the past decade (Gillespie and
Seaver, [n. d.]).

Within computer science, the machine learning and mechanism design communities
have been particularly active in taking up these concerns. Both fields have
been heeding the call for attention to values, politics, and “social good”
more generally, holding more than twenty technical workshops and conferences
between them on some variation of fairness, bias, discrimination,
accountability, and transparency in the last five years (e.g., (Ekstrand and
Levy, [n. d.]; Abebe and Goldner, 2018)).

And yet, these recent efforts have been met with concern that computer science
has failed to target the right point of intervention. In focusing on changes
to decision-making and allocation, these endeavors risk obscuring the
background conditions that sustain injustices. For instance, a computational
intervention that aims to equalize offers of college admission across
demographic groups might function as a less ambitious substitute for the
deeper and more challenging work of improving high school instruction in low-
income neighborhoods. Similarly, an intervention at the selection phase in an
employment context might mask the impact of a hostile workplace culture or
other barriers to long-term employee success — problems for which other (and
perhaps non-technological) responses might be indicated (Barocas, 2014).

There is a long-standing tension between strategies that seek to intervene
incrementally within the contours of an existing social and political system
and those that seek more wholesale social and political reform. Existing work
has made clear how computational approaches may contribute to the former style
of intervention. Here, we ask whether, and to what extent, computing can
contribute to the latter style as well. We pose this question while
recognizing the critical scholarship we have described above, and we
emphatically reject the idea that technological interventions can unilaterally
“solve” injustice in society — an approach some critics condemn as
“solutionism” (Morozov, 2013). Our goal is to cut a path between solutionist
and critical perspectives by describing potential roles through which
computing work can support, rather than supplant, other ways of understanding
and addressing social problems.

Meaningful advancement toward social change is always the work of many hands.
We explore where and how technical approaches might be part of the solution,
and how we might exploit their unique properties as a route to broader
reforms. In this way, we seek to address two distinct audiences: this paper is
a call to our colleagues in computer science to reflect on how we go about our
work in this area, as well as a response to our fellow critical scholars who
question computing’s value in addressing social problems. In what follows, we
propose a series of four potential roles for computing research that may be
well-aligned with efforts for broader social change.111These proposals are in
the spirit of other scholars’ recent calls to recognize the political nature
of computational work and articulate new modes of engagement for computing
(e.g., (Green, 2018)).

The roles we offer here are intentionally modest: they are ways to leverage
the particular attributes of computational work without overclaiming its
capacity. We argue that these are worthy and plausible aspirations for our
nascent field. Our list is illustrative, not exhaustive, and our categories
are not mutually exclusive. And like any attempt to effectuate change, the
approaches we outline carry hazards of their own, which we also explore
below.222While we include some examples from low- and middle-income nations,
many of the examples and hence discussions are focused around the United
States and other developed nations. There is an emerging set of discussions
around risks and challenges in using machine learning specifically in the
context of developing nations, including the annual Machine Learning for
Development Workshop Series (De-Arteaga et al., 2018), which also faces many
of the structural challenges we engage here.

##  2\. Computing as Diagnostic

_Computing can help us measure social problems and diagnose how they manifest
in technical systems._

While computing cannot solve social problems on its own, its methods can be
used to diagnose and precisely characterize those problems. Computational
approaches, used in tandem with other empirical methods, can provide crucial
evidentiary support for work that attends to values in technology — even if
computing itself is an insufficient remedy. In this sense, there is a role for
computer science and its methods to play in critically interrogating computing
itself.

Many now-classic studies in the field take this approach, giving us a new
sense of the shape and depth of a long-standing problem by applying a
computational lens. Latanya Sweeney’s analysis of an ad delivery platform
demonstrated, among other things, that arrest-related ads were more likely to
appear in response to searches for first names commonly associated with
African-Americans (Sweeney, 2013), likely reflecting Internet users’
disproportionate propensity to click on ads suggesting that African-Americans,
rather than people of other races, have criminal records. Teams of computer
science researchers have demonstrated the gender biases inherent in word
embeddings and the difficulties they create for machine translation and other
language tasks (Caliskan et al., 2017; Bolukbasi et al., 2016). More recently,
Joy Buolamwini and Timnit Gebru demonstrated that several commercially
available facial analysis systems perform significantly worse on women and
individuals with darker skin tones (Buolamwini and Gebru, 2018). These
analyses have enhanced our ability to document discriminatory patterns in
particular sociotechnical systems, showing the depth, scope, and pervasiveness
of such problems and illuminating the mechanisms through which they occur.

And yet, while these studies sometimes point toward improvements that could be
made (e.g., to ensure that ads appear at comparable rates across groups, to
use caution with language models trained on text corpora with ingrained human
biases, or to train facial analysis systems on a more diverse dataset), they
do not purport to offer computational solutions to the problems they
illustrate. From this perspective, recent attempts to develop formal
definitions of fairness, while often presented as a solution to bias, can be
understood as diagnostics first and foremost — as new methods and metrics for
evaluating normatively relevant properties of computational systems (Barocas
et al., 2019, Chapter 2).

Diagnostic work of this sort can be particularly valuable when confronting
systems that are “black-boxed”: when the criteria of decision-making (and the
values that inhere therein) are obscured by complexity, trade secret, or lack
of transparency, diagnostic studies can provide an important means of auditing
technical processes (Sandvig et al., 2014). And such an approach can help to
highlight technological dimensions of a social problem in a way that would be
difficult to interrogate otherwise. For example, Abebe et al. leverage search
data to surface unmet health information needs across the African continent —
demonstrating when and how search engines display low-quality health
information to users. A lack of high-authority websites relevant to users’
search queries might mean that results highlight natural cures for HIV, rather
than scientifically sound medical advice (Abebe et al., 2019).

Other recent work has sought to advance the diagnostic role that computing can
play by providing a principled approach to interrogating the machine learning
pipeline (Gebru et al., 2018; Mitchell et al., 2019). These diagnostic efforts
do not present themselves as solutions, but rather as tools to rigorously
document practices. Thus, when compared with other computing interventions
that aim directly at incremental improvements, they are less vulnerable to
becoming a substitute for broader change. These efforts are not intended to
absolve practitioners of the responsibility to critically examine the system
in question, but instead to aid in that investigation.

Without purporting to resolve underlying social problems, diagnostic studies
that use computational techniques can nevertheless drive real-world impacts on
the systems they investigate. For example, in response to Buolamwini and
Gebru’s findings (Buolamwini and Gebru, 2018), Microsoft and IBM reported that
they had improved the accuracy of their facial analysis technologies along
gender and racial lines (Roach, 2018; Puri, 2018). Continued research (e.g.,
(Raji and Buolamwini, 2019)) and advocacy following this work has led to
policy-making and government action that questions, limits, or prohibits the
use of facial recognition in a number of contexts.

Some important caveats are warranted. First, computing is not unique in its
capacity to help us diagnose social problems, even those manifest in technical
systems. Disciplines like science and technology studies (STS), sociology, and
economics provide their own sets of tools to interrogate sociotechnical
phenomena — including tools that capture important dimensions poorly addressed
by computational approaches. For example, descriptive ethnographic research is
essential for understanding how social and organizational practices intersect
with technical systems to produce certain outcomes (e.g., (Brayne, 2017;
Christin, 2018). Computing is only one of multiple approaches that should be
brought to bear on the analysis — even when it may appear that the system in
question (e.g., facial recognition technology) is primarily technical. A
holistic analysis of a sociotechnical system must draw from a wide range of
disciplines in order to comprehensively identify the issues at stake (Crawford
and Calo, 2016; Selbst et al., 2019).

Second, our optimism as to the potential benefits of computing as diagnostic
must be tempered by a healthy degree of skepticism. Once metrics and formulae
are used to characterize the performance of a system, individuals and
organizations often have incentives to optimize towards those metrics in ways
that distort their behavior, and corrupt the meaning of the metric. This
process puts any targeted metric at risk of becoming a less useful measure
over time — a phenomenon known as Goodhart’s Law (Hoskin, 1996) or Campbell’s
Law (Campbell, 1979). We can see this worry instantiated, for example, in the
Equal Employment Opportunity Commission’s 4/5ths rule. The rule applies to
employee selection procedures, and holds that when the selection rate for one
protected group is less than 80% of that of another group, such a gap is
strong evidence of proscribed disparate impact. Initially intended as a
guideline to aid in diagnosis of potentially discriminatory practices, it has
become a target in itself for practitioners who strictly enforce the 4/5ths
rule while sometimes failing to consider other aspects of discrimination and
bias (Raghavan et al., 2020). Thus, when using computational techniques as
diagnostic tools, care must be taken to prevent diagnostics from implicitly
becoming targets.

Diagnostic approaches may be stymied when technical systems have been
insulated from outside scrutiny (Pasquale, 2015). For example, while a number
of studies have used computational methods to characterize proprietary
algorithms used in news curation (Lurie and Mustafaraj, 2019), resume search
(Chen et al., 2018), and ad delivery (Datta et al., 2015; Ali et al., 2019),
their methodologies must work around the constraints imposed by the
institutions that operate these systems. Moreover, some testing methods can be
further impeded by legal restrictions on researchers’ activities (e.g., the
disputed use of the Computer Fraud and Abuse Act to attach criminal penalties
to audit methods that involve violating a website’s terms of service (Patel,
2018)). In such cases, it can be infeasible to provide a fully comprehensive
or conclusive diagnosis.

Finally, it can be tempting to view diagnosis itself as a goal: precisely
stating the problem, we might hope, will naturally lead to a solution. Indeed,
a good diagnosis can motivate the relevant parties to work towards remedying
the concerns it surfaces. The above examples, and others that follow in
subsequent sections, demonstrate that illuminating a problem through technical
examination can lead to positive change. However, it is important not to
confuse diagnosis with treatment: there are a number of domains in which we
are well aware of the extent of the problem (e.g., mass incarceration or
homelessness), yet do not have sufficient will or consensus to adequately
address it. As Ruha Benjamin notes, the production of audit data about a
social problem must be accompanied by narrative tools that help to drive
change: “[d]ata, in short, do not speak for themselves and don’t always change
hearts and minds or policy” (Benjamin, 2019).

##  3\. Computing as Formalizer

_Computing requires explicit specification of inputs and goals, and can shape
how social problems are understood._

People and institutions charged with making important decisions often speak in
general terms about what they are doing. A standard that says that social
workers must act in the “best interests of the child,” for instance, or an
employer’s stated intent to hire the “most qualified applicant,” leave wide
latitude for interpretation. This vagueness is a double-edged sword. At its
best, such broad flexibility lets decision-makers consider factors that are
specific to a particular case or situation, and that could not be stated in a
rigid rule. Vagueness is also an important political tool: laws are often
worded broadly because no majority of legislators could agree on a more
specific plan. Yet an underspecified standard may effectively delegate
important choices to people and situations that are less open to scrutiny and
supervision, and where individual bias may play a larger role. The relative
merits of holistic and flexible “standards” versus more rigid and consistent
“rules” are a prominent topic of debate among legal scholars (Kaplow, 1992).

Increasing the role of computing within high-stakes decisions often moves
decision-making away from generalized standards and toward more explicitly
specified, rule-based models (Citron, 2018). A computational model of a
problem is a statement about how that problem should be understood. To build
and use a model is to make, and to promote as useful, a particular lens for
understanding what the problem is. The nature of computing is such that it
requires explicit choices about inputs, objectives, constraints, and
assumptions in a system. The job applicant who is ranked first by a
statistical model or other algorithm will not simply be the one holistically
deemed most qualified; she will be the one ranked first on the basis of
discrete numbers and specific rules. Those rules will reflect a range of
concrete judgments about how job performance should be defined, measured, and
forecasted.

This quality of computing is often bemoaned: Algorithms are cold calculators
that collapse nuance and execute their tasks in ignorance of the histories and
contexts that precede and surround them (Noble, 2018; Selbst et al., 2019;
Eubanks, 2018). But this same quality may also be a source of political
potential. Because they must be explicitly specified and precisely formalized,
algorithms may help to lay bare the stakes of decision-making and may give
people an opportunity to directly confront and contest the values these
systems encode (Kleinberg et al., 2016). In the best case, the need to
disambiguate general policy aims may provide a community with important
touchpoints for democratic deliberation within policy processes.

A model may be rigid in the way that it formalizes the structure of a problem,
but the act of formalization is, paradoxically, a creative one, and
increasingly important to social and political outcomes. In many settings
where automated decision-making tools are used, this creative process of
designing a system is a potential opportunity for non-technical stakeholders,
including responsible officials and members of the public, to hash out
different ways in which a problem might be understood. Questions in this vein
include: what is the specific predicted outcome that serves as the basis for
decision-making, and why was it chosen over competing alternatives (Passi and
Barocas, 2019)? Which outcomes should be treated as indicia of “good” job
performance (Barocas and Selbst, 2016)? How much risk should be considered
“high” risk, meriting special treatment or attention from a court or a social
services agency (Koepke and Robinson, 2018)? The process of formalization
requires that someone make these decisions — and gives us the opportunity to
explicitly consider how we would like them to be made.

The formalism required to construct a mathematical model can serve as an
opportune site of contestation, a natural intermediate target for advocacy.
Transparency and accountability, moreover, are themselves intermediate
virtues: Advocates will most often pursue these ends not out of an abstract
interest in procedural questions, but rather as a way to influence the
substance of decisions that the eventual algorithm will reach. Calls for
transparency, accountability, and stakeholder participation — while crucial in
their own right — ultimately do not resolve matters of substantive policy
debate. These procedural values concern how rules are made, but leave
unaddressed what those rules should actually be. The process of formalization
can bring analytic clarity to policy debates by forcing stakeholders to be
more precise about their goals and objectives.

This observation may seem out of step with the widely recognized risk that
machine learned models may be so complex as to defy understanding. It may be
difficult to succinctly describe how a model weighs different features or to
provide a meaningful explanation for such a weighing. But all models are
surrounded by technical and policy choices that are amenable to broad
understanding and debate. The choice of objective function, for instance, and
debates over which features to use as candidates for inclusion in the eventual
model, are frequently delicate and politically important questions.

For example, using statistical models to assess people who have been accused
of crimes is a controversial and widespread practice. These tools are
described as “risk assessment” tools, but the probabilities that they actually
forecast — such as the chance that the accused person will miss a future
appointment related to the case — do not directly correspond to the narrow
sense of “risk” that is legally salient at a bail hearing, namely the risk
that the defendant will abscond from the jurisdiction or will violently harm
another person before a trial can be held (Koepke and Robinson, 2018). In
situations like this, where the relevant risk is substantially narrower and
more serious than the risks actually being measured and predicted by an
algorithm, the algorithm effectively paints with too broad a brush,
stigmatizing the accused by implicitly exaggerating the hazard that they pose
(Koepke and Robinson, 2018). Many failures to appear at a courtroom hearing
are traceable to anodyne causes like a lack of transportation, or confusion
about the time and place of the appointment. Formalizing the problem in a way
that conflates these risks — as some pretrial instruments do — is a
substantive and consequential decision, one that here operates to the
detriment of the accused. For this among many other reasons, a broad coalition
of more than a hundred civil rights organizations, as well as a substantial
and growing number of technical experts on algorithms and criminal law, either
oppose the use of these instruments in the forms they currently take or else
have raised serious concerns about their use (Leadership Conference on Civil
and Human Rights, 2018).

The debate over how to formalize pretrial risk — and over how and indeed
whether to use these instruments — is highly active at the time of this
writing. Some advocates and scholars have argued that any feasible
formalization of the problem, given the available data, will have drawbacks so
serious as to draw into question the use of actuarial methods at all (Mayson,
2019; Eckhouse et al., 2018; Leadership Conference on Civil and Human Rights,
2018; Koepke and Robinson, 2018). For instance, differing base rates of arrest
across racial groups may mean that any feasible predictive system will amplify
longstanding disparities by over-predicting arrests among stigmatized minority
groups. Other activists, even while objecting to data-driven methods for these
and other reasons, are also seeking to generate new kinds of data for the
pretrial system to use, such as formalized and measurable evidence of the
community support available to an accused person (Jayadev, 2019). The inherent
challenges of formally modelling this problem are driving _both_ changes to
the models being used, and a reconsideration of whether risk assessment should
be used at all.

In another context, Abebe et al.’s work (Abebe et al., 2020) on income shocks
demonstrates that alternative objective functions can result in very different
allocations, even when the broad policy goal is the same. When allocating
subsidies to households to prevent them from experiencing adverse financial
outcomes due to income shocks, we might reasonably want to minimize the
expected number of people that will experience a certain negative financial
state (a min-sum objective function). Alternatively, we might instead
reasonably determine that we want to minimize the likelihood that the worst-
off family experiences this financial state (a min-max objective function).
Abebe et al. show that these alternative policy goals — both wholly plausible
and defensible — can result in some instances in the exact reverse ordering of
which households to prioritize for subsidies. Formalization, then, requires us
to think precisely about what we really want when we say we want to accomplish
some goal.

Of course, just because decisions must be made about how to formalize a
problem does not mean those decisions will necessarily be made in a
transparent, accountable, or inclusive way. There are many reasons why they
may not be.

Some values may be harder to incorporate into formal models than others,
perhaps because they are difficult to quantify (Friedman and Nissenbaum,
1996). What we choose to incorporate into models is largely driven by
available data, and this constraint may press both scholars and practitioners
to rely on measures that elide or distort important aspects of a situation, or
that are not conducive to advocating for broader change. Although moral
considerations are often important in determining system design, practical
factors — such as the cost savings involved in using readily-available data,
rather than gathering or generating different evidence — often play a vital
role as well (Clarke, 1988; Citron, 2018; Passi and Barocas, 2019).

As a result, for stakeholders primarily committed to values that may be ill-
served by the process of formalization, the decision to involve computing in a
decision process may itself be a morally controversial one. The opportunity
that formalization poses for constructive intervention has a negative
corollary — that pragmatic technical concerns can draw attention away from the
underlying policy goal that a model is supposed to serve. At the same time,
researchers may be able to help illuminate the constraints and biases in
existing sources of data — such as child welfare “substantiation” outcomes,
official findings of disability, or police arrest patterns — and to underline
both the importance and the expense of generating alternative data that may be
a necessary precondition for socially responsible forecasting (e.g., (Wald and
Woolverton, 1990)).

If we fail to pay attention to the question of whether our formulation
carefully reflects the true goals of the domain, models can easily fall prey
to inaccurate assumptions or failures of imagination. In particular, the
formalisms that a powerful institution adopts to judge individual people risk
focusing moral evaluation and attention on individuals rather than on systems,
a trend that some experts have long recognized as invidious. As far back as
1979, Donald Campbell argued that those who study public programs “should
refuse to use our skills in ad hominem research …We should be evaluating not
students or welfare recipients but alternative policies for dealing with their
problems” (Campbell, 1979). More recent work has echoed this call for an
evaluative focus on systemic “interventions over [individual] predictions”
(Barabas et al., 2018).

For instance, a discussion about the quality of employees in an organization
might implicitly assume that the relevant metrics for each employee could be
computed as a function of their attributes in isolation. This approach,
however, would be unable to assess the quality of the team of employees that
results, or the differing ways in which alternative candidates might alter the
team’s performance, since a focus on individual attributes would fail to model
anything about interactions or complementarities among multiple employees
(Page, 2008).

##  4\. Computing as Rebuttal

_Computing can clarify the limits of technical interventions, and of policies
premised on them._

In a world where practitioners are tempted to pursue computational
interventions, technical experts have a unique contribution to make in
illustrating the inherent limits of those approaches. Critical reflections on
the limits of computing may drive some stakeholders — and at times, the
political process as a whole — to reject computational approaches in favor of
broader change. Technical experts can be particularly well positioned to
recognize and declare these limits.

The belief that the design and deployment of computational tools is a neutral
process — and one that can be assumed to be beneficial — may be long debunked
in academic circles, but it remains a powerful force among policymakers and
the general public. When scholars of computing recognize and acknowledge the
political valence of their technical work, they can make it more difficult for
others to leverage computing — both practically and rhetorically — for
political ends. Technical experts can be particularly effective in contesting
claims about technologies’ capabilities and neutrality. This opportunity is
the converse of the risk that the technical research community may “fail to
recognize that the best solution to a problem may not involve technology”
(Selbst et al., 2019), and that exploration of technological approaches may
distract from broader aims.

For example: a group of computing scholars recently called on Immigration and
Customs Enforcement (ICE) to reconsider its plans to use an algorithm to
assess whether a visa applicant would become a “positively contributing member
of society” as part of its “Extreme Vetting” program. The experts explained
that “no computational methods can provide reliable or objective assessments
of the traits that ICE seeks to measure” (Abelson and et. al, 2016), and the
program was later abandoned (Harwell and Miroff, 2018). Other advocates —
drawing on computer science research — have warned of the limits of natural
language processing tools for analyzing social media posts for purposes of
“solving” the problems of identifying fake news, removing extremist content,
or predicting propensity for radicalization. The advocates noted that such
tools are “technically infeasible” for such purposes and advised that
“policymakers must understand these limitations before endorsing or adopting
automated content analysis tools” (Duarte et al., 2018). Computing scholars
and practitioners can play a critical role in advocating against inappropriate
use of computational tools or misunderstandings of what they can accomplish.

Another mode of computing as rebuttal is work that uses a formalization of the
underlying computational problem to establish mathematically rigorous limits
on the power of algorithms to provide certain guarantees. One recent example
comes from the study of prediction algorithms for risk assessment: formal
analysis has shown that when two groups differ in their base rates for some
behavior of interest, any well-calibrated algorithm assigning probabilities of
this behavior to individuals must necessarily produce differences between
groups in the rate at which people are inaccurately labeled “high-risk” or
“low-risk” (Chouldechova, 2017; Kleinberg et al., 2017). This result thus
establishes that no matter what algorithm is employed, any way of assigning
risk estimates to two groups of differing base rates will necessarily produce
some kind of disparity in outcomes between the groups; we cannot eliminate the
problem through a better choice of algorithm — or better process for making
predictions, even those involving human judgment. Formal results of this type
can expose the limitations of an entire category of approaches — in this case,
the assignment of risk scores to individuals — in a way that the deficiencies
of any one specific algorithm cannot.

Critiques of computing research can also illustrate the limitations of
existing policy frameworks. Much computational research on fairness is built
on frameworks borrowed from discrimination law — for instance, the definition
of protected categories, the 4/5ths rule as a metric for assessing disparate
impact, and, perhaps most crucially, the belief that fairness can be achieved
by simply altering how we assess people at discrete moments of decision-making
(e.g., hiring, lending, etc.) (Barocas et al., 2019). At best, discrimination
law is an incomplete mechanism to remedy historic injustices and deeply
entrenched structures of oppression. Work on computational fairness inherits
these limitations (Hoffmann, 2019). Yet, exposing the limits of algorithmic
notions of fairness has exposed the limits of the underlying legal and
philosophical notions of discrimination on which this work has built. In this
regard, computer science has not simply taken normative concerns on board; it
has helped to clarify and deepen our understanding of the values at stake
(Xiang and Raji, 2019; Mayson, 2019; Hellman, 2019).

Methods from computer science can also change how stakeholders perceive a
problem domain, effectively serving as a rebuttal to entrenched policy
thinking. For example, researchers who work on matching mechanisms for refugee
resettlement have argued that by using more information about local
communities — for instance, matching refugees to places that already have a
successful cluster of earlier immigrants speaking the same language — they can
improve resettlement outcomes and in turn increase the number of refugees that
communities are willing to accept (Kominers, 2018; Delacrétaz et al., 2016;
Jones and Teytelboym, 2018). Such steps are important because, as Robert
Manduca has argued, “many of our pressing social problems cannot be solved by
better allocating our existing sets of outcomes” (Manduca, 2019). In some
cases, computing can upend long-standing beliefs about the constraints under
which policymakers are expected to allocate a scarce resource or opportunity.
It can rebut needlessly narrow conceptualizations of a problem, expanding the
set of outcomes considered achievable and the scope of the political debate.
Conversely, by exposing the limits of what a more optimal allocation can
accomplish on its own, computing can also help justify the non-computational
changes that are necessary for effective reform. A system for allocating
scarce housing beds may make better use of a limited stock (Eubanks, 2018),
and yet may ultimately highlight the need for more beds.333Eubanks (Eubanks,
2018) discusses the January 2016 LA homelessness strategy report by Mayor Eric
Garcetti which benefited from a previously-implemented coordinated entry
system for allocating homelessness services in the city. This report was
followed by policy changes that increased funding for low-income housing and
homelessness services.

Computing research has demonstrated the impossibility, infeasibility, or
undesirability of proposed policies in other contexts as well. In the area of
electronic voting, more than a decade of research and effort has demonstrated
that secure, anonymous, and fully electronic voting systems are infeasible
with present and reasonably foreseeable computer science methods. This view is
now widely understood by policymakers, and has led large numbers of
policymakers away from initial misplaced enthusiasm for paperless high-tech
voting equipment. Similarly, an authoritative consensus among computing
researchers about the infeasibility of secure “backdoors” in encryption
technology has played a major role in dampening policymaker enthusiasm for
broad surveillance mandates (Abelson et al., 2015).

Using computing as a tool for rebuttal carries risks. Perhaps the most
significant is that proclamations about what a computational tool is incapable
of may focus attention on improving said tool — which may or may not be the
desired policy outcome. This risk often accompanies critiques about inaccuracy
and bias in predictive systems: if these critiques are perceived as the system
not being (yet) “good enough” to accomplish designated policy aims well,
technical improvements to the tool may be perceived as sufficient to address
these problems. The danger, then, is that rebuttals run the risk of
transforming a policy discussion into one about what is technically possible,
rather than what social aims are ultimately desirable.

A decade ago, Kevin Haggerty observed this exact dynamic in debates about CCTV
surveillance. The campaign against it had tried to push back against its
adoption by pointing out its lack of efficacy. Haggerty noted that these
debates were “insidious precisely because they fixate exclusively on a
standard of ‘functioning.’ Such a narrow frame ignores the prospect that the
true nightmare scenario might be that all of these technologies might actually
work; that they might function perfectly, with full enrollment, complete
transparency, seamless integration and exacting discriminatory power. Indeed,
when critics point out that a surveillance technology does not work, one
wonders if they would be thrilled if it did. Rather than confronting the
dystopian potentials inherent in the maximum surveillance scenario, the
political/methodological knife fight seems to unwittingly help drive systems
towards developing ever-greater capacities” (Haggerty, 2009).

Researchers focused on the risks of facial recognition seem to have avoided
the same trap this round, raising alarm about both its likely failures and
threatening successes. Nabil Hassein was (to our knowledge) the first to
publicly observe that working to equalize the accuracy of facial recognition
across racial groups is an entirely different undertaking than seeking to
restrict the use of surveillance based on facial recognition by law
enforcement altogether (Hassein, 2017). The former approach addresses specific
deficiencies in algorithms used by government actors and others, while the
latter argues that the use of even a perfectly accurate facial recognition
algorithm by police would be an amplifier for oppression and injustice. On
this account, the best alternative to a bad algorithm might not be a better
algorithm — it might be no algorithm at all. Channeling these concerns, a
number of scholars published an open letter calling on Amazon to stop selling
its facial recognition technology to law enforcement altogether (Concerned
Researchers, 2019). Several cities in the United States have issued bans
against police use of facial recognition, with further bans under
consideration across various states, at the federal level, and outside the
United States.444For an updated list of jurisdictions that have already
adopted or are considering regulations, see:
https://www.policingproject.org/face-rec-all-legislation

A second risk of the rebuttal approach is that focusing on what is not
possible may encourage policymakers to throw up their hands at a problem and
unduly write off computational approaches altogether, when they may still have
a positive role to play. Analysis of social media posts for hate speech, for
example, is impossible to execute with complete fidelity; but it does not
necessarily follow that platforms have no responsibility to try to filter such
content. Rather, the incapabilities and imperfections of computational tools
must be objectively and pragmatically considered when evaluating potential
solutions. Scholars and practitioners engaging in computing as rebuttal must
be cautious against overclaiming for this reason.

##  5\. Computing as Synecdoche

_Computing can foreground long-standing social problems in a new way._

Virginia Eubanks’s acclaimed ethnography Automating Inequality tells the
stories of three automated systems used to administer public services in
different parts of the country (Eubanks, 2018). We learn about an attempt to
automate welfare eligibility determinations in Indiana which wreaks havoc on
the lives of the state’s most vulnerable. In Los Angeles, the county’s
“coordinated entry” system ranks homeless individuals in order to apportion
the city’s limited housing supply — treating basic human needs as resources to
be strategically allocated, not rights to be ensured. And in Allegheny County,
Pennsylvania, Eubanks tells the story of a risk model used to predict child
abuse and neglect that targets poor families for far greater scrutiny.

Eubanks’s book draws much-needed attention to these systems. But in discussing
the book, and in the text itself, Eubanks is explicit that her core concern is
poverty, not technology. For Eubanks, computing is just one mechanism through
which long-standing poverty policy is manifested. As she terms it, data
analytics are “more evolution than revolution”: they’re a new instance of the
tools we’ve used for generations, built on the same notions of desert and
blame that have long characterized poverty discourse. Automated systems sit
alongside broader social policies and cultural attitudes that divert poor
people from the resources they need. Yet a technological lens does important
work for Eubanks: by framing her book through algorithmic instantiations of
poverty policy, she brings renewed attention to the plight of the poor writ
large. It’s safe to say that Eubanks’s work has garnered more attention (and
attention from different spheres of influence) as a book about inequality
through technology than it might have if it were a book about inequality in
general.

In this way, computing acts as a synecdoche — a part that stands in for the
larger whole in discourse and critique. Computing can offer us a tractable
focus through which to notice anew, and bring renewed attention to, old
problems. This approach is not uncommon in political discourse. Social
problems are by nature complex and multivalent; we rarely obtain purchase on a
problem by focusing on its entirety. In policymaking, we often chip away at
big social issues by concentrating on their components — and for both better
and worse, technology critique often captures public attention. Even when we
are ultimately concerned about a broader problem and see computing as but one
(and perhaps not even the most important) facet of that problem, framing it as
a technology problem may be quite pragmatic. Such a focus can leverage
resources and attention that might not accrue otherwise. Put most bluntly,
many people would not pick up a book about poverty policy in general — but are
game to read a critique of the algorithms used to administer it.555As Eubanks
writes, the United States stands in “cultural denial” of poverty, “a social
process organized and supported by schooling, government, religion, media, and
other institutions” on both the left and the right (Eubanks, 2018).

Jack Balkin describes this as a salience function of new technologies. He
proposes that, rather than focusing entirely on technological novelty,
researchers should ask: “What elements of the social world does a new
technology make particularly salient that went relatively unnoticed before?
What features of human activity or of the human condition does a technological
change foreground, emphasize, or problematize?” (Balkin, 2004). In his own
analysis of the Internet and free speech, Balkin emphasizes that digital
technologies “place[] freedom of speech in a new light” and “bring[] features
of the system of free expression to the forefront of our concern, reminding us
of things about freedom of expression that were always the case” (Balkin,
2004). In writing about Internet speech, Balkin tells us something about
characteristics of speech more generally.

The significant risk, of course, is that a focus on the technological aspects
of a problem can restrict our attention to merely those aspects. A computing
lens can have the effect of masking and pulling political capital away from
other and more insidious facets of a problem, as well as other (non-technical)
means of addressing it.666Eubanks laments this narrowed horizon in the context
of poverty policy: “When the digital poorhouse was born, the nation was asking
difficult questions: What is our obligation to each other in conditions of
inequality? How do we reward caregiving? How do we face economic changes
wrought by automation and computerization? The digital poorhouse reframed
these big political dilemmas as mundane issues of efficiency and systems
engineering: How do we best match need to resource? How do we eliminate fraud
and divert the ineligible? How do we do the most with the least money?”
(Eubanks, 2018). It can also make computing something of a scapegoat; to
reprehend computing for broad social wrongs may give us a convenient target
for outrage at systemic injustice, but in a way that does not build momentum
toward change. Further, using computing as a synecdoche strategically exploits
computing’s hegemony, but does not, at root, challenge it — and may in fact
reinforce tendencies to center the computational dimensions of problems while
dismissing their other aspects.

Some of these tensions have recently emerged in critiques of the labor
practices that underpin the operation of algorithmic systems. In Finland,
prison laborers train a classifier on Finnish-language business articles; the
startup running the project paid the prison the equivalent of what it would
have paid Mechanical Turk workers for the same tasks. (It is not clear what
proportion of the payment went to prisoners themselves.) Though the story was
reported predominantly within tech media verticals, and the prison’s practices
decried by notable critics of technology, others noted that there was “nothing
special about AI” (Chen, 2019) in the story: its technological framing was
merely a new illustration of long-standing practices. As Lilly Irani noted,
“[t]he hook is that we have this kind of hype circulating around AI” as a
gloss on “really old forms of labor exploitation” (Chen, 2019). Similar
critiques focus on the working conditions of human content moderators who
review violent, traumatic imagery for very low wages, and without proper
support for the toll such work takes on their mental and physical health
(Roberts, 2019; Gillespie, 2018). Low-wage and exploitative work existed long
before computing; computing snaps them into focus and exacerbates them, but
these are not merely computing problems, and we should not treat them as
though they were.777In another labor context, concerns about automation in the
workplace (of the “robots will take all the jobs” ilk) may also represent a
technological scapegoat for deeper and more pernicious concerns about work
precarity, capital accumulation, and the demise of affordable education and
the social safety net. The latest waves of workplace automation may be
exciting so much concern not because the technology is fundamentally different
from prior advances, but because “the programs that helped Americans deal with
how technology is always upending the job market were dismantled” (Spross,
2019) (emphasis added). An overemphasis on robots obscures these broader
problems and runs the risk of diverting further political capital from them.

Sebastian Benthall makes a pointed critique on this theme. Channeling comments
by Luke Stark, Benthall explains that, while debates about technology may at
root be debates about capitalism, “it’s impolite to say this because it cuts
down on the urgency that might drive political action. …The buzz of novelty is
what gets people’s attention” (Benthall, 2018b). Rather than viewing a
technology lens as a pragmatic route into a broader social or economic
problem, Benthall contends that the AI ethics research community’s focus on
engineers and tech companies ultimately “serves as a moral smokescreen” that
impedes effective critique of root problems. Benthall notes, for example, that
the emphasis on AI ethics in the critical community is “an awkward synecdoche
for the rise of major corporations like Google, Apple, Amazon, Facebook, and
Netflix” (Benthall, 2018a) — and that the focus on technology rather than
institutionalism or political economy necessarily circumscribes the issues
that can be brought to the table.

To recognize that technology is only one component of a broader sociopolitical
system is not to give technology a free pass. The existence of a technology
may help to create the conditions to support and intensify a particular
arrangement of power. Langdon Winner described this quality as technology’s
inherent compatibility with particular sociopolitical systems (noting, for
instance, that nuclear power is inherently compatible with centralized and
hierarchical decision-making as the social “operating environment” which
allows the technology to function practically, whereas solar energy may be
more compatible with distributed egalitarian systems of decision-making)
(Winner, 1980). Content moderation systems seem naturally to invite
exploitative labor practices based on the scale and speed they require and the
nature of the content to be moderated; the technology does not just happen to
be paired with these practices, but is a close fit for it. A synecdochal focus
on computing must walk a pragmatic — and tenuous — line between overemphasis
on technical aspects, on one hand, and due recognition of the work computing
does to reinforce social systems, on the other.

##  6\. Conclusion

Technical work on prediction and optimization in policy domains can sometimes
seem to favor slow and incremental approaches to social change — taking a
side, without necessarily intending to, against broader and more sweeping
redesigns of existing institutional arrangements. But as we have sought to
show, technical work can also operate as a constructive ally for broad social
change. In this paper, we have described four ways computing research can
support and reinforce more fundamental changes in society and politics. Such
research can help to diagnose problems, shape through formalization the ways
people understand social problems and possibilities, illuminate the boundaries
of what can and cannot be achieved by technical means, and make long-standing
problems newly salient. And it can do so in ways that are compatible with
taking less, rather than more, of today’s social landscape for granted.

## References

  * (1)
  * Abebe and Goldner (2018) Rediet Abebe and Kira Goldner. 2018.  Mechanism design for social good.  _AI Matters_ 4, 3 (2018), 27–34.
  * Abebe et al. (2019) Rediet Abebe, Shawndra Hill, Jennifer Wortman Vaughan, Peter M Small, and H Andrew Schwartz. 2019\.  Using search queries to understand health information needs in Africa. In _Proceedings of the International AAAI Conference on Web and Social Media_ , Vol. 13. 3–14.
  * Abebe et al. (2020) Rediet Abebe, Jon Kleinberg, and S. Matthew Weinberg. 2020\.  Subsidy Allocations in the Presence of Income Shocks. In _Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence_.
  * Abelson et al. (2015) Harold Abelson, Ross Anderson, Steven M Bellovin, Josh Benaloh, Matt Blaze, Whitfield Diffie, John Gilmore, Matthew Green, Susan Landau, Peter G Neumann, et al. 2015\.  Keys under doormats: mandating insecurity by requiring government access to all data and communications.  _Journal of Cybersecurity_ 1, 1 (2015), 69–79.
  * Abelson and et. al (2016) Hal Abelson and et. al. 2016.  Letter to the Honorable Elaine C. Duke.  https://www.brennancenter.org/sites/default/files/Technology%20Experts%20Letter%20to%20DHS%20Opposing%20the%20Extreme%20Vetting%20Initiative%20-%2011.15.17.pdf
  * Agre (1997) Philip E Agre. 1997\.  Lessons Learned in Trying to Reform AI.  _Social science, technical systems, and cooperative work: Beyond the Great Divide_ (1997), 131\.
  * Ali et al. (2019) Muhammad Ali, Piotr Sapiezynski, Miranda Bogen, Aleksandra Korolova, Alan Mislove, and Aaron Rieke. 2019.  Discrimination through Optimization: How Facebook’s Ad Delivery Can Lead to Biased Outcomes.  _Proceedings of the ACM on Human-Computer Interaction_ 3, CSCW (2019), 199.
  * Balkin (2004) Jack M Balkin. 2004\.  Digital speech and democratic culture: A theory of freedom of expression for the information society.  _NYU Law Review_ 79 (2004), 1.
  * Barabas et al. (2018) Chelsea Barabas, Karthik Dinakar, Joichi Ito, Madars Virza, and Jonathan Zittrain. 2018.  Interventions over Predictions: Reframing the Ethical Debate for Actuarial Risk Assessment. In _Proceedings of the 1st Conference on Fairness, Accountability and Transparency_ , Vol. 81. 62–76.
  * Barocas (2014) Solon Barocas. 2014\.  Putting Data to Work.  In _Data and Discrimination: Collected Essays_ , Seeta Peña Gangadharan, Virginia Eubanks, and Solon Barocas (Eds.). Open Technology Institute.
  * Barocas et al. (2019) Solon Barocas, Moritz Hardt, and Arvind Narayanan. 2019\.  _Fairness and Machine Learning_.  fairmlbook.org.  http://www.fairmlbook.org.
  * Barocas and Selbst (2016) Solon Barocas and Andrew D Selbst. 2016.  Big data’s disparate impact.  _Calif. L. Rev._ 104 (2016), 671.
  * Benjamin (2019) Ruha Benjamin. 2019\.  _Race after technology: Abolitionist tools for the new jim code_.  John Wiley & Sons.
  * Bennett and Keyes (2019) Cynthia L Bennett and Os Keyes. 2019.  What is the Point of Fairness? Disability, AI and The Complexity of Justice. In _ASSETS 2019 Workshop — AI Fairness for People with Disabilities_.
  * Benthall (2018a) Sebastian Benthall. 2018a.  Computational institutions.  https://digifesto.com/2018/12/22/computational-institutions/
  * Benthall (2018b) Sebastian Benthall. 2018b.  The politics of AI ethics is a seductive diversion from fixing our broken capitalist system.  https://digifesto.com/2018/12/18/the-politics-of-ai-ethics-is-a-seductive-diversion-from-fixing-our-broken-capitalist-system/
  * Bolukbasi et al. (2016) Tolga Bolukbasi, Kai-Wei Chang, James Y Zou, Venkatesh Saligrama, and Adam T Kalai. 2016.  Man is to computer programmer as woman is to homemaker? Debiasing word embeddings. In _Advances in neural information processing systems_. 4349–4357.
  * Brayne (2017) Sarah Brayne. 2017\.  Big data surveillance: The case of policing.  _American Sociological Review_ 82, 5 (2017), 977–1008.
  * Broussard et al. (2019) Meredith Broussard, Nicholas Diakopoulos, Andrea L. Guzman, Rediet Abebe, Michel Dupagne, and Ching-Hua Chuan. 2019.  Artificial Intelligence and Journalism.  _Journalism & Mass Communication Quarterly_ 96, 3 (2019), 673–695.  https://doi.org/10.1177/1077699019859901
  * Buolamwini and Gebru (2018) Joy Buolamwini and Timnit Gebru. 2018.  Gender shades: Intersectional accuracy disparities in commercial gender classification. In _Conference on Fairness, Accountability and Transparency_. 77–91.
  * Caliskan et al. (2017) Aylin Caliskan, Joanna J Bryson, and Arvind Narayanan. 2017\.  Semantics derived automatically from language corpora contain human-like biases.  _Science_ 356, 6334 (2017), 183–186.
  * Campbell (1979) Donald T. Campbell. 1979\.  Assessing the impact of planned social change.  _Evaluation and Program Planning_ 2 (1979), 67–90.  Issue 1.
  * Chen (2019) Angela Chen. 2019\.  Inmates in Finland are training AI as part of prison labor.  _The Verge_ (2019).  https://www.theverge.com/2019/3/28/18285572/prison-labor-finland-artificial-intelligence-data-tagging-vainu
  * Chen et al. (2018) Le Chen, Ruijun Ma, Anikó Hannák, and Christo Wilson. 2018.  Investigating the impact of gender on rank in resume search engines. In _Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems_. ACM, 651\.
  * Chouldechova (2017) Alexandra Chouldechova. 2017\.  Fair prediction with disparate impact: A study of bias in recidivism prediction instruments.  _Big data_ 5, 2 (2017), 153–163.
  * Christin (2018) Angèle Christin. 2018\.  Counting clicks: Quantification and variation in web journalism in the United States and France.  _Amer. J. Sociology_ 123, 5 (2018), 1382–1415.
  * Citron (2018) Danielle Keats Citron. 2018\.  Technological Due Process.  _Washington University Law Review_ (2018).
  * Clarke (1988) David A Clarke. 1988\.  Digital data processing arbitration system.  US Patent 4,789,926.
  * Concerned Researchers (2019) Concerned Researchers. 2019\.  On Recent Research Auditing Commercial Facial Analysis Technology.  _Medium.com_ (2019).  https://medium.com/@bu64dcjrytwitb8/on-recent-research-auditing-commercial-facial-analysis-technology-19148bda1832
  * Costanza-Chock (2018) Sasha Costanza-Chock. 2018\.  Design justice, AI, and escape from the matrix of domination.  _Journal of Design and Science_ (2018).
  * Crawford ([n. d.]) Kate Crawford. [n. d.].  You and AI – the politics of AI.  https://www.youtube.com/watch?v=HPopJb5aDyA.  Accessed: 2019-08-01.
  * Crawford and Calo (2016) Kate Crawford and Ryan Calo. 2016.  There is a blind spot in AI research.  _Nature News_ 538, 7625 (2016), 311.
  * Datta et al. (2015) Amit Datta, Michael Carl Tschantz, and Anupam Datta. 2015\.  Automated experiments on ad privacy settings.  _Proceedings on privacy enhancing technologies_ 2015, 1 (2015), 92–112.
  * De-Arteaga et al. (2018) Maria De-Arteaga, William Herlands, Daniel B Neill, and Artur Dubrawski. 2018.  Machine learning for the developing world.  _ACM Transactions on Management Information Systems (TMIS)_ 9, 2 (2018), 9.
  * Delacrétaz et al. (2016) David Delacrétaz, Scott Duke Kominers, and Alexander Teytelboym. 2016.  Refugee resettlement.  _University of Oxford Department of Economics Working Paper_ (2016).
  * Dencik et al. (2018) Lina Dencik, Fieke Jansen, and Philippa Metcalfe. 2018\.  A conceptual framework for approaching social justice in an age of datafication.  _DATAJUSTICE project_ 30 (2018).
  * D’Ignazio and Klein (2019) Catherine D’Ignazio and Lauren Klein. 2019.  _Data feminism_.  Cambridge, MA: MIT Press.
  * Duarte et al. (2018) Natasha Duarte, Emma Llanso, and Anna Loup. 2018.  Mixed Messages? The Limits of Automated Social Media Content Analysis. In _Proceedings of the 1st Conference on Fairness, Accountability and Transparency_ _(Proceedings of Machine Learning Research)_ , Sorelle A. Friedler and Christo Wilson (Eds.), Vol. 81. PMLR, New York, NY, USA, 106–106.
  * Eckhouse et al. (2018) Laurel Eckhouse, Kristian Lum, Cynthia Conti-Cook, and Julie Ciccolini. 2018.  Layers of Bias: A Unified Approach for Understanding Problems With Risk Assessment.  _Criminal Justice and Behavior_ 46, 2 (2018), 185–2019.
  * Ekstrand and Levy ([n. d.]) Michael Ekstrand and Karen Levy. [n. d.].  FAT* Network.  https://fatconference.org/network/.  Accessed: 2019-08-01.
  * Eubanks (2018) Virginia Eubanks. 2018\.  _Automating inequality: How high-tech tools profile, police, and punish the poor_.  St. Martin’s Press.
  * Friedman and Hendry (2019) Batya Friedman and David G Hendry. 2019.  _Value sensitive design: Shaping technology with moral imagination_.  Mit Press.
  * Friedman and Nissenbaum (1996) Batya Friedman and Helen Nissenbaum. 1996.  Bias in computer systems.  _ACM Transactions on Information Systems (TOIS)_ 14, 3 (1996), 330–347.
  * Gangadharan and Niklas (2019) Seeta Peña Gangadharan and Jedrzej Niklas. 2019.  Decentering technology in discourse on discrimination.  _Information, Communication & Society_ 22, 7 (2019), 882–899.
  * Gebru (2019) Timnit Gebru. 2019\.  Oxford Handbook on AI Ethics Book Chapter on Race and Gender.  arXiv:cs.CY/1908.06165
  * Gebru et al. (2018) Timnit Gebru, Jamie Morgenstern, Briana Vecchione, Jennifer Wortman Vaughan, Hanna Wallach, Hal Daumeé III, and Kate Crawford. 2018\.  Datasheets for datasets.  _arXiv preprint arXiv:1803.09010_ (2018).
  * Gillespie (2018) Tarleton Gillespie. 2018\.  _Custodians of the Internet: Platforms, content moderation, and the hidden decisions that shape social media_.  Yale University Press.
  * Gillespie and Seaver ([n. d.]) Tarleton Gillespie and Nick Seaver. [n. d.].  Critical Algorithm Studies: a Reading List.  https://socialmediacollective.org/reading-lists/critical-algorithm-studies/.  Accessed: 2019-08-01.
  * Green (2018) Ben Green. 2018\.  “Fair” Risk Assessments: A Precarious Approach for Criminal Justice Reform. In _5th Workshop on Fairness, Accountability, and Transparency in Machine Learning_.
  * Greene et al. (2019) Daniel Greene, Anna Lauren Hoffmann, and Luke Stark. 2019\.  Better, nicer, clearer, fairer: A critical assessment of the movement for ethical artificial intelligence and machine learning. In _Proceedings of the 52nd Hawaii International Conference on System Sciences_.
  * Haggerty (2009) Kevin D Haggerty. 2009\.  Methodology as a knife fight: The process, politics and paradox of evaluating surveillance.  _Critical Criminology_ 17, 4 (2009), 277.
  * Harwell and Miroff (2018) Drew Harwell and Nick Miroff. 2018.  ICE just abandoned its dream of ’extreme vetting’ software that could predict whether a foreign visitor would become a terrorist.  _Washington Post_ (2018).  https://www.washingtonpost.com/news/the-switch/wp/2018/05/17/ice-just-abandoned-its-dream-of-extreme-vetting-software-that-could-predict-whether-a-foreign-visitor-would-become-a-terrorist/
  * Hassein (2017) Nabil Hassein. 2017\.  Against black inclusion in facial recognition.  https://digitaltalkingdrum.com/2017/08/15/against-black-inclusion-in-facial-recognition/
  * Hellman (2019) Deborah Hellman. 2019\.  Measuring Algorithmic Fairness.  _Virginia Public Law and Legal Theory Research Paper_ 2019-39 (2019).
  * Hoffmann (2019) Anna Lauren Hoffmann. 2019\.  Where fairness fails: data, algorithms, and the limits of antidiscrimination discourse.  _Information, Communication & Society_ 22, 7 (2019), 900–915.
  * Hoskin (1996) Keith Hoskin. 1996\.  The ‘awful idea of accountability’: inscribing people into the measurement of objects.  _Accountability: Power, ethos and the technologies of managing_ 265 (1996).
  * Introna and Nissenbaum (2000) Lucas D Introna and Helen Nissenbaum. 2000.  Shaping the Web: Why the politics of search engines matters.  _The information society_ 16, 3 (2000), 169–185.
  * Jasanoff (2006) Sheila Jasanoff. 2006\.  Technology as a site and object of politics.  In _The Oxford handbook of contextual political analysis_. Oxford University Press.
  * Jayadev (2019) Raj Jayadev. 2019\.  The Future of Pretrial Justice is Not Bail or System Supervision — It Is Freedom and Community.  _Silcon Valley Debug_ (2019).  https://www.siliconvalleydebug.org/stories/the-future-of-pretrial-justice-is-not-money-bail-or-system-supervision-it-s-freedom-and-community
  * Jones and Teytelboym (2018) Will Jones and Alexander Teytelboym. 2018.  Matching Systems for Refugees.  _Journal on Migration and Human Security_ 5 (2018), 667–681.  Issue 3.
  * Kaplow (1992) Louis Kaplow. 1992\.  Rules versus standards: An economic analysis.  _Duke Lj_ 42 (1992), 557.
  * Kleinberg et al. (2016) Jon Kleinberg, Jens Ludwig, and Sendhil Mullainathan. 2016\.  A guide to solving social problems with machine learning.  _Harvard Business Review_ (2016).
  * Kleinberg et al. (2017) Jon M. Kleinberg, Sendhil Mullainathan, and Manish Raghavan. 2017\.  Inherent Trade-Offs in the Fair Determination of Risk Scores. In _8th Innovations in Theoretical Computer Science Conference, ITCS 2017, January 9-11, 2017, Berkeley, CA, USA_. 43:1–43:23.
  * Koepke and Robinson (2018) John Logan Koepke and David G Robinson. 2018.  Danger ahead: Risk assessment and the future of bail reform.  _Wash. L. Rev._ 93 (2018), 1725.
  * Kominers (2018) Scott Duke Kominers. 2018\.  Good Markets (Really Do) Make Good Neighbors.  _ACM SIGecom Exchanges_ 16, 2 (2018), 12–26.
  * Leadership Conference on Civil and Human Rights (2018) Leadership Conference on Civil and Human Rights. 2018.  The Use of Pretrial “Risk Assessment” Instruments: A Shared Statement of Civil Rights Concerns.  http://civilrightsdocs.info/pdf/criminal-justice/Pretrial-Risk-Assessment-Full.pdf
  * Lessig (2009) Lawrence Lessig. 2009\.  _Code: And other laws of cyberspace_.  Basic Books.
  * Lurie and Mustafaraj (2019) Emma Lurie and Eni Mustafaraj. 2019.  Opening Up the Black Box: Auditing Google’s Top Stories Algorithm. In _Proceedings of the International Florida Artificial Intelligence Research Society Conference_ , Vol. 32.
  * Manduca (2019) Robert Manduca. 2019\.  Mechanism Design for Social Good.  _RobertManduca.com_ (2019).  http://robertmanduca.com/portfolio/mechanism-design-4-social-good/
  * Mayson (2019) Sandra G. Mayson. 2019\.  Bias In, Bias Out.  _Yale Law Journal_ 128 (2019), 2218.  Issue 8.
  * Mitchell et al. (2019) Margaret Mitchell, Simone Wu, Andrew Zaldivar, Parker Barnes, Lucy Vasserman, Ben Hutchinson, Elena Spitzer, Inioluwa Deborah Raji, and Timnit Gebru. 2019.  Model cards for model reporting. In _Proceedings of the Conference on Fairness, Accountability, and Transparency_. ACM, 220–229.
  * Morozov (2013) Evgeny Morozov. 2013\.  _To save everything, click here: The folly of technological solutionism_.  Public Affairs.
  * Noble (2018) Safiya Umoja Noble. 2018\.  _Algorithms of oppression: How search engines reinforce racism_.  NYU Press.
  * Overdorf et al. (2018) Rebekah Overdorf, Bogdan Kulynych, Ero Balsa, Carmela Troncoso, and Seda Gürses. 2018.  Questioning the assumptions behind fairness solutions.  _arXiv preprint arXiv:1811.11293_ (2018).
  * Page (2008) Scott E. Page. 2008\.  _The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies_.  Princeton University Press.
  * Pasquale (2015) Frank Pasquale. 2015\.  _The black box society_.  Harvard University Press.
  * Pasquale (2018) Frank Pasquale. 2018\.  Odd Numbers.  _Real Life Mag_ (2018).
  * Passi and Barocas (2019) Samir Passi and Solon Barocas. 2019.  Problem formulation and fairness. In _Proceedings of the Conference on Fairness, Accountability, and Transparency_. ACM, 39–48.
  * Patel (2018) Komal S Patel. 2018\.  Testing the Limits of the First Amendment: How Online Civil Rights Testing Is Protected Speech Activity.  _Columbia Law Review_ 118, 5 (2018), 1473–1516.
  * Powles (2018) Julia Powles. 2018\.  The seductive diversion of ‘solving’ bias in artificial intelligence.
  * Puri (2018) Ruchir Puri. 2018\.  Mitigating Bias in AI Models.  _IBM Research Blog_ (2018).
  * Raghavan et al. (2020) Manish Raghavan, Solon Barocas, Jon Kleinberg, and Karen Levy. 2020.  Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices. In _Proceedings of the Conference on Fairness, Accountability, and Transparency_. ACM.
  * Raji and Buolamwini (2019) Inioluwa Deborah Raji and Joy Buolamwini. 2019.  Actionable Auditing: Investigating the Impact of Publicly Naming Biased Performance Results of Commercial AI Products.  _AAAI/ACM Conf. on AI Ethics and Society_ (2019).
  * Reidenberg (1997) Joel R Reidenberg. 1997\.  Lex informatica: The formulation of information policy rules through technology.  _Tex. L. Rev._ 76 (1997), 553.
  * Roach (2018) John Roach. 2018\.  Microsoft improves facial recognition technology to perform well across all skin tones, genders.  _The AI Blog_ (2018).
  * Roberts (2019) Sarah T Roberts. 2019\.  _Behind the Screen: Content Moderation in the Shadows of Social Media_.  Yale University Press.
  * Sandvig et al. (2014) Christian Sandvig, Kevin Hamilton, Karrie Karahalios, and Cedric Langbort. 2014.  Auditing algorithms: Research methods for detecting discrimination on internet platforms.  _Data and discrimination: converting critical concerns into productive inquiry_ 22 (2014).
  * Selbst et al. (2019) Andrew D Selbst, Danah Boyd, Sorelle A Friedler, Suresh Venkatasubramanian, and Janet Vertesi. 2019\.  Fairness and abstraction in sociotechnical systems. In _Proceedings of the Conference on Fairness, Accountability, and Transparency_. ACM, 59–68.
  * Spross (2019) Jeff Spross. 2019\.  How robots became a scapegoat for the destruction of the working class.  _The Week_ (2019).  https://theweek.com/articles/837759/how-robots-became-scapegoat-destruction-working-class
  * Sweeney (2013) Latanya Sweeney. 2013\.  Discrimination in online ad delivery.  _ACM Queue_ (2013).
  * Wald and Woolverton (1990) Michael S Wald and Maria Woolverton. 1990.  Risk assessment: The emperor’s new clothes?  _Child Welfare: Journal of Policy, Practice, and Program_ (1990).
  * Whittaker et al. (2018) Meredith Whittaker, Kate Crawford, Roel Dobbe, Genevieve Fried, Elizabeth Kaziunas, Varoon Mathur, Sarah Mysers West, Rashida Richardson, Jason Schultz, and Oscar Schwartz. 2018\.  _AI now report 2018_.  AI Now Institute at New York University.
  * Winner (1980) Langdon Winner. 1980\.  Do artifacts have politics?  _Daedalus_ (1980), 121–136.
  * Xiang and Raji (2019) Alice Xiang and Inioluwa Deborah Raji. 2019.  On the Legal Compatibility of Fairness Definitions.  _arXiv preprint arXiv:1912.00761_ (2019).


# The pseudoscalar meson and baryon octet interaction with strangeness $S=-2$
in the unitary coupled-channel approximation

Bao-Xi Sun<EMAIL_ADDRESS>Faculty of Science, Beijing University of
Technology, Beijing 100124, China  Xin-Yu Liu  Faculty of Science, Beijing
University of Technology, Beijing 100124, China

###### Abstract

The interaction of the pseudoscalar meson and the baryon octet is investigated
by solving the Bethe-Salpeter equation in the infinite and finite volume
respectively. It is found that there is a resonance state generated
dynamically, which owns a mass about 1550MeV and a large decay width of
120-200MeV. This resonance state couples strongly to the $\pi\Xi$ channel.
Therefore, it might not correspond to the $\Xi(1620)$ particle announced by
Belle collaboration. At the same time, this problem is studied in the finite
volume, and an energy level at 1570MeV is obtained, which is between the
$\pi\Xi$ and $\bar{K}\Lambda$ thresholds and independent of the cubic box
size.

###### pacs:

12.40.Vv, 13.75.Gx, 14.20.Gk

##  I Introduction

The experimental data on double strange baryons $\Xi(1620)$ and $\Xi(1690)$
are scarce, and the spin-parity of them are not determined, so they are
labeled with one star and three stars respectively in the review of Particle
Data GroupPDG . Recently, the $\Xi(1620)$ particle has been reported to be
observed in the decay of $\Xi_{c}^{+}\rightarrow\Xi^{-}\pi^{+}\pi^{+}$ by
Belle collaboration, and the mass and decay width are measured as

$\displaystyle M$ $\displaystyle=$ $\displaystyle 1610.4\pm
6.0(stat){}^{+6.1}_{-4.2}(syst)MeV,$ $\displaystyle\Gamma$ $\displaystyle=$
$\displaystyle 59.9\pm 4.8{stat}{}^{+2.8}_{-7.1}(syst)MeV,$ (1)

respectively. Moreover, there are also some evidences of the $\Xi(1690)$
particle with the same data sampleBelle .

The masses of these two particle are about 300MeV higher than that of the
$\Xi$ hyperon, and thus they can be regarded as excited states of the $\Xi$
hyperon. However they are difficult to be described within the framework of
the constituent quark model.

In Ref. Ramos:2002xh , the $\Xi(1620)$ particle was assumed to be a resonance
state of the pseudoscalar meson and baryon octet with strangeness $S=-2$ and
spin $J=1/2$ in the unitary coupled-channel approximation of the Bethe-
Salpeter equation. It shows that this resonance state couples strongly to the
$\pi\Xi$ and $\bar{K}\Lambda$ channels, and its width is sensitive to the
subtraction constants related to these two channels. The properties of
$\Xi(1620)$ was studied by solving the Bethe-Salpeter equation in Ref.
Guoxinheng , Apparently, the method is the same as that used in Ref.
Ramos:2002xh , but with the kernel introduced by the vector meson exchange
interaction. It manifests that the $\Xi(1620)$ particle might be a
$\bar{K}\Lambda$ or $\bar{K}\Sigma$ bound state. Moreover, the decay width of
$\Xi(1620)\rightarrow\Xi\pi$ is calculated, where $\bar{K}\Lambda$ and
$\bar{K}\Sigma$ are treated as the intermediate state respectively, and the
results indicates that the component of $\bar{K}\Lambda$ is larger than
$\bar{K}\Sigma$ in the $\Xi(1620)$ particle. Sequently, the radiative decay
process of $\Xi(1620)$ is analyzed systematically in Ref. Huang:2021ahp  by
assuming the $\Xi(1620)$ particle to be a $\bar{K}\Lambda$ and $\bar{K}\Sigma$
bound state with spin-parity $J^{P}=1/2^{-}$. In Ref. Hyodo , a series of non-
leptonic weak decays of $\Xi_{c}$ into $\pi^{+}$ and a meson-baryon final
state are discussed, and the invariant mass distribution of the meson-baryon
final state is analyzed within three different chiral scheme. However, it is
found that the peak appeared in the $\pi\Xi$ and $\bar{K}\Lambda$ spectra is
more possible to be $\Xi(1690)$, but not the $\Xi(1620)$ particle.

The unitary coupled-channel approximation of Bethe-Salpeter equation in the
finite volume has made a great success in the study of the meson-meson
interactionDoringmeson ; AlbertoKD ; Albaladejopipi ; Gengf1285  and the
meson-baryon interactionAlbertoKN . Actually, a scheme to simulate the Lattice
data in order to obtain the kernel of Bethe-Salpeter equation in the unitary
coupled-channel approximation is proposed in these articles, which is called
the inverse problem. However, the parameters in the kernel are fit to the
calculation results of the Bethe-Salpeter equation in the finite volume, but
not the real Lattice data. Finally, an attempt has been made to fit the
lattice finite volume energy levels from $\pi\eta$ scattering and the
properties of $a_{0}(980)$ is evaluatedGuozhpieta . This method is also
extended to study the interaction of the $\pi D$, $\eta D$ and $\bar{K}D_{S}$
channels in $J^{P}=0^{+}$ in the finite volume by fitting the lattice QCD
calculation resultsAlbaladejo2400 .

In this work, the interaction between the pseudoscalar meson and baryon octet
with strangeness $S=-2$ will be studied, and then the Bethe-Salpeter equation
in the infinite and finite volume will be solved within the unitary coupled-
channel approximation respectively. We will try to distinguish whether there
are resonance state generated dynamically or not, and if so, whether the
resonance state can be treated as a counterpart of the $\Xi(1620)$ particle.

This article is organized as follows. In Section II, the potential of the
pseudoscalar meson and baryon octet is constructed. In Section III, a basic
formula on how to solve the Bethe-Salpeter equation in the unitary coupled-
channel approximation is shown. Sequently, the pole position in the complex
energy plane is obtained by solving the Bethe-Salpeter equation in the
infinite volume, and its coupling constants to different channels are
calculated. The chiral unitary approach in a finite box is introduced in
Section IV Finally, the summary is given in Section V.

##  II Framework

The effective Lagrangian of the pseudoscalar meson and the baryon octet can be
written as

$\displaystyle{\sl
L}=\langle\bar{B}(i\gamma_{\mu}D^{\mu}-M)B\rangle+\frac{D/F}{2}\langle\bar{B}\gamma_{\mu}\gamma_{5}[u^{\mu},B]_{\pm}\rangle.$
(2)

In the above equation, the symbol $\langle...\rangle$ denotes the trace of
matrices in the $SU(3)$ flavor space, and
$D^{\mu}B=\partial^{\mu}B+\frac{1}{2}\left[[u^{\dagger},\partial^{\mu}u],B\right]$
with $u^{2}=U=\exp\left(i\frac{\Phi}{f_{0}}\right)$ and
$u^{\mu}=iu^{\dagger}\partial^{\mu}u-iu\partial^{\mu}u^{\dagger}$, where
$f_{0}$ is the meson decay constant in the chiral limit.

The matrices of the pseudoscalar meson and the baryon octet are given as
follows

$\displaystyle\Phi={}$
$\displaystyle\sqrt{2}\begin{pmatrix}\frac{1}{\sqrt{2}}\pi^{0}+\frac{1}{\sqrt{6}}\eta&\pi^{+}&K^{+}\\\
\pi^{-}&-\frac{1}{\sqrt{2}}\pi^{0}+\frac{1}{\sqrt{6}}\eta&K^{0}\\\
K^{-}&\bar{K}^{0}&-\frac{2}{\sqrt{6}}\eta\end{pmatrix}$ (3)

and

$\displaystyle B={}$
$\displaystyle\begin{pmatrix}\frac{1}{\sqrt{2}}\Sigma^{0}+\frac{1}{\sqrt{6}}\Lambda&\Sigma^{+}&p\\\
\Sigma^{-}&-\frac{1}{\sqrt{2}}\Sigma^{0}+\frac{1}{\sqrt{6}}\Lambda&n\\\
\Xi^{-}&\Xi^{0}&-\frac{2}{\sqrt{6}}\Lambda\end{pmatrix}.$ (4)

The first term in the Lagrangian in Eq. (2) supplies the contact interaction
of the pseudoscalar meson and the baryon octet, which is usually called as
Weinberg-Tomozawa term, while the other terms which are relevant to the
coefficients $D$ and $F$ give a contribution to the $s-$ and $u-$ channel
interactions, as shown in Fig. 1.

Figure 1: Feynman diagrams of the pseudoscalar meson-baryon octet interaction.
$(a)$ contact term, $(b)$ $u-$ channel and $(c)$ $s-$ channel.

The Weinberg-Tomozawa contact term of the pseudoscalar meson and the baryon
octet takes the form of

$\displaystyle V^{con}_{ij}={}$ $\displaystyle-
C_{ij}\frac{1}{4f_{i}f_{j}}(2\sqrt{s}-M_{i}-M_{j})\left(\frac{M_{i}+E}{2M_{i}}\right)^{\frac{1}{2}}\left(\frac{M_{j}+E^{\prime}}{2M_{j}}\right)^{\frac{1}{2}},$
(5)

where $\sqrt{s}$ is the total energy of the system, $M_{i}$ and $M_{j}$ denote
the initial and final baryon masses, $E$ and $E^{\prime}$ stand for the
initial and final baryon energies in the center of mass frame, respectively.
The coefficient $C_{ij}$ for the sector of strangeness $S=-2$ and charge zero
is listed in Table 1, Moreover, we assume the values of the decay constants
are only relevant to the pseudoscalar meson with $f_{\eta}=1.3f_{\pi}$,
$f_{K}=1.22f_{\pi}$ and $f_{\pi}=92.4$MeV, as given in Refs. Inoue ; Bruns ;
DongSun ; SunZhao .

In the interaction of pseudoscalar meson and baryon octet, the contact
potential originated from Weinberg-Tomozawa term plays a dominant role, and
the correction from the $s-$ and $u-$ channel potentials can be neglected. The
Weinberg-Tomozawa term of the pseudoscalar meson and the baryon octet are only
related to the Mandelstam variable $s$, therefore, it only gives a
contribution to the S-wave amplitude in the scattering process of the
pseudoscalar meson and the baryon octet.

$C_{ij}$ | $\pi^{+}\Xi^{-}$ | $\pi^{0}\Xi^{0}$ | $\bar{K}^{0}\Lambda$ | $K^{-}\Sigma^{+}$ | $\bar{K}^{0}\Sigma^{0}$ | $\eta\Xi^{0}$
---|---|---|---|---|---|---
$\pi^{+}\Xi^{-}$ | $1$ | $-\sqrt{2}$ | $-\sqrt{\frac{3}{2}}$ | $0$ | $-\frac{1}{\sqrt{2}}$ | $0$
$\pi^{0}\Xi^{0}$ |  | $0$ | $\frac{\sqrt{3}}{2}$ | $-\frac{1}{\sqrt{2}}$ | $-\frac{1}{2}$ | $0$
$\bar{K}^{0}\Lambda$ |  |  | $0$ | $0$ | $0$ | $-\frac{3}{2}$
$K^{-}\Sigma^{+}$ |  |  |  | $1$ | $-\sqrt{2}$ | $-\sqrt{\frac{3}{2}}$
$\bar{K}^{0}\Sigma^{0}$ |  |  |  |  | $0$ | $\frac{\sqrt{3}}{2}$
$\eta\Xi^{0}$ |  |  |  |  |  | $0$
Table 1: The coefficients $C_{ij}$ in the pseudoscalar meson and baryon octet
interaction with strangeness $S=-2$ and charge $Q=0$, $C_{ji}=C_{ij}$.

In the sector of strangeness $S=-2$ and isospin $I=\frac{1}{2}$, the wave
function in the isospin space can be written as

$|\pi\Xi;\frac{1}{2},\frac{1}{2}\rangle=\sqrt{\frac{2}{3}}|\pi^{+}\Xi^{-}\rangle-\sqrt{\frac{1}{3}}|\pi^{0}\Xi^{0}\rangle,$
(6)

$|\eta\Xi;\frac{1}{2},\frac{1}{2}\rangle=|\eta\Xi^{0}\rangle,$ (7)

$|\bar{K}\Lambda;\frac{1}{2},\frac{1}{2}\rangle=|\bar{K}^{0}\Lambda\rangle,$
(8)

and

$|\bar{K}\Sigma;\frac{1}{2},\frac{1}{2}\rangle=-\sqrt{\frac{2}{3}}|K^{-}\Sigma^{+}\rangle+\sqrt{\frac{1}{3}}|\bar{K}^{0}\Sigma^{0}\rangle,$
(9)

respectively. Thus the coefficients $C_{ij}$ in the Weinberg-Tomozawa contact
potential of the pseudoscalar meson and the baryon octet can be obtained in
the isospin space, which are summarized in Table 2.

$C_{ij}$ | $\pi\Xi$ | $\bar{K}\Lambda$ | $\bar{K}\Sigma$ | $\eta\Xi$
---|---|---|---|---
$\pi\Xi$ | $2$ | $-\frac{3}{2}$ | $-\frac{1}{2}$ | $0$
$\bar{K}\Lambda$ |  | $0$ | $0$ | $-\frac{3}{2}$
$\bar{K}\Sigma$ |  |  | $2$ | $\frac{3}{2}$
$\eta\Xi$ |  |  |  | $0$
Table 2: The coefficients $C_{ij}$ in the pseudoscalar meson and baryon octet
interaction with strangeness $S=-2$ and isospin $I=1/2$, $C_{ji}=C_{ij}$.

In the case of isospin $I=3/2$ and strangeness $S=-2$, the interaction of the
pseudoscalar meson and the baryon octet are repulsive, therefore, no resonance
states can be generated dynamically.

##  III Bethe-Salpeter equation

The Bethe-Salpeter equation can be expanded as

$\displaystyle T$ $\displaystyle=$ $\displaystyle V+VGT$ (10) $\displaystyle=$
$\displaystyle V+VGV+VGVGV+....$

When the Bethe-Salpeter equation in Eq. (10) is solved, only the on-shell part
of the potential $V_{ij}$ gives a contribution to the amplitude of the
pseudoscalar meson and the baryon octet, and the off-shell part of the
potential can be reabsorbed by a suitable renormalization of the decay
constants of mesons $f_{i}$ and $f_{j}$. More detailed discussion can be found
in Refs. Oller97 ; Ramos97 ; DongSun ; SunZhao . If the relativistic kinetic
correction of the loop function of the pseudoscalar meson and the baryon octet
is taken into account, the loop function $G_{l}$ can be written as

$\displaystyle G^{D}_{l}={}$ $\displaystyle
i\int\frac{d^{d}q}{(2\pi)^{4}}\frac{\hbox
to0.0pt{/\hss}q+M_{l}}{q^{2}-M_{l}^{2}+i\epsilon}\frac{1}{(P-q)^{2}-m_{l}^{2}+i\epsilon},$
(11)

with $P$ the total momentum of the system, $m_{l}$ the meson mass, and $M_{l}$
the baryon mass, respectively.

The loop function in Eq. (11) can be calculated in the dimensional
regularization (See Appendix 1 of Ref. DongSun  for details), and thus the
loop function takes the form of

$\displaystyle G^{D}_{l}={}$
$\displaystyle\frac{\gamma_{\mu}P^{\mu}}{32P^{2}\pi^{2}}\left[(a_{l}+1)(m_{l}^{2}-M_{l}^{2})+(m_{l}^{2}\ln\frac{m_{l}^{2}}{\mu^{2}}-M_{l}^{2}\ln\frac{M_{l}^{2}}{\mu^{2}})\right]$
(12)
$\displaystyle+\left(\frac{\gamma_{\mu}P^{\mu}[P^{2}+M_{l}^{2}-m_{l}^{2}]}{4P^{2}M_{l}}+\frac{1}{2}\right)G_{l}^{\prime},$

where $a_{l}$ is the subtraction constant and $\mu$ is the regularization
scale, and $G_{l}^{\prime}$ is the loop function in Ref. Oller ,

$\displaystyle G^{\prime}_{l}(s)$ $\displaystyle=$
$\displaystyle\frac{2M_{l}}{16\pi^{2}}\left\\{a_{l}(\mu)+\ln\frac{m_{l}^{2}}{\mu^{2}}+\frac{M_{l}^{2}-m_{l}^{2}+s}{2s}\ln\frac{M_{l}^{2}}{m_{l}^{2}}+\right.$
(13)
$\displaystyle\phantom{\frac{2M}{16\pi^{2}}}+\frac{\bar{q}_{l}}{\sqrt{s}}\left[\ln(s-(M_{l}^{2}-m_{l}^{2})+2\bar{q}_{l}\sqrt{s})+\ln(s+(M_{l}^{2}-m_{l}^{2})+2\bar{q}_{l}\sqrt{s})\right.$
$\displaystyle\left.\phantom{\frac{2M}{16\pi^{2}}+\frac{\bar{q}_{l}}{\sqrt{s}}}\left.-\ln(-s+(M_{l}^{2}-m_{l}^{2})+2\bar{q}_{l}\sqrt{s})-\ln(-s-(M_{l}^{2}-m_{l}^{2})+2\bar{q}_{l}\sqrt{s})\right]\right\\},$

with $\bar{q}_{l}$ the three-momentum of the meson or the baryon in the center
of mass frame.

Since the total three-momentum $\vec{P}=0$ in the center of mass frame, only
the $\gamma_{0}P^{0}$ part remains in Eq. (12). Similarly, This matrix
$\gamma_{0}$ can be replaced by the unit matrix $I$ since the
$U(p_{i},\lambda_{i})$ and $\bar{U}(p_{j},\lambda_{j})$ denote the wave
functions of the initial and final baryons, respectively. Thus the loop
function of the intermediate pseudoscalar meson and baryon octet becomes

$\displaystyle G^{D}_{l}={}$
$\displaystyle\frac{\sqrt{s}}{32\pi^{2}s}\left[(a_{l}+1)(m_{l}^{2}-M_{l}^{2})+(m_{l}^{2}ln\frac{m_{l}^{2}}{\mu^{2}}-M_{l}^{2}ln\frac{M_{l}^{2}}{\mu^{2}})\right]$
(14)
$\displaystyle+\left(\frac{s+M_{l}^{2}-m_{l}^{2}}{4M_{l}\sqrt{s}}+\frac{1}{2}\right)G_{l}^{\prime}.$

The off-shell part of the potential is reabsorbed in a renormalization
process, so the decay constants of mesons, the masses of intermediate baryons
all take physical values when the Bethe-Salpeter equation is solved.

In the calculation of the present work, we make a transition of

$\displaystyle\tilde{V}$ $\displaystyle=$ $\displaystyle
V~{}\sqrt{M_{i}M_{j}},$ $\displaystyle\tilde{G}_{l}$ $\displaystyle=$
$\displaystyle G_{l}/M_{l},$ (15)

so the scattering amplitude

$\tilde{T}=[1-\tilde{V}\tilde{G}]^{-1}\tilde{V}$ (16)

becomes dimensionless.

The subtraction constants in the loop function of Eqs. (13) and (14) are
listed in Table 3, which are the same as those used in Ref. Ramos:2002xh .
With these subtraction constants and the regularization scale $\mu=630$MeV,
the amplitudes of pseudoscalar meson and baryon octet are evaluated by solving
the Bethe-Salpeter equation in the unitary coupled-channel approximation. A
pole is detected around 1550MeV in the complex energy plane and the pole
position and coupling constants obtained with the loop functions in Eqs. (13)
and (14) are summarized in Tables 4 and 5, respectively. Since the real part
of the pole position is higher than the $\pi\Xi$ threshold, and lower than the
$\bar{K}\Lambda$ threshold, it lies in the second Riemann sheet and can be
regarded as a resonance state with strangeness $S=-2$ and isospin $I=1/2$.
When the values of these subtraction constants change, the mass of this
resonance state changes slightly, while the decay width of it changes in the
range of 120-200MeV. Apparently, both the mass and the decay width of this
resonance state are far away from the experimental value supplied by Belle
collaboration, and the results are also different from those in Ref.
Ramos:2002xh .

The coupling constants are calculated according to

$\frac{g_{i}g_{j}\sqrt{M_{i}M_{j}}}{\sqrt{s}-\sqrt{s_{0}}}=\tilde{T},$ (17)

with $\sqrt{s_{0}}$ the pole position in the complex energy plane. This
resonance state couples strongly to the $\pi\Xi$ channel, as listed in Tables
4 and 5.

| $a_{\pi\Xi}$ | $a_{\bar{K}\Lambda}$ | $a_{\bar{K}\Sigma}$ | $a_{\eta\Xi}$
---|---|---|---|---
Set 1 | -2.0 | -2.0 | -2.0 | -2.0
Set 2 | -2.2 | -2.0 | -2.0 | -2.0
Set 3 | -2.0 | -2.2 | -2.0 | -2.0
Set 4 | -2.5 | -1.6 | -2.0 | -2.0
Set 5 | -3.1 | -1.0 | -2.0 | -2.0
Table 3: The subtraction constants $a_{ij}$ used in the calculation, where the regularization scale takes the value of 630MeV, i.e., $\mu=630$MeV. | Set 1 | Set 2 | Set 3 | Set 4 | Set 5
---|---|---|---|---|---
Pole position | 1566-i119 | 1557-i99 | 1558-i113 | 1558-i83 | 1553-i60
$g_{\pi\Xi}$ | 2.2-i1.5 | 2.2-i1.3 | 2.1-i1.5 | 2.2-i2.4 | 2.1-i0.8
$g_{\bar{K}\Lambda}$ | -1.8+i0.6 | -1.8+i0.5 | -1.7+i0.6 | -1.9+i0.5 | -2.1+i0.4
$g_{\bar{K}\Sigma}$ | -0.5+i0.3 | -0.5+i0.3 | -0.5+i0.3 | -0.6+i0.3 | -0.7+i0.2
$g_{\eta\Xi}$ | 0.1-i0.3 | 0.1-i0.3 | 0.2-i0.3 | -0.0-i0.1 | -0.3-i0
Table 4: The pole position and corresponding coupling constants $g_{i}$ for different parameter sets calculated with the loop function in Eq. (13), where the pole position in the complex energy plane is in units of MeV. | Set 1 | Set 2 | Set 3 | Set 4 | Set 5
---|---|---|---|---|---
Pole position | 1557-i104 | 1550-i89 | 1552-i100 | 1551-i78 | 1546-i60
$g_{\pi\Xi}$ | 2.2-i1.4 | 2.2-i1.2 | 2.1-i1.4 | 2.2-i1.0 | 2.1-i1.0
$g_{\bar{K}\Lambda}$ | -1.7+i0.5 | -1.7+i0.5 | -1.7+i0.5 | -1.8+i0.5 | -2.0+i0.4
$g_{\bar{K}\Sigma}$ | -0.5+i0.3 | -0.5+i0.3 | -0.5+i0.3 | -0.6+i0.3 | -0.6+i0.2
$g_{\eta\Xi}$ | 0.1-i0.3 | 0.1-i0.2 | 0.2-i0.3 | 0.0-i0.1 | -0.2-i0.0
Table 5: The pole position and corresponding coupling constants $g_{i}$ for
different parameter sets calculated with the loop function in Eq. (14), where
the pole position in the complex energy plane is in units of MeV.

##  IV The chiral unitary approach in a finite box

In order to obtain the energy level in a finite box, the loop function in Eq.
(14) should be be replaced by a $\bar{G}$ when the Bethe-Salpeter equation is
solved, where

$\displaystyle\bar{G}(E)=G^{D}(E)+\lim_{q_{\rm
max}\to\infty}\Bigg{[}\frac{1}{L^{3}}\sum_{q_{i}}^{q_{\rm
max}}I(q_{i})-\int\limits_{q<q_{\rm
max}}\frac{d^{3}q}{(2\pi)^{3}}I(q)\Bigg{]},$ (18)

where

$\displaystyle I(q)$ $\displaystyle=$
$\displaystyle\frac{2M_{l}}{2\omega_{j}(\vec{q})\,\omega^{\prime}_{j}(\vec{q})}\frac{\omega_{j}(\vec{q})+\omega^{\prime}_{j}(\vec{q})}{E^{2}-(\omega_{j}(\vec{q})+\omega^{\prime}_{j}(\vec{q}))^{2}+i\epsilon},$
(19)

and

$\displaystyle\vec{q}$ $\displaystyle=$
$\displaystyle\frac{2\pi}{L}\,\vec{n},\vec{n}\in Z^{3},$ (20)

with $\omega_{l}(\vec{q})=\sqrt{\vec{q}^{2}+m_{l}^{2}}$,
$\omega^{\prime}_{l}=\sqrt{(\vec{q}^{2}+M_{l}^{2})}$AlbertoKD .

Instead of integrating over the energy states in the infinite volume, we sum
over the discrete momenta allowed in a finite box of side $L$ with periodic
boundary conditions. The three dimensional sum in Eq. (18) can be reduced to
one dimension considering the multiplicities of the cases having the same
$\vec{n}^{\,2}$.

When calculating the limit of $q_{max}$ going to infinity in Eq. (18) we
obtain oscillations which gradually vanish as $q_{max}$ goes to infinity, as
shown in Fig. 2. Note that the imaginary part of $G^{D}$ and of the integral
in Eq. (18) are identical and they cancel in the construction of $\tilde{G}$,
which is a real function. The integral in Eq. (18) has an analytical form as
shown in the appendix part of Ref. Olleroset (See erratum), and it repeats the
value calculated with Eq. (18), but without fluctuation.

The eigenenergies of the box correspond to energies that produce poles in the
$T$ matrix. Thus we search for these energies by looking for zeros of the
determinant of $1-\tilde{V}\tilde{G}$

$\det(1-\tilde{V}\tilde{G})=1-\tilde{V}_{11}\tilde{G}_{1}-\tilde{V}_{22}\tilde{G}_{2}+(\tilde{V}_{11}\tilde{V}_{22}-\tilde{V}_{12}^{2})\tilde{G}_{1}\tilde{G}_{2}=0\,.$
(21)

Figure 2: Real part of the last two terms of the right hand side of Eq. (18)
for the $\bar{K}\Lambda$ channel. The solid line indicates the analytical form
in Ref. Olleroset , while the dashed line represents oscillation results
calculated with Eq. (18) directly. Figure 3: Energy levels as functions of the
cubic box size $L$, derived from the chiral unitary approach in a box and
using $\bar{G}(E)$ from Eq. (18).

The energy levels obtained in the box for different values of $L$ are depicted
in Fig. 3, and a smooth behavior of energy levels as a function of $L$ is
observed. In Fig. 3, the first 3 energy levels are almost invariant when the
cubic box size $L$ increases. Especially, the lowest and third levels are
close to the $\pi\Xi$ and $\bar{K}\Lambda$ thresholds, respectively,
therefore, they do not correspond to bound states of the pseudoscalar meson
and baryon octet, but indicate the threshold effect in the finite volume. The
second level lies at 1570MeV, which is higher than the $\pi\Xi$ threshold, and
can be regarded as a resonance state with strangeness $S=-2$ and isospin
$I=1/2$. Apparently, this energy level is far away from the mass of the
$\Xi(1620)$ particle announced by Belle collaboration.

##  V Summary

In this work, the interaction of the pseudoscalar meson and the baryon octet
with strangeness $S=-2$ and isospin $I=1/2$ is investigated by solving the
Bethe-Salpeter equation in the unitary coupled-channel approximation. It is
found that a resonance state is generated dynamically around 1550MeV, which
owns a decay width about 120-200MeV. Thus this resonance state is not
consistent with the $\Xi(1620)$ particle announced by Belle collaboration. The
coupling constants of this resonance state to different channels are
calculated, and it couples strongly to the $\pi\Xi$ channel. Furthermore, this
problem is also studied by solving the Bethe-Salpeter equation in the finite
volume, and the energy levels at different cubic box sizes are obtained. It is
found that the second energy level near 1570MeV might be a resonance state of
the pseudoscalar meson and baryon octet, while the first and third levels
might comes from the $\pi\Xi$ and $\bar{K}\Lambda$ thresholds, respectively.

## References

  * (1) P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020) and 2021 update
  * (2) M. Sumihama et al. [Belle Collaboration], Phys. Rev. Lett. 122, 072501 (2019).
  * (3) A. Ramos, E. Oset and C. Bennhold, Phys. Rev. Lett. 89, 252001 (2002)
  * (4) Z. Y. Wang, J. J. Qi, J. Xu and X. H. Guo, Eur. Phys. J. C 79, 640 (2019)
  * (5) Y. Huang, F. Yang and H. Zhu, Chin. Phys. C 45, 073112 (2021)
  * (6) K. Miyahara, T. Hyodo, M. Oka, J. Nieves and E. Oset, Phys. Rev. C 95, 035212 (2017)
  * (7) M. Doring, U. G. Meissner, E. Oset and A. Rusetsky, Eur. Phys. J. A 47, 139 (2011) idem Eur. Phys. J. A 48, 114 (2012)
  * (8) A. Martinez Torres, L. R. Dai, C. Koren, D. Jido and E. Oset, Phys. Rev. D 85, 014027 (2012)
  * (9) M. Albaladejo, J. A. Oller, E. Oset, G. Rios and L. Roca, JHEP 1208 071 (2012)
  * (10) L. S. Geng, X. L. Ren, Y. Zhou, H. X. Chen and E. Oset, Phys. Rev. D 92, 014029 (2015)
  * (11) A. Martinez Torres, M. Bayar, D. Jido and E. Oset, Phys. Rev. C 86, 055201 (2012)
  * (12) Z. H. Guo, L. Liu, U. G. Meissner, J. A. Oller and A. Rusetsky, Phys. Rev. D 95, 054004 (2017)
  * (13) M. Albaladejo, P. Fernandez-Soler, F. K. Guo and J. Nieves, Phys. Lett. B 767, 465 (2017)
  * (14) T. Inoue, E. Oset and M. J. Vicente Vacas, Phys. Rev. C 65, 035204 (2002)
  * (15) P. C. Bruns, M. Mai and U. G. Meissner, Phys. Lett. B 697, 254 (2011)
  * (16) F. Y. Dong, B. X. Sun and J. L. Pang, Chin. Phys. C 41, 074108 (2017)
  * (17) B. X. Sun, S. Y. Zhao and X. Y. Wang, Chin. Phys. C 43, 064111 (2019)
  * (18) J. A. Oller and E. Oset, Nucl. Phys. A 620, 438 (1997)
  * (19) E. Oset and A. Ramos, Nucl. Phys. A 635, 99 (1998)
  * (20) J. A. Oller and U. G. Meissner, Phys. Lett. B 500, 263 (2001)
  * (21) J. A. Oller, E. Oset and J. R. Pelaez, Phys. Rev. D 59, 074001 (1999), [Erratum-ibid. D 60, 099906 (1999)] [Erratum-ibid. D 75, 099903 (2007)]