Andrew Miller is UK editor of ESPNcricinfo. He tweets at @miller_cricket
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Rory Burns also misses the trip, as his wife Victoria is expecting their first child in the second week of January, while Burns' Surrey team-mate Ollie Pope will join the squad as a non-playing member, with a view to being fit in time for the four Tests in India as he continues his rehab from the shoulder injury that he sustained against Pakistan in August.
With England facing a busy schedule on all fronts in the coming 12 months, with the Ashes in Australia following hot on the heels of away and home series against India and the T20 World Cup, the absences of Archer and Stokes come as part of a commitment from England's selectors to provide blocks of rest for all their multi-format players at various points this winter.
Speaking to the media after the announcement, Ed Smith, England's national selector, indicated that Stokes, Archer and Burns would fly directly to India on or around January 22-23 to acclimatise ahead of the first Test of that series, at Chennai on February 5, with further changes to England's squad also likely ahead of the third and fourth Tests of the India tour at Ahmedabad.
"The way to think about this winter is in three blocks of two Tests: Sri Lanka, India 1 and 2, India 3 and 4," Smith said. "We think that's the only way to make sure we balance having the right number of resources in each position, and also getting rest into those multi-format players like Jos Buttler, Jofra Archer, Ben Stokes, and also Sam Curran, Mark Wood, Chris Woakes, etc."
In the absence of Pope, Stokes and Burns - three players who would have been automatic picks for England's top five - Essex's Dan Lawrence could be in line to earn his first Test cap, after being named in the senior squad for the first time, a year on from his starring role on the England Lions tour of Australia in 2019-20.
"This is a great opportunity for Dan Lawrence," Smith said. "He's a really talented cricketer, a confident player in good form, and he is absolutely delighted about being selected in the full squad.
"He's an unusual player, but he's got that real quality about him," Smith added. "He has his own style, and a real confidence and presence at the crease. He's inventive, he's versatile. He's also a good short-format player, and he really impressed on the England Lions just under a year ago."
Jonny Bairstow is the other player likely to challenge for a middle-order berth. He has been recalled to the Test set-up for the first time since featuring in the first Test against South Africa at Centurion 12 months ago, with Smith indicating that he was back in contention as a batsman only - the role he performed when making a century from No.3 in England's most-recent Test in Sri Lanka two years ago.
Ben Foakes, who scored a century on debut and was named Player of the Series on that same tour, is the designated back-up to the current incumbent, Jos Buttler, with Smith suggesting he will be in line for a recall when Buttler is given his break from action during the India series. "Jonny has a really great opportunity here to get back into the Test mix as a batter, and that's a really exciting possibility for him," Smith said.
With spin playing a central role in England's 3-0 series win in 2018-19, Moeen Ali is back in the squad after opting out of last winter's tours of New Zealand and South Africa, and is in line to play his first Test since the opening match of the 2019 Ashes.
Jack Leach, who along with Moeen was England's leading wicket-taker on that last Sri Lanka trip with 18 scalps, is also included, and is set to link up once again with his former Somerset team-mate and current first-choice England spinner, Dom Bess.
However, there is no return for the third spinner of the 2018-19 triumvirate, legspinner Adil Rashid, who had been an outside bet for a recall given his importance to England's white-ball plans ahead of next year's T20 World Cup. He has been left out as he continues to manage a shoulder problem and is likely also to miss the subsequent tour of India.
"Adil has had a long-running shoulder injury, and though he has made really good strides, he does have concerns about that shoulder in the strain of five-day cricket," Smith said. "Obviously he's got to weigh up his one-day and T20 form, which is outstanding. He is among the most irreplaceable players in a very, very strong white-ball set-up, and that's where he stands at the moment."
England have, however, named three spinners among their seven-man list of reserves - legspinners Matt Parkinson and Mason Crane, whose one-off Test came at Sydney in the 2017-18 Ashes, and the Surrey offspinner, Amar Virdi.
All the reserves will travel and train with the main squad, with the series once again being played behind closed doors and in biosecure environments, initially at Hambantota and then in Galle for the two Test matches, commencing January 14 and 22 respectively.
Despite playing limited roles on the 2018-19 tour, England have named both of their veteran fast bowlers James Anderson and Stuart Broad in their main touring party, alongside Chris Woakes and two 90mph options in Mark Wood and Olly Stone, who made his international debut in the ODI leg of England's last tour of Sri Lanka.
Archer's omission from the squad had been telegraphed in South Africa last week, after he had spent most of the preceding five months in biosecure environments, while Stokes' absence comes in the wake of the death of his father Ged from brain cancer. He also missed the final two Tests of last summer's Pakistan series, as well as the subsequent one-day series, to travel to New Zealand to spend time with his family.
"It is a very difficult time for Ben and all our thoughts and with him and his family," Smith said. "[In the circumstances], it made sense for Ben to take his rest for the Sri Lankan tour, and to get ready for India."
England men's Test squad: Joe Root (capt), Moeen Ali, James Anderson, Jonathan Bairstow, Dom Bess, Stuart Broad, Jos Buttler, Zak Crawley, Sam Curran, Ben Foakes, Dan Lawrence, Jack Leach, Dom Sibley, Olly Stone, Chris Woakes, Mark Wood.
Reserves: James Bracey, Mason Crane, Saqib Mahmood, Craig Overton, Matt Parkinson, Ollie Robinson, Amar Virdi.