Experimental data of the DNA cyclization (J-factor) at short length scales, as a way to study the elastic behavior of tightly bent DNA, exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths... To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study (B. Eslami-Mossallam and M. Ejtehadi, Phys. Rev. E 80, 011919 (2009)). Exploiting a coarse grained representation of DNA molecule at base pair (bp) level, and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that, for DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data. (read more)