Rubber composition containing specialized styrene/butadiene elastomer and precipitated silica reinforcement and tire with component

A pneumatic rubber tire having a component of a rubber composition containing, based on parts by weight per 100 parts by weight of the rubber (phr),

• (A) conjugated diene-based elastomers comprised of:
• (1) about 40 to about 90 phr of a specialized styrene/butadiene elastomer having a molecular weight profile comprised of a weight average molecular weight (Mw) in a range of from about 500,000 to about 800,000 with a low molecular weight content limited to a maximum of six percent of said styrene/butadiene elastomer having a number average molecular weight (Mw) of up to 150,000, and
• (2) about 60 to about 10 phr of at least one additional conjugated diene-based elastomer,
• (B) about 40 to about 150 phr of reinforcing filler comprised of a combination of rubber reinforcing carbon black and precipitated silica together with a coupling agent having a moiety reactive or interactive with hydroxyl groups on said precipitated silica and another different moiety reactive or interactive with said diene-based elastomers.