# Role of left-hand cut contributions on pole extractions from lattice data:
Case study for $T_{cc}(3875)^{+}$

Meng-Lin Du  0000-0002-7504-3107 School of Physics, University of Electronic
Science and Technology of China, Chengdu 611731, China  Arseniy Filin
0000-0002-7603-451X Institut für Theoretische Physik II, Ruhr-Universität
Bochum, D-44780 Bochum, Germany  Vadim Baru  0000-0001-6472-1008 Institut für
Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany
Xiang-Kun Dong  0000-0001-6392-7143 CAS Key Laboratory of Theoretical Physics,
Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, China  School of Physical
Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Evgeny Epelbaum  0000-0002-7613-0210 Institut für Theoretische Physik II,
Ruhr-Universität Bochum, D-44780 Bochum, Germany  Feng-Kun Guo
0000-0002-2919-2064 CAS Key Laboratory of Theoretical Physics, Institute of
Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, China  School of Physical
Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Peng Huanwu Collaborative Center for Research and Education, Beihang
University, Beijing 100191, China  Christoph Hanhart  0000-0002-3509-2473
Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center
for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany  Alexey
Nefediev  0000-0002-9988-9430 Jozef Stefan Institute, Jamova 39, 1000
Ljubljana, Slovenia  CeFEMA, Center of Physics and Engineering of Advanced
Materials, Instituto Superior Técnico, Avenida Rovisco Pais 1, 1049-001
Lisboa, Portugal  Juan Nieves  0000-0002-2518-4606 Instituto de Física
Corpuscular (centro mixto CSIC-UV),
Institutos de Investigación de Paterna, Apartado 22085, 46071, Valencia, Spain
Qian Wang  0000-0002-2447-111X Guangdong Provincial Key Laboratory of Nuclear
Science, Institute of Quantum Matter, South China Normal University, Guangzhou
510006, China  Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  Guangdong-Hong Kong Joint Laboratory of Quantum Matter,
Southern Nuclear Science Computing Center, South China Normal University,
Guangzhou 510006, China

###### Abstract

We discuss recent lattice data for the $T_{cc}(3875)^{+}$ state to stress, for
the first time, a potentially strong impact of left-hand cuts from the one-
pion exchange on the pole extraction for near-threshold exotic states. In
particular, if the left-hand cut is located close to the two-particle
threshold, which happens naturally in the $DD^{*}$ system for the pion mass
exceeding its physical value, the effective-range expansion is valid only in a
very limited energy range up to the cut and as such is of little use to
reliably extract the poles. Then, an accurate extraction of the pole locations
requires the one-pion exchange to be implemented explicitly into the
scattering amplitudes. Our findings are general and potentially relevant for a
wide class of hadronic near-threshold states.

Introduction.—The last two decades have witnessed the discovery of a large
number of the so-called exotic hadronic states in the heavy quark sector that
do not fit into the scheme of simple quark models [1, 2, 3, 4, 5, 6, 7, 8, 9].
For some of them only particular properties like masses or decays strongly
deviate from expectations, for others already the quantum numbers
unambiguously indicate their multiquark content—the most prominent
representatives of this class are the isotriplet $Z_{c}$ and $Z_{b}$ states
that decay to a heavy quarkonium plus a single pion. For an overview of the
experimental situation see, e.g., [7].

The pressing theoretical question is what clusters the quarks form in these
exotic hadrons. One popular scenario is that diquarks and anti-diquarks emerge
as relatively compact building blocks carrying a color charge [1, 2]. Then, if
there are light quarks in the system, the size of the emerging states is
governed by the confinement radius, $\sim 1/\Lambda_{\text{QCD}}$
($\Lambda_{\text{QCD}}\sim 300$ MeV), and does not depend on the binding
energy $E_{b}$ defined as the difference between the mass of the state and the
energy of the closest threshold. Alternatively, the building blocks could be
color-neutral conventional hadrons. Then, the size of these so-called hadronic
molecules is given by the inverse of the binding momentum $\gamma=\sqrt{2\mu
E_{b}}\ll\Lambda_{\rm QCD}$, with $\mu$ for the reduced mass, resulting in
large radii of near-threshold states. Thus, the size of hadronic molecules is
limited by the binding momentum rather than by the structure of the
interaction. This difference in size leads to significant differences in some
observables [4]. Because of confinement, only color singlet multi-hadron
intermediate states can go on-shell thereby generating a unitarity or right-
hand cut (rhc) in the amplitude. The argument can be further generalized to
unstable constituents [10, 11], as long as they are not too broad [12], with
lifetime larger than the range of forces [13].

So far little is known about the potential that leads to exotics—this changes
with identifying the potentially strong impact of left-hand cuts (lhcs) from
the one-pion exchange on the pole extraction for doubly heavy near-threshold
states, which is demonstrated here for the first time. For concreteness, we
present our findings with the focus on the double-charm meson $T_{cc}^{+}$
reported in [14, 15] and treated as a $DD^{*}$ molecule. Among many exotic
candidates, the $T_{cc}^{+}$ is of particular interest since its width, apart
from a tiny electromagnetic contribution, stems almost entirely from the only
available strong decay channel $DD\pi$. Then, the only relevant cut of the
amplitude on the real axis is the three-body $DD\pi$ cut (blue dashed vertical
lines in Fig. 1), while the $DD^{*}$ branch cut (green dashed vertical line)
splits into a pair of cuts on the second sheet in the complex energy plane
[16, 17]. The branch point of the $DD\pi$ cut is located below the nominal
$DD^{*}$ threshold.

Figure 1: The cut structure in the $DD^{*}$ system: (i) the blue dotted
vertical lines ($c_{3}$) indicate the three-body right-hand cuts, (ii) the
green dotted vertical line ($c_{2}$) shows the two-body cut, and (iii) the red
dotted horizontal line ($c_{\rm L}$) is for the left-hand cut. $T$ and $V$
denote the amplitude and interaction potential, respectively.

The cut structure of the amplitude severely changes for a heavier pion, which
can be studied using lattice QCD and chiral effective field theories. As soon
as the pion mass $m_{\pi}$ exceeds the $D^{*}$-$D$ mass difference $\Delta
M=M_{D^{*}}-M_{D}$, the $T_{cc}^{+}$ is stable with respect to the strong
interaction, the $DD\pi$ three-body cut branch point appears above the
$DD^{*}$ two-body threshold, and the pion exchange induces the lhc (the red
dashed horizontal line in Fig. 1) [18, 19]. Since the location of the branch
point is related to the range of the potential and the discontinuity depends
on its strength, the lhc is also called dynamical [20]. Other relevant cuts
present in the system are discussed below.

The $T_{cc}^{+}$ was recently studied in lattice QCD [21, 22, 23]. The last
work employs the HAL QCD method to extract the $DD^{*}$ scattering potential
and then use it to calculate the phase shifts above the two-body threshold.
Our consideration does not directly apply to that approach. In the first two
works the Lüscher method is employed to extract the $DD^{*}$ phase shifts
$\delta(E)$ at $m_{\pi}=280$ and 350 MeV, respectively. However, in [22],
there is only one data point in the near-threshold region and only a single
lattice volume is investigated, so the authors themselves argue that a proper
discussion of the pole structure of the amplitude is not possible yet.
Therefore, we stick to the phase shifts extracted in [21] and related to the
scattering $T$-matrix as

$\displaystyle-\frac{2\pi}{\mu}T^{-1}(E)=p\cot\delta-ip,$ (1)

with $E$ and $p$ the energy and the magnitude of the relative momentum in the
center-of-mass (c.m.) frame, respectively. A pole of the $T$-matrix appears if

$p\cot\delta=ip.$ (2)

To exploit condition (2), the phase shifts extracted from the lattice
calculations were parameterized retaining the first two terms in the effective
range expansion (ERE) 111If one of the scattering particles is unstable, it is
convenient to make ERE around the complex branch point connected to the two-
body channels [51, 52].,

$p\cot\delta=\frac{1}{a}+\frac{1}{2}rp^{2}+\mathcal{O}(p^{4}),$ (3)

where $a$ and $r$ are the scattering length and effective range, respectively.
However, the convergence radius of ERE is set by the location of the nearest
singularity irrespective of its origin. We argue that, in the settings of
[21], the physics related to the lhc is relevant and cannot be ignored. In
particular, we demonstrate that the simple approximation (3) has to be
abandoned in favor of the exact solution of the dynamical equation in the
presence of pions, which have a strong effect on both $p\cot\delta$ and the
extracted pole. Thus, the physics discussed in this Letter is related to the
lhcs from long-range potentials and is quite general.

Importantly, the phase shifts extracted from the lattice data and employed in
our analysis may need to be revisited since the presence of the lhc requires a
modification of the Lüscher method [25, 26] and may induce sizable partial-
wave mixing effects [27]. Being unable to assess quantitatively the importance
of these effects, we take the phase shifts extracted above the lhc for
granted.

Cut structure of the $DD^{*}$ amplitude.—In line with the lattice setting
employed to analyze the $DD^{*}$ system, we work in the isospin limit and use
isospin-averaged masses for all mesons. Then the $T_{cc}(3875)^{+}$ is a
purely isoscalar state. The relevant degrees of freedom are $DD^{*}$ and
$DD\pi$, introducing two- and three-body branch points in the amplitude,
respectively. For the physical pion mass, pions contribute to the $DD^{*}$
dynamics in two ways: through the $D^{*}$ selfenergy and $DD^{*}$ scattering
potential. Both induce rhcs to the amplitude (upper and lower blue dashed
vertical lines in Fig. 1, respectively). The three-body $DD\pi$ Green’s
function generating the most relevant cut in the $DD^{*}$ scattering amplitude
reads [28, 29, 30, 31] (for details on time-ordered perturbation theory see,
e.g., [32, 33, 34])

$\begin{split}G_{\pi}^{-1}(E,\bm{k}\,^{\prime},\bm{k})&=E-E_{D}(k^{2})-E_{D}(k^{\prime
2})-\omega_{\pi}(q^{2})\\\ &\approx E-2M_{D}-\frac{k^{2}+k^{\prime
2}}{2M_{D}}-\omega_{\pi}(q^{2})\,,\end{split}$ (4)

where $E$ is the total energy, $\bm{k}$ ($\bm{k}^{\prime}$) is the incoming
(outgoing) $DD^{*}$ relative momentum in the c.m. frame,
$E_{D}(k)=\sqrt{M_{D}^{2}+k^{2}}$,
$\omega_{\pi}(q^{2})=\sqrt{m_{\pi}^{2}+q^{2}}$, with
${\bm{q}}=\bm{k}-\bm{k}^{\prime}$, and $k^{(\prime)}=|{\bm{k}}^{(\prime)}|$,
$q=|{\bm{q}}|$.

For the physical pion mass, $m_{\pi}<\Delta M$, and one can find real values
of $k$ and $k^{\prime}$ such that $G_{\pi}^{-1}=0$ for each energy $E$ above
the three-body threshold $E_{\rm thr}\equiv 2M_{D}+m_{\pi}$, with the
interpretation of the $DD\pi$ state going on-shell. At the same time, the
$DD^{*}$ Green’s function has two branch points in the complex $s$ plane
($s=E^{2}$), giving rise to the two-body unitarity cuts in the scattering
amplitude—see Fig. 2 (b).

If $m_{\pi}$ increases, $\Delta M$, governed by heavy-quark spin symmetry
violation and not chiral dynamics, changes very little, but the phase space
for the $DD\pi$ state shrinks. For $m_{\pi}>\Delta M$, $D^{*}$ becomes stable
(its radiative decays are not considered in lattice calculations, so we
neglect them too), and the $DD^{*}$ branch cut moves to the real axis. We
measure the energy relative to the $DD^{*}$ threshold to write
$E=M_{D^{*}}+M_{D}+p^{2}/(2\mu)$, where
$\mu=M_{D^{*}}M_{D}/(M_{D^{*}}+M_{D})$. The two-body branch point is located
at $E=M_{D}+M_{D^{*}}$, which implies

$p_{{\rm rhc}_{2}}^{2}=0.$ (5)

Then,

$G_{\pi}^{-1}(E,{\bm{k}}^{\prime},{\bm{k}})=\Delta
M+\frac{p^{2}}{2\mu}-\frac{k^{2}+k^{\prime^{2}}}{2M_{D}}-\omega_{\pi}(q^{2}),$
(6)

so the three-body branch point (we set $k=k^{\prime}=0$) is

$p_{{\rm rhc}_{3}}^{2}=2\mu(m_{\pi}-\Delta M).$ (7)

In addition, new singularities emerge from (6) in the on-shell partial-wave
amplitudes at imaginary values of the momenta, $k^{2}=k^{\prime 2}=p^{2}<0$.
The smallest in magnitude value of $p^{2}$ where this happens ($\mu\approx
M_{D}/2$) is given by $\omega_{\pi}(4p^{2})\approx\Delta M$ (backward
scattering),

$(p_{\rm lhc}^{1\pi})^{2}\approx\frac{1}{4}[(\Delta M)^{2}-m_{\pi}^{2}].$ (8)

This sets the location of the branch point for the lhc nearest to the
threshold. The other, remote, end-point of this lhc is set by forward
scattering [34]. The cut structure in the complex $s$ plane for
$m_{\pi}>\Delta M$ (stable $D^{*}$) is shown in Fig. 2 (a) with the lhc
located below the two-body $DD^{*}$ threshold. Decreasing $m_{\pi}$, the lhc
shrinks and moves towards the threshold. For $m_{\pi}=\Delta M$ both branch
points of the lhc and 3-body rhc (see (7)) hit the threshold. After that, as
the $D^{*}$ becomes unstable, the only relevant cut left on the real axis is
the 3-body $DD\pi$ cut—see Fig. 2 (b). Meanwhile, the other possible lhcs from
the two-pion or heavier meson exchanges may still be present. Those are much
further away from the threshold and irrelevant to the discussion here.

A lhc introduces nonanalyticity to $p\cot\delta$ defined in (1) and,
accordingly, sets the upper bound on the convergence radius of ERE (3). For
the case at hand, $p\cot\delta$ acquires an imaginary part for energies below
the lhc and cannot be treated as real-valued.

Figure 2: Sketch of the locations of various branch cuts and poles in the
complex $s$-plane for: (a) $m_{\pi}=280$ MeV and (b) the physical pion mass.
The left-hand, two-body $DD^{*}$, and three-body $DD\pi$ cuts are shown in
red, green, and blue, respectively. The black symbols show typical locations
for the $T_{cc}^{+}$ poles: they can correspond to a pair of virtual states
(dots) or a resonance (stars) in case (a) and to a quasi-bound state, which
would be a bound state for stable $D^{*}$, in case (b). In cases (a) and (b),
the poles are on the second and first Riemann sheets, respectively, with
respect to the $DD^{*}$ cut. Figure 3: Fit results for the lattice data from
[21]. The solid and dashed vertical lines indicate the $DD^{*}$ threshold and
the lhc, respectively, while the green dashed curve shows the function $ip$.
The gray line and gray band show the fit and its 1$\sigma$ uncertainty,
respectively, found in [21] using ERE formula from (3) in the entire energy
range both above and below lhc. The red solid line and the orange band show
the best fit and its 1$\sigma$ uncertainty, respectively, calculated in this
work. In the right panel, only the three most right data points were used in
the fit while in the left panel, in addition, a part of the error bar of the
fourth (from right to left) point located above the lhc (for
$(p/E_{DD^{*}})^{2}>-0.0010$) is included in the fit for illustrative purpose.
Below the lhc, $p\cot\delta$ acquires an imaginary part, which is shown as the
blue line with the pink uncertainty band.

Results and discussion.—For an illustration of the general concept, we focus
on the lattice data from [21] collected at $m_{\pi}=280$ MeV, $M_{D}=1927$ MeV
and $M_{D^{*}}=2049$ MeV (the second data set provided in [21] leads to
analogous results [34]). Then, with $\Delta M=122~{}\mbox{MeV}<m_{\pi}$, we
find

$(p_{\rm lhc}^{1\pi})^{2}=-(126\
\mbox{MeV})^{2}\Longrightarrow\left(\frac{p_{\rm
lhc}^{1\pi}}{E_{DD^{*}}}\right)^{2}=-0.0010,$ (9)

where $E_{DD^{*}}=M_{D}+M_{D^{*}}$. In Fig. 3 the location of this lhc branch
point is indicated with the dashed vertical line. The $DD\pi$ rhc branch point
is located far away,

$p_{{\rm rhc}_{3}}^{2}=(552\ \mbox{MeV})^{2}\Longrightarrow\left(\frac{p_{{\rm
rhc}_{3}}}{E_{DD^{*}}}\right)^{2}=+0.019,$ (10)

and is irrelevant for the current analysis.

In [21] the $T$-matrix pole is extracted from the lattice data using a linear
(in $p^{2}$) fit, as defined in (3), in the full energy range, thereby
yielding a pole location at $p_{0}^{2}/(2\mu)=-9.9$ MeV
[$(p_{0}/E_{DD^{*}})^{2}=-0.0012$], on the second Riemann sheet of the complex
$s$ plane. In Fig. 3 this fit is shown as the gray line including its
1$\sigma$ uncertainty band in light gray. Thus, the pole extracted using only
the first two terms in ERE is located below the lhc. However, since the lhc
sets the radius of convergence of ERE, the latter is only valid in a small
range $|(p/E_{DD^{*}})^{2}|<0.0010$, where no lattice data exist. Furthermore,
the central values of the two data points crucial for the fit lie below the
lhc, though $p\cot\delta$ should be complex in this case. Therefore, this pole
extraction procedure cannot be regarded as reliable.

To improve on the extraction of the pole parameters from the phase shifts we
fit the lattice data from [21] with an amplitude that includes the lhc 222An
important role played by the lhc from pion exchanges for $NN$ scattering at
unphysical pion masses was pointed out in [53, 54].. More precisely, we solve
the $DD^{*}$ scattering equation employing a potential that incorporates the
OPE and two contact terms (one momentum-independent and one momentum-
dependent) treated as fitting parameters. This is a simplified version of the
full amplitude of [31], where $D$ waves are now switched off to be in line
with [21]. The chiral extrapolation of the pion decay constant is considered
using chiral perturbation theory [36] and that of the $D^{*}D\pi$ coupling is
taken from [37, 38]. To reliably extract the $T$-matrix pole, the amplitude
needs to be put into a finite volume to determine the parameters directly from
a fit to the lattice energy levels; however, to demonstrate the effect of the
lhc it is sufficient to fit to the existing lattice data. The results are
shown in Fig. 3 in red with orange uncertainty band 333These results were
obtained with the $D$-meson recoil terms included, however their impact is
negligible since the three-body cut (10) is sufficiently remote.. Uncertainty
in [21] is given by the probability distribution for each phase shift data
point. The nonzero probability of real phase shift data below the lhc is an
artifact of the lhc being ignored in [21]. Therefore, the lowest data point in
[21] is discarded in our analysis. We perform two fits: one where we use the
part of the second data point that is above the lhc (left panel of Fig. 3) and
the other one where we ignore it (right panel of Fig. 3). The upper three data
points are included in both fits.

The poles of the $T$-matrix are now extracted using (2). From the left panel
of Fig. 3 we conclude that, for the majority of the $1\sigma$ parameter space
including the best fit, the amplitude contains two virtual states, both
residing closer to the $DD^{*}$ threshold than the pole extracted in [21],
where only a single virtual state was found. Those fits within the $1\sigma$
band, where $p\cot\delta$ does not cross the $ip$ curve above the lhc,
describe the presence of a very narrow resonance showing up as a pair of
complex poles below the $DD^{*}$ threshold. The appearance of a pair of
virtual states is natural near the point where they are about to turn to a
narrow resonance, as discussed in detail in [40, 41, 42, 43]. The position of
the lhc sets the upper bound on the virtual pole binding energy—the collision
between the virtual pole and its counterpart always takes place between the
lhc branch point and the two-body threshold. The fit results presented in the
right panel of Fig. 3 are also consistent with the picture just drawn, with
the narrow resonance scenario preferred.

In both fits $p\cot\delta$ contains a near-threshold pole as a result of a
subtle interplay of the repulsive OPE and the attractive short-range
interaction. According to (1), this pole manifests itself as a zero in the
$T$-matrix and provides yet another illustration that, in the current setting,
$p\cot\delta$ cannot be approximated by a polynomial with a finite number of
terms. Moreover, it emphasizes the important role played by the OPE for
understanding the analytic structure of the scattering amplitude. The
existence of such a pole in $p\cot\delta$ for the neutron-deuteron scattering
was already investigated half a century ago [44, 45]. Here the location of the
pole in $p\cot\delta$ very close to the lhc branch point is dictated by the
particular lattice data points taken from [21]. Indeed, while the lhc branch
point depends only on the masses involved, the exact location of the pole is
sensitive to the interaction strength. If the pion coupling constant is
artificially decreased or increased by some factor and the lattice data are
refitted to fix the contact terms, the pole in $p\cot\delta$ either disappears
below the lhc or moves closer to the two-body threshold [34]. In the latter
case, it may impose a stronger constraint on the ERE convergence radius than
the lhc branch point.

Concluding remarks.—An interesting question is what our findings imply for the
nature of the $T_{cc}^{+}$ given an intriguing relationship between the
location of a near-threshold bound state pole and the size of the molecular
component [46, 47] 444The equivalence of the two approaches was first
discussed in [55], generalization to virtual states is provided in [56] and,
for a positive effective range to be the case for the lattice analyses of
$T_{cc}^{+}$ [21, 22], in [57, 58].. This formalism relies on the assumption
that the binding momentum $\gamma$ is by far the smallest scale in the
problem. However, the lhc induces an additional small scale, which not only
strongly limits the range of applicability of ERE (see [30] for a related
discussion), but also calls for an improvement of the entire Weinberg approach
to describe the compositeness of a hadronic state 555That zeros in the
$T$-matrix invalidate the original Weinberg formalism was discussed in [46,
59, 60].. On the other hand, a clear visibility in the amplitude of the lhc
induced by the OPE provides an additional strong support for the molecular
nature of the $T_{cc}(3875)^{+}$.

In summary, we have demonstrated that the lhcs from the long-range
interactions, with the nearest one originating from the OPE, strongly restrict
the range of validity of ERE in extracting the pole positions of near-
threshold states. In order to increase this range and thereby extract the
poles reliably, at least the OPE needs to be considered explicitly. Our
findings clearly suggest that a direct comparison of the below-threshold
energy levels predicted by our formalism, put in a finite volume, with the
lattice energy levels should be made. The described feature is general, and we
illustrated it by reanalyzing the lattice data of [21] for the
$T_{cc}(3875)^{+}$. The same effect may be operative in other hadronic systems
where the lhc appears within the range covered by the theory and should be
taken into account not only in lattice studies but also in analytical
approaches already for physical parameters. These might include not only
$BB^{*}$ and $B\bar{B}^{*}$, but also $\Sigma(\Lambda)N$,
$\Sigma_{c}^{(*)}\bar{D}^{(*)}$, $ND^{(*)}$, $N\bar{D}^{(*)}$ systems and so
forth. Consequently, the effect of the lhc could be of relevance for probing
the $\Sigma$ hyper-nuclei, $D$-mesic nuclei and the properties of charmed and
bottom mesons in nuclear matter. Moreover, the $D\bar{D}^{*}$ is of particular
interest for its obvious similarity to the $T_{cc}^{+}$ case studied above.
The lattice simulations performed in [50] predict the $X(3872)$ as a shallow
bound state $(11\pm 7)$ MeV below the $D\bar{D}^{*}$ threshold. Within the
uncertainty, the $X$ pole may appear either below or above the lhc, so the
influence of the latter is hard to foresee, and a reanalysis of the system on
the lattice seems necessary.

Lattice QCD enters the era of precise calculations for low-lying near-
threshold states, which have been a focus of experimental and theoretical
hadron physics for two decades and will clearly remain a hot topic in the
foreseeable future. Our finding can be crucial in accurately extracting the
pole locations of the benchmark systems such as $DD^{*}$ and $D\bar{D}^{*}$
from lattice data. Thus, the consequences of taking it into account are
potentially very important for understanding various exotic hadrons, e.g.,
whether they exist and what their internal structure is, from first principles
of QCD.

###### Acknowledgements.

The authors would like to thank Sasa Prelovsek for reading the manuscript and
valuable comments. This work is supported in part by the National Natural
Science Foundation of China (NSFC) and the Deutsche Forschungsgemeinschaft
(DFG) through the funds provided to the Sino-German Collaborative Research
Center TRR110 “Symmetries and the Emergence of Structure in QCD” (NSFC Grant
No. 12070131001, DFG Project-ID 196253076); by the Chinese Academy of Sciences
under Grant No. YSBR-101 and No. XDB34030000; by the NSFC under Grants No.
12125507, No. 11835015, and No. 12047503; by the EU STRONG-2020 project under
the program H2020-INFRAIA-2018-1 with Grant No. 824093; by the Spanish
Ministerio de Ciencia e Innovación (MICINN) under Grant No.
PID2020-112777GB-I00; by Generalitat Valenciana under Grant PROMETEO/2020/023;
by BMBF (Contract No. 05P21PCFP1) and by the MKW NRW under the funding code
NW21-024-A. A.N. is supported by the Slovenian Research Agency (research core
Funding No. P1-0035). Q.W. is also supported by Guangdong Provincial funding
with Grant No. 2019QN01X172.

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##  Appendix A Theoretical framework and fitting procedure

###  A.1 Left-hand cuts from pion exchanges

Figure 4: The two contributions to the OPE interaction between the $D^{*}$
(double solid line) and $D$ (single solid line) mesons; the dashed line
corresponds to the pion. The thin vertical line picks up the relevant
intermediate state: $DD\pi$ and $D^{*}D^{*}\pi$ for the left and right plot,
respectively.

Here we briefly outline the relation between the pion propagator in the
Feynman technique and in the time-ordered perturbation theory (TOPT), for
details see, e.g., [32, 33].

We start from the Feynman propagator,

$D^{\pi}(q)=\frac{1}{q_{\mu}q^{\mu}-m_{\pi}^{2}}=\frac{1}{q_{0}^{2}-\omega_{\pi}^{2}(q^{2})},$
(11)

where $\omega_{\pi}(q^{2})=\sqrt{q^{2}+m_{\pi}^{2}}$, and rewrite it
identically in the form

$D^{\pi}(q)=\frac{1}{{2}\omega_{\pi}(q^{2})}\left(\frac{1}{q_{0}-\omega_{\pi}(q^{2})}-\frac{1}{q_{0}+\omega_{\pi}(q^{2})}\right).$
(12)

The derivation of the integral equations yields that the energy transfer
$q_{0}$ in the first and second terms in the parentheses can be substituted as
$q_{0}=E-E_{D}(k^{2})-E_{D}(k^{\prime 2})$ and
$q_{0}=-E+E_{D^{*}}(k^{2})+E_{D^{*}}(k^{\prime 2})$, respectively, with
${\bm{k}}$ and ${\bm{k}}^{\prime}$ for the momenta in the initial and final
state, respectively. Then the pion propagator (12) finally reads

$\displaystyle D^{\pi}(q)$ $\displaystyle=$
$\displaystyle\frac{1}{{2}\omega_{\pi}(q^{2})}\left[\frac{1}{E-E_{D}(k^{2})-E_{D}(k^{\prime
2})-\omega_{\pi}(q^{2})}\right.$ (13)
$\displaystyle+\left.\frac{1}{E-E_{D^{*}}(k^{2})-E_{D^{*}}(k^{\prime
2})-\omega_{\pi}(q^{2})}\right],$

which can be recognized as the TOPT form of the propagator, with the two terms
in square brackets for the two time orderings corresponding to the TOPT
diagrams shown in Fig. 4.

The lhc branch points from the OPE for the $DD^{*}$ scattering can be found as
the end-point singularities of the $DD\pi$ TOPT Green’s function in the on-
shell kinematics,

$\displaystyle E-E_{D}(k^{2})-E_{D}(k^{\prime
2})-\omega_{\pi}(q^{2})\xrightarrow[\text{on shell:
}k=k^{\prime}=p]{\cos\theta=\pm 1}$ (14) $\displaystyle
E_{D*}(p^{2})-E_{D}(p^{2})-\omega_{\pi}(2p^{2}(1-\cos\theta))\big{|}_{\cos\theta=\pm
1}=0,$

which gives for the lhc branch point near the two-body threshold
($\cos\theta=-1$)

$\displaystyle(p_{\rm lhc}^{1\pi})^{2}$ $\displaystyle=$
$\displaystyle\frac{1}{4}\Bigl{[}(\Delta
M)^{2}-m_{\pi}^{2}\Bigr{]}\frac{(M_{D}+M_{D^{*}})^{2}-m_{\pi}^{2}}{2M_{D}^{2}+2M_{D^{*}}^{2}-m_{\pi}^{2}}$
$\displaystyle=$ $\displaystyle\frac{1}{4}\Bigl{[}(\Delta
M)^{2}-m_{\pi}^{2}\Bigr{]}\left[1+{\cal O}\left(\frac{(\Delta
M)^{2}}{M_{D}^{2}}\right)\right].$

Since $\Delta M\ll M_{D}$, the relativistic correction is negligible for the
problem at hand and we arrive at equation (8) in the main text. The position
of the more distant branch point corresponding to $\cos\theta=+1$ depends on a
particular relation between the masses of the particles involved. In the
kinematics discussed in this paper, we have

$\sqrt{M_{D}^{2}+m_{\pi}^{2}}\leqslant M_{D^{*}}\leqslant M_{D}+m_{\pi},$ (16)

which gives

$\displaystyle(\tilde{p}_{\rm lhc}^{1\pi})^{2}$ $\displaystyle=$
$\displaystyle\frac{1}{4}\Bigl{[}(\Delta
M)^{2}-m_{\pi}^{2}\Bigr{]}\frac{(M_{D}+M_{D^{*}})^{2}-m_{\pi}^{2}}{m_{\pi}^{2}}$
$\displaystyle=$ $\displaystyle\frac{1}{4}\Bigl{[}(\Delta
M)^{2}-m_{\pi}^{2}\Bigr{]}\frac{4M_{D}^{2}}{m_{\pi}^{2}}\left[1+{\cal
O}\left(\frac{\Delta M}{M_{D}}\right)\right].$

It follows from (LABEL:Eq:lhc1pi) and (LABEL:Eq:lhc1pidist) that both lhc
branch points move towards the two-body threshold when $m_{\pi}$ decreases, so
in the limit $m_{\pi}=\Delta M$ the lhc disappears. We would like to highlight
that the $D^{*}D^{*}\pi$ TOPT Green’s function generates only a remote lhc for
the $DD^{*}$ scattering that is irrelevant to the discussion and is thus
disregarded.

The next in importance lhc comes from the two-pion exchange (TPE)
contributions. A rough estimate of its near-threshold branch point can be done
if one employs that $(\Delta M)^{2}/m_{\pi}^{2}\ll 1$ for the lattice settings
in [21] to neglect the difference in the mass squared relative to the pion
mass squared, which gives $(p_{\rm lhc}^{2\pi})^{2}\approx-m_{\pi}^{2}$. This
implies that although the TPE contributions may introduce certain corrections,
the relatively large distance of $(p_{\rm lhc}^{2\pi})^{2}$ from the threshold
suggests that there should be no qualitative changes in the extracted poles.
Furthermore, it is argued in [53, 54] that a significant portion of the multi-
pion-exchange cut contributions is already accounted for through iterations of
the OPE.

###  A.2 $\bm{T}$-matrix

In the isospin limit, the contact potential up to next-to-leading order in the
nonrelativistic expansion for the $S$-wave $DD^{*}$ isoscalar ($I=0$) state
reads

$\displaystyle V_{C}^{I=0}(k,k^{\prime})=c_{0}+c_{2}(k^{2}+k^{\prime 2}),$
(18)

where $c_{0}$ and $c_{2}$ are the low-energy constants and $k$ $(k^{\prime})$
is the 3-momentum of the incoming (outgoing) particle in the the center-of-
mass (c.m.) frame. In the framework of the time-ordered-perturbation theory,
the one-pion exchange (OPE) potential is written as

$\displaystyle V_{\text{OPE}}^{I=0}(E,k,k^{\prime})$ $\displaystyle=$
$\displaystyle\frac{g^{2}}{8f_{\pi}^{2}}\int_{-1}^{1}dzD^{\pi}(E,k,k^{\prime},z)$
(19) $\displaystyle\hskip 17.34189pt\times(k^{2}+k^{\prime 2}-2kk^{\prime}z),$

where, according to (13),

$D^{\pi}(E,k,k^{\prime},z)=-\frac{D_{1}(E,k,k^{\prime},z)+D_{2}(E,k,k^{\prime},z)}{2\omega_{\pi}(q^{2})},$

with

$\displaystyle D_{1}^{-1}(E,k,k^{\prime},z)$ $\displaystyle=$ $\displaystyle
2M_{D}+\frac{k^{2}+k^{\prime 2}}{2M_{D}}+\omega_{\pi}(q^{2})-E-i\epsilon,$
$\displaystyle D_{2}^{-1}(E,k,k^{\prime},z)$ $\displaystyle=$ $\displaystyle
2M_{D^{*}}+\frac{k^{2}+k^{\prime
2}}{2M_{D^{*}}}+\omega_{\pi}(q^{2})-E-i\epsilon,$

and $\omega_{\pi}(q^{2})=\sqrt{m_{\pi}^{2}+k^{2}+k^{\prime 2}-2kk^{\prime}z}$,
that is, the pion is treated fully relativistically while the $D^{(*)}$ mesons
are nonrelativistic.

The $T$-matrix (amplitude) is obtained as a solution of the Lippmann-Schwinger
equation

$\displaystyle T(E,k,k^{\prime})$ $\displaystyle=$ $\displaystyle
V(E,k,k^{\prime})$
$\displaystyle-\int\frac{\text{d}^{3}{\bm{q}}}{(2\pi)^{3}}V(E,k,q)G(E,q)T(E,q,k^{\prime}),$

where the potential is a sum of the contact term and OPE,

$V(E,k,k^{\prime})=V_{C}(k,k^{\prime})+V_{\text{OPE}}(E,k,k^{\prime}).$ (21)

In order to render the integral in (A.2) well defined, we set a sharp cutoff
$\Lambda$. To arrive at the results in Fig. 3, $\Lambda$ is chosen to be 500
MeV. The $DD^{*}$ propagator is expressed as

$\displaystyle
G(E,q)=\left[M_{D^{*}}+M_{D}+\frac{q^{2}}{2\mu}-E-\frac{i}{2}\Gamma(E,q)\right]^{-1},~{}~{}$
(22)

where $\mu=M_{D}M_{D^{*}}/(M_{D}+M_{D^{*}})$ is the reduced mass,

$\Gamma(E,q)=\frac{g^{2}M_{D}}{8\pi
f_{\pi}^{2}M_{D^{*}}}\Big{[}\Sigma(s)-\Sigma_{0}(s)\theta(M_{D}+m_{\pi}-M_{D^{*}})\Big{]},$

with $s=[E-M_{D}-q^{2}/(2\mu)]^{2}$, and

$\displaystyle\Sigma(s)=\left[\frac{\sqrt{\lambda(s,M_{D}^{2},m_{\pi}^{2})}}{2\sqrt{s}}\right]^{3},$
(23)

where $\lambda(a,b,c)=a^{2}+b^{2}+c^{2}-2ab-2bc-2ca$ is the Källén triangle
function. Here

$\displaystyle\Sigma_{0}(s)$ $\displaystyle=$
$\displaystyle\Sigma(M_{D^{*}}^{2})$
$\displaystyle+2M_{D^{*}}\left(E-M_{D^{*}}-M_{D}-\frac{q^{2}}{2\mu}\right)\Sigma^{\prime}(M_{D^{*}}^{2}),$

where the first and second terms renormalize the $D^{*}$ mass and wave
function, respectively, if $M_{D^{*}}<M_{D}+m_{\pi}$.

Figure 5: Fits for the OPE potential artificially suppressed by a factor of
1/10 (the left plot) or artificially enhanced by a factor of 5 (the right
plot). The inset in the left panel magnifies the red curve in the vicinity of
the lhc branch point. See the caption of Fig. 3 in the main text for further
details. Here only the three data points not affected by the lhc are
considered in the fits.

###  A.3 Chiral extrapolation of $\bm{f_{\pi}}$ and $\bm{g}$

For convenience, we introduce the ratio $\xi=m_{\pi}/m_{\pi}^{\text{ph}}$ with
$m_{\pi}^{\text{ph}}$ the physical pion mass. For the masses of the $D$ and
$D^{*}$ we stick to the values used in the lattice calculations and quoted
explicitly in [21]. For the pion decay constant $f_{\pi}$, we resort to the
result of the one-loop chiral perturbation theory [36] and cast it into the
form [37]

$\displaystyle
f_{\pi}(\xi)=f_{\pi}^{\text{ph}}\left[1+\left(1-\frac{f_{0}}{f_{\pi}^{\text{ph}}}\right)(\xi^{2}-1)-\frac{(m_{\pi}^{\text{ph}})^{2}}{8\pi^{2}f_{0}^{2}}\xi^{2}\log\xi\right],$

where $f_{0}\equiv f_{\pi}(m_{\pi}=0)=85$ MeV [38] and
$f_{\pi}^{\text{ph}}=92.1~{}\text{MeV}$.

Figure 6: The behavior of the pole position (left) and the residue (right) of
$p\cot\delta$ with the variation of the OPE strength while keeping the pion
mass fixed. Only the central values are shown. The horizontal dashed line in
the left panel indicates the lhc. The data points used in the fits for the
artificially suppressed/enhanced OPE potential are the same as Fig. 5.

For the chiral extrapolation of the $DD^{*}\pi$ coupling $g$, we employ the
lattice results of [38] and express it in terms of the physical value
$g^{\text{ph}}$ and $g_{0}\equiv g(m_{\pi}=0)$ as [37]

$g(\xi)=g^{\text{ph}}\left[1+C_{1}(\xi^{2}-1)+C_{2}\xi^{2}\log\xi\right],$
(24)

where $g^{\text{ph}}=0.57$ is determined from the experimentally measured
$D^{*+}\to D^{0}\pi^{+}$ decay width [31],

$\displaystyle
C_{1}=1-\left[1-\frac{1+2g_{0}^{2}}{8\pi^{2}f_{0}^{2}}(m_{\pi}^{\text{ph}})^{2}\log\frac{m_{\pi}^{\text{ph}}}{\mu_{\text{lat}}}+\alpha_{\text{lat}}(m_{\pi}^{\text{ph}})^{2}\right]^{-1},$
$\displaystyle
C_{2}=-\frac{1+2g_{0}^{2}}{8\pi^{2}f_{0}^{2}}(m_{\pi}^{\text{ph}})^{2}(1-C_{1}),$

and the parameters take the values [38]

$\displaystyle
g_{0}=0.46,\quad\alpha_{\text{lat}}=-0.16~{}\text{GeV}^{-2},\quad\mu_{\text{lat}}=1~{}\text{GeV}.$

Specifically, for $m_{\pi}=280$ MeV this gives

$g(m_{\pi}=280\,{\rm MeV})=0.65.$ (25)

The variation of the strength of the OPE potential (within approximately 30%,
driven by the pion mass dependence of both $f_{\pi}$ and $g$) due to changing
$m_{\pi}$ between its physical and lattice values provides only a subleading
effect on the dynamics of the system at hand while the leading effect comes
from the position of the lhc branch point, as given in (8). Specifically, for
$m_{\pi}>\Delta M$ the lhc is on the real axis in the energy plane with the
lhc branch point being close to the threshold.

Figure 7: Fits for the alternative set of parameters provided in [21] and
quoted in (27). See the caption of Fig. 3 in the main text for further
details.

###  A.4 Fitting procedure

In this appendix we describe the procedure employed to fit
$p\cot\delta(p^{2})$ extracted from the lattice data in [21] using the model
described above which explicitly takes into account the OPE interaction.

In particular, the function $p\cot\delta(p^{2})$ is related to the $DD^{*}$
$S$-wave on-shell scattering $T$-matrix $T(E)$ as

$p\cot\delta(p^{2})=-\frac{2\pi}{\mu}T^{-1}(E)+ip,$ (26)

where $T(E)\equiv T(M_{D}+M_{D^{*}}+p^{2}/(2\mu),p,p)$ is a solution of the
Lippmann-Schwinger equation (A.2).

Since the lattice data points for $p\cot\delta(p^{2})$ are extracted using the
Lüscher method, their uncertainties have non-Gaussian shapes, which prevents
us from performing a naive $\chi^{2}$ fit. Instead, we employ the probability
distribution extracted for each lattice data point from [21] and generate 1000
sets of quasi-data points according to these distributions. Each generated set
(with 3 or 4 data points depending on the fit) is then fitted with our model
by minimizing

$\chi^{2}=\sum_{i}\left(p_{i}\cot\delta{(p_{i}^{2})}\big{|}_{\text{model}}-p_{i}\cot\delta{(p_{i}^{2})}\big{|}_{\text{quasi-
data}}\right)^{2}$

as a function of the parameters $c_{0}$ and $c_{2}$, where $i$ enumerates the
data points used in the fit—see the main text for the details of the selection
procedure of the data points. The resulting 1000 pairs $\\{c_{0},\,c_{2}\\}$
are used then to evaluate the most probable values of these low-energy
constants, $p\cot\delta(p^{2})$, and the corresponding 68% confidence
intervals. The correlations between lattice data points are not available in
[21], so that we do not consider them in our fits. It is sufficient for the
illustrative purpose of the significant impact of the OPE potential on the
pole extraction as we do not aim at a strict and comprehensive analysis of the
lattice data from [21], which calls for a well-justified approach taking the
lhc into account.

###  A.5 Pionic dynamics for unphysically small and large pion coupling

Here we discuss the effect of the pionic dynamics in case of the OPE potential
artificially suppressed by a factor of 1/10 (the left plot in Fig. 5) or
enhanced by a factor of 5 (the right plot in Fig. 5). From these plots, in
agreement with the natural expectations, one can see that, for a weaker pion
exchange, the fit approaches the ERE linear formula. On the contrary, for the
enhanced OPE interaction, the singularity of $p\cot\delta(p^{2})$ moves closer
to the two-body threshold, thus limiting the range of convergence of the ERE
even stronger than the lhc. Therefore, an approximate coincidence of the pole
in $p\cot\delta$ and lhc, that takes place for the physical value of the pion
coupling, comes as a result of fitting the particular data points taken from
[21].

In order to show the essential effect of the OPE on the pole of $p\cot\delta$,
we demonstrate how the pole moves if we vary the OPE strength while keeping
the pion mass fixed—see the left panel in Fig. 6. For the lattice OPE strength
from (25), the pole of $p\cot\delta$ appears just above the lhc. Then, if the
pion coupling (labeled as $g_{\text{Modified}}$) is artificially decreased,
the pole gradually approaches the lhc. Finally, as the OPE strength vanishes
($\beta=(g_{\text{Modified}}/g_{\text{lat}})^{2}\to 0$), the residue at the
pole also vanishes (see the right panel in Fig. 6), ensuring that OPE is
essential for producing the pole in $p\cot\delta$.

##  Appendix B Analysis of the lattice data for the smaller charm quark masses

In this appendix we provide the fit results for the lattice data from [21]
corresponding to the smaller charm quark masses, namely

$M_{D}=1762~{}\mbox{MeV},\quad M_{D^{*}}=1898~{}\mbox{MeV},$ (27)

while the pion mass remains the same as before, $m_{\pi}=280$ MeV. The
obtained 3- and 4-point fits are shown in Fig. 7. In these settings, the lhc
position corresponds to ${(p/E_{DD^{*}})}^{2}=-0.0011$. As stated in the main
text, these fits demonstrate essentially the same behaviour as those shown in
Fig. 3 and as such lead to the same conclusions.


1 Dept. of BioHealth Informatics, Indiana University Purdue University
Indianapolis, Indianapolis, IN.

# Evaluation of accessibility of open-source EHRs for visually impaired users

Megha M Moncy  BDS1 Manya Pilli  BTech1 Manasi Somasundaram  PharmD1 Saptarshi
Purkayastha  PhD1 Cathy R. Fulton  DNP  RN  ANP-BC  FNP  BC1

## Abstract

This study investigates the accessibility of open-source electronic health
record (EHR) systems for individuals who are visually impaired or blind.
Ensuring the accessibility of EHRs to visually impaired users is critical for
the diversity, equity, and inclusion of all users. The study used a
combination of automated and manual accessibility testing with screen readers
to evaluate the accessibility of three widely used open-source EHR systems. We
used three popular screen readers - JAWS (Windows), NVDA (Windows), and Apple
VoiceOver (OSX) to evaluate accessibility. The evaluation revealed that
although each of the three EHR systems was partially accessible, there is room
for improvement, particularly regarding keyboard navigation and screen reader
compatibility. The study concludes with recommendations for making EHR systems
more inclusive for all users and more accessible.

##  1 Introduction

Open source Electronic Health Records (EHRs) have revolutionized healthcare
delivery by providing efficient access and management of patient information,
resulting in improved decision-making, reduced medical errors, and enhanced
quality of care 1. Their increased popularity is attributed to their cost-
effectiveness and community-driven development 2. Even though EHRs have become
ubiquitous in healthcare delivery, there has been a lack of attention to
ensuring these systems are accessible to all users, including visually
impaired individuals 3. There are an estimated 8 million visually impaired
people in the USA, and many providers who need access to EHRs might be denied
access due to visual impairment. Many of them face challenges when using EHRs
due to their inability to read text, distinguish colors, or navigate complex
interfaces 4. The American Disability Act requires that anyone with
disabilities should have equal opportunity, but EHR systems may be denying
this opportunity due to accessibility problems. This can compromise the
quality of healthcare that visually impaired users might give or receive and
potentially worsen healthcare outcomes 5. Therefore, it is critical to ensure
that EHR systems are designed with accessibility in mind so that all patients
can benefit from the advancements in digital healthcare technology 6. Despite
the significant population of visually impaired individuals, many open-source
EHR systems have not been developed with their usability in mind 7. To provide
inclusive and accessible healthcare delivery, EHR developers must prioritize
accessibility in their designs.

OpenEMR, OpenMRS, and OSHERA VistA are three open-source EHRs that are widely
used in healthcare delivery 8. OpenEMR is primarily used in small to medium-
sized practices due to its cost-effectiveness and community-driven development
9. OpenMRS, on the other hand, is designed to manage patient information in
resource-limited settings and is widely used in developing countries 10.
Although the VA is replacing it, OSHERA VistA, which was initially developed
by the US Department of Veterans Affairs (VA), still has a robust user base in
the US and outside. Moreover, it is widely recognized as some of the most
user-friendly and usable EHR systems in the US 11. There have been several
studies examining the features and capabilities of open-source EHRs. However,
a significant research gap exists in evaluating their accessibility for
visually impaired users.

This study aims to evaluate the accessibility of three open-source EHR
systems, namely OpenEMR, OpenMRS, and OSHERA VistA, for blind and low-vision
users through the use of screen readers. JAWS, NVDA, and Apple VoiceOver are
examples of popular screen readers used by visually impaired individuals to
access digital content, including EHRs. In our research, we utilized these
screen readers to evaluate the accessibility of OpenEMR, OpenMRS, and OSHERA
VistA for blind and low-vision users. These screen readers provide audio
feedback, allowing users to navigate interfaces and access content through
keyboard commands 12. By using these screen readers to assess the
accessibility of the EHR systems, we identified specific challenges faced by
visually impaired users and provided recommendations for improving
accessibility in EHR design. Our research findings can guide the creation of
EHR systems that are more inclusive and accessible for visually impaired
patients, ultimately leading to better healthcare delivery.

##  2 Literature Review

Open-source Electronic Health Record (EHR) systems have been widely adopted by
healthcare systems globally because they offer cost-effective solutions for
managing patient data, which are crucial components of modern healthcare
systems. However, despite their increasing popularity, making these systems
accessible to visually impaired users remains a significant challenge. Back in
2014, the ONC Health IT curriculum had clear learning outcomes to train
informaticians to assess EHR systems with accessibility in mind 13. However,
the lack of published research and the lack of robust, large-scale
accessibility evaluation of EHR systems makes us question the scale-up and
reach of the curricular guidance.

OpenEMR is designed with accessibility in mind, but several studies have
identified some accessibility issues that must be addressed. A study by
Dimauro et al. (2018) also reported that OpenEMR had usability issues. The
study identified problems with the system’s keyboard navigation and labeling
of controls 14.

Although OpenMRS was not originally designed for visually impaired users,
recent studies have shown that the system has significantly enhanced
accessibility. For instance, a study by Verma et al. (2021) found that OpenMRS
had good accessibility features, including keyboard navigation, focus
management, labeling of controls, and color contrast 15. Other studies
highlight the potential of OpenMRS having good accessibility for visually
impaired users 16. However, our findings with screen readers provide a
different evaluation.

However, using EHRs has also introduced accessibility issues for individuals
with disabilities, including visual, auditory, physical, and cognitive
impairments.

  * •

Visual Accessibility: One of the primary accessibility issues with EHRs is
related to visual impairments. EHRs are typically designed with small fonts
and low-contrast colors, making it difficult for individuals with visual
impairments to read the content. Additionally, EHRs often require users to
navigate through multiple screens and menus, which can be challenging for
individuals with low vision or blindness.

  * •

Auditory Accessibility: EHRs also pose accessibility issues for individuals
with hearing impairments. Many EHRs rely on auditory alerts and notifications,
which can be missed by individuals with hearing impairments.

  * •

Physical Accessibility: EHRs can also pose physical accessibility issues for
individuals with mobility impairments. Many EHRs require users to navigate
through multiple screens and menus, which can be challenging for individuals
with limited dexterity or range of motion. Additionally, some EHRs require
users to use a mouse or trackpad, which can be difficult for individuals with
physical disabilities to operate.

  * •

Cognitive Accessibility: EHRs can also pose cognitive accessibility issues for
individuals with cognitive impairments, such as learning disabilities or
dementia. Many EHRs use complex medical terminology and require users to
navigate through multiple screens and menus, which can be challenging for
individuals with cognitive impairments to understand.

The accessibility of websites for visually impaired users has been extensively
studied, and the findings can be useful in improving the accessibility of
open-source EHRs 17. Various methods have been identified to enhance the
readability of web pages for people with low vision, such as increased letter
spacing and wider letters. Moreover, better layout and design, consistent font
usage, and color contrast are also considered important factors in improving
accessibility 18. Assistive technologies, such as screen readers that convert
text into synthesized speech have been found to improve the usability of
websites for the blind significantly. While there are multiple approaches to
improving accessibility, screen readers are considered one of the easiest to
implement. They offer a relatively simple and cost-effective way to enhance
the usability of websites for visually impaired users. By converting text into
speech, screen readers allow users to access and interact with web content
without relying on visual cues 19. Thus, ensuring EHR user interfaces work
with screen readers can significantly improve accessibility and enable
visually impaired individuals to benefit from these systems.

Screen readers are essential tools for visually impaired individuals to access
and interact with digital content. Popular screen readers include JAWS, NVDA,
and Apple VoiceOver. JAWS, a proprietary software developed by Freedom
Scientific, is widely used in Windows-based applications due to its
compatibility and advanced features 20. NVDA, an open-source screen reader,
has gained popularity due to its cost-free accessibility and compatibility
with Windows-based applications 21. Apple VoiceOver, an integrated screen
reader in Mac OS X, iOS, and iPad OS, provides seamless accessibility for
Apple device users. These screen readers enable visually impaired users to
access and interact with EHR systems, ensuring that the systems are inclusive
and accessible to all users 22.

##  3 Methodology

### Data Collection and Source of Information

We ensured that we covered all the relevant literature on the accessibility of
EHR systems by conducting a robust literature review. We utilized PubMed and
IEEE Xplore databases to gather information from diverse sources. Furthermore,
we examined the official websites of three open-source EHR systems to collect
more details on their accessibility considerations and found little to no
evidence that accessibility was actively considered by the developer community
of these EHR systems. By incorporating these multiple sources of information,
we aimed to provide a thorough and reliable analysis of screen reader
accessibility in various open-source EHR platforms.

### Methods

The research methodology used in this study was developed in three distinct
phases. The first phase involved deploying the open-source EHR software on
institutional servers, using the available documentation from their official
websites. This allowed us to create a controlled testing environment and
ensured the EHR systems were tested similarly. In the second phase, we
established evaluation criteria by identifying eight parameters through a
literature review and qualitative content analysis, similar to our prior work
comparing open-source EHR systems 8. These parameters were chosen to encompass
common tasks that users might need to perform when using an EHR system, such
as logging in, finding a patient, creating a new password, logging out,
entering and modifying demographics, entering medication orders, scheduling an
appointment, and ordering a lab. Using a comprehensive set of evaluation
criteria, we aimed to evaluate the EHR systems’ accessibility thoroughly. In
the final phase, we utilized three different screen readers - JAWS, NVDA, and
Apple VoiceOver - to evaluate using the specified set of criteria. These
screen readers were chosen based on their popularity among visually impaired
users and their availability across different platforms. To better understand
the functionality of these screen readers, we consulted various resources,
including IEEE Xplore and Google Scholar.

### Comparison Criteria

Each open-source EHR system was evaluated using established criteria (see
Table 1, ensuring the evaluation was objective and consistent. We tested each
system with multiple screen readers and noted accessibility issues. This
approach allowed for identifying any differences in accessibility between the
three EHR systems and screen readers for blind users.

The results of this study can inform developers and designers to make EHR
systems more accessible and inclusive for all users, including those with
visual impairments. By doing so, EHR systems can better serve their intended
purpose of improving patient care and outcomes by ensuring that all users can
easily and effectively use them, regardless of their abilities.

##  4 Results

Table 1: A Comparative Table Evaluating Screen Reader Accessibility in Various
Open-Source EHR Platforms

Open Source EHRs | TASK CRITERIA | JAWS | NVDA | AppleVoiceOver
---|---|---|---|---
|  | Success | Issues | Success | Issues | Success | Issues
OpenEMR | Login | Yes | * | Yes | * | Yes | *
| Find a patient | Yes |  | Yes |  | Yes |
| Create a new patient | Yes | * | Yes | * | Yes | *
| Logout | No | * | No | * | No | *
| Enter and modify demographics | Yes |  | Yes |  | Yes |
| Enter in medication order | Yes | * | Yes | * | Yes | *
| Schedule an appointment | Yes |  | Yes |  | Yes |
| Order a lab | Yes | * | Yes | * | Yes | *
OpenMRS | Login | Yes |  | Yes | * | Yes | *
| Find a patient | Yes | * | Yes | * | Yes | *
| Create a new patient | Yes | * | Yes | * | Yes |
| Logout | Yes |  | Yes |  | Yes |
| Enter and modify demographics | Yes | * | Yes | * | Yes | *
| Enter in medication order | Yes |  | Yes |  | Yes |
| Schedule an appointment | Yes | * | Yes | * | Yes | *
| Order a lab | Yes |  | Yes |  | Yes |
OSHERA VistA | Login | Yes |  | Yes |  |  |
| Find a patient | Yes | * | Yes | * |  |
| Create a new patient | No | * | No | * |  |
| Logout | No | * | No | * |  |
| Enter and modify demographics | No | * | No | * |  |
| Enter in medication order | Yes | * | Yes | * |  |
| Schedule an appointment | Yes | * | Yes | * |  |
| Order a lab | Yes | * | Yes | * |  |

* - issue details are provided in the sections below

As seen in Table 1, all 3 EHR systems have issues with one or more screen
readers. Although these EHR systems may perform well in terms of their
intended functionality, there are still some accessibility issues that may
hinder visually impaired users from utilizing them fully. It is important to
note that the experience of using these systems may vary depending on the
assistive technology being used, as different screen readers have varying
features and functionalities.

We have identified Login, Find a patient, Create a new patient, Logout, Enter
and modify demographics, Enter in medication order, and Schedule an
appointment as critical parameters to evaluate the compatibility of EHRs with
screen readers. These parameters are commonly used by healthcare
professionals, and their compatibility with screen readers is crucial to
ensure that visually impaired professionals can use EHRs effectively and
efficiently. For instance, accurate reading of demographic fields and
medication order fields is essential for healthcare professionals with visual
impairments to enter data or modify patient records. Similarly, accurate
reading of the schedule an appointment field is essential to enable visually
impaired healthcare professionals to schedule appointments with patients.
Therefore, evaluating EHRs compatibility with screen readers while performing
these tasks is critical to ensure that visually impaired healthcare
professionals can access and use EHRs effectively.

### OpenEMR

Figure 1: Dashboard of OpenEMR

Based on our considered parameters, OpenEMR appears to be mostly compatible
with popular screen readers such as JAWS, NVDA, and Apple Voiceover.

  * •

Login: The screen readers read out the selected fields for login, finding a
patient, and creating a new patient, which indicates that the EHR’s basic
accessibility functions are in place. Although screen readers read the login
information accurately, they could not report error messages or provide
feedback to users when incorrect information was entered in the login fields.

  * •

Create a new patient: While creating a patient in OpenEMR, the consecutive
tabs such as demographics, contact information, and so on were reliably
reported by the three screen readers we tested (JAWS, NVDA, and Apple
VoiceOver). This allowed users to navigate through different fields and enter
the appropriate information easily. An exception is that the screen readers
could not report which required field was left blank, making it challenging
for visually impaired users to complete the patient creation process.

  * •

Logout : The process of logging out was found to be inefficient when using
keyboard clicks, and it was discovered that users couldn’t log out using the
Tab key. Additionally, no audible confirmation was provided to indicate that
the user had successfully logged out when using the cursor.

  * •

Enter and modify demographics: It’s noteworthy that the use of screen readers
proved to be efficient in assisting users with editing and updating patient
demographics. This capability is particularly valuable when there is a need to
include any missing information for a patient.

  * •

Enter in medication order: Entering medication details was a straightforward
process. However, the medication list was not read out, which could create
difficulties for visually impaired users to input medication information
accurately.

  * •

Order a lab: During the lab ordering process, it was discovered that certain
required options could not be accessed using the Tab key and required using a
mouse. This presents a significant challenge for visually impaired users who
rely on keyboard navigation to complete tasks.

While OpenEMR has some accessibility concerns, it appears to be a generally
functional and efficient system for users who rely on screen readers. However,
there may be room for further improvements to ensure all users can fully
utilize the software’s features.

### OpenMRS

Figure 2: Dashboard of OpenMRS

OpenMRS is an accessible platform that meets all the parameters considered.

  * •

Login: The login and log-out features were particularly efficient and user-
friendly. However, we did observe a difference in performance among the three
screen readers we tested (JAWS, NVDA, and Apple Voiceover) regarding the
reporting of incorrect login information. While JAWS reported when incorrect
information was entered into the system, NVDA and Apple Voiceover did not.
NVDA does not allow users to navigate the department options and automatically
selects the registration desk.

  * •

Find a patient: We found it easy to navigate and find a patient in OpenMRS,
although the feature to select from a list of existing names is not compatible
with the screen readers, making it difficult for users to find patients
efficiently.

  * •

Create a new patient: Creating a new patient is relatively easy, although
relationships cannot be entered using the tab key, which can slow down the
data entry process.

  * •

Enter and modify demographics: Entering demographics in OpenMRS was relatively
easy, as the screen readers provided clear and concise navigation options.
When modifying demographics, the screen readers provide clear and concise
navigation options, but entering conditions and allergies requires a mouse,
which can be challenging for keyboard-only users. Also, the ”Save form” and
”Exit form” options are inaccessible on Apple Voiceover, which could confuse
users who want to save or exit a form.

  * •

Schedule an appointment: Scheduling appointments works well with all screen
readers, but entering the date and time using the keyboard is impossible,
which could be a significant barrier for some users.

Overall, OpenMRS is an accessible platform that could benefit from further
improvements, especially regarding keyboard navigation and screen reader
compatibility for certain features.

### OSHERA VistA

Figure 3: Dashboard of VistA

OSHERA VistA has several accessibility features that work well, but there are
also some areas where improvement is needed. We evaluated using JAWS and NVDA,
as the system is incompatible with Apple VoiceOver.

  * •

Login: The login feature in OSHERA VistA worked efficiently with both JAWS and
NVDA, without any significant issues.

  * •

Find a patient: When finding a patient, we found that NVDA performed better
than JAWS as the latter could not read out the names being scrolled through in
the drop-down list.

  * •

Create a new patient: We faced an issue creating a new patient with both JAWS
and NVDA on OSHERA VistA. These screen readers did not read out the respective
feature despite accessing all the tabs on the interface.

  * •

Logout: There was an issue with the logout feature in the EHR system.
Specifically, there was no option to log out and sign in with a different
account, and the system directly exited from the entire EHR.

  * •

Enter and modify demographics: Although it was possible to review the selected
patient’s demographics, there is no option to enter new information or modify
the demographics that are reported by both the screen readers (JAWS and NVDA).

  * •

Enter in medication order: In the medication order feature, JAWS incorrectly
guided the user to use the Ctrl + Page Up keys to shift pages, and neither
JAWS nor NVDA read out the missing required fields when the order failed to
save. These issues can make it difficult for users to complete medication
orders accurately and efficiently.

  * •

Schedule an appointment: Scheduling an appointment had pertinent accessibility
issues, such as the inability to move past the ”Reason for Request” box with
the tab key and the lack of feedback from both screen readers upon quitting.
Also, JAWS and NVDA failed to read out the number being selected in the
calendar when picking a date, which could make it difficult for users to
select the correct date for their appointment.

  * •

Order a lab: The screen readers provided clear and concise navigation options,
making it easy for users to fill in the appropriate fields. However, both
screen readers failed to read the message of an unsaved order dialogue box
when quitting a window. Finally, the lack of feedback from both screen readers
upon successfully adding a lab test was another pertinent issue, as users may
not know whether the test has been added successfully, which could lead to
confusion.

##  5 Discussion

Much effort has been spent making internet websites accessible to the blind or
visually challenged 23. While various tools are available to improve
accessibility, including screen readers, Braille displays, software for
magnifying objects, Windows Voice Recognition, Microsoft Narrator, and Dragon
Naturally Speaking, not all individuals with visual impairments are proficient
in using computers 24. To enhance the accessibility of websites for those with
visual impairments, it is necessary to modify the color contrast and font
sizes, use informative headers, and ensure that the content is straightforward
to access with a keyboard 25. However, choosing the right tools to improve
accessibility is crucial. Among the various tools available, we have chosen
JAWS, NVDA, and Apple VoiceOver as they are widely used and have proven to be
effective in enhancing the accessibility of websites. They are effective,
compatible, and popular among blind users. By using these tools, we can
enhance the accessibility of websites and other digital content, making it
easier for individuals with visual impairments to access the same information
as those without such impairments.

The small user base of blind healthcare providers may contribute to why
vendors are not prioritizing accessibility improvements for this particular
user group. With a small user base, vendors may not see the potential return
on investment for developing more accessible tools and features. However, this
mindset overlooks the significant impact that such enhancements could have on
the usability and productivity of blind providers who do exist. Therefore,
while developing and implementing EHR systems, accessibility is crucial. A
wide variety of features are available in JAWS and NVDA, including
sophisticated navigation, customizability, and compatibility for several file
formats and web browsers. Although it supports certain accessibility
functions, such as basic navigation and typing, Apple VoiceOver was found to
be not as advanced as JAWS and NVDA.

We have noticed that OpenMRS and OpenEMR both provide high levels of
accessibility for individuals who are blind or visually impaired. Both EHRs
have user interfaces that enable visually impaired users to access the
system’s content and operate the interface, such as text-to-speech and
keyboard navigation. The analysis demonstrates that designing an EHR system
with accessibility for users who are blind or visually impaired is essential.
They have all the required key components that blind users require, which can
make it easier for them to access the system’s information.

When it comes to procedures like logging into the account, ordering a lab and
medications, scheduling an appointment for a patient, editing their
demographics and contact details, taking vital signs, etc., they were all
easily completed consistently. By providing an audible description of the user
interface and allowing users to navigate through menus, links, and other
elements, screen readers increase the usability of open-source EHRs for people
with visual impairments, ensuring they can interact with the system’s user
interface and input data accurately. Additionally, screen readers can help
identify compatibility issues that may prevent users with visual impairments
from using the system.

The study found a few accessibility barriers, including the complex interfaces
and screen readers’ sporadic partial completion of recitations, which made
them difficult for users to comprehend and perceive. The most accessible EHR
was determined to be OpenMRS, whereas OpenEMR and OSHERA VistA had some
accessibility issues regarding compatibility with Apple VoiceOver, which was
later corrected and evaluated as a part of the study. EHRs frequently have
intricate user interfaces that may not be designed with screen readers in
mind, making them challenging to navigate and interact with. This was evident
in OpenMRS, where we were unable to use the keyboard to mention a patient’s
relationship and were unable to exit the form while editing the patient’s
demographics and contact information. For example, in OpenEMR, the screen
reader could not recite that the login password was incorrect for the user to
understand that they were typing the wrong password. This is because open-
source EHRs are developed by a diverse range of contributors, so there may be
inconsistencies in the way that different components of the software are
labeled and organized. The patient finding was challenging in OpenMRS since we
needed a mouse to scroll down. However, only a limited number of tasks in each
of the three EHRs required the usage of a mouse rather than the keyboard’s tab
key.

Despite the valuable insights derived from this study, a key limitation lies
in our inability to capture the perspectives of visually impaired individuals
directly. This introduces potential bias in our understanding of screen reader
use with EHRs, as our findings may not entirely align with the actual user
experiences. Future research endeavors should seek to address this gap by
actively incorporating the experiences and feedback of visually impaired
individuals using EHRs with screen readers. Incorporating their feedback will
allow us to more accurately and empathetically design, test, and improve EHR
systems for those with visual impairments.

##  6 Conclusion

In conclusion, this study highlights the importance of accessibility in open-
source EHR systems for users who are blind or visually impaired. The findings
suggest that developers can make EHR systems more inclusive and accessible by
incorporating text-to-speech and keyboard navigation features. Additionally,
users and organizations should prioritize accessibility when selecting and
implementing EHR systems to ensure all users can access and benefit from the
system’s content. Our next steps are to conduct wider functionality testing
across these EHRs and include proprietary EHRs like Epic, Meditech,
eClinicalWorks, and Cerner.

The study shows that all three open-source EHR systems evaluated offer a
respectable level of accessibility for visually impaired users. However, there
is still room for improvement in specific areas, such as the user interface of
OSHERA VistA and the forms and navigation of OpenEMR. Comparatively, OpenMRS
was found to have the fewest accessibility concerns among the three systems.
Overall, this study provides valuable insights into how open-source EHR
systems can be made more accessible for individuals with visual impairments.
It emphasizes the need to prioritize accessibility in EHR system design and
implementation to improve access to healthcare information and services for
individuals with disabilities. The findings presented in this research paper
can serve as a valuable resource for developers, users, and organizations
looking to design and implement accessible EHR systems that prioritize the
needs of visually impaired users.

## Acknowledgments

We acknowledge the invaluable contributions of our teaching assistants, tech
staff, and instructors supporting the deployment of the Educational EHR for
which we started the accessibility review. We acknowledge Pallavi Singh, who
helped review prior work on EHR accessibility. We acknowledge the support of
the IUPUI STEM Education Innovation & Research Institute’s 2022 seed grant.

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