Why lambda capture by value provide reference type in the lambda body

Question

I was writing some code dependent on type of variable and found out that referenced argument to function captured by value detected as reference type inside lambda body. I checked it with static_assert for std::is_same_v and decltype. Given code will be successfully compiled, but if I replace std::is_same_v<decltype(a),Loud&> to std::is_same_v<decltype(a),Loud>, the static_assert will fail.

void foo(Loud& a) {
    auto lamb = [a]() {
        static_assert(std::is_same_v<decltype(a),Loud&>);
    };
}

I expected that decltype(a) is equal to Loud, because it was copied.

Then I tried to check was it really copied with given code:

class Loud{
public:
    Loud() {
        cout << "ctor" << endl;
    }
    
    Loud(Loud& other) {
        cout << "copy ctor" << endl;
    }
};

void foo(Loud& a) {
    auto lamb = [a]() {
        static_assert(is_same_v<decltype(a),Loud&>);
    };
}

int main()
{
    Loud a;
    foo(a);
    return 0;
}

And I found that it was copied because I had copy ctor line in my output.

After all of this I continued to experiment and was suprised that following code was successfully compiled

void foo(Loud& a) {
    Loud b;
    auto lamb = [a, b]() {
        static_assert(is_same_v<decltype(a),Loud&>);
        static_assert(is_same_v<decltype(b),Loud>);
    };
}

Finally I am totally confused with this behavior. Can you please explain me what is going on here?