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Posts Tagged ‘Penta’

Finding a five-leafed clover

Wednesday, July 15th, 2015
Photo Credit: Cathy Händel, Published on http://www.suttonelms.org.uk/olla12.html

Photo Credit: Cathy Händel, Published on http://www.suttonelms.org.uk/olla12.html

Sometimes when you’re looking for something else, you happen across an even more exciting result. That’s what’s happened at LHCb, illustrated in the paper “Observation of \(J/\psi p\) resonances consistent with pentaquark states in \(\Lambda_b^0\to J/\psi K^-p\) decays”, released on the arXiv on the 14th of July.

I say this is lucky because the analysts found these states while they were busy looking at another channel; they were measuring the branching fraction of \(B^0\to J/\psi K^+ K^-\). As one of the analysts, Sheldon Stone, recalled to me, during the review of the \(B^0\) analysis, one reviewer asked if there could be a background from the decay \(\Lambda_b^0\to J/\psi K^- p\), where the proton was misidentified as a kaon. As this was a viable option, they looked at the PDG to see if the mode had been measured, and found that it had not. Without a certain knowledge of how large this contribution would be, the analysts looked. To their surprise, they found a rather large rate of the decay, allowing for a measurement of the lifetime of the \(\Lambda_b^0\). At the same time, they noticed a peak in the \(J/\psi p\) spectrum. After completing the above mentioned analysis of the \(B^0\), they returned to the channel.

It’s nice to put yourself in the analysts shoes and see the result for yourself. Let’s start by looking at the decay \(\Lambda_b^0\to J/\psi p K^-\). As this is a three body decay, we can look at the Dalitz Plots.

Dalitz plots from the decay Lambda_b^0\to J/\psi K p. Compiled from http://arxiv.org/abs/1507.03414

Dalitz plots from the decay \(\Lambda_b^0\to J/\psi K^- p\). Compiled from http://arxiv.org/abs/1507.03414

The above Dalitz plots show all combinations of possible axes to test. In the one on the left, around \(m^2=2.3\) GeV\(^2\), running vertically, we see the \(\Lambda(1520)\) resonance, which decays into a proton and a kaon. Running horizontally is a band which does not seem to correspond to a known resonance, but which would decay into a \(J/\psi\) and a proton. If this is a strong decay, then the only option is to have a hadron whose minimum quark content is \(uud\bar{c}c\). The same band is seen on the middle plot as a vertical band, and on the far right as the sloping diagonal band. To know for sure, one must perform a complete amplitude analysis of the system.

You might be saying to yourself “Who ordered that?” and think that something with five quarks hadn’t been postulated. This is not the case. Hadrons with quark content beyond the minimum were already thought about by Gell-Mann and Zweig in 1964 and quantitatively modeled by Jaffe in 1977  to 4 quarks and 5 quarks by Strottman in 1979. I urge you to go look at the articles if you haven’t before.

It appears as though a resonance has been found, and in order to be sure, a full amplitude analysis of the decay was performed. The distribution is first modeled without any such state, shown in the figures below.

Projections of the fits of the Lambda_b^0\to J/\psi K^- p spectrum without any additional components. From http://arxiv.org/abs/1507.03414

Projections of the fits of the\( \Lambda_b^0\to J/\psi K^- p\) spectrum without any additional components. Black is the data, and red is the fit. From http://arxiv.org/abs/1507.03414

Try as you might, the models are unable to explain the invariant mass distribution of the \(J/\psi p\). Without going into too much jargon, they wrote down from a theoretical standpoint what type of effect a five quark particle would have on the Dalitz plot, then put this into their model. As it turns out, they were unable to successfully model the distribution without the addition of two such pentaquark states. By adding these states, the fits look much better, as shown below.

Mass projection onto the J/\psi p axis of the total fit to the Dalitz plot. Again, Black is data, red is the fit. The inset image is for the kinematic range...  From http://arxiv.org/abs/1507.03414

Mass projection onto the \(J/\psi p\) axis of the total fit to the Dalitz plot. Again, Black is data, red is the fit. The inset image is for the kinematic range \(m(K p)>2 GeV\).
From http://arxiv.org/abs/1507.03414

The states  are called the \(P_c\) states. Now, as this is a full amplitude analysis, the fit also covers all angular information. This allows for determination of the total angular momentum and parity of the states. These are defined by the quantity \(J^P\), with \(J\) being the total angular momentum and \(P\) being the parity. All values for both resonances are tried from 1/2 to 7/2, and the best fit values are found to be with one resonance having \(J=3/2\) and the other with \(J=5/2\), with each having the opposite parity as the other. No concrete distinction can be made between which state has which value.

Finally, the significance of the signal is described by under the assumption \(J^P=3/2^-,5/2^+\) for the lower and higher mass states; the significances are 9 and 12 standard deviations, respectively.

The masses and widths turn out to be

\(m(P_c^+(4380))=4380\pm 8\pm 29 MeV\)

\(m(P_c^+(4450))=4449.8\pm 1.7\pm 2.5 MeV\)

With corresponding widths

Width\((P_c^+(4380))=205\pm 18\pm 86 MeV\)

Width\((P_c^+(4450))=39\pm 5\pm 19 MeV\)

Finally, we’ll look at the Argand Diagrams for the two resonances.

Argand diagrams for the two P_c states. From http://arxiv.org/abs/1507.03414

Argand diagrams for the two \(P_c\) states.
From http://arxiv.org/abs/1507.03414

 

Now you may be saying “hold your horses, that Argand diagram on the right doesn’t look so great”, and you’re right. I’m not going to defend the plot, but only point out that the phase motion is in the correct direction, indicated by the arrows.

As pointed out on the LHCb public page, one of the next steps will be to try to understand whether the states shown are tightly bound 5 quark objects or rather loosely bound meson baryon molecule. Even before that, though, we’ll see if any of the other experiments have something to say about these states.

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Hi All,

Exciting news came out the Japanese physics lab KEK (@KEK_jp, @KEK_en) last week about some pretty exotic combinations of quarks and anti-quarks. And yes, “exotic” is the new “tantalizing.” At any rate, I generally like assuming that people do not know much about hadrons so here is a quick explanation of what they are. On the other hand, click to jump pass “Hadrons 101” and straight to the news.

Hadrons 101: Meeting the Folks: The Baryons & Mesons

Hadrons are pretty cool stuff and are magnitudes more quirky than those quarky quarks. The two most famous hadrons, the name for any stable combination of quarks and anti-quarks, are undoubtedly the proton and the neutron:

According to our best description of hadrons (Quantum Chromodynamics), the proton is effectively* made up two up-type quarks, each with an electric charge of +2/3 elementary charges**; one down-type quark, which has an electric charge of -1/3 elementary charges; and all three quarks are held together by gluons, which are electrically neutral. Similarly, the neutron is effectively composed of two down-type quarks, one up-type quark, and all the quarks are held strongly together by gluons. Specifically, any combination of three quarks or anti-quarks is called a baryon. Now just toss an electron around the proton and you have hydrogen, the most abundant element in the Universe! Bringing together two protons, two neutrons, and two electrons makes helium. As they say, the rest is Chemistry.

However, as the name implies, baryons are not the only type of hadrons in town. There also exists mesons, combinations of exactly one quark and one anti-quark. As an example, we have the pions (pronounced: pie-ons). The π+ (pronounced: pie-plus) has an electric charge of +1 elementary charges, and consists of an up-type quark & an anti-down-type quark. Its anti-particle partner, the π (pronounced: pie-minus), has a charge of -1, and is made up of an anti-up-type quark & a down-type quark.

 

If we now include heavier quarks, like strange-type quarks and bottom-type quarks, then we can construct all kinds of baryons, mesons, anti-baryons, and anti-mesons. Interactive lists of all known mesons and all known baryons are available from the Particle Data Group (PDG)***. That is it. There is nothing more to know about hadrons, nor has there been any recent discovery of additional types of hadrons. Thanks for reading and have a great day!

 

* By “effectively,” I mean to ignore and gloss over the fact that there are tons more things in a proton, like photons and heavier quarks, but their aggregate influences cancel out.

** Here, an elementary charge is the magnitude of an electron’s electron charge. In other words, the electric charge of an electron is (-1) elementary charges (that is, “negative one elementary charges”). Sometimes an elementary charge is defined as the electric charge of a proton, but that is entirely tautological for our present purpose.

*** If you are unfamiliar with the PDG, it is arguably the most useful site to high energy physicists aside from CERN’s ROOT user guides and Wikipedia’s Standard Model articles.

The News: That’s Belle with an e

So KEK operates a super-high intensity electron-positron collider in order to study super-rare physics phenomena. It’s kind of super. Well, guess what. While analyzing collisions with the Belle detector experiment, researchers discovered the existence of two new hadrons, each made of four quarks! That’s right, count them: 1, 2, 3, 4 quarks! In each case, one of the four quarks is a bottom-type quark and another is an anti-bottom quark. (Cool bottom-quark stuff.) The remaining two quarks are believed to be an up-type quark and an anti-down type quark.

The two exotic hadrons have been named Zb(10610) and Zb(10650). Here, the “Z” implies that our hadrons are “exotic,” i.e., not a baryon or meson, the subscript “b” indicates that it contains a bottom-quark, and the 10610/10650 tell us that our hadrons weigh 10,610 MeV/c2 and 10,650 MeV/c2, respectively. A proton’s mass is about 938 MeV/c2, so both hadrons are about 11 times heavier than the proton (that is pretty heavy). The Belle Collaboration presser is really great, so I will not add much more.

Other Exotic Hadrons: When Barry met Sally.

For those keeping track, the Belle Collaboration’s recent finding of two new 4-quark hadrons makes it the twelfth-or-so “tetra-quark” discovery. What makes this so special, however, is that all previous tetra-quarks have been limited to include a charm-type quark and an anti-charm-type quark. This is definitely the first case to include bottom-type quarks, and therefore offer more evidence that the formation of such states is not a unique property of particularly charming quarks but rather a naturally occurring phenomenon affecting all quarks.

Furthermore, it suggests the possibility of 5-quark hadrons, called penta-quarks. Now these things take the cake. They are a sort of grand link between elementary particle physics and nuclear physics. To be exact, we know 6-quark systems exist: it is called deuterium, a radioactive stable isotope of hydrogen (Thanks to @incognitoman for pointing out that deuterium is, in fact, stable.). 9-quark systems definitely exist too, e.g., He-3 and tritium. Etc. You get the idea. Discovering the existence of five-quark hadrons empirically establishes a very elegant and fundamental principle: That in order to produce a new nuclear isotope, so long as all Standard Model symmetries are conserved, one must simply tack on quarks and anti-quarks. Surprisingly straightforward, right? Though sadly, history is not on the side of 5-quark systems.

Now go discuss and ask questions! 🙂

Run-of-the-mill hadrons that are common to everyday interactions involving the Strong Nuclear Force (QCD) are colloquially called “standard hadrons.” They include mesons (quark-anti-quark pairs) and baryons (three-quark/anti-quark combinations). Quark combinations consisting of more than three quarks are called “exotic hadrons.”

 

 

 

 

Happy Colliding.

– richard (@bravelittlemuon)

 

PS, I am always happy to write about topics upon request. You know, QED, QCD, OED, etc.

http://en.wikipedia.org/wiki/Neutron
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