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We present the pulsar timing analysis of the accreting millisecond X-raypulsar SWIFT J1749.4-2807 monitored by NICER and XMM-Newton during its latestoutburst after almost eleven years of quiescence. From the coherent timinganalysis of the pulse profiles, we updated the orbital ephemerides of thesystem. Large phase jumps of the fundamental frequency phase of the signal arevisible during the outburst, consistent with what was observed during theprevious outburst. Moreover, we report on the marginally significant evidencefor non-zero eccentricity ($e\simeq 4\times 10^{-5}$) obtained independentlyfrom the analysis of both the 2021 and 2010 outbursts and we discuss possiblecompatible scenarios. Long-term orbital evolution of SWIFT J1749.4-2807suggests a fast expansion of both the NS projected semi-major axis $(x)$, andthe orbital period $(P_{\rm orb})$, at a rate of $\dot{x}\simeq 2.6\times10^{-13}\,\text{lt-s}\,\text{s}^{-1}$ and $\dot{P}_{\rm orb}\simeq 4 \times10^{-10}\,\text{s}\,\text{s}^{-1}$, respectively. SWIFT J1749.4-2807 is theonly accreting millisecond X-ray pulsar, so far, from which the orbital periodderivative has been directly measured from appreciable changes on the observedorbital period. Finally, no significant secular deceleration of the spinfrequency of the compact object is detected, which allowed us to set aconstraint on the magnetic field strength at the polar caps of$B_{PC}<1.3\times 10^{8}~\text{G}$, in line with typical values reported forAMXPs.

On the peculiar long-term orbital evolution of the eclipsing accreting millisecond X-ray pulsar SWIFT J1749.4-2807