We present a spectroscopic follow-up of photometrically-selected young stellar object (YSO) candidates in the Central Molecular Zone of the Galactic center. Our goal is to quantify the contamination of this YSO sample by reddened giant stars with circumstellar envelopes and to determine the star formation rate in the CMZ. We obtained KMOS low-resolution near-infrared spectra (R ~4000) between 2.0 and 2.5 um of sources, many of them previously identified, by mid-infrared photometric criteria, as massive YSOs in the Galactic center. Our final sample consists of 91 stars with good signal-to-noise ratio. We separate YSOs from cool late-type stars based on spectral features of CO and Br_gamma at 2.3 um and 2.16 um respectively. We make use of SED model fits to the observed photometric data points from 1.25 to 24 um in order to estimate approximate masses for the YSOs. Using the spectroscopically identified YSOs in our sample, we confirm that existing colour-colour diagrams and colour-magnitude diagrams are unable to efficiently separate YSOs and cool late-type stars. In addition, we define a new colour-colour criterion that separates YSOs from cool late-type stars in the H-Ks vs H-[8.0] diagram. We use this new criterion to identify YSO candidates in the |l| < 1.5, |b|<0.5 degree region and use model SED fits to estimate their approximate masses. By assuming an appropriate initial mass function (IMF) and extrapolating the stellar IMF down to lower masses, we determine a star formation rate (SFR) of ~0.046 +/- 0.026 Msun/yr assuming an average age of 0.75 +/- 0.25 Myr for the YSOs. This value is lower than estimates found using the YSO counting method in the literature. Our SFR estimate in the CMZ agrees with the previous estimates from different methods and reaffirms that star formation in the CMZ is proceeding at a lower rate than predicted by various star forming models.
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