In this sorry age for Supersymmetry (SUSY) phenomenologists, it is quite easy to step on an aching toe while discussing the results of the Large Hadron Collider experiments, whose results have let these physicists down by excluding the presence of SUSY where most of them used to put their moneys until yesterday.
The knee-jerk reaction I frequently observe (e.g. see the thread of my recent post on the cMSSM) in the most stubborn SUSY enthusiasts is to seek refuge in a concept which could be summarized as follows: "There is only one true realization of SUSY in Nature, and one point of the parameter space which corresponds to it; the fact that the LHC has kept excluding parameter space points that do not correspond to the true realization of SUSY says nothing on the correctness of SUSY anyway".
Now, let us step back for a second and make a few simple-minded examples of the implications of this kind of reasoning, to put it in the correct context.
1) In some cultures a popular game played in special events is to hide a small coin or jewel in a big cake; everybody then gets a slice, and the person who finds the precious treasure can keep it. Now imagine you play such a game, and you start eating your slice bit by bit, to be sure you are not gulping down the treat with the cake. You keep finding nothing, and your dish is soon close to empty; only the tip of your slice remains to be checked. You therefore now grow extremely excited: surely you're going to find it in the next bit !
2) You arrive at a deserted train station in the evening. You know that there's one train exactly every hour to your destination; however, you do not know the minutes at which trains pass. You also seem to remember that at some time late in the evening trains stop circulating. You sit and wait, and after 58 minutes have passed your train has not come yet. You then rise from the bench and pick up your suitcase, certain that the train is about to arrive.
3) In a science-fiction story (I believe it is Ray Bradbury's "The Martian Chronicles", but I could be mistaken) a man decides to seek the help of a private detective. The detective explains that his client can be confident the case will be solved: he failed to solve the previous 150 ones, so it's extremely improbable that he'll fail on this one, too.
In the three above examples, there is an obvious flaw in the reasoning of the protagonist: a wrong a priori assumption. The failure to account for the unknown probability that reality is according to one's wish is a childish mistake that we sometimes fall in even as adults.
What SUSY enthusiasts in fact do when they resort to the "Nature chose elsewhere to hide" argument is to manifest that their prior belief in SUSY being the correct theory of nature is 100%. This, in a Bayesian formalism, can be mathematically described as a "point mass" prior probability density function (PDF): a Dirac delta function, containing all the probability at one value (whatever value we choose to describe "SUSY is true" on a real axis). Now, the problem with a point mass prior PDF is that no experimental observation -none at all- inserted in the Bayesian equation can produce a posterior which is different from the prior: a granitic belief cannot be shaken, regardless of the evidence against it !
I believe Science progresses more rapidly if scientists keep their minds open to the widest range of possibilities. Well, let me restate that: I believe Science does not progress at all if scientists fail to do so ! I am therefore inclined to believe that choosing a point mass PDF for one's beliefs on the correctness of a unconfirmed theory is a wrong, anti-scientific attitude. I certainly acknowledge that SUSY is a beautiful idea, and I indeed would be happy if it were found some day (even better, if I myself found it ! I am indeed searching for SUSY particles in my research time with the CMS experiment!); yet the failure to observe SUSY as we raise the energy of proton-proton collisions and the accumulated size of our datasets in ATLAS and CMS cannot be dismissed as "no information". It is important information !
Keeping oneselves anchored to a point-mass PDF that "SUSY is correct" equates to dismissing as garbage all the negative results of the LHC searches. I will say more: it equates to saying that it is useless to do experimental research, because SUSY might be hiding where we have no access with particle collisions or other experiments. Given that, and given that we must already be sure that SUSY is correct, why searching for it ?
I am confident, though, that the attitude of those SUSY enthusiasts who choose the point-mass PDF is going to change if we continue excluding parameter space points at the LHC. Phenomenologists are pragmatic and smart people (someone funnily used the word "street-smart" in connection to one of them in the comments thread I mentioned above), so even the stubborn among them will soon choose some other point mass to anchor themselves and their careers to.
The knee-jerk reaction I frequently observe (e.g. see the thread of my recent post on the cMSSM) in the most stubborn SUSY enthusiasts is to seek refuge in a concept which could be summarized as follows: "There is only one true realization of SUSY in Nature, and one point of the parameter space which corresponds to it; the fact that the LHC has kept excluding parameter space points that do not correspond to the true realization of SUSY says nothing on the correctness of SUSY anyway".
Now, let us step back for a second and make a few simple-minded examples of the implications of this kind of reasoning, to put it in the correct context.
1) In some cultures a popular game played in special events is to hide a small coin or jewel in a big cake; everybody then gets a slice, and the person who finds the precious treasure can keep it. Now imagine you play such a game, and you start eating your slice bit by bit, to be sure you are not gulping down the treat with the cake. You keep finding nothing, and your dish is soon close to empty; only the tip of your slice remains to be checked. You therefore now grow extremely excited: surely you're going to find it in the next bit !
2) You arrive at a deserted train station in the evening. You know that there's one train exactly every hour to your destination; however, you do not know the minutes at which trains pass. You also seem to remember that at some time late in the evening trains stop circulating. You sit and wait, and after 58 minutes have passed your train has not come yet. You then rise from the bench and pick up your suitcase, certain that the train is about to arrive.
3) In a science-fiction story (I believe it is Ray Bradbury's "The Martian Chronicles", but I could be mistaken) a man decides to seek the help of a private detective. The detective explains that his client can be confident the case will be solved: he failed to solve the previous 150 ones, so it's extremely improbable that he'll fail on this one, too.
In the three above examples, there is an obvious flaw in the reasoning of the protagonist: a wrong a priori assumption. The failure to account for the unknown probability that reality is according to one's wish is a childish mistake that we sometimes fall in even as adults.
What SUSY enthusiasts in fact do when they resort to the "Nature chose elsewhere to hide" argument is to manifest that their prior belief in SUSY being the correct theory of nature is 100%. This, in a Bayesian formalism, can be mathematically described as a "point mass" prior probability density function (PDF): a Dirac delta function, containing all the probability at one value (whatever value we choose to describe "SUSY is true" on a real axis). Now, the problem with a point mass prior PDF is that no experimental observation -none at all- inserted in the Bayesian equation can produce a posterior which is different from the prior: a granitic belief cannot be shaken, regardless of the evidence against it !
I believe Science progresses more rapidly if scientists keep their minds open to the widest range of possibilities. Well, let me restate that: I believe Science does not progress at all if scientists fail to do so ! I am therefore inclined to believe that choosing a point mass PDF for one's beliefs on the correctness of a unconfirmed theory is a wrong, anti-scientific attitude. I certainly acknowledge that SUSY is a beautiful idea, and I indeed would be happy if it were found some day (even better, if I myself found it ! I am indeed searching for SUSY particles in my research time with the CMS experiment!); yet the failure to observe SUSY as we raise the energy of proton-proton collisions and the accumulated size of our datasets in ATLAS and CMS cannot be dismissed as "no information". It is important information !
Keeping oneselves anchored to a point-mass PDF that "SUSY is correct" equates to dismissing as garbage all the negative results of the LHC searches. I will say more: it equates to saying that it is useless to do experimental research, because SUSY might be hiding where we have no access with particle collisions or other experiments. Given that, and given that we must already be sure that SUSY is correct, why searching for it ?
I am confident, though, that the attitude of those SUSY enthusiasts who choose the point-mass PDF is going to change if we continue excluding parameter space points at the LHC. Phenomenologists are pragmatic and smart people (someone funnily used the word "street-smart" in connection to one of them in the comments thread I mentioned above), so even the stubborn among them will soon choose some other point mass to anchor themselves and their careers to.
http://blog.vixra.org/2012/05/10/bayes-and-susy/
A more general calculation of the same thing is here:
http://motls.blogspot.com/2012/05/thomas-bayes-and-supersymmetry.html
As someone stated at a different place, the conclusion of the calculation above is that the absence of evidence isn't the evidence of absence. Of course, in all these debates, the discussion is about the precise numbers but the precise numbers are such that the exclusions accumulated by the LHC so far are equivalent to less-than-one-sigma evidence against the SUSY. In any other context, the existence of less-than-one-sigma bumps sold as an argument for or against something would be ridiculed. But when it comes to some key dogmas underlying your unscientific opinions about particle physics – such as the dogma that SUSY can't be right – you're ready to sell less-than-one-sigma bumps as proofs.
If you think anything else, you are making a brutal mistake in the way you try to use your brain if you have any.
If one's prior probability of SUSY is very low to start with, the elimination of 2/3 of a parameter space reduces the subjective probability to 1/3 of its prior value. But this approximation becomes very invalid once the prior probabilities are close to 50 percent or higher. And they should be because if someone thinks that a non-falsified prior probability is much smaller than 50 percent to start with, he suffers from dogmas – by definition. For 50 percent or so – one is neutral about SUSY Yes/No to start with – the decrease of the probability by the 2/3 exclusion is very weak.
At any rate, you're rather likely to be proved wrong by the LHC in a foreseeable future. You will say that it's a shocking surprise but it won't be a surprise. The absence of a signal in the first 5/fb of the data at 7 TeV doesn't imply the absence of a signal in the first 15/fb data at 8 TeV, assuming any reasonably scientific standard for an "implication".
You may try to populistically scream that if 6,000 physicists work for a year and write dozens of exclusion papers, they must have an impact. Well, they have an impact on the detailed models and regions of the parameter space that are being investigated by the phenomenologists and model builders. But their impact on the question SUSY Yes/No may be quantified and it is equivalent to a less-than-one-sigma bump in a graph. This result of the collective ATLAS and CMS efforts is easily beaten e.g. by a single paper by Christoph Weniger who finds traces of a 130 GeV dark matter particle in the Fermi gamma-ray data. It's easy to calculate that there's almost no evidence for or against the big SUSY question coming from the LHC papers so far whether or not someone finds this fact inconvenient.