CTS 500K vintage taper audio potentiometer, long bushing .750", 3/8" diameter, for carved tops LP USA

CTS 500k Ohm vintage audio taper (30% Log) potentiometer. Dished back, solid shaft, long 19mm length bushing. Check the actual bushing length required!

Value:
Typically 250K pots are used for single coil pickups and 500K pots for humbucker pickups. The bigger the resistance value, the brighter the sound will be/ less highs will bleed off. 1MEG can be used to make humbuckers sound brighter.

Taper:
The taper of a pot refers to the way its resistance changes as the shaft is rotated. A linear taper pot will work in a linear way related to shaft rotation. As the human ear is not linear in response to increasing volume, an audio (aka. logarithmic) pot will work best for volume applications.
A third option available is vintage audio taper. These pots are 30% logarithmic: with the pot halfway open, the audio response/output is at 30%. Audio/log pots have an output of 10% in the same setting, linear pots are at 50% output. So, their taper is roughly halfway in between audio/log and linear taper pots. They are very similar to the original spec for vintage Stratocaster guitar pots and can be used for both tone and volume controls.

Shaft:
A split, knurled shaft will hold most knobs. Sometimes the knob is mounted using a set screw. You should order a solid shaft pot, or align the set screw with the split for correct mounting.

Bushing:
The standard bushing diameter is 3/8" or 9,5mm, used in most made in USA guitars. Another industry standard is M8, as used by guitar builders outside of the USA. When space is limited mini pots are used with a shaft diameter of 7mm.
The standard bushing length is .375" for inch type pots and 10mm for metric type pots. Using two nuts it is very easy to set the correct bushing length for knob placement. Specially for pickguard (ST, PB) or control plate mount (TE, JB) the .250" short bushing will fit perfectly using only one nut.
For use with a thick or carved top (LP USA) you should order a bushing length of .750".

CTS is (and has been since the 50's) a factory standard for most USA brands like Fender and Gibson. Alpha is a good alternative, nowadays used as a factory standard by Ibanez, Epiphone and Squier.