## 1 Introduction
Engagement plays a significant role in guaranteeing naturalness and effectiveness during human-robot interaction (HRI). Robots maintaining user engagement give the impression of being competent, relate to them on a social scale, and possess high degrees of social competence [13]. These situations are relevant for applications including education, therapies, and entertainment, whose impacts depend directly on the sustained engagement a user expresses [14]. Similarly, in the field of social robotics, where the purpose of these robots is to establish relationships and coexist with humans [15], JA is of interest as a capacity to be considered to allow the robots to respond correctly to user cues, not only promoting natural interactions but also generating trust and acceptance by the users [16]. RJA, in particular, allows robots to react in real time to user behaviors, demonstrating awareness and adaptability. However, the effects of JA capabilities in a social robot in terms of engagement remain unexplored. Most existing research on JA has focused on implementing specific attentional mechanisms in robots, such as gaze following [17], imitation [18], or turn-taking [19], demonstrating the technical advances and their integration. Nevertheless, while most of these studies have successfully replicated this capability, analyzing the user perception of the robots regarding JA and engagement is still an area of interest. Most importantly, this will be necessary for understanding effectiveness beyond technical functionality. Bridging the gap between replicating attentional mechanisms and assessing their effects on user experience could provide valuable insights into how to create more engaging and socially competent robots. In a previous study, we presented a biologically inspired responsive joint attention system (RJAS) that enables a social robot to perform RJA by recognizing and following user attentional cues such as gaze and gestures [20]. Subsequent evaluations of this system revealed that, when active, it enhanced the user's perception of the robot's social presence, as well as its perceived competence and warmth [21]. Building on these results, the present work shifts the focus towards user engagement. Although the experimental framework remains consistent with our previous studies--centered on the \"Odds and Evens\" turn-taking game and using the same two experimental conditions (_RJAS Active_ vs. _RJAS Inactive_)--the current study introduces a novel analytical perspective. This work draws from principles in developmental and cognitive psychology related to joint attention, implementing them in a social robot designed to detect and respond to user social cues such as gaze direction and pointing gestures. We expect these capabilities to enable the robot to behave in a socially attentive manner, potentially shaping how it is perceived during interaction. **The main contribution of this work is to examine whether this socially responsive behavior affects user engagement, specifically if users stay attentive, avoid distraction, and remain involved in the interaction during a collaborative task. **  
To do so, we assess engagement through a dual approach: from a questionnaire, using the User Engagement Scale Short Form (UES-SF) [22]; and using a telemetry system, referred to in this work as the user behavior tracking (UBT) system. The described telemetry system monitored head pose orientation to indicate user distractions and attentional focus during the interaction. This combination of self-reports and behavioral data is still relatively uncommon in HRI studies, where engagement is often assessed through either questionnaires or manual observational grids. However, both approaches present limitations: self-reports suffer from time-discrepancy issues, and observational methods can be affected by annotator subjectivity [23].