Observation of e(+)e(-) -> phi chi(c1) and phi chi(c2) at root s=4.600 GeV

Using a data sample collected with the BESIII detector operating at the BEPCII storage ring at a center-of-mass energy of root s = 4.600 GeV, we search for the production of e(+)e(-) -> phi chi(c0,1,2). A search is also performed for the charmonium-like state X(4140) in the radiative transition e(+)e(-) -> gamma X(4140) with X(4140) subsequently decaying into phi J/psi The processes e(+)e(-) -> phi chi(c1) and phi chi(c2) are observed for the first time, each with a statistical significance of more than 10 sigma, and the Born cross sections are measured to be (4.2(-1.0)(+1.7) +/- 0.3) and (6.7(-1.7)(+3.4) +/- 0.5) pb, respectively, where the first uncertainties are statistical and the second systematic. No significant signals are observed for e(+)e(-) -> phi chi(c0) and e(+)e(-) -> gamma X(4140) and upper limits on the Born cross sections at 90% C. L. are provided at root s = 4.600 GeV