There is no earth/ground out on the HLD-X0.
Do you thing it is better to just plug it without earth, or better to attach a cable from earth to the case ?

I would not worry about an earth connection for it. On such high end player with no expenses spared, I'm sure they would at least include a screw terminal on the back that allowed it to be connected to earth, if it were necessary. Unless you experience some interference issues, I wouldn't bother adding one. I doubt the chassis will become a shock hazard either. I'm sure Pioneer took precautions to avoid that.

ok, then i could maybe even worst to connect it to the earth ?

No, it would not hurt it to connect it to earth.

thank you for your advices !

It would not 'hurt' it, but could cause audible noise.
Probably why they didn't have a ground terminal for power.

thank you for the detail !

Audible noise? I know this is not LD related, but I'm getting a buzzing sound when I attempt to digitize my vinyl. When I touch the ground lug on the turntable it disappears. I'm still confused why there is a ground lug on a turntable as the turntable and amplifier power cords only have the two prongs (hot and neutral, although hot and neutral are tied together at the breaker box). Plus my house was wired before they had ground, and the boxes that hold the outlets in are plastic so I know they didn't ground that. I did add a few outlets in my house and ran a ground from the breaker box to those particular outlets. So thinking I could get rid of the buzzing ground noise I made my own ground wire that runs from the turntable to the ground prong on the newly grounded outlet. That made the buzzing worse.

I'm wondering if the outlet where my computer is plugged in needs to be grounded? As my set up is: turntable to ART Phono Plus (usb computer interface. This device also has a ground terminal which in the past I tied to the turntable ground) to my computer to record. Maybe the ground on the ART is relying on the computer ground since that has the computer has a three prong cord. Although in my situation there is no ground at that particular outlet.