I am reading a paper that I find very hard to follow.
This is partially due to my lack of experience in the subfield, but also I think because the paper is unclearly written.
Is it acceptable for me to email the writer of the paper, and ask for explanations of basic concepts in the paper? i.e. I would ask for things that I think could have been explained more clearly.
It's okay, and more than okay, to ask for clarifications on specific bits that you were unable to follow. Academics love talking about their work, and they love spreading knowledge.
It's less okay to email someone out of the blue and say "explain yourself better". As SolarMike said, this paper has already been peer-reviewed; people in the field have looked over it and said "yep, that looks good". It may indeed be true that the paper was not written clearly enough to be understandable to someone without extensive knowledge of the subfield, and it may also be true that a better written version of the paper would have been more widely understandable without compromising its concision or its organization, but that's not a sin the author is required to atone for.
Try reading a few of the papers that paper cites, particularly ones sharing one or more authors; authors will often introduce and explain formalisms in one paper, and then take them "as read" in later papers (either accidentally or because they see the later paper as incorporating the earlier one by reference). If you still can't follow it, definitely contact the author... but make sure your request comes off as a request, not a criticism.
Is it acceptable for me to email the writer of the paper, and ask for explanations of basic concepts in the paper?
Not really, no. When somebody writes a paper about something, they're not offering to explain the basics of that field to every stranger in the world who might be interested. Rather, they're explaining their particular advances to people who are already expected to be familiar with the basics.
You should try to find other sources for the basics. Textbooks, websites, earlier papers in the same field, members of your own department, a relevant Stack Exchange site, and so on. If you can't find appropriate resources on your own, it would definitely be appropriate to ask the authors of the paper if they have any recommendations of resources you could use to learn about the area.
I'm assuming here that, by "basic concepts", you mean the basic concepts of the field, rather than the concepts that they introduce. For example, if the paper is about prime numbers, it wouldn't be appropriate to ask the authors what a prime number is, or what Euler's totient function is. If, on the other hand, their whole paper is about their new concept of "squiggle primes" and you can't follow their definition, it's reasonable to ask about that, if no more local person can help you. But do try to ask something specific rather than, "You define squiggle primes but I don't get it. Please explain more."
'I would ask for things that I think could have been explained more clearly.' : wrong approach.
'I would ask for help in understanding something that isn't fully clear to me at present' : right approach.
Your objective is to understand/learn, not to correct/improve the authors' writing style. If the latter is indeed your objective, this is not the time. You're a reader, not a reviewer.
The way you think about it manifests in your words, in your tone, and is very likely to influence the response you get.
It really depends on how you do it. I am only speaking from personal experience, as I tend to receive mails like that a couple of times a month or more. This is due to me implementing my academic work into software, which people can then use to make calculations.
If you just imagine the person you are writing giving the rant below, and then ask your question accordingly, you will be fine.
I can immediately tell if you made an effort understanding it. Please do so before you write me. While I will surely answer your question, I can certainly have more fun than trying to paraphrase one of my papers in an email.
Ask genuine questions, don't try to hide anything out of fear that I will steal your idea. I wont, I have enough to do. I all too often have to drag out of people what they are actually trying to accomplish, enabling me to give them better answers.
If you are a student, ask your supervisor first. While I will be happy to help, I don't run a correspondence course.
For God's sake: spell check. Your English does not have to be perfect - mine certainly isn't - but I need to be able to understand your mail before answering it.
Don't open simultaneous, parallel mail threads with both me and my co-author. We do not often discuss "help" mail, and if we do, it's for giggles in the coffee room. We will not know that you reached out to both of us, and when we find out we will be annoyed.
I don't think it would be a good use of the author's time to answer questions on basic concepts, however I think there are specific situations where asking questions is appropriate.
For my MedChem MSc we reviewed a number of papers on structure analysis that included statistical results. As I previously did statistics undergrad I was keen to replicate their steps (as their methods were fairly straight-forward) and replication should be a matter of plugging their data into Rstudio with the appropriate model. This approach worked fine, except for one particular paper.
After a week of messing around with variations, I couldn't get the same results. I asked some fellow students who suggested it was much more likely that I was wrong somewhere, than the paper was wrong, which was my feeling.
However eventually I emailed the author who quickly responded that indeed, the paper was missing some required details, and their clarifications allowed me to come up with the same results.
So sometimes, I assume rarely, papers have mistakes and omissions, and usually the author can help you with that.
It's certainly acceptable to ask the author of a paper questions when you don't understand something.
However, when corresponding with the author, take into account that the author will probably answer only two or three emails before giving up on you as somebody who is wasting too much of their time.
So if you have a basic question, try to answer it yourself, or get somebody at your institution who knows more about the field, before emailing them; save your emails for questions that you really need help on, and that only the author will be able to answer.
I follow GEdgar in his answer. That strategy works for me. I get my self several (text) books on the subject underlying the paper. Often there is (mathematical) notation in papers that is explained clearly in books. Once you understand that language, the papers suddenly aren’t that difficult anymore. When I started my PhD some papers took me months to fully grasp. It is also a normal process, I guess. I have never emailed authors but I do not see why you shouldn’t if that feels right for you.
