PSR B0656+14 is a middle-aged pulsar with a characteristic age $tau_c=110$ kyr and spin-down power $dot{E}= 3.8times 10^{34}$ erg s$^{-1}$. Using Chandra data, we searched for a pulsar wind nebula (PWN) and found evidence of extended emission in a 3.5-15 arcsec annulus around the pulsar, with a luminosity $L_{rm 0.5-8,keV}^{rm ext} sim 8times 10^{28}$ erg s$^{-1}$ (at the distance of 288 pc), which is a fraction of $sim 0.05$ of the non-thermal pulsar luminosity. If the extended emission is mostly due to a PWN, its X-ray efficiency, $eta_{rm pwn} = L_{rm 0.5-8,keV}^{rm ext}/dot{E} sim 2times 10^{-6}$, is lower than those of most other known PWNe but similar to that of the middle-aged Geminga pulsar. The small radial extent and nearly round shape of the putative PWN can be explained if the pulsar is receding (or approaching) in the direction close to the line of sight. The very soft spectrum of the extended emission ($Gammasim 8$), much softer than those of typical PWNe, could be explained by a contribution from a faint dust scattering halo, which may dominate in the outer part of the extended emission.
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