The jeweler, age 59, was taken to a local hospital and is expected to survive.
The store owners said the thieves took about $1 million in valuables.
A vigil for Arguello, who was well-known in the community, was held on Saturday.
The robberies and thefts occurred on highways and streets, in parking lots, outside hotels and retail stores and at a gas station.
The communities listed in the alert are Lowell, Tyngsborough, Chelmsford, Dracut, Billerica and Tewksbury.
About $50,000 in custom jewelry was stolen.
The store had recently posted the Patek Philippe timepiece on Instagram.
Police said the suspects wore hoodies and used hammers to smash display cases.
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They hoisted the safe onto a truck and drove away.
The crime happened Sept. 8 at Jewelers On Time.
The workers, who are family members, hit and kicked the suspect and struck him with a stick.
Police are still searching for the four suspects.
It happened Tuesday at Gold Estate Jewelry.
Brazen theft at LA store follows similar incident in San Francisco.
The crimes are alleged to have happened between September 2019 and December 2022.
Thieves tied up two workers and made another get jewelry from display cases.
Paul Prosano, also known as “Tony Pro,” of New York was sentenced July 5.
An employee 'was assaulted during the robbery and sustained non-life threatening injuries.'
The total number of crimes committed against U.S. jewelry firms was 2,211.
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