A tyre for a vehicle carrying heavy loads, and comprising a tread having at least a rubber composition containing at least one elastomeric matrix comprising, as a major component, a styrene and butadiene copolymer with a glass transition temperature Tg strictly higher than -65°C and not exceeding -30°C; a reinforcing filler comprising silica as a major component; a chemical cross-linking system; a coupling agent for coupling the elastomeric matrix and the reinforcing filler; a plasticiser system comprising 2 to 15 phr of at least one plasticiser resin having a glass transition temperature Tg of at least 20°C, the total proportion of the plasticiser system in the composition ranging from 2 to 17 phr; and a modifier agent for modifying the styrene and butadiene copolymer, optionally already grafted onto said copolymer, which modifier agent is a 1,3-dipolar compound of general formula (I): A-E-D (I). The symbol D is a functional group comprising at least one nitrogen atom and capable of binding to the copolymer via a [3 +2]-type cycloaddition on a carbon-carbon double bond of the chain of said copolymer; the symbol E is a divalent spacer group linking group D to group A; A is a functional group selected from C1-C20 alkyls, C7-C18 alkylaryls, C7-C18 arylalkyls, optionally substituted, 5 to 6 atom nitrogen heterocycles, optionally substituted, 5 to 6 atom sulfur heterocycles, ester groups, phosphate groups, dialkylamino groups and associative groups comprising at least one nitrogen atom.
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