I'm considering a user journey which will be hosted on a single site, but will launch into another site (e.g. PayPal) for the user to make a payment. I'm concerned that launching into a different site midway through a user journey may have a detrimental impact on trust. Is there any research available (or even anecdotal evidence) to support or reject this idea?
The fact that you're integrating with a third party means that you are, to some extent, reliant on the credibility they bring to the table. Are they recognized, trusted, reliable?
In PayPal's case the experience is awful but recognition is ubiquitous. Their miserable bounce around UX is how they choose retain control over brand and security. If you changed that workflow, PayPal users would wonder why your path deviates from their past experiences. PP doesn't give partners the option to deviate. They also have the scale and market recognition to make that demand. And some would argue that the simple presence of their logo brings credibility to your experience.
If you have to jump domains because of business or systems limitations, just be sure you keep the user informed. They need to know what to expect and understand why the hand-off is happening in the first place. Put it in positive, user-centric terms and most importantly make sure you're partnering with someone worthy of your user's trust.