## Thursday, May 05, 2005

### Yuval & B-physics

Yuval Grossman who is with us right now - but who is otherwise affiliated with Technion and now also with Boston University - made a very good job in defending B-physics. Note that "B" stands for "bottom" or "beauty" and it is the second heaviest quark.

Why do we pay for B-physics?

Because it's the right way to test flavor physics, he argues. Well, then the next natural question is why not T-physics, C-physics, S-physics, D-physics, and U-physics. Yuval answered all these questions. For example, we do not produce too many tops so far - tens or hundreds, and it will jump by a factor of ten at the LHC. There are other problems with the charm quarks, while the u,d,s quarks are viewed as "known".

B-physics is (together with K-physics) a precision science that can be used to argue for new physics indirectly, and I will explain some numbers at the bottom of the text.

It costs a quarter to produce a B today. Another thing that Yuval had to explain is: Why do we need two B-factories instead of one? One of them is in Japan (at KEK) while the other is in California (at SLAC). The answer is that you always want to check things and replicate everything at two places. When Yuval was asked whether we also want to build two LHCs, the answer was "almost yes" - we will have two detectors (ATLAS, CMS) that will compete, and it is always a better approach to build two detectors than one better detector. Well, there will be two more detectors to be built at the LHC - ALICE and LHC-B which is gonna test B-physics.

Yuval continued with "orientation". He explained all the bound states of the b-quark and b-antiquark - B0, B0bar (with the down quark and antiquark, respectively), B+ (with up-quark), Bs (with strange quark) - these are the mesons and heavier relatives of the pion (mesons are quark-antiquark bound states; those without bars contain an anti-b-quark) - and then the less interesting baryons with a single B.

The Upsilon (with "b" and "b-bar") has played a less important role, but he was still producing it from "e+ e-" scattering at a resonant energy.

Every acceptable physics talk today must apparently refer to the anthropic principle. So Yuval explained that the mass of the lightest B meson is 5280 MeV, where 5280 is the number of feet in a mile. Because a mile is an American length unit and both feet as well as America are necessary for intelligent life, the mass of the B meson had to be exactly this number and billions of dollars for B-physics are necessary for intelligent life, too. Because in the context of the anthropic reasoning it is often unclear what is meant seriously and what is a joke, let me mention that I believe that this particular comment about the number 5280 was a joke. Maybe.

Yuval then discussed experiments that have three stages:
• produce many B's
• trigger
• tag
He mentioned that the worst enemy of all the people who study B-physics is QCD. And I hope that both Betsy as well as David will have understanding for this statement - in light of Yuval's scary 30% uncertainties of various decay rates and so forth (the worst uncertainties are, of course, connected with non-perturbative QCD and the uncertainty which quark inside a hadron is really responsible for the decay). He explained why we want to create B's moving and not at rest - which requires asymmetric colliders with different energies of the positron and the electron (3 GeV vs. 9 GeV). It's because we want to create a moving B, because when it decays at two points, the distance in between them can be used to determine the oscillations.

Yuval explained that one can get information about one "b" from the "anti-b" that went in the opposite direction because they're entangled, and he mentioned that the B-factories have been using the EPR phenomenon as a standard identification tool for decades while the people in quantum information and atomic physics pretend that it is extremely original and revolutionary to measure the EPR phenomenon experimentally.

The oscillation rate of B0 to B0bar used to be a big surprise decades ago, but today it's standard physics that is used for calibration purposes and the frequency is known quite well. In the case of B-physics, we are very lucky because the oscillations are almost as fast as the decay of the B's (the ratio is 0.73, and I forgot which way), which is very good for measurements. Similar mesons constructed from other quarks have corresponding ratios that are much smaller or much bigger than one which causes problems.

Yuval also discussed theory. He explained basics about the CKM U(3) matrix (transforming the mass eigenstates of the u,c,t quarks to the SU(2) partners of the mass eigenstates of the d,s,b quarks) with the three CP-conserving angles and a CP-violating phase, and the triangle presentation of its parameters. For the matrix to be unitary, the following sum must vanish:
• sum_{i=u,c,t} V_{bi} V*_{di}
Note that it is a sum of three complex numbers. You can draw them as vectors in the complex plane, and because they sum to zero, you obtain a closed triangle. This picture is used to test the consistency of the Standard Model: first 4 measurements are used to determine the 4 parameters of the CKM matrix and the remaining (N-4) experiments are consistency checks.

Note that if the CP-violating phase were zero, the three terms above would be real and the triangle would collapse into a degenerate line (two of its angles would be zero). Yuval has also explained why we choose the orthogonality between the b-row and the d-row - the pairs of rows involving the s-row lead to nearly degenerate triangles while the orthogonality of the columns associated with the upper u,c,t quarks is hard to measure.

There have been many details that I don't want to repeat right now - how the different B mesons decay; what are the rates; which processes violate CP and how they're measured; how precisely can we measure various decay rates; how does the box diagram induce the oscillations of B0 into B0bar; which processes in the MSSM can induce the dimensions 6 flavor violating operators such as
• lambda . (d sbar) (d sbar) / Lambda^2.
Well, the exchange of a sbottom squark is an example. I should have written it at the beginning, but the existence of these problematic flavor changing processes is strongly constrained by experiments. For "lambda" of order one, it is known that the energy scale "Lambda" in the interaction above must be at least 10^{4} TeV. Detailed SUSY models have problems and "universality" (of flavors) and R-parity are the principles that improve the situation.

Note that 10^{4} TeV is a pretty large energy scale that you indirectly test if you study B-physics. The previous sentence should be, however, understood in analogy with the statement that by observing neutrino oscillations, we study the GUT scale physics at 10^{16} GeV. The information is very indirect.

There are several 2-sigma apparent discrepancies known, and most of them will go away. Some of those discrepancies can grow to 3 sigma and higher, but we don't know which ones. Finally, honestly, let me guess that they won't find any deviation from the Standard Model, and if they will, it won't really be clear what is the source.

1. Lubos:

The 5280 MeV figure, just like the rest of elementary particle masses, are easily explained in GUITAR, which accept a fundamental mass unit which is exactly equal to the electron mass divided by the big alpha, i.e., 137.03599911 times the electron mass of 0.511 MeV.

The Botton quark mass is simply expressed in integer form as:

Mb = 3 * 4*PI * M0

Not convinced? Pull a calculator and try it. The discrepancy from 5280 MeV is only 0.004%. And that's purely due to the measurement error of the 5280 MeV figure.

It is not yet completely clear why Mb = 3*4*PI. But that is definitely the correct relationship, not a conincidence.

Quantoken

2. Lubos:

In case you still haven't figured it out: The precise non-perturbative definition of M-theory and the way it gives rise to the unique vacuum we live in is easily explained by VIOLIN.

The sense of life, on the other hand, is concisely summarized in PIANO.

I dare you to figure it out in 2 minutes, since it took me just 1:30.

3. Lubos:

In case you still haven't figured it out: The precise non-perturbative definition of M-theory and the way it gives rise to the unique vacuum we live in is easily explained by VIOLIN.

The sense of life, on the other hand, is concisely summarized in PIANO.

I dare you to figure it out in 2 minutes, since it took me just 1:30.

4. I should be happier if someone can explain me why there are 5280 feet in an mile. I suppose you should have some smaller unit of length amounting to 440 feet, do you?

Classically :-) a mile, 1000 steps, is taken to be 8 stadium. One stadium is the length of the Olimpian Stadium, as kept in Athenas (and buried somewhere at Olimpia).

5. Dear Leucipo,

it just happens that there are 3 feet in a yard, which is almost a meter, and 1760 yards in a mile, which gives 5280 feet. Miracle?

Best
Lubos

6. Lubos said:
"it just happens that there are 3 feet in a yard, which is almost a meter, and 1760 yards in a mile, which gives 5280 feet. Miracle?"

No not a miracle. It's anthropic principle :-) If Ancient Europeans had not defined a mile the way it was defined, we would not be wondering today where the 5280 came from.

But B_Quark_Mass = 3*4*PI*Electron_Mass/ALPHA

That is really a miracle that has nothing to do with human unit sets. And only GUITAR gave an explanation of the coincidence.

Quantoken

7. Leucipo said:
"Classically :-) a mile, 1000 steps"

I guess it's got to be a small step for Leucipo, a giant leap for mankind. I do not think I can walk one mile in just 1000 steps, unless I am making giant leaps :-)

Quantoken

8. Quantoken, I also need a time to realise that a latin "step" was supposed to be a complete 'one-two' or left foot + right foot sequence. This is, the sequence of two 'chiral' steps, so after the move you are in the same position that at the start, but about 1.5 meters forward.

Interestingly, road engineers already had a counting device to measure miles. It was based in the mechanism you can currently observe in buble-gum machines, where a wheel turns and as a consequence a small sphere is served.

9. "it just happens that there are 3 feet in a yard, which is almost a meter, and 1760 yards in a mile, which gives 5280 feet. Miracle?"

I would say Miracle, yep. 1760 is
11*5*2^5. No decent unit system would use a factor 11 relating two units, it makes the calculations terribly ugly. Even the factor 5, that we use in our modern powers-of-ten system, was not easy to implement (British resisted to it bravely, sticking to their powers-of-12 system for monetary calculations).

As for the yard, it is a 12-based subunit. In fact the double-yard was also a very common unit in Spain (yard="vara", doubleyard="caña"). N

According the internet (hmm...) the conversion factor is implemented using a cricket pitch! A cricket pitch (chain), is 1/10 of 1 stadium (english furlong, a horse race unit. I believe to remember it is also a work-related unit: field to be ploughed in one day).

So we have:
"Sport/work/militaty units", based on multiples of 2 and 5

1 mile = 8 stadium or furlongs
1 furlong= 10 cricket pitches or chains
1 chain = 4 poles

"trading units", on multiples of 2 and 3
12 lines = 1 inch
12 inches = 1 foot
3 feet = 1 yard
12 feet = ???

And both systems of units are joined in the imperial system with the conversion factor, declared exact:
22 yards = 1 chain

It is not rare to declare exact a factor. In the International System, c is declared exact.

10. Leucipo said:
"It is not rare to declare exact a factor. In the International System, c is declared exact."

C has to be exactly because fundamentally C is a ruler you use to make spacetime measurements. If C is not constant we don't even know how to construct a ruler to measure distance. All physical rulers you can construct, whether it is metal or wood or any material, rely on the gap between atoms remain roughly constant. And that atomic gap is proportional to the Bohr Radius, which boils down to hbar*C/(alpha*Me*C^2). The denorminator is the energy equivalent of electron mass times alpha, and the anominator ceratin contains a C.

Clearly, here, three natural rulers are needed to make measurements: hbar, C, and electro mass. If any of three is missing, or is not constant, you can't even have a constant bohr radius, and you will be unable to make any physical ruler of any material.

In GUITAR, the third ruler is taken to be the electron mass-energy divided by alpha, because the electron mass-energy itself is proportional to alpha. And that's because a bigger alpha, meaning stronger EM interaction, would have meant heavier electrons.

As for the 1760 figure. It's purely because mile and foot had two unrelated origin. The foot was correlated to the size of the feet of a particular British King, but mile probably did not have something to do with that. So the tatio number probably originated as something like 1759.87354436546 or sort of thing. And later purely for convenience it became 1760. So the fact 1760 contains a 11 is a pure coincidence. Had the kind be over weight a bit it might have been 1759 :-)

Quantoken