What's the default scope for a bean created by a @Produces method without a scope annotation?

It's @Dependent.

According to "2.4.4. Default scope" from the CDI (1.2) specification:

When no scope is explicitly declared by annotating the bean class or producer method or field the scope of a bean is defaulted.

The default scope for a bean which does not explicitly declare a scope depends upon its declared stereotypes:

• If the bean does not declare any stereotype with a declared default scope, the default scope for the bean is @Dependent.

• If all stereotypes declared by the bean that have some declared default scope have the same default scope, then that scope is the default scope for the bean.

• If there are two different stereotypes declared by the bean that declare different default scopes, then there is no default scope and the bean must explicitly declare a scope. If it does not explicitly declare a scope, the container automatically detects the problem and treats it as a definition error.

If a bean explicitly declares a scope, any default scopes declared by stereotypes are ignored.

As you do not define any Scope, your produced bean will be @Dependent by defaut.

It means that lifecycle of the produced bean will be the lifecycle of the bean which in which it is injected (contains the @Inject).

So if you have the following producer :

public class AppleProducer {
    @Produces
    public Apple createApple() {
        return new Apple();
    }
}

If you Inject an Apple in an @ApplicationScoped Pie Bean :

@ApplicationScoped
public class Pie {

    @Inject
    private Apple apple;
}

Then the Apple bean will be @ApplicationScoped, so created just one time.

If Pie bean is @RequestScoped then the Apple bean will be created at each request.