I'm not affiliated with a physics department and I want to do independent research. I'm working my way through Peskin et. al. QFT now. Let's say that I've finished Peskin et. al. and Weinberg QFT books and want to do some independent research on phenomenology although I don't have a specific topic in mind. Would I be prepared for doing research at this level? Where should I start? Should I just begin reading papers until I figure out current unanswered problems in the field? What journal would accept my paper provided that It doesn't have scientific errors and well-written? Can some-one knowledgeable in these topics give me an advice? I didn't go to graduate school so I don't know how one usually do research in particle physics. EDIT: Can I just visit a physics department and seek advice from some-one working on the field who can also give me an endorsement so that I can publish my papers on arXiv?
There are usually no formal restrictions on who can publish in a journal. But, for a paper to be published, it has to be read, reviewed, and edited. The reason journals usually expect some sort of creditation is to avoid having to dredge through the work of people who don't know what they're talking about.
It is true that most people have no desire to be published in a scientific journal, but the draw is big enough that journals get plenty of crack-pot submissions. The big name journals are more prone to this, and will be more likely to reject unaccredited authors out of hand. If you want to get published without co-authors and without going to grad school, your best bet would be to focus on a small journal serving a small topical area.
That being said, whatever your goal, your best bet would be to work with a professor. For anyone who is serious about pursuing upper-level academic research, a graduate program is a first step. But, if you just don't have the time for graduate school (money shouldn't be a problem as these programs are usually paid for), you should at the very least communicate with a couple of professors who specialize in your particular field of interest. Granted, professors are busy people too, and will likely be hard to get ahold of around mid-terms and finals, but if you show yourself to be serious, intelligent, knowledgeable, and passionate, you will likely find them to be friendly and helpful people.
I will complete @AdamRedwine 's good advice by:
Try to be close to a large laboratory which supports particle physics. Every week there will be lectures on various subjects, experimental, phenomenological, theoretical. These are open to all , so try to attend as many as you can. This will accomplish two things: if you ask intelligent questions people will start to know you and secondly you will get a feel of the real research and how it is conducted, even if not in a group/program. It will be easier to approach professors or researchers if they know you from the lectures.