No one knows exactly how the system works, but the comment about a digital mark is not correct.
When any border agent in any country swipes your passport, the number is checked against their own systems to see if any alerts flag up. In the case of the EU/EEA, your PPU raises an alert on SISII, which is an EU wide computer system linked to border control. Therefore, when you enter an EU country and they swipe your passport, the border official sees a flag on his screen that there is an alert. That's usually a section 36 alert which asks the border official to make a discrete check on who you're travelling with and where you are going to/from.
When you land in the US and they swipe your passport, the number is checked against US databases (FBI, Homeland Security etc.). Only if there is an alert on the US system would you be flagged up.
So the real question is this - do the UK provide information to the US systems? This is how it's meant to work - if your PPU considers you a risk and that the foreign country should be notified, they have to raise an Interpol green notice - this goes to every country including the US. Of course, some countries get the information but don't have the computer systems capable of processing or using it.
So in theory, you should only be flagged in the US if an Interpol notice is issued.
Now the scary bit. If you have to notify, you will be on the ViSOR database in the UK. This database is synced with the Home Office Warnings Index (HOWI) - this is the database that UK border use when they scan your passport back in the UK.
If you apply for a US visa, the US can ask to cross reference the details with HOWI. I don't know if the ESTA process can also do this. If you apply for an ESTA while you are notifying and get it, it would suggest that the link is not there.
And finally, you have to provide advanced passenger information to your airline before you fly to the US. The US and UK authorities screen this against their own databases. In theory, the US database would not have your information on it unless an interpol notice has been issued.
What we don't know as citizens, is what really goes on behind the scenes in the name of public protection. Despite the official rules, does the UK give ViSOR/HOWI data to the US to put into their databases?
Unless you jump on a p[lace and try, you'll never know - the worse that can happen is you get turned back and lose a few hours of your life flying.