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We apply, for the first time, the Transit Least Squares (TLS) algorithm tosearch for new transiting exoplanets. TLS is a successor to the Box LeastSquares (BLS) algorithm, which has served as a standard tool for the detectionof periodic transits. In this proof-of-concept paper, we demonstrate how TLSfinds small planets that have previously been missed. We showcase TLS'capabilities using the K2 EVEREST-detrended light curve of the star K2-32(EPIC205071984) that was known to have three transiting planets. TLS detectsthese known Neptune-sized planets K2-32b, d, and c in an iterative search andfinds an additional transit signal with a high signal detection efficiency(SDE_TLS) of 26.1 at a period of 4.34882 (-0.00075, +0.00069) d. We show thatthis signal remains detectable (SDE_TLS = 13.2) with TLS in the K2SFF lightcurve of K2-32, which includes a less optimal detrending of the systematictrends. The signal is below common detection thresholds, however, if searchedwith BLS in the K2SFF light curve (SDE_BLS = 8.9) as in previous searches.Markov Chain Monte Carlo sampling shows that the radius of this candidate is1.01 (-0.09, +0.10) Earth radii. We analyze its phase-folded transit lightcurve using the vespa software and calculate a false positive probability FPP =3.1e-3, formally validating K2-32e as a planet. Taking into account themultiplicity boost of the system, FPP < 3.1e-4. K2-32 now hosts at least fourplanets that are very close to a 1:2:5:7 mean motion resonance chain. Theoffset of the orbital periods of K2-32e and b from a 1:2 mean motion resonanceis in very good agreement with the sample of transiting multi-planet systemsfrom Kepler, lending further credence to the planetary nature of K2-32e. Weexpect that TLS can find many more transits of Earth-sized and smaller planetsin the Kepler data that have hitherto remained undetected with BLS and similaralgorithms.

Transit least-squares survey - I. Discovery and validation of an Earth-sized planet in the four-planet system K2-32 near the 1:2:5:7 resonance