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Posts Tagged ‘quark’

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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Getting to the Bottom of the Higgs

Thursday, January 30th, 2014

Updated Friday, January 31, 2014: Candidate event of Higgs boson decaying to bottom quarks has been added at the bottom.

CMS has announced direct evidence of the Higgs coupling to bottom quarks. This is special.

Last week, the Compact Muon Solenoid Experiment, one of the two general purpose experiments at the CERN Large Hadron Collider (LHC), submitted two papers to the arXiv. The first claims the first evidence for the Higgs boson decaying directly to tau lepton pairs and the second summarizes the evidence for the Higgs boson decaying directly to bottom quarks and tau leptons. (As an aside: The summary paper is targeted for Nature Physics, so it is shorter and more broadly accessible than other ATLAS and CMS publications.) These results are special, and why they are important is the topic of today’s post. For more information about the evidence was obtained, CERN posted a nice QD post last month.

Event display of a candidate Higgs boson decaying into a tau lepton and anti-tau lepton in the CMS detector.

Fig 1. Event display of a candidate Higgs boson decaying into a tau lepton and anti-tau lepton in the ATLAS detector.

There is a litany of results from ATLAS and CMS regarding the measured properties of the Higgs boson. However, these previous observations rely on the Higgs decaying to photons, Z bosons, or W bosons, as well as the Higgs being produced from annihilating gluons or being radiated off a W or Z. Though the top quark does contribute to the Higgs-photon and Higgs-gluon interactions, none of these previous measurements directly probe how fermions (i.e., quarks and leptons) interact with the Higgs boson. Until now, suggestions that the Higgs boson couples to fermions (i) proportionally to their masses and (ii) that the couplings possess no other scaling factor were untested hypotheses. In fact, this second hypothesis remains untested.

CMS-Htautau1

Fig. 2: Event display of a candidate Higgs boson decaying into a tau lepton and anti-tau lepton in the CMS detector.

As it stands, CMS claims “strong evidence for the direct coupling of the 125 GeV Higgs boson” to bottom quarks and tau leptons. ATLAS has comparable evidence but only for tau leptons. The CMS experiment’s statistical significance of the signal versus the “no Higgs-to-fermion couplings” hypothesis is 3.8 standard deviations, so no rigorous discovery yet (5 standard deviations is required). For ATLAS, it is 4.1 standard deviations. The collaborations still need to collect more data to satisfactorily validate such an incredible claim. However, this should not detract from that fact that we are witnessing phenomena never before seen in nature. This is new physics as far as I am concerned, and both ATLAS and CMS should be congratulated on discovering it.

Event display of a candidate Higgs boson decaying into a tau lepton and anti-tau lepton in the CMS detector.

Fig. 3: Event display of a candidate Higgs boson decaying into a bottom quark and anti-bottom quark in the ATLAS detector. HT to Jon Butterworth for the link.

The Next Step

Once enough data has been collected to firmly and undoubtedly demonstrate that quarks and leptons directly interact with the Higgs, the real tests of the Standard Model of particle physics start up. In the Standard Model, the strength at which a fermion interacts with the Higgs is proportional to the fermion mass and inversely proportional to the ground state energy of the Higgs field. There is no other factor involved. This is definitively not the case for a plethora of new physics models, including scenarios with multiple Higgs bosons, like supersymmetry, as well as scenarios with new, heavy fermions (heavy bottom quark and tau lepton partners). This is definitely a case of using newly discovered physics to find more new physics.

Happy Colliding.

– Richard (@bravelittlemuon)

PS I was unable to find an event display of a Higgs boson candidate decaying into a pair of bottom quarks. If anyone knows where I can find one, I would be very grateful.

PSS Much gratitude toward Jon Butterworth for providing a link to Higgs-bbar candidate events.

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