A Quantum Diaries Survivor

Scientists should be bold. They are expected to think out of the box, and to pursue their ideas until these either trickle down into a new stream, or dry out in the sand. Of course, not everybody can be a genuine “seer”: the progress of science requires few seers and many good soldiers who do the lower-level, dirty work. Even soldiers, however, are expected to put their own creativity in the process now and then -and that is why doing science is appealing even to us mortals.

You do not need to be a Einstein, or a Fermi, or a Witten, to do good science: but you need to be bold sometimes. You study, understand, ponder on something, and you come up with your own perception of the matter: you create a model of it in your brain, and this enables you to look in the shady corners, and make a bold claim about what one should find there. The claim may have the function of a working hypothesis, or remain a wild bet, a guess you do not pursue further. Usually a working hypothesis allows you to continue your investigation in one direction, giving you some guidance into new territory. A wild bet is more risky, since it exposes you more: if somebody else proves you wrong it hurts much more than if you prove yourself you were on a dead track.

I have made my own very wild and risky bet a couple of years ago, when I predicted that the LHC will not find any signal for new physics beyond the Standard Model. Definitely a bold statement, motivated by my frustration with observing the lack of any real indication that our current understanding of the subnuclear world may be finally crumbling down. Indeed, it was a real bet, which will pay real money. I perceive it as an insurance: I definitely would rather lose it than win it!

Other scientists have made their own, virtual or real bets: claims about what we will eventually discover on the organization of reality. I salute with enthusiasm the latest one, which I read today. Here is what Peter Woit says:

To go out on a limb and make an absurdly bold guess about where this is all going, I’ll predict that sooner or later some variant (”twisted”?) version of N=8 supergravity will be found, which will provide a finite theory of quantum gravity, unified together with the standard model gauge theory.

How’s that for boldness ? This is not about not finding something. It is about predicting how things stand: definitely a high-level claim. And Peter then continues in kinds:

String theory will turn out to play a useful role in providing a dual picture of the theory, useful at strong coupling, but for most of what we still don’t understand about the SM, it is getting the weak coupling story right that matters, and for this quantum fields are the right objects. The dominance of the subject for more than 20 years by complicated and unsuccessful schemes to somehow extract the SM out of the extra 6 or 7 dimensions of critical string/M-theory will come to be seen as a hard-to-understand embarassment, and the multiverse will revert to the philosophers.

This is called going “all in” in Texas hold’em poker: being consistent to the end. The criticism of string theory contained in his successful, highly readable book Not Even Wrong finds here its final justification: string theory is not by itself bad, but investigating it with momentum in the last two decades has not resulted in finding a new stream, but rather in a folding into itself of the discipline along with its extra dimensions, in one of the 10^500 possible ways which all together threatened the perception that most of us have of what doing science should be. Congratulations for your Friday evening boldness, Peter!

Just a quick note to congratulate with Marni Dee Sheppeard, who has reached her 200th online lesson on Category theory (actually she is already at 201!). And she has recently posted some wonderful views of New Zealand, with the pretext of investigating on the potential site of a new university - one more reason to pay her a visit.

These days my honest yet slightly anarchical style of blogging is becoming harder and harder to maintain. I am curiously receiving a synchronous input from the two opposing sides of the Atlantic Ocean: a true coincidence, because the origins of these inputs are totally uncorrelated. And yet the push goes in the same direction. Worse still: since the input is coming from authoritative sources, it would be idiotic to ignore it.

Good science works by encouraging an open exchange of information only in fairy tales. In reality, the human factor weighs in to modify that optimal picture. Man is ambitious, selfish, vain. And hundreds, or even thousands, such individuals gathered together in the same project make a sociological bomb that is only begging to be set off. Handling such a bomb is not an easy matter: therefore, I do understand the concerns of these giant collaborations.

Time and again I am told by readers that one of the things that make this blog interesting to read is the cut-away view I occasionally provide of the inner workings of the scientific collaborations I work in. Well, that feature of this site is bound to be slightly dampened. Posts such as this one, or even this one, might be considered a diffusion of internally exchanged information, and as such they would create trouble (the first one did, in fact).

I decided I will unwillingly oblige. Not so much because of the harm that my own scientific career might be exposed to if I were unreasonable: I am not ambitious -I have a good life, my job satisfies me fully, and I do not depend for my living on my ridiculous salary. Rather, I will oblige because I fully understand that keeping a blog with some audience requires a good dose of responsibility. One of the things that makes me proud is to have belonged and still belong to CDF, the longest-lasting and one of the most successful physics experiments ever; and nowadays, I am spending most of my time to earn the right to be proud of belonging to CMS too. I certainly want to help these experiments!

What this all boils down to is, I think, only that I will not post any more about the humorous sides of internal meetings -the rest has never made it to this blog anyway- and that I will compensate by writing a bit more about the physics. Not such a terrible deal after all. I will have to save my irony for other matters.

Rick Ryals, a frequent visitor of this site, wrote a guest post here some time ago, on Dirac’s theory and the Einstein constant. He sent me today another text about his views on the Anthropic principle, which I am happy to host here. Of course, his views and mine need not be the same for me to find the following text fit for this site. -TD

Ever wonder why David Gross calls the inability of science to produce a “dynamical principle” that would “make the landscape go away”, the biggest failure of science in the last twenty years?

I would assert that it’s quite obviously because scientists can’t or won’t add one and one.

The anthropic principle is possibly the most misunderstood and misused observation in all of science, whose mere mention brings about the most extreme reactions from just about everyone who comes into contact with it. Creationists read-in the hand of god, while some String theorists find hope for a real theory, but most others find only utter disgust and complete disdain, as very few actually get the point. If this post was about a “variant interpretation”, then it would be called “The Unpopular Anthropic Principle”, because that’s exactly what it will be, since it includes all of the dirty little truths that nobody on any highly motivated side of the popular issues really wants to know about.

The physics concerns the unexpected carbon-life orientation of certain structure defining features of our universe that do not concur with the cosmological projections of modern physics.

The pointed nature of the physics indicates the direction that one might look in for the as yet undefined dynamical structure mechanism that is normally expected to explain why the universe is configured the way that it is, rather than some other way. Brandon Carter called this “a line of reasoning that requires further development”. But the Anthropic Principle was originally formalized by Carter as an ideological statement against the dogmatic non-scientific prejudices that scientists commonly harbor, that cause them to consciously deny anthropic relevance in the physics, so they instead tend to be willfully ignorant of just enough pertinent facts to maintain an irrational cosmological bias that leads to absurd, “Copernican-like” projections of mediocrity that contradict what is actually observed.

Carter was talking about an equally extreme form of counter-reaction-ism to old historical beliefs about geocentricism that cause scientists to automatically dismiss evidence for anthropic “privilege” right out of the realm of the observed reality. I intend to put very heavy emphasis on this point, because people go to unbelievable lengths to distort what Carter said on that fateful day in Poland, in order to willfully ignore this point as it applies to modern physics speculations and variant interpretations, which are neither, proven, nor definitively justified, theoretically.

Why do none of the popular definitions of the anthropic principle include what Carter actually said?
…a reaction against conscious and subconscious - anticentrist dogma.

This a the real problem for science.

Carter’s example was as follows:

Unfortunately, there has been a strong and not always subconscious tendency to extend this to a most questionable dogma to the effect that our situation cannot be privileged in any sense. This dogma (which in its most extreme form led to the “perfect cosmological principle” on which the steady state theory was based) is clearly untenable, as was pointed out by Dicke (Nature 192, 440,
1961). -Brandon Carter

Carter expounded on the anthropic coincidence that Robert Dicke had deduced from Dirac’s Large Numbers Hypothesis. Dicke had noted that “the forces are not random, but are constrained by biological factors” that cause the universe to evolve contrarily to the standard cosmological prediction in a unique manner that favors carbon life. It is important to note that this evolving physics includes all carbon-based-life, and this also limits life to a very narrow range of time in the history of the universe. But this feature also dictates that the same combination of “homeostatic” environmental balances that define the Goldilocks Enigma will occur on similarly developed planets in similarly developed galaxies that exists along the same fine “layer” or time/location “plane” that our galaxy evolved on, so there is absolutely no apparent reason to assume that the physics applies exclusively to only one planet, or to a single form of carbon-based life.

Circumstellar Habitable Zone - Ecobalance - Ecosphere

How Carter’s anti-political statement applies, including its strength, depends on the cosmological model that physics is being applied to, so Brandon Carter’s own “strong” multiverse interpretation differs from what is actually observed. Carter’s point was that unscientific ideological bias should be honestly weighed into consideration whenever a scientist is faced with anomalous features of the universe that are also relevant to our place in it, in order to serve as a counterbalancing constraint on their preconceived prejudices against evidence for “preference” or “specialness”. Unfortunately for science, this is rarely the case, as these words will fly right past the theoretical confidence of the “cutting-edge”.

Add to that the creation/evolution “debate” and you have all the makings for a very bad situation for science, where zealots will either, embrace what physicists commonly call the “appearance of design”, as being just that, or, on the other side of the fanatical coin, anti-zealots will all together deny that there is any such implication for “specialness” in the physics whatsoever, while appealing to multiverses and quantum uncertainty, in lieu of causality and first principles. This is done in order to “explain-away” the evidence, rather than to honestly recognize and give credible time to the most readily apparent implication for a biocentric cosmological principle that is indicated by the “appearance of design”. The anticentrist’s tendency to deny the significance of the observation is an over-reaction to pressure from religious extremists and from ill-considered assumptions about human arrogance, which doesn’t even make sense if we’re spread-out across the universe like bacteria on a thin slide of time. Unfortunately for science, it is also a perfectly true example of Carter’s point, as anticentrists typically and wrongly believe that such an admission constitutes evidence in favor of the religious fanatic’s argument, so willful ignorance takes the place of science when the argument is a culture war between zealots and their antifanatical counterparts.

But it is an unavoidable fact that the anthropic physics is directly observed to be uniquely related to the structuring of the universe in a way that defies the most natural expectation for the evolution of the universe in a manner that is also highly-pointed toward the production of carbon based life at a specific time in its history, (and over an equally specific, fine-layer or region of the Goldilocks zone of the observed universe).

If you disallow unproven and speculative physics theory, then an evidentially supported implication does necessarily exist that carbon-based life is somehow intricately connected to the structure mechanism of the universe, and weak, multiverse interpretations do not super cede this fact, unless a multiverse is proven to be more than cutting-edge theoretical speculation.

That’s the “undeniable fact” that compels Richard Dawkins and Leonard Susskind to admit that the universe “appears designed” for life! There is no valid “weak” interpretation without a multiverse, because what is otherwise unexpectedly observed without the admission of speculation, is most-apparently geared toward the production of carbon-base life. Their confidence comes from the fact that their admissions are qualified by their shared “belief” in unproven multiverse theories, but their interpretation is strictly limited to equally non-evidenced “causes”, like supernatural forces and intelligent design.

These arguments do not erase the fact that the prevailing evidence still most apparently does indicate that we are somehow relevantly linked to the structure mechanism, until they prove it isn’t so, so we must remain open to evidence in support of this, or we are not honest scientists, and we are no better than those who would intentionally abuse the science. We certainly do not automatically dismiss the “appearance” by first looking for rationale around the most apparent implication of evidence.

That’s like pretending that your number one suspect doesn’t even exist! There can be nothing other than self-dishonesty and pre-conceived prejudicial anticipation of the meaning that motivates this approach, and often *automatically* elicits false, ill-considered, and, therefore, necessarily flawed assumptions, that most often elicit equally false accusations about “geocentricism” and “creationism”. That’s not science, it’s irrational reactionary skepticism that is driven without justification by sheer disbelief and denial.

And then along came this highly inconvenient… WHOOPS! WHAT’S THIS SUPPORTING HERESY that we must only work to explain-away?!?!

Does the motion of the solar system affect the microwave sky? http://cerncourier.com/cws/article/cern/29210

Lawrence Krauss even talks about this direct observation:

THE ENERGY OF EMPTY SPACE THAT ISN’T ZERO But when you look at CMB map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That’s crazy. We’re looking out at the whole universe. <b>There’s no way there should be a correlation of structure with our motion of the earth around the sun — the plane of the earth around the sun — the ecliptic. That would say we are truly the center of the universe.
-Lawrence Krauss

“That’s Crazy”… “There’s no way”… Really, Larry?… Are you sure that it isn’t more-like… willful ignorance and denial?

Or isn’t it actually compounded supporting evidence for the life-oriented cosmological structure principle that we already have theoretical precedence for?

The problem here isn’t that we don’t have evidence, (make that, compounded evidence, and/or independently supportive evidence), the problem is that nobody is looking into this from any perspective that isn’t aimed at refuting the significance of the evidence.

They have had some success at this, too, because it has been discovered that the correlation applies to a specific region of galaxies like ours, but they act like they don’t have a clue, (and I’m sure that they don’t), that this is exactly what the Goldilocks Enigma predicts will be found.

It isn’t a case of not having evidence, rather, it is a matter of unscientific interpretation and an unwillingness to look at the physics straight-up, without automatically dragging some abstract and unproven assumptions about quantum observers into it, to see if maybe something that we do quite naturally might make us entirely necessary to the energy-economy of the physical process.

If you take Brandon Carter’s statement and bring it with you to the “consensus of opinion”, then you might begin to understand why the problem doesn’t get resolved:

And it ain’t pretty:

http://arxiv.org/abs/0705.2462

Tough blogging these days. On Friday I was in Florence for a day, to discuss organizational matters with the colleagues of the italian CMS-Tracker community: a long meeting void of physics or anything vaguely resembling my field of expertise, to decide on funds, candidacies for the new project leader of the CMS Tracker, and other trivialities. Basically I was offline all day, given the seven hours I spent driving and the six at the meeting.

Then yesterday I had my hands itching from the lack of typing. I very much wanted to comment on the new paper by Mangano and Giddings, but I had to yield to the prospects of a boat trip on the sea with family, kids, and friends.

And today, I left early for a flight to Cyprus, via Wien. I am now typing from the lobby of Hotel Adriatica Miramare, in Limassol, after a taste of the Mediterranean sea (warm and calm, but the water was less clear than I expected - I think there are better beaches if one moves away from Limassol). What on Earth is going on there, you might well ask. Well, 190 members of CMS are gathering for the yearly off-site CMS week. The focus of the workshop will be on the final preparations before first collisions.

I also learned yesterday evening that I will be speaking here, this Wednesday morning, at the Electroweak session. Kind of a late warning, but I know what I am going to say. The problem, though, is that what I will be able to show depends entirely on the fate of a few batch jobs I submitted yesterday evening on the CERN batch system… But I am not going to let that spoil my week here. The sun is shining, the level of decibels is really low, and all I have to worry about tonight is what kind of food to eat. Oh, and a certain TV event. Spain will meet Italy at the quarter-finals of the European soccer championship. I am no soccer fan, but I will certainly watch the show!

This just in: the report on the safety of the LHC is out. I have no time to comment it here, will do it tomorrow after a more thorough reading.

In order of increasing complexity, you can start from the CERN press release, look directly at the LSAG report, or concentrate on the physics in the paper by Mangano and Giddings.

After a spoiler warning, I can say that…

(more…)

A recent analysis by CDF, based on 2 inverse femtobarns of data (approximately 160 trillion proton-antiproton collisions) has searched for events featuring a rare mixture of striking objects: high-energy photons, significant missing transverse energy, and energetic b-quark jets. Photons at a proton-antiproton collider are by themselves a sensitive probe of several new physics processes, and the same can be said of significant missing energy. The latter, in fact, is the single most important signature of supersymmetric decays, since the latter usually feature a non-interacting, neutral particle, as I had a chance of explaining in a lot of detail in two posts on the searches for dark matter at colliders (see here for part 1, here for part 2, and here for part 3). Add b-quark jets to boot, and you are looking at a very rare signature within the standard model, but one that may in fact be due to hypothetical exotic processes.

The idea of such a signature-based search is simple: verify whether the sum of standard model processes account for the events observed, without having to be led by any specific model for new physics. The results are much easier to interpret in terms of models that theorists might not have cooked up yet. A specific process which could provide the three sought objects together is not hard to find, in any case: in supersymmetric models where a photino decays radiatively emitting a photon and turning into a Higgsino -a lightest particle which escapes the detector, one gets both photons and missing energy; the additional b-jet is then the result of the decay of an accompanying chargino.

If the above paragraph makes no sense to you, worry not. Just accept that there are possible models of new physics where such a trio of objects arise rather naturally in the final state.

However, there is another, much more intriguing, motivation for the search described below. So let me open a parenthesis.

In Run I, CDF observed a single striking, exceedingly rare event which contained two high-energy electrons, two high-energy photons, and significant missing transverse energy. A unexplicable event by all means! Below you can see a cut-away view of the calorimeter energy deposits: pink bars show electromagnetic energy (both electrons and photons leave their energy in the electromagnetic portion of the calorimeter), but photon candidates have no charged track pointing at them. The event possesses almost nothing else, except for the large transverse energy imbalance, as labeled.

The single event shown above was studied with unprecedented detail, and some doubts were cast on the nature of one of the two electron signals. Despite that, the event remained basically unexplained: known sources were conservatively estimated at a total of millionth of an event! A definitive answer on it was thought would be given by the larger dataset that the Tevatron Run II would soon provide. You can read a very thorough discussion of the characteristics of the infamous event in a paper on diphoton events published in 1999 by CDF.

Closing the parenthesis, we can only say that events with photons and missing transverse energy are hot! So, CDF looked at them with care, by defining each object with simple cuts -such that theorists can understand them. No kidding: if an analysis makes complicated selections, a comparison with theoretical models coming after the fact becomes hard to achieve.

The cuts are indeed straightforward. A photon has to be identified with transverse energy above 25 GeV in the central calorimeter. Two jets are also required, with and ; Rapidity is just a mesure of how forward the jet is going; a rapidity of 2.0 corresponds to about 30 degrees away from the beam line, if I remember correctly. Selecting these events leads to about 2 million events! These are dominated by strong interactions where a photon is faked by a hadronic jet.

The standard selection is tightened by requiring the presence of missing transverse energy above 25 GeV. Missing transverse energy is measured as the imbalance in the energy flowing in the plane transverse to the beam axis; 25 GeV are usually already a significant amount, which is hard to fake by jets whose energy has been under- or overestimated. The two jets are also required to be well separated between each other and from the photon, and this leads to 35,463 events: missing Et has killed alone about 98% of our original dataset. But missing Et is most of the times due to a jet fluctuation, even above 25 GeV: thus it is further required that it is not pointing along the direction of a jet in the azimuthal angle (the one describing the direction in the plane orthogonal to the beam, which for missing transverse energy is indeed defined). A cut halves the sample, which now contains 18,128 events.

Finally, a b-tagging algorithm is used to search for the secondary vertex B mesons produce inside the jet cones. Only 617 events survive the requirement that at least a jet is b-tagged. These events constitute our “gold mine” and they are interpreted as a sum of standard model processes, to the best of our knowledge.

One last detail is needed: not all the b-tagged jets are originated from real b-quarks! A sizable part of them is due to charm quarks and even lighter ones. To control the fraction of real b-quarks in the sample, one can study the invariant mass of the system of charged tracks which are fit together to a secondary vertex inside the jet axis. The invariant mass of the tracks is larger for b-jets, because b-quarks weigh much more than lighter ones, and their decay products reflect that difference. Below, you can see the “vertex mass” for b-tagged jets in a loose control sample of data (containing photons and jets with few further cuts): the fraction of b-jets is shown by the red histogram, while the blue and green ones are the charm and light-quark components. Please also note the very characteristic “step at about 2 GeV, which is due to the maximum mass of charmed hadrons.

The vertex mass fit in the 617 selected events allows to extract the fractions of events due to real photons accompanied by b-jets, c-jets, and fake b-tags (light quark jets). In addition, one must account for fake photon events. Overall, the background prediction is extracted by a combination of methods, well-tested by years of practice in CDF. The total prediction is of events (the uncertainties are statistical and systematic, respectively), in excellent agreement with observed counts. A study of the kinematics of the events, compared with the sum of predicted backgrounds, provides a clear indication that Standard Model processes account very well for their characteristics. No SUSY appears to be lurking!

Below you can see the missing transverse energy distribution for the data (black points) and a stack of backgrounds (with pink shading for the error bars on background prediction).

Below, a similar distribution for the invariant mass of the two jets.

A number of kinematic distirbutions such as those shown above is available in the paper describing the preliminary results. Interested readers can also check the public web site of the analysis.

Time and again, knowledgeable readers of this blog point out some inaccuracy in the physics I describe in a post. Often, it is just a simplification I made to make the matter understandable; more rarely, it is a blatant mistake, or a wrong statement that exposes my ignorance. I thank those who exposed me  -correcting wrong physics is a commendable action, and in some instances it has allowed me to increase my own understanding of a topic I had not completely digested. Sometimes, those readers are surprised by my naive reaction. The question, however, is whether I should worry about it.

After all, physics is my job, and I could well be concerned with my reputation at stake. Exams are never over in the life of a scientist, and this site has enough traffic to guarantee that now and then some of those who might one day be members of a committee which decides on my career advancement do read what is written here (I could name a half dozen).

The other side of the coin is that by occasionally (and accidentally) showing my own ignorance I actually make this site more appealing to many. The hidden but powerful message is that a reader who does not have a Ph.D. in high-energy physics does not need to feel an intruder if he lingers around or comments posts in this blog. This is very important since, in my opinion, when doing science outreach it is fundamental to bridge the gap with non-scientists, providing places where researchers and people with a real job can meet and interact. If scientists continue to stay in their ivory tower, they risk losing the support of society. I discussed this issue in some detail in a recent contribution to a symposium about science divulgation, Sci.bzaar.net (video here -unfortunately, in Italian only!). Another video with some further ideas, which I produced for the event, is available here.

So how would you run your own blog, if it was aimed at education in physics ?  Would you fact-check every sentence, or maybe remove those you would like to keep but fear could expose your fallacy ? Would you read wikipedia first ? Hell, I do not even spell-check my texts (I recently discovered wordpress does provide an automatic tool for that -but I do not think I am not going to try it), and I am not an English native speaker!

I guess the message of this post is the following: I am not an encyclopedia. I have holes in my education, delusions, misconceptions. I believe I understand things which I actually do not. I am only human, and not one of the most knowledgeable ones. But that really is ok: I do not need to be encyclopedic to run this site. And guess what, I am learning a lot by doing it! And I do not even have to pay attention: by being natural and by speaking my mind, I achieve my goals. This is important when writing a blog in my opinion.

Now, I hope the above facts are appreciated by those who are so glad to pay me a visit now and then…

I was slightly surprised this morning to read the following comment from my friend Kea, after I had answered in slightly provocative terms to the umpteenth comment of some anti-LHC activist promoting the modern-day equivalent of a raid with torches:

Tommaso, to be honest, I am a bit tired of this LHC-safety-case bashing. Even given all the usual reasonable arguments, how sure are you that you have accounted for all your hidden assumptions? I’m a theorist, and the only I thing I know for sure is that NOBODY knows what we’ll see at the LHC.

I wish to paste here my answer to Kea, because I think the heart of the matter must not be mistaken.

I am of course unable to be sure of what the LHC will produce, if black holes or red dragons. But I am sure that the advancement of science calls for boldness in opening doors leading into the unknown. And I am in favor of the small risks the package includes. The question, to me, is not whether the risk is zero or tiny. It is whether we must insist for rationality in our choices or be led by hysteria. And I have my own answer. Therefore I will, sorry, insist in bashing these clowns whenever they pester this site with their oddities.

Now, I am sure Kea agrees with my statement. I think she just wants to communicate that we might end up feigning more confidence than we really possess. After all, it is not so uncommon to find fanatics among scientists too: we are humans. Granted: but fear mongering is to be addressed before we clean up our own home.

UPDATE: on a second thought, there is nothing wrong in principle with raising objections about the LHC or whatever other scientific endeavour, if done respectfully. And following Voltaire, I have to remind myself that I defend the right to speak of those who disagree with me. So I have to offer a partial retractatio: I will not “bash those clowns” as they “pester this site with their oddities”, but rather counter their arguments with rationality. Not forgetting that I want to have my share of fun as I do it

Massimo Passera is an esteemed colleague in Padova. Our Physics department is not very big, but if one is immersed in one’s own work, the activities going on around are easy to overlook. In fact, I only became aware of Massimo’s recent study by checking the ArXiV for recent phenomenological papers -funny, if you think our offices are only a 30 second walk from one another.

I thus asked him to give a short review of the results of his work at the CMS-Padova analysis meeting which I chair monthly with my colleague Ezio Torassa. The analysis he performed has important implications for Higgs searches in CMS, and in general they shed light on the details of electroweak fits that check the internal consistency of the standard model. Massimo kindly agreed, and yesterday he presented his review.

In the first part of this post I gave some sort of background information on the physics of the muon anomaly, at a level which I hoped would keep non-physicist readers alive through the end. That first part now helps me to write a summary of Massimo’s talk in a way which is hopefully both understandable and lightweight. Let us see what I manage below, where I make use of some concepts I explained yesterday.

Massimo started by giving some background information on the measurements of anomalous magnetic moments for leptons. For electrons, the anomaly is measured with exquisite precision, and it provides us with a precise estimate of the fine structure function . The tau anomaly, on the other hand, it is very hard to measure, and so comparisons with theory -which is much more advanced in this case- are not meaningful.

For the muon, the experimental uncertainty has reached down to : here the ball is on the court of theorists, who have to lower the uncertainty on their prediction if they want to challenge the experimental accuracy. Here are the numbers, for reference: experiment E821 finds (PRD73 (2006) 072003); while theory predicts different things depending on the method, as we will discuss below:

The first numbers in the table above are those to which most credit is given nowadays, so one can really talk about a 3.something standard deviation between theory and experiment.

It is to be noted that the muon anomaly, measured so far with the best precision at Brookhaven in a dedicated experiment, could see the experimental uncertainty decrease to (units of will be assumed throughout this post in the following) if a proposed experiment, E969, could see the light. The jury is still out on whether to fund that experiment, or even a more challenging one called “Legacy”, which would bring the error down further.

Theorists are not ready to compare their result with a muon anomaly experimentally determined with the accuracy promised by E969 or Legacy: the reason is that their current estimates have errors in the range of 60 or 70 parts in 10^-11, as shown above (numbers in parenthesis are the uncertainties). And when you compare two numbers, their difference -which ultimately tells us whether they agree or whether it is necessary to hypothesize unforeseen effects that make them different- is plagued with its own uncertainty: if is the difference between experimental and theoretical determination of the anomaly, the error on is simply , the quadratic sum of the two uncertainties. Now, it is easy to see that if one of the two contributions is much larger than the other, there is no gain in decreasing the smaller one.

A numerical example will clarify this point: if and , their difference is : something we address colloquially as “a two-sigma effect”, meaning that the number is different from zero at the level of two standard deviations (40/20=2). Now imagine you halve the error on : your effort will not repay you with much more insight in whether the two numbers differ, because the uncertainty on the difference will go from to , or : your understanding of the value of has progressed by just 10%! Now go back to your funding agent and explain that!

After this introduction on the numbers we have to play with if we are to analyze the status of g-2 in the Standard Model, Massimo gave a short didactical review of the physics of the anomalous magnetic moment. I discussed the matter in the former post, so I will just note here that the issue of g being different from 2 is a problem which is exactly 60 years old: it was Schwinger, in 1947 (but he published in 1948), who first realized that quantum corrections affected its value. Theorists have continued increasing the precision of the their calculation of the anomaly due to quantum electrodynamical (QED) interactions during all this time, and their advancement is spectacular.

The QED contribution to the anomaly is in truth by far the largest, although, as I described yesterday, not the only one. It has been computed to incredible accuracy, up to what is called “four loop” level (diagrams with up to four loops of virtual particles): this is a result that took twenty years to achieve! Imagine sitting on a desk for 20 years, drawing thousands of complicated diagrams and computing them using fixed rules. A unforgiving, maddening task; but not a useless one: the four-loop QED contribution to the muon anomaly is six times larger than the current theoretical uncertainty! Without a complete four-loop computation, the muon anomaly would be utterly useless for our understanding of the Standard Model.

And the four-loop calculation is not the only hard piece as far as QED corrections go: once you fully compute diagrams to a given order, you have to estimate the contribution of the following order. The “five-loop” correction -a slight additive modification to the anomaly which attempts to account for the enormous number of diagrams including five fermion loops- have been estimated with what appears great precision by now. So, the QED part of the theoretical estimate of the muon anomaly is not what worries theorists the most these days: the total QED uncertainty amounts to one part (in 10^11,remember?), or one hundredth of a billionth.

The contribution from exchanges involving electroweak bosons (EW) is small, 195 parts at one loop level. But this has been computed up to two-loops, and it is precisely the first time that electroweak corrections to two-loops have been determined in any subatomic process. Thus, the total contribution to the muon anomaly from EW exchanges has decreased to 154, with an error of two parts only.

Massimo pointed out here that those diagrams are indeed sensitive to the Higgs boson mass -we in fact know that the Higgs does couple strongly to W and Z bosons: but a variation of the Higgs mass from 114 GeV (the lowest value it may have, otherwise LEP would have discovered it already) to 300 GeV changes the electroweak correction to almost imperceptibly -and in fact, these variations are included as systematics in the 2-parts-per-hundred-billions error.

Now, of course, as I was mentioning yesterday, the most problematic contribution is the hadronic one, the one due to QCD diagrams. Even the simplest sub-diagram where a photon fluctuates into hadrons and then returns to be a photon is not calculable with perturbative QCD! That is because the dominant contributions come from the lowest energy circulating in the virtual loop of hadrons: and the lowest the energy, the harder it gets with QCD, since becomes unmanageably large and perturbation series are not meaningful.

So what one does is to take formulas from the ‘60, the so-called optical theorem. This is not something I want to get into, but suffices to say that one uses the measured cross section of (hadrons) at very low energy. It is hard to use those measurements. Unfortunately, their contribution is large to the muon anomaly: 7000 parts! So to match the experimental precision on it has to be known with 1% or better precision, to keep the overall error at 70 parts in 10^-11.

To determine the electron-positron cross section into hadrons, energy scans (beam collisions where the beam energy is varied in small increments to study the dependence of physical processes on the center-of-mass energy) have been made at Novosbirsk. They provide the best input for the hadronic contribution of the muon anomalous magnetic moment. There are other methods: In Frascati the KLOE experiments, which collides electrons and positrons at the energy of creation of the , a 1-GeV resonance, they use events with a “radiative return” to obtain a determination of the hadronic cross section at lower energies. Radiative return means that the electron or positron before colliding emit a real photon, which carries away a sizable fraction of the center-of-mass energy. The collision thus happens at a lower energy, and one may compute the cross section for that value, if -as KLOE- one can measure the outgoing photon energy.

A third method involves studying the hadronic decays of tau leptons, . With some black magic called “isospin rotation” one can transform the decay parameters into a spectral function which… Ok, I leave the details to another time: the bottomline is that this black magic works, but there are subtleties which cast some doubts on this method. In particular, “isospin violations”, i.e. non-perfect conservation of the symmetry called “isospin” may affect the result at the 1% level: just the precision we wanted to achieve.

It is unfortunate that the general consensus appears to be to discard the tau decay estimate of the hadronic contribution: that is because, if one were to use that method to estimate QCD contributions to the muon anomaly, the discrepancy we observe between experiment and theory -a 3.4 standard deviations difference- would almost totally go away! This can be seen by checking the last line in the table I pasted at the beginning of this mile-long post (it is line number 5 in the table).

A final contribution which cannot be estimated because it has never been measured is the so-called “light by light” scattering, shown in the graph on the right: three photons emitted by the muon line connect to a quark loop, the quarks do what strongly interacting particles do (exchange gluons by QCD interactions), and at the end they annihilate, vanishing in a single photon which carries the electromagnetic interaction of the muon. This appears at higher order in the QCD part of the calculation: no perturbative calculations are possible -too low energy-, and this time not even any measurements come to the rescue. So theoretical models are used, and they have a large uncertainty. Suffices to say that the contribution of the light-by-light scattering diagram has changed sign four times in the last twenty years! Nowadays, the sign of the contribution finds physicists in agreement, but its size is of the order of 100 parts: even a large relative uncertainty does not spoil totally the overall calculation of g-2. However, this is ultimately the limitation to our present capability of determining a prediction for the muon anomaly.

Once all is said and done, we have a discrepancy of 300 units between theory and experiment. The light-by-light scattering diagram is too small to be the single source of the disagreement. Other unforeseen QED or EW contributions are unthinkable. So, if we look the experimental measurement at face value, we have two possibilities only: either the difference is due to some new physics -new particles circulating in virtual loops, affecting the muon anomaly- or the hadronic calculation at leading order is wrong.

Massimo explained that this was the starting point of their analysis: what happens in the second case ? Does this error have other consequences that may be visible elsewhere ? We can change g-2 by changing the hadronic contribution, but this has consequences in other observable quantities.

The hadronic contribution we have been discussing with regards to of course also impacts the calculation of the fine structure constant, albeit in a less critical way. The value of -the value of the constant calculated for processes where the relevant energy scale is the large mass of the Z boson- is one crucial input in electroweak global fits to the Standard Model, which as we know have these days the ultimate goal of telling us not only that the Standard Model is alive and well -from the experimental standpoint, of course-, but to suggest what the heck the value of the Higgs boson mass really is.

Massimo showed in detail how a hypothetical modification of the hadronic cross section in different ranges of center-of-mass energy affects the fits. If we impose that the change in cross section “fixes” the discrepant value of the muon g-2 value, bringing it in agreement with the experimental determination, we
modify as shown in the figure below.

In the graph you see that the higher the energy where you modify the hadronic cross section enough to bring agreement in the muon anomaly, the larger the modification you have to make (because, for g-2, lower energies weigh more). This in turn modifies more the value of , the value shown on the y axis.

Now, using the modified values of the fine structure constant, Massimo can perform different global fits to electroweak observables, and obtain in every case a different upper bound (at 95% of confidence level) on the Higgs boson mass. This is shown in the figure below: on the y axis now there’s the allowed range of Higgs masses. The lower bound is experimental and cannot be touched: 114.4 GeV. The upper bound in the unmodified case is 150 GeV according to Massimo’s fits. This, however, gets smaller as we consider modifications to the hadronic cross section in different ranges of center-of-mass energy. Recall that the larger the energy, the more we have to change the cross section to bring g-2 of the muon in agreement with experiment: this is why we get a larger and larger effect on the Higgs mass upper bound.

The plot also shows the upper bound one would get if one assumed the starting value of the hadronic contribution to g-2 as the one obtained from tau hadronic decays: in that case, the discrepancy in g-2 is smaller, so the correction in the estimated hadronic cross section can be smaller, and the effect is milder: the upper limit moves around following the hatched red line in that case. Note, though, that even in the unmodified case the upper bound on the Higgs mass is only 138 GeV, if we accept the tau hadronic “isospin rotation” black magic.

Now, all this is good and fancy, but we have to ask ourself the question: is it realistic to move around the hadronic cross section in a given region of energy by several percents, to bring agreement with g-2 and thus obtain different results for the Higgs ? In other words, do the low-energy electron-positron collider data allow these variations, or are they ruled out by the Novosbirsk determinations ?

This is answered by just another plot, shown below. Here, on the y axis you see the variation you are required to make in the hadronic cross section to fix , while on the x axis you still have the energy bin where you apply it. On each bar, representing a possible modification of y% of the cross section, you can read off the resulting upper bound on the Higgs mass. Massimo warns that the lowest modifications in cross section that are effective are of the order of a few percents, and this is already stretching the experimental results of low-energy electron-positron colliders. However, the study shows that under those circumstances, even forgetting about the tension in low energy data, one would trade the agreement in g-2 with a restricted range for the mass values of the Higgs boson, down to levels where the Higgs may live only in a very small region of parameter space.

In conclusion, the enlightening seminar by Massimo Passera taught me quite a few things. The 3.4 standard deviation between theory and experiment in the value of may be a signal of new physics or a problem in hadronic cross sections. Which is more likely ? If you’ve read this blog long enough, you know
my very own, personal answer.