Howdy Sir.
Always a good idea to check your local and state laws for clarification on the particular legality in your area as some states do not allow residents to own firearms that are allowed by the federal government. That being said, as far as the feds are concerned there are only three ways you can legally use a 14.5" barrel on your carbine:
1. Have a flash hider or other muzzle device permanently affixed (pinned and welded) to the 14.5" barrel so that the overall length is 16" or more. It is important that this is done as quickly as possible after receiving the barrel to avoid any appearance of "intent" to manufacture an unregistered SBR. The smart play is to have a gunsmith or other means to pin and weld the flash hider ready and waiting before the barrel arrives. Remember, possession is 9/10 of the law.
2. Start with a stripped lower receiver and build up a pistol lower from scratch, or purchase a complete pistol lower. A pistol configuration will allow you to use any length barrel you like provided that the overall length of the weapon exceeds 26".
3. Fill out and submit an ATF Form 1 to register your lower as an SBR. This will require your CLEO signature before you submit the required forms to the ATF with a $200 check for the tax stamp. Once the paperwork is approved and you receive your tax stamp, takes around 8-12 months nowadays, you can legally put any length barrel you like on the upper that is used with your new SBR lower...