I think we agree that their null hypothesis is &quot;there is a background, with events coming from all the known particles&quot;. I think we agree that their conclusion is &quot;these results provide conclusive evidence for the discovery of a new particle&quot;. I don&#x27;t see how can they say that there is a new particle without rejecting the hypothesis that there is no such new particle. Of course you can say that the null hypothesis can never be rejected (relevant Dilbert strip: <a href="http:&#x2F;&#x2F;dilbert.com&#x2F;strip&#x2F;2001-10-25" rel="nofollow">http:&#x2F;&#x2F;dilbert.com&#x2F;strip&#x2F;2001-10-25</a>) but then they can never discover a new particle either.<p>Regarding p-values in general, your definition is the same I&#x27;ve been using all along. But I don&#x27;t think it is meaningless when the null hypothesis does not hold. The meaning is clear: &quot;the probability of getting a value for the statistic as high as the observed one if the null hypothesis was true&quot;. For example, there would be one chance in several millions of observing the kind of data they found at the LHC if the Higgs boson didn&#x27;t exist.<p>You might want to look into the theory yourself, because the notion of p-values trending towards 1 if the null hypothesis is true is nonsense. By definition, if the null hypothesis is true the p-value is uniformly distributed between 0 and 1. If you have at some point a p-value close to one (or to any other number for that matter) and keep adding data, in the long run it will still be uniformly distributed between 0 and 1.