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The purpose of this paper is to share the iterative process we used to design a task that elicits causal mechanistic reasoning and how the subsequent student responses can be analyzed. Our goal in this task is to strike a balance between eliciting as much student knowledge as possible without providing so much structure that the answer becomes obvious. The task development was approached using (1) a resources perspective of learning, (2) principles of scaffolding, and (3) evidence-centered design, for which we specified evidence that would be considered a fully causal mechanistic explanation. That is, an explanation which pays explicit attention to the properties, interactions, and behaviors of entities that are involved at a scalar level below the phenomenon under consideration. Since our eventual goal is to characterize how students use knowledge across disciplinary boundaries, the phenomenon of protein–ligand binding was chosen as the context for this task, because it requires students to apply ideas learned in chemistry courses to a biological phenomenon. After three rounds of iterative refinement, a final task was developed. To characterize students’ responses to this task, we developed a coding scheme which can be used to code explanations based on the presence or absence of three key ideas relevant to this phenomenon. In this paper, we share the detailed processes and approaches used in task development, which we hope will provide insight into instructors and researchers as they, too, develop such tasks to explore student reasoning. 

A<sc>bstract</sc> This paper presents a study of the charmless three-body decays$$ {B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-} $$ $B_{\left(s\right)}^0\to K_S^0{h}^{+}h{\prime }^{-}$ (whereh⁽′⁾=π, K), using a sample ofppcollision data collected by the LHCb experiment during Runs 1 and 2 of the LHC, corresponding to an integrated luminosity of 9 fb⁻¹. The decay$$ {B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-} $$ $B_s^0\to K_S^0{K}^{+}{K}^{-}$ is observed for the first time, and the following ratios of branching fractions are measured:$$ {\displaystyle \begin{array}{l}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.578\pm 0.007\pm 0.017,\\ {}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{K}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.1363\pm 0.0035\pm 0.051,\\ {}\begin{array}{l}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.269\pm 0.011\pm 0.015\pm 0.008,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.0303\pm 0.0041\pm 0.0025\pm 0.0009,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=1.818\pm 0.021\pm 0.031\pm 0.056,\end{array}\end{array}} $$ $\begin{array}{c}\frac{B\left(B^0\to K_S^0{K}^{+}{K}^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.578\pm 0.007\pm 0.017,\\ \frac{B\left(B^0\to K_S^0{K}^{\pm }{K}^{\mp }\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.1363\pm 0.0035\pm 0.051,\\ \begin{array}{c}\frac{B\left(B_s^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.269\pm 0.011\pm 0.015\pm 0.008,\\ \frac{B\left(B_s^0\to K_S^0{K}^{+}{K}^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.0303\pm 0.0041\pm 0.0025\pm 0.0009,\\ \frac{B\left(B_s^0\to K_S^0{K}^{\pm }{\pi }^{\mp }\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=1.818\pm 0.021\pm 0.031\pm 0.056,\end{array}\end{array}$ where the uncertainties are statistical, systematic, and due to knowledge of the ratio of hadronisation fractions of the$$ {B}_s^0 $$ $B_s^0$ andB⁰mesons, respectively. 

The time-dependent $CP$ asymmetry in $B^0\to J/\psi \rho (770{)}^0$ decays is measured using proton-proton collision data corresponding to an integrated luminosity of $6{\mathrm{fb}}^{-1}$ , collected with the LHCb detector at a center-of-mass energy of 13 TeV during the years 2015–2018. The $CP$ -violation parameters for this process are determined to be $2{\beta }_{c\overline{c}d}^{\mathrm{eff}}=0.710\pm 0.084\pm 0.051\mathrm{rad}$ and $\left|\lambda \right|=1.019\pm 0.034\pm 0.024$ , where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent $CP$ violation in $B^0\to J/\psi \rho (770{)}^0$ decays. Assuming approximate SU(3) flavor symmetry, these results are combined with the previous consistent LHCb measurement to set the most stringent constraint on the penguin contribution, $\mathrm{\Delta }{\varphi }_s$ , to the $CP$ -violating phase ${\varphi }_s$ in $B_s^0\to J/\psi \varphi \left(1020\right)$ decays, yielding $\mathrm{\Delta }{\varphi }_s=5.0\pm 4.6\mathrm{mrad}$ . 

Muon-electron universality is tested in $B^0\to K^{*0}{\ell }^{+}{\ell }^{-}$ decays, in the dilepton-invariant-mass region above the $\psi \left(2S\right)$ resonance. The analysis uses beauty mesons produced in proton-proton collisions recorded by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The ratio of branching fractions between the muon and electron channels $R_{K^{*0}}$ is measured to be ${1.08}_{-0.12}^{+0.14}\left(\mathrm{stat}\right)\pm 0.07\left(\mathrm{syst}\right)$ for a dilepton-invariant-mass squared above $14.0{\mathrm{GeV}}^2/c^4$ , consistent with the standard model prediction. This result represents the most precise measurement of $R_{K^{*0}}$ in this region and the first such measurement performed at a hadron collider.