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During my Ph.D. in condensed-matter physics, I published a paper together with two other students. The research group of the university that I am originally from (in Madrid, Spain) happened to work on the same subject and, later on, published another paper where they criticize our work, propose their own, and claim that theirs ‘works’ better. This group includes a famous and highly influential professor.

I could finally get around to study their results, reproduce every single bit of them, and found a major flaw, which invalidates their conclusions, including the superiority of their approach over ours.

I am now a permanent researcher in another country, but would like to go back to Madrid some day for personal reasons. It is a small world, and it is likely that I will have to interact/negotiate with that group if I ever want to go back.

On the one hand, I would like to publish this work where I found the flaw, in order to get things straightened out and properly settle the scientific issue. On the other hand, this may cause a strong embarrassment for them and be detrimental on a relational/political level, possibly implying a revenge from their side.

I could certainly write them a polite email before publishing, trying to be as delicate as possible and frame the whole thing in a positive way. However, I doubt that this will make a difference on the long term.

How can I deal with this?

Don't make it personal. Keep it about the science. You can inform them of the flaw and let them fix it or you could just publish a new paper with better results, pointing out the flaw if needed. That would depend on whether you want the new result under your name or are happy enough for it to be under theirs.

If you write, however, and get pushback, evaluate it fully and then publish or not as you choose. But I wouldn't get into an argumentative back and forth about it. And if you just decide to publish it, as a courtesy you can send them your paper when you submit it to a publisher: For Your Information...

The science is the important thing.

I'm no physicist, but speaking from common sense: Depending on how "ground-breaking" your discovery of their mistake is, here are the options I would consider:

• Silly mistake that could have been avoided by being careful or by knowing a bit more math: Write up a correction, contact the group and offer to co-author the correction with them, so that way everyone "saves face" and you are likely to remain friends and future colegas.




• Fundamental mistake that some of their team members may not pick up even after lengthy communication: proceed as above initially, knowing that you may end up publishing alone (if you're correct about the mistake and manage to convince a journal). Friendships may or may not be damaged.




• Earth-shattering stuff that requires a gestalt shift: write up, contact them for the sake of politeness and to give them a chance for a rebuttal, but publish alone. Science wins, but friendships not so much.

In all cases, remain super polite and respectful, obviously.

A diplomatic way to title your write-up: "Corrigendum" or even "Comment" rather than "Rebuttal."

It's clear that you have your own interests in this special situation that you outlined. Other researchers have other interests. If you believe your work is better, as a physicist/reader I would expect you to publish your work/method or comment their critics in a new publication. Writing privately an email to them is the worst thing you can do for the readers of these articles from both groups and therefore for academia in general.

Don't put your personal interests over the scientific need to publish the flaw you found, especially when you are in a permanent position paid by taxes. You are in a permanent position.

The first thing to do is to typeset your work and check it - if possible ask someone else to look over it if only superficially to make sure there is no obvious oversight on your part. Typesetting is a form of deep proofreading so this will also force you re-evaluate your own work with the mindset of explaining to others what you have done.

The next thing is to contact one of the persons involved (presumably the senior author if possible) in the erroneous paper, asking for clarifications and supplying your notes as evidence that you cannot duplicate or disagree with the original result. Statements like I am quite puzzled as to how you got from here to here because... or Could you clarify why you make this approximation because it seems to me... are useful for softly directing attention to the contentious issues.

Presumably this would be enough to get some sort of discussion going. The key point is to allow plenty of time for the other group to assess your own work and compare it to theirs.

Finally, you can eventually write your own rebuttal, including in the conclusion or acknowledgments discussions with authors of said papers if such a back-and-forth took place.

I have been on the receiving end of such papers, i.e. some groups have published results challenging work done with collaborators, whereas in fact we had never made the claims under challenge. I have also received advanced copies of manuscript citing my papers and found the authors to have overlooked a crucial details. I much prefer the second scenario, irrespective of where an error was to be found.

There are four possibilities, for this moment:

1) They are wrong, you are right.

2) You are wrong, they are right.

3) Both you and them are wrong;

4) Both you and them are right.

It is also possible that future will cast new light on the situation - but that no one can predict.

Hence, publish as-is, reference the other study, say that your result is different and explain why it is different. There are nicer ways of putting forward why the other party is mistaken, ranging from:

"However, if the term is omitted, ..."

all the way up/down to:

"... which appears to be a typesetting error ..."