Cross-domain authentication based on token

Question

There are two servers:

• one on domain A
• another on different domain B.

Let's call them A-server and B-server respectively.

A-server is a main server with its own authentication and also frontend part. B-server is a service with its own authentication.

How could I authenticate user on server B from server A within js?

I think about token-based authentication and add it to server B.

Now it could response to /sign.json path and well authenticate with token.

But token is placed in http-headers. So, everything should be normal, right?
But these headers are hidden for js, because servers ( main A with js and B with token-based authentication ) have different domains.

Could somebody point to appropriate implementation of such kind of authentication?

Also, how it should be done well?

( For now it is too difficult to put authentication in one place and use it for all services/servers. )

It is a general question about http and tokens, but I have specific implementation:

B - Rails 4.2
gem 'devise_auth_token'
gem 'rack-cors'

//setup for rack-cors:
//in middlewares.rb
  config.middleware.insert_before 0, "Rack::Cors" do
    allow do
      origins ENV['CONFIG_ACTION_DISPATCH_DEFAULT_HEADERS_CONTROL_ALLOW_ORIGIN'] || '*'
      resource '*', headers: :any, 
      methods: [:get, :post, :options, :put, :patch, :delete],
      expose: ['access-token', 'expiry', 'token-type', 'uid', 'client']
    end
  end

As you see from setup I add Expose-Headers from Token-based authentication.