## A QCD measurement and why you should care about it August 25, 2008

Posted by dorigo in news, physics, science.
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Quantum ChromoDynamics, the theory of strong interactions, is admittedly not considered the most exciting branch of particle physics at colliders these days. QCD processes make up 99.99% of what happens in hadronic collisions at the Tevatron, or what will happen at the LHC starting this fall: they are usually backgrounds to those much more interesting reactions involving electroweak bosons and leptons, or to the searches for the Higgs boson.

I would like to point out that QCD is in truth a wonderfully complex and beautiful theory, and that QCD measurements are very important. Only by understanding strong interactions in detail can we hope to find new phenomena lying underneath. And don’t even get me started on the need for more studies on low-energy strong interactions -they are really not well understood yet, and in fact precise measurements of strong interaction cross sections are direly needed in cosmology. But let me go back to high-energy high-energy physics.

Today I would like to discuss a precise measurement by CDF which will prove very useful when somebody -me and Mia, for instance- will start studying CMS data in search for the decay $h \to ZZ \to \mu^+ \mu^- b \bar b$: the production of a higgs boson and its subsequent decay into a pair of Z bosons, with a final state including one leptonic Z very easy to identify, and a second one which can be separated from backgrounds by the identification of b-quark jets.

The signal is buried in a large background, namely $Z+ b \bar b$ production where the pair of b-quarks is not coming from a Z boson decay. How large ? Well, we have theoretical calculations, Monte Carlo simulations incorporating them, detector simulations… We have a pretty good idea, but unless we check that these calculations are precise, we are stuck with large systematic uncertainties. One good part of these is due to our limited knowledge of the probability to find a b-quark inside the proton, the b-quark PDF.

A recent result which improves matters has been obtained on the cross section for $Z + b$ production by Andrew Mehta and Beate Heinemann, two very skilled colleagues from Liverpool and Berkeley, respectively. The comparison of the result with theoretical predictions provides a nice confirmation that the latter are in the right ball-park, and an estimate of the level of trust we can put in them. Let me try and describe very briefly how the measurement is produced.

Events with a leptonic Z boson decay are selected from 2.0 inverse femtobarns of proton-antiproton collisions produced by the Tevatron 1.96 TeV synchrotron in the core of the CDF detector. Both $Z \to ee$ and $Z \to \mu \mu$ decays are selected, for a total of about 200,000 events. Among these, the analysis selects those events containing one hadronic jet which has a secondary vertex reconstructed with its charged tracks: the vertex is the signal of the decay of a B-hadron, which contains the long-lived b-quark. By selecting jets with a secondary vertex, their b-purity is increased tremendously.

Below you can see the Z mass peak for events containing a b-quark jet accompanying the dilepton system. The black points are CDF data, the black line is the total of the various contributions, which include, together with the signal, few small backgrounds.

To compute a cross-section for $Z + b$ production, there remains one step (ok, I am making things simpler than they really are, for the sake of clarity and space): understanding the fraction of these jets really due to b-quark hadronization. This can be accomplished by studying the invariant mass of all the measured charged tracks originating from the secondary vertex: the mass is larger for real b-quark jets and smaller for charm-quark jets or jets due to lighter quarks or gluons, for which the secondary vertex is due to a random mismeasurement of tracks rather than the true decay of a long-lived particle.

Above you can see a fit to the secondary vertex mass distrbution, with the three components. The cyan histogram represents the b-jet fraction, which has a larger vertex mass and amounts for 40% of the total. By measuring the fraction of b-jets one can proceed to measure the cross section, if one knows the efficiency of the selection of Z boson decays and the efficiency of the vertex-finding b-tag algorithm. What I am talking about is the following formula:

$\large \sigma_{Zb} = f_b N_{ev} / ( \epsilon_{Z \to ll} \epsilon_{sv} \int L dt )$.

Don’t be scared: the ingredients have all been introduced to you already. $\sigma_{Zb}$ is the cross-section of the process, i.e. the thing that is measured in the analysis. $f_b$ is the fraction of b-jets among those with a secondary vertex, and is extracted by the figure shown above. $\epsilon_{Z \to ll}$ is the fraction of Z bosons which are detected and reconstructed from two observed muons or electrons; $\epsilon_{sv}$ is the efficiency of finding the b-jet with the required energy and with a secondary vertex inside it. Finally, $\int L dt$ is the integrated luminosity of the data used, 2.0/fb.

What is the result ? CDF finds $\sigma_{Zb} = 0.86 \pm 0.14 \pm 0.12 pb$, a small number -eight times smaller than the cross-section for producing a pair of top quarks! Theory calculations at Next-to-Leading-Order (a good level of precision for this calculation) predict $0.53 \pm 0.07 pb$, a figure smaller but not utterly incompatible with the data.

Maybe the most interesting part of the measurement is the ratio between the measured $Zb$ cross section and the cross section for production of one Z boson alone. It is shown in the plot below as a function of the transverse energy of the b-jet, compared to three different Monte Carlo calculations. As you can see, the fraction of Z bosons which are produced together with a b-jet is tiny! The reason has to do with the smallness of the b-quark PDF.

1. carlbrannen - August 26, 2008

“And don’t even get me started on the need for more studies on low-energy strong interactions -they are really not well understood yet”

This is exactly what Kea and I are working on. The very lowest energy strong interactions are the bound states of quarks. In a sort of duality, we’re hoping that these states, instead of being mathematically intractable in perturbation theory, will instead be mathematically simple.

The model for this is the Lamb shift, where the bound states of the hydrogen are slightly different from what QM predicts. The bound state itself is computed to first order using simple QM, Schroedinger’s equation and all that. Then the corrections are computed in QFT.

Of course people have tried this sort of thing before, but our method is to do the first order QM calculation in qubits; by ignoring momentum, we look just at the influence of the color force (i.e. between 1S states in position).

So when we get this complete, maybe you will allow us a guest post on the odd structure of the bound states of heavy quarkonium.

2. dorigo - August 26, 2008

Carl, you are welcome here. Let me know when you’re done with your investigations.

On a side note, perhaps you might be interested in Eric Braaten’s recent preprint on a topic of relevance for the issue you’re dealing with.

3. mfrasca - August 26, 2008

Hi Tommaso,

I understand that in these times of deep problems in physics like unification of interactions, quantum gravity, multi-verse and anthropic principle, the question of low-energy QCD is something like kindergarten and one can quietly avoid to consider it seriously. But let me emphasize a point about this matter. Low-energy QCD represented a great chance for the community and the reason relies on the fact that one could have developed new approaches to manage theories with a large parameter rather than do weak perturbation theory. If a general method would exist for this it is a major scientific revolution having an impact on all areas of physics. Do we have got it? Time will say. But if we missed it a great chance would have been lost.

I used to think that all physics research is worthwhile and the reason is that we cannot know a priori where the breakthrough can come from.

Ciao,

Marco

4. Luca S. - August 26, 2008

Hi Tommaso,
surfing on interner I have found a very “strange”
(from our point of view) article of Maurizio Blondet,
this one:
http://www.effedieffe.com/content/view/3820/171/
on the Higgs boson.

Unfortunately, there are a lot of Italians that have the same opinions of Maurizio Blondet on physics and basic research.
Their equation is:
italian physicists = comunists.

Well, somehow this equation finds support in your blog.
What do you think?

Ciao,
L.

5. dorigo - August 26, 2008

Hi Luca,

I think I can live happily without bothering to read such rubbish as the thing you point to. I am afraid I cannot thank you for offering the link. I had never heard before of Maurizio Blondet, and I think I will forget him now.

As for italians and what they believe, I have long lost any hope.
That is what I think, in a nutshell. It is not by chance that this blog is in English…

Cheers,
T.

6. dorigo - August 26, 2008

Hi Marco,

I agree with your statement that one does not know where the next breakthrough is coming. That, by the way, is the reason of my disgust at the article Luca linked to, above.

Cheers,
T.

7. carlbrannen - August 26, 2008

Tommaso,

It’s interesting what that reference does with the Y(4008), Y(4260), etc. 1– sates. If these eventually get renamed as J/psi or psi it will throw a wrench in my works.

A reason to keep these separate is given in the fairly recent review article Charmonium which is to be published in Prog. Part. Nucl. Phys. 2008, see page 59:

“Such behavior is next to impossible to explain by considering the resonance as a charmonium state even though the mass of Y is close to the expectation for the 4S state[209], since lower JPC = 1−− resonances ψ(3770), ψ(4040) decay practically exclusively to D meson pairs.”

However, the mass is close to the expectation for the psi(4S), so there is a strong theoretical inclination to believe one’s BS and to assign it that way.

By the way, in those places where the standard “radial excitation” theory is able to be fit to quarkonium masses, the resonances are renamed to be XX(nS) or appropriate, instead of XX(####).

What I’m doing, basically, is supposing that non perturbative color interactions figure predominantly in the bound states and are more important than the radial excitations per se. That is, at any given radial excitation, there will be also “color excitations”, which consist of changes in the phase relationship between the sea quarks and the valence quarks. These phase relationships come in three choices, which correspond to the generation structure of the leptons, hence the use of the Koide formula.

The standard way of doing business here is to assume that the appropriate symmetry is purely SU(2), hence the radial excitations and the 1S, 2P, 3D, etc. nomenclature. This is basically about spin and position dependence in Schroedinger’s equation. That is, they are fitting quarkonia to the periodic table of the elements. So they try to assign appropriate quantum numbers to the resonances and they talk about “chemistry”.

I think that this is naive, and that the appropriate symmetry for excitations of color bound states needs to have color built into it. To first order, color excitations should be a matter of what is happening to the sea quarks, not necessarily what is happening to the radial excitations of the valence quarks.

8. mfrasca - August 26, 2008

Carl,

check my blog http://marcofrasca.wordpress.com for some computations of charmonium and bottomonium ground states from the gluon propagator. I think you should check the reference by Nora Brambilla and QWG Collaboration that is a must in this field.

Marco

9. mfrasca - August 26, 2008

Tommaso,

I thought Maurizio Blondet was universally known: if you know him you avoid him. But I am forged by the reading of Italian newsgroups where you can find several good physicists fighting against such a junk.

Ciao,

Marco

10. Luca S. - August 27, 2008

Tommaso,
you are surely right. But guys like Blondet are able to infuence a lot of people (in the past he wrote in the catholic newspaper “Avvenire”).

It is very important, in particular in this period, we explain very well what we are doing (and the many technological applications)
at the Italian public opinion, and also at the students.

I have many frinds (engineeres and physicians) that hate physics simply because the univ. teachers were too arrogant.
I think that, unfortunately, we (Italian physicists) are educated to be quite arrogant and “aristocratic”.

By the way, the number of high-energy faculty members
(of a Physics Department) in a generic US University is usually
much much smaller than in an Italian University.

Hasta la victoria,
L.

11. dorigo - August 27, 2008

Hi Carl,

I think HQET does a good job with figuring out what is going on with those excited states, but I am very ignorant on the subject and so I should no doubt like to let Marco speak instead. Probably his advice above is a good one…

Cheers,
T.

12. dorigo - August 27, 2008

Hi Luca,
physics professors are no doubt arrogant in general. About the fraction of HEP faculty: it does not surprise me, because italian universities are publically funded, and so there is more freedom to invest in pure research. I would not use it as an indicator of something wrong in Italy… I would tend to look at it the other way round.

Cheers,
T.

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