A Quantum Diaries Survivor

I am not qualified to write a detailed post on this but, good lord, the latest verbal hemorrage of pope Ratzinger leaves me bewildered and nauseated. And stimulates an insolent post. 

I will be brief: I sure do not intend to read all the 77 pages of his enciclica “spe salvi” to discuss it here. I just mention a few sentences I found reported on today’s newspapers in Italy. Atheism has caused “the greatest cruelty and violations of justice”, according to Nazinger. Illuminism is a failed hope. Progress may lead to abysses of evil.

Sure, I am biased. I am uninformed, my theology is not up-to-date, and I’m stuck with Religion 111, which I never really digested. But I can smell a Rat when it’s on my desk. Progress is dangerous ? It sure is, like life itself on this planet ridden with wars declared in the name of gods. Atheism caused cruelties ? The purposeless cruelties of the christian crusaders have nothing to envy to what came after them, and actually set the tune for a millennium of hatred between different ethnicities. Nothing can save us, as beings and as a race. Progress, however, has the potential to improve our lives. God could save us if she existed, but she never did, and if there was one, she is long dead now.

1. The United States does not torture. That is stuff for fascist sudamerican countries, and of course the US are above that.
2. It is in principle possible to store large amounts of greenhouse gases underground, and possibly fight successfully the global warming threats our world is facing.
3. Forza Italia, Silvio Berlusconi’s party, will not be terminated, as he had previously announced, but will constitute the basis of a new movement. Repubblica reports that Silvio appears still unsure on the name of the new political entity which will gradually substitute FI.  The man is for sure a bit more lazy with restyling than with liftings, but he is catching up. This weekend he announces a poll in all italian cities, where the name of the party will be chosen. Here the three choices he mentioned:
   1. “Popolo delle libertà”.
   2. “Partito del popolo delle libertà”.
   3. “Partito del popolo italiano delle libertà”. No kidding. I wonder if one can instead chose something more descriptive, like the bold “Partito italiano libero del libero popolo partitico italiano della libertà”, or something similarly easy and catchy. Should be fun to see people amassing at the poll booths for such a crucial step in the final crowning of italian democracy.
4. Homeopathy is losing ground, and will soon be confined to its place in the shelves of pseudosciences. New evidence and a critical review of past results (also published on the prestigious The Lancet)  shows that the vast majority of double blind tests with placebos confirm what many had known for decades: it is a scam! Nyaah nyaah!

After overwhelming requests, I hereby make available the slides of yesterday’s lecture on the web. Beware: they are in italian, they are probably inaccurate here and there, they have not been proofread, and finally, they are nothing special… But here you go: they are viewable online here.

Actually, since it is a single file, you also get to see -in world premiere- the slides of the second lecture, which I will give tomorrow. In case you should find some blatant mistake or nagging inaccuracy, please let me know today before 10PM UT. Thank you.

UPDATE: I was asked to provide a file readily downloadable. Get it here.

Today was the first day of my course in subnuclear physics in Padova. I had given similar lectures in the past -to PhD students, both in Padova and in Catania- but I felt more responsibility this time, partly because I was going to discuss basic concepts of particle physics to students that had not had prior exposure to them.

The lecture I gave today was about the need for gauge symmetries, the lagrangian formalism for scalar and fermion fields, the issue of endowing with mass the bosons mediating weak interactions, and the connected problems of divergences and renormalizability. It was a fairly theoretical discussion, although I tried to give as much experimental perspective as I could to the various issues treated. I tried to make it quite clear just why one needs to insist that a lagrangian function retain local gauge invariance, and on the other hand why it is mandatory to add terms that at first glance spoil the invariance. I spent some time also describing the connection between observed and only hypothesized weak processes, their divergent behavior, the need for neutral vector bosons, and the resulting predictions of the GSW theory. The next lesson will start with the Higgs mechanism.

I was a bit worried before the lecture - I usually keep a cool mind in such occasions, but admittedly my knowledge of the theoretical nuisances below the surface of the simplified treatment I offered  in the lecture is not very deep. What worried me was not the chance of incurring in a tough question I was unable to answer - I have no trouble admitting my ignorance if that is the case- so much as the risk of embarking in a discussion of details which I would have explained in a less than satisfactory, inaccurate way: the responsibility of writing garbled physics concepts on the clean slates of my students’ minds. I have to admit I did not sleep well last night: but I prefer to ascribe that to my jetlag, and to Ilaria’s contribution -she woke everybody up at 4 in the morning with symptoms of a flu.

I did well. I recorded myself, and later analyzed the recording by noticing how much time I had spent on several topics, how repetitive I had been on some issues, and how clearly I had expressed the most important concepts. Overall I am mildly satisfied with the result. One thing I noticed, though, is that I have a mannerism in my speech, which consists in interspersing a sound like “errrr…” between sentences when I am thinking at what to say. I should just silence myself during those short, 1-second intervals. I will be working at that in the next lectures… Room for improvement there.

The next lesson will be the hardest for me, since the full theoretical formalism of the Standard Model will be explained in its details, and I will take care to derive a few important consequences for vector boson and Higgs phenomenology, and the shortcomings of the theory. From then on, I will start delving with the phenomenology of Higgs production and decay at colliders, things on which it will be much easier for me to produce a decent lecture. Following that, I will discuss top quark physics and other topics in hadron collider physics at the Tevatron and the LHC. I believe my students will also be happier with the latter part of the course…

Banks -at least in Italy- are little short than criminal associations. They offer a poor service to private customers, and in exchange they get to steal money from their accounts every time they have a chance - by changing the rules of the account, lowering the interest rate every other day, charging fees for anything conceivable, delaying the crediting of bank deposits, and in a number of other ways. As a private citizen it is really hard to defend from these practices, but one cannot live with no bank account these days, so each of us soon learns to accept the abuse and bow his or her head. The robbery, although nasty, is usually on small change, and one can well ignore its effect on one’s own pockets, although it is hard to swallow the abuse.

In addition to these practices, one sometimes gets to touch with one’s own hand the total disdain of the bank for their clients’ interest. Just to mention one case, last year Deutsche Bank deduced from my account more than 3000 euros, leaving me with a negative balance - and without a warning!, because INPS, a government institute that used to pay the retirement salary to my father, had fallaciously requested a refund (we did not owe them a cent). The bank paid the sum without letting me know, as if I had signed a blank check! It was only through threatening a legal action that they agreed to refund me without waiting the government to acknowledge the mistake.

While they act this way with their less important customers, banks use to grant huge loans to industries and businesses with ridiculous warranties in return, often getting the worst of it when their credits cannot be recovered. If you are asking for a loan they will turn you down, unless it is a seven digit one. In Italy we sure have mafia and camorra, but much worse is the delinquent link between politicians, bankers, and businessmen which is emerging only recently through bankruptcy cases much like what has been happening in the US a few years ago.

For a serene life it is better to ignore this annoying reality. However, if one ever has a chance to get revenge, one should take it fully and make sure to enjoy every bit of it. That is what luckily happened to me very recently.

I have a loan from Deutsche Bank, where I have had a bank account for the last fifteen years. I got it three years ago when I remodeled my new house: 200,000 euros - little short of 300 grands-, to be given back in 20 years. Getting a loan was a sound thing to do back then, when interest rates were very low. However, the latter have since almost doubled, and the loan is now costing us more money than we find reasonable. I was able to reduce the amount of the debt to 100,000 euros recently by making a partial refund with some money that had poured on my head in the meantime, and then started to investigate whether a renegotiation of the loan with other banks would allow a reduction of the interest rate.

I soon discovered that Unicredit -another pond full of sharks, so to speak- would reduce by 0.3 percentage points the interest with respect to my original loan; a friend of mine works there, and he explained to me things the way they are, with no frills and fine prints. The conditions were favorable, so I made a phone call and told Deutsche Bank I was going to close the account with them, leave them for good, and transfer the loan, unless they would lower the interest rate: could they please make their best offer ? They could, and they would call me back.

They answered after three weeks of silence, calling me on the phone to say they could reduce the interest rate by 0.1% -as if they were doing me a great favor. I answered bluntly: fine, I found another bank which lowers it by two more points, so I will be happy to close everything in a few months, just give me the time. After that phone call they waited much less time to call again: a week later they called me again to announce they had been authorized to lower the rate by 0.3%, matching the offer of the other bank. I then said, fine: I would face some expenses if I transferred everything to Unicredit, so I will stay.

But the devil is always in the details: I soon learned that to change the interest rate Deutsche Bank would require a formal intervention of a notary, which would cost me 600 euros. That upset me since I knew other banks do not require that, and allow the modification to be described in a private document that is exchanged between the bank and the client. I requested the bank to check whether they could waive the fomal act through the notary, and the vice-director agreed to try it.

I went to visit the vice-director a couple of weeks ago, and got the news that my request had been turned down, because “the bank has to make things correct formally, to reduce its risks”. That made me snap. I said I was fed up with them and their politics of feeding notaries by forcing their clients to spend inordinate amounts of money to register even the most insignificant agreement. I said that it was up to them to decide whether they wanted one client more or one client less, and that I found outrageous their bullying the less wealthy customers while they bowed to every wink of larger businesses. I said plainly what I thought of the bank and its practices: misdemeanor was an euphemism. I said that forcing a client to throw away 600 euros in a useless piece of paper was a tell-tale sign of how little they cared for their customers’ interest. The vice-director and his colleague had to listen to it all, and could not even reply - they knew I was right.

At the end of my tirade I gave them an ultimatum: either they accepted to renegotiate the loan with no notary act, or I’d wave bye bye. The vice-director then said he would check again with the central offices, but he had to say he would in earnest hope the request would be declined again, because otherwise he would feel quite embarassed. I replied I could not care less, and left. Behind the polite mannerism and the slightly shaded eyeglasses, I could feel the irritation in the vice-director’s eyes.

Last night, I was waken up by his call. He did not know I was in Chicago and expressed his excuses for disturbing me in the middle of the night, but he was pleased to announce that the central offices of Deutsche Bank in Milano had agreed to waive the notary act. I was sorry for the guy, torn between sharks and angry customers.

So, in the end I got what I wanted: a lower interest rate, and no further expenses. And in the meantime I was able to dump all my anger and disgust at the way banks behave with customers, in an occasion when they could not help but listening to me. Admittedly a redundancy, but a very sweet one. This only confirms what I have known for a while: banks (and insurance companies, I may add) are weak with the strong, and strong with the weak. Just put your balls on the table with them and you’ll see their tail immediately hide between their legs.

4 -Searches for the top quark: the techniques 

I left the discussion of top quark history in the last post of this series by mentioning that among the three basic strategies for producing new massive particles - and thus search for the top quark, the massive isospin partner of the bottom quark found by Lederman and collaborators in 1977 - the one that was going to win the house was soon recognized to be the same one that had bagged the W and Z boson discoveries at CERN: colliding a intense, high energy proton beam against a beam of antiprotons traveling in the opposite direction within the same vacuum chamber, and bent and kicked by the same electromagnetic field.

That does not mean that electron-positron colliders did not attempt at producing pairs of top quarks: they did, in fact, but only were able to report the failure to observe the production of two heavy quarks, which would produce an increase in the R ratio (see the discussion in the former post of this series), some spectacular resonances, and a more spherical distribution of hadrons in the detector. The latter signature is due to the large mass of the produced quark, which can impart high energy to all the bodies it decays into - and thus allow them to deviate from the original flying direction of the parent particle.

And in fact, the UA1 and UA2 experiments at CERN 546 GeV (later 630 GeV) proton-antiproton collider took the challenge quite seriously: not satiated with the weak bosons - which would soon fruit Carlo Rubbia and Simon Van der Meer a Nobel prize - they wanted to put their hands on the top quark. And they indeed could have, had the top mass been lower.

What happens if the top quark has a mass of, say, 50 GeV ? At a proton-antiproton collider you can produce top quarks in pairs by strong interactions - and that is exactly how it is done at the Tevatron these days, roughly once every hour during data taking- but if the sum of top and bottom quark masses are lower than 80 GeV, an enticing new possibility arises: electroweak production of a W boson, followed by a decay into a top-antibottom pair. The energy balance allows the W to decay into top quarks, and in subatomic physics everything that is not forbidden is compulsory, as I mentioned earlier.

In the plot on the right - a vintage one, in fact - you can see the then still fairly uncertainty prediction for the top quark cross section at the Tevatron (top curves) and at the SppS collider (bottom curves) as a function of the top quark mass. The sudden decrease as the 80 GeV mass is reached is due to the strong suppression of electroweak single top production by W decay at about that mass value. The lower of each two sets for top masses below 80 GeV represents the contribution to the cross section of the pair production process alone.

So what would the CERN experiments expect to see from a 50 GeV top? Well, typically a lepton, missing transverse energy from an escaping neutrino, and two hadronic jets from the two remaining b-quarks: something like  , where we assumed the top decayed semileptonically, and X denotes whatever else the two incoming hadrons fragmented into. A signature like that is sought nowadays at the Tevatron in the study of single top production, in fact: a single top is produced by electroweak interaction.

The UA1 experiment in fact did see the above signature, and from the observed 12 events claimed discovery of the top quark in 1984! They had predicted to see 3.5 events in their dataset due to background sources (mainly due to W production accompanied by QCD radiation), and 12 events looked like a signal: from it they could also measure a top quark mass of ! Unfortunately, the roads of particle physics are paved with tombstones of 3-sigma effects, fluctuations, unexplained effets. These invariably go away after more data is collected, and so it happened with UA1. UA2, the competitor experiment, could not confirm the discovery, and a few years later, it set the highest lower limit on top mass at 69 GeV (1990).

What had happened to UA1 then ? It so happened that QCD, the theory of strong interactions, dictating the phenomenology of interactions between quarks and gluons, was already a well-tested, mature theory, but its description by Monte Carlo simulations and models was not perfect yet. Physicists need simulations of the subatomic processes  in their detectors, in order to estimate backgrounds when searching for a signal - and that was the weak link of the chain of deductions that had led UA1 to broadcast the false claim. W production occurred way more often in association with hadronic jets than predicted by simulations, and so it had been heavily underestimated.

The top mass was soon realized to be higher than 77 (1990) and then 91 GeV (1992) when the CDF experiment published their analysis of the first 4 inverse picobarns of collisions collected between1988 and 1989. That simply meant that the top quark could not be produced copiously by W decay. That process was kinematically forbidden unless the W was strongly “off-mass-shell”, that is if it was produced with an unusually large mass. The business of discovering a top quark was harder than earlier thought, because not only the quark was heavy - and thus more rarely produced in the collisions (the cross section dependence on the mass has been shown in the plot above)- but it was to be produced in pairs, and so with a doubled effort. A task to be left to the upgraded CDF detector and its competitor, D0, in the run foreseen for 1992….

A final candy: the plot below shows a very interesting feature of W decay. The W boson has a total width of about 2.1 GeV. That means it decays “quite quickly” - in a trillionth of a trillionth of a second, more or less. More interesting is to note that the W is “democratic” in its decay: it generates an electron-electron neutrino pair once every nine times, and with the same frequency a $\mu \nu_\mu$ pair or a  pair; the other six out of nine decays are shared evenly between the three and the three $c \bar s$ quark pairs (remember, quarks are colored and they come in three colors!). So physicists talk about the “partial width” of W decay into one specific final state. Now, in the presence of a light top quark, the latter would claim its right to be generated in W decays as well, and each of the possible pairs would then have to be content with a 12th of the total share, there being now three more quark pairs allowed, the $t \bar b$ ones. By measuring the partial width of W decay into leptons, one can thus determine if the W does also decay to top quarks!

This exceptionally simple result was however obtained only later, when a very precise determination of the partial widths of W decay were possible with the large Tevatron data. The plot shows the ratio between total W width and partial width to electron-neutrino pairs (the black curve  turning down to a constant) as a function of the top quark mass. The CDF measurement (bottom horizontal line with hatched 1-sigma region) implies that the W width is shared in nine equal parts, and the top must be heavier than about 62 GeV at 95% confidence level. (Also note the curved structure of the dependence of the inverse partial width in the standard model, due to the “turning off” of the decay which becomes progressively kinematically forbidden as the top mass becomes closer to the W mass).

[To be continued...]

“If I have seen further than others, it is because I was standing in between the shoulders of dwarfs.”

 S.Coleman (via Betsy Devine)

The CDF control room is the place where the detector is operated during data taking. It is a place full of monitors of all kinds, with notices and instructions posted all over to make sure the shift crew knows how to handle every part of the system. This serious business does not prevent some humor from springing up here and there. Look at the picture below, which shows two members of my shift crew today taking care of a problem:

In the background you can see the notice reproduced enlarged below:

The notice just warns in a friendly way the crew to be precise in their log-book entries - something which is very difficult to teach people to do. The names of collaborators who handle any problem worth mentioning in the CDF electronic logbook are needed to trace back any further issues more promptly. Of course, within a large collaboration it is not always easy to keep track of everybody’s name. I find the task one of the most complex among my shift duties.

For a change (or is it) let me write about personal issues, i.e., about what I have been doing this week. I have been in the US for four days only, but it looks like a long time already… And I need a post of the kind “dear diary” to sort things out.

I arrived to O’Hare last Thursday at noon after a uneventful flight - the same route through Munich I’ve flown three dozen times in the last few years. This time I found some company in a colleague who was going to attend the workshop Peter mentioned the other day - we met on the lounge in Venice and traveled together.

Thursday was spent cursing myself for missing a toll on I-88 while driving out of the airport towards Fermilab. It so upsets me to have to lose time for silly things! I soon learned I could pay over the internet the .80$ toll charge, but once I went through the instructions I realized the procedure only works for US residents. I then proceeded to pretend I lived here, but got stuck at the last page of the web interface because my credit cards have an italian billing address and got refused. I then tried my american VISA debit card, and that one got refused too. At that point, after almost 40 minutes wrestling with the site and at the peak of frustration, I found out that my US account was blocked for inactivity - and 6 dollars a month had been charged by the kind people at CHASE because of that. I then proceeded to call the tollway office, but they told me I could not pay with a card, and I would have to send in the credit card information. However, sending a simple letter may become a difficult task if you have no stamps and you work day shifts from 8AM to 4PM every day.

On Friday I took service as a Scientific Coordinator in the CDF control room. The accelerator works 24/7 and each experiment has to provide three shift crews a day to attend data taking and care for our detector. I arrived impeccably on time, at 7.55, only to find frowned people staring at me, and I soon realized that on the first day of shift the incoming SciCo has to be there one hour earlier, to overlap with the one that did the owl shift and refresh his or her training.

Disappointing people is not an activity I particularly enjoy, but I soon forgot the incident as I started to sort out what I did not remember about the procedures I had to refresh. However, my attention was distracted by repeated attempts at finding out whether Mia, who had taken the written test for admission to PhD courses in Padova that same day, had done a good exam or not. I would only hear from her on Monday (! students have lost all their respect to their mentors, apparently), and fortunately she did pass the exam! So if all goes well at the oral test, I will enjoy her company doing research together in CMS for the next three years!

Friday evening was spent in a very uncommon way. I visited a person I had never met before, and with whom I had only played a game or two in an internet Bridge site. This lady was the late Riqie Arneberg’s best friend, and I intended to meet her to hear Riqie’s story from her. We spent a lovely evening together, and we remembered Riqie. I think Riqie would be jealous if she knew - I know our mail and blog comment exchanges and our bridge games made her very happy, and I had promised her I would visit her next time I’d come to the US. Sadly, I could only fulfil virtually that promise, by spending the evening with the last person who saw her alive.

Oh, and I finally saw a few pictures of Riqie. What an interesting person she must have been. She had a tragic life, and she died quite young, but you could see the wit in her eyes from afar. I will collect in another post a few things she wrote in my blog, and if I find it in the wayback machine I will dig out her own blog, which she discontinued about a year ago due to a hacker attack.

Saturday was uneventful, but yesterday I had another very nice evening. I drove to north Chicago, picked up Vincent and Jadwiga - two dear friends of mine, an elderly couple who lives in a very nice apartment overlooking the lake on the north lakefront. I’ve talked about them elsewhere. We had a dinner in Evanston and then attended a chamber music concert by the Chicago Chamber Musicians. Here is the program:

• Richard Strauss, Till Eulenspiegel, Op. 28 (arr. Hasenohrl):
  • Larry Combs, clarinet
  • Gail Williams, horn
  • Jasmine Lin, violin
  • Peter Lloyd, double bass
• Franz Schubert, Fantasy for Violin and Piano in C major, Op. 159 (D.934):
  • Joseph Genualdi, violin
  • Alan Chow, piano
• Dana Wilson, Shallow Streams, Deep Rivers - world premiere
  • Gail Williams, horn
  • Joseph Genualdi, violin
  • Alan Chow, piano
• Ludwig van Beethoven, String Quartet in F Major, Op. 59, n.1 (Razumovsky):
  • Jasmine Lin, violin
  • Joseph Genualdi, violin
  • Rami Solomonow, viola
  • Katinka Kleijn, cello

I especially enjoyed the new piece by Dana Wilson (who presented the piece himself). What a great composition! The three instruments fought at the beginning, retaining their own personality, to later merge perfectly into a single deeper stream of music. A very melodic piece, surprisingly balanced despite the presence of the horn.

And today was a really positive day for me. Because of the news about Mia which I already mentioned, and because I got good news about a friend of mine who is being treated with liver cancer and who feared his liver was not going to allow more radiation therapy. Instead, his doctor confirmed his bilirubin is within limits, which allows him to be treated with a third injection of radioactive microspheres in the liver artery, and there are good chances that the tumor will recede.

Life goes on. When one touches with one’s hand the fragility of human life, things get back in their place and the view is restored to a more meaningful perspective - we do not care too much any longer about the insolence of office or other silly incidents. I myself have recently been diagnosed with a relapsing carcinoma, but it does not seem a life-threatening condition - I hope. As soon as I get back to Italy I will be summoned to remove it surgically. After which, I will shrug my shoulders again and pretend to forget about my own vulnerability - something human beings have learned to do a bit too well. 

My non-physicist readers will excuse me if this post is above their head… I intend to explain the matter in a more readable way very soon… 

In the process of writing about the need for the top quark in the Standard Model,  it occurred to me yesterday that the need for a renormalizable theory of subnuclear interactions - which implies the absence of axial-vector-vector anomalies, and thus a cancellation of all electric charges of the matter fields of the theory - could be combined with the requirement of the existence of charged currents among these fields imposed by the group structure of electroweak interactions, to yield more or less a priori requirements on the number of colors in quantum chromodynamics, the theory of strong interactions which keep atomic nuclei together. Here is an excerpt:

[...]if you were some deity and you were constructing the standard model from scratch, one could argue you would care for renormalizability - it would allow you to compute stuff in a simple mathematical framework. Then, having introduced doublets of quarks and leptons -you need both to construct molecular structures-, you would be facing the choice on the number of colors of quarks (which you need in order to provide stability to nuclear matter, as well as to satisfy the antisymmetric form of the total wavefunction of baryons) and the simultaneous choice of their electric charge.  These are bound to satisfy the rule in order to cancel axial-vector-vector anomalies, as well as the requirement that (so that W bosons allow charged current interactions between quarks as well as leptons). You would be hard pressed to choose any different from three if you wanted to build integer-charge mesons and baryons from and states! That follows from the fact that the two relations above imply . [...] If you know some literature on the topic of building a consistent, alternative version of the SM with different quark charges, I would be glad to get a reference [...]

Well, a blog is a wonderful thing, because it sometimes fulfils your wishes! In fact, I was extremely pleased by receiving today an answer to my prayer by a distinguished professor in Stony Brook, Robert Shrock. I was even more pleased to read that the question I had posed to myself was by no means a silly one. Here is Robert’s answer:

Let me respond to your question about quark charges as a function of . It is certainly true that is special. The condition for the cancellation of anomalies in gauged currents in the standard model is

where denotes weak isospin, and and denote the left-handed quark and lepton doublets (with notation for the first generation, but the relation holds, of course, for each generation). This yields the relations (e.g., see eqs. (2.15), (2.16) in my paper R. Shrock, Phys. Rev. D53, 6465 (1996) (hep-ph/9512430)):

In general, one may consider lepton charges different from the usual ones, which leads to a general set of several classes of quark charges, as displayed in Table 1 of that paper. Note that the relation is independent of and only depends on the gauge structure with the relation and the electroweak representation content of the fermions. In section VIII of the paper I discussed some of the phenomenological properties of theories with the various classes of quark charges. For example, for , if one required the usual lepton charges, then , and baryons would be composed of 5 quarks. The proton-like and neutron-like baryons would be given by eqs. (8.3), (8.4), namely and with their usual charges, eqs. (8.5) and (8.6).

The value is also special for the idea of grand unification. If one constructs a grand unified theory based on an SO(N) group with , , then the condition that the SM fermions of a given generation (including an electroweak-singlet neutrino) fit exactly into a spinor representation is (see eq. (9.7))

which has a solution only for .

Interestingly, if one considers the -extended standard model and studies possible embeddings in a (supersymmetric) GUT, then imposing the conditions of unbroken electromagnetic gauge invariance, asymptotic freedom of color, and three generations of quarks and leptons forces one to choose . See my recent paper ArXiv:0704.3464, published as Phys. Rev. D76, 055010 (2007).

I am writing this now, but I am feeling guilty, because I should be reading those papers first! The fact is, I want to give them more attention than what I can deserve to them in the control room of the CDF experiment, which is where I am now, with an eye on the keyboard and another on the monitors of the beam, the data taking efficiency, the silicon bias voltages…  And I wanted to give my readers access to those papers as well. So let’s all read about it and get educated on this fascinating issue - I think I will twist Robert’s arm into making a guest post on the matter here!