The blue plus points with the error bar represent the observed photometry and its uncertainty, and the red solid line represents the best-fit SED. The black open circle with the arrow represents the upper limit of the photometry at 2$\sigma$ level. In the bottom right three panels, we show the $\chi^{2}$ map of our SED fitting analysis on one-dimensional space. The vertical axis represents the $\chi^{2}$ value and the horizontal axis represents the photometric redshift, dust attenuation, and age. The horizontal black dashed line in each panel represents the minimum $\chi^{2}$ value. We emphasize that the two examples we show here are categorized as faintest objects, and most of the other objects are fitted better than the examples. Our SED fitting procedure performs well due to the deep imaging data of UKIRT/*HK* which covers the wavelength of Balmer break for LBGs at *z* $\sim$ 4.

![image](im10051_comb.eps){width="140mm"}

![image](im10643_comb.eps){width="140mm"}

 Measurement method of UV slope $\beta$  {#S3Mmuvb}
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According to the original definition of @Calz94, the UV slope $\beta$ value should be estimated from the Spectral Energy Distribution (SED) from 1250Å to 2600Å through the 10 fitting windows. However, spectroscopic observation generally requires a long exposure time for measuring the continuum flux from 