Earlier today, the LHC finished its 2009 run. They did everything they said they were going to do: provide physics-quality 900 GeV collisions and break the world record by colliding protons with a combined energy of 2.36 TeV (that happened Monday), as well as many other studies to make sure that everything will work for 7 TeV collisions next year. We’ve been busily finding the familiar particles of the Standard Model— I wrote two weeks ago about the re-discovery of the π^{0}; since then new particles been dropping in almost daily. I’ll explain some of the already-public results below the cut, but first I want to point out that there will be another LHC Report this Friday at 12:15 (European Central Time = 6:15 AM Eastern U.S. = 3:15 AM Pacific) on CERN’s webcast site. This is where all of the LHC experiments will present their results and probably make a few more public.

Also, in case you haven’t heard, there have been a lot of rumors that the Cryogenic Dark Matter Search (CDMS) has discovered something interesting. They’ll be presenting whatever it is tomorrow with a paper on the arXiv, a Fermilab presentation at 4:00 PM Central U.S. (webcast here), and a SLAC presentation at the same time, 2:00 PM Pacific (webcast here). It might be the direct detection of dark matter particles, which would be incredibly exciting.

In the past month of LHC running, we’ve seen evidence or hints of the following particles:

Particle |
Original discovery |

Muon | 1936 |

Pion | 1950 (π^{0}) |

Kaon | 1947 (K_{S}) |

Lambda | 1947 (Λ^{0}) |

Quarks and gluons (partons)* | 1968 et seq |

J/ψ candidate* | 1974 “November Revolution” |

* The two with asterisks require qualification: see below.

The muon is an easy one: as soon as the tracking detectors were turned on, they saw muons raining down from cosmic rays. CMS collected hundreds of millions of muons in a month-long campaign in 2008, the basis of 23 detector-commissioning papers submitted to JINST (a personal point for me, since I edited one of those papers). Muons originating from proton collisions are more rare, but were observed.

The neutral pion (π^{0}) was seen in the first 900 GeV LHC collisions this November. Most of the charged particles produced in proton collisions are also pions (π^{+} and π^{–}), and the tracking detectors saw plenty of tracks originating from the collision point as well. But the first LHC run required the experiments’ magnetic fields to be turned off to avoid complicating the orbits of the proton beams, and this meant that all of the tracks from charged collision products were straight lines, providing little information about their momenta. The energy of the two photons (γγ) from neutral pion decays (π^{0}→ γγ), measured by calorimeters, gives us a handle on the mass of the parent particle, and therefore confirm it definitively as a π^{0}.

The December run was conducted with full magnetic fields, allowing for some precision tracking. Two absolutely beautiful resonance peaks came out of that: K_{S} → π^{+}π^{–} and Λ^{0}→ π^{+}p^{–}/Λ^{0}→ π^{–}p^{+}. (These are the ones that I know have been approved by the collaboration so far: there’s a nice article on them in the CMS Times.)

Much like the π^{0} peak, the distributions above are the mass of the particle from which the pair of charged pions (top) or proton-pion pair (bottom) were assumed to originate. The calculation is pretty simple: in special relativity, the relationship between mass (), energy (), and momentum is

so

.

The distributions above are histograms of , calculated for pairs of observed particles (1 and 2). More charged pion pairs have an invariant mass of 0.497 GeV than would be expected from random combinations, so we see a K-short peak (K_{S}) on top of a low, flat background. Similarly, pairs of protons and π^{–}, and of antiprotons and π^{+}, pile up at 1.116 GeV, the neutral Lambda (Λ^{0}) mass. Red lines are fits to the distributions and the blue lines are the masses measured from experiments before the LHC.

When I flew home from CERN yesterday, I couldn’t resist and brought a reduced sample from the dataset with me on the plane. Poking around, finding vertices where pairs of charged particle tracks intersect and calculating their masses, I saw our two friends K_{S} and Λ^{0} and tried looking for more. It reminded me of why I became an experimental physicist: these things really are there! The guy next to me on the plane asked if I was programming, and I had to say, “not exactly,” because even though it looks like computer work, it’s reaching beyond the computer to something physical, if not tangible, that was happening inside a beryllium beampipe in France. The beam quality was better in some runs than others, and you could see that in the backgrounds.

Quarks and gluons (collectively called “partons”) have a weird history in that they were considered computational devices before the physics community begrudgingly, then whole-heartedly, considered them real particles. The three “colors” of quarks and three anticolors of antiquarks were a physicist’s mneumonic for the algebra of the Lie group SU(3), with the 8 two-colored gluons being the group generators. The problem with their interpretation as particles was that single quarks and single gluons were never seen in isolation, a phenomenon today known as confinement: a single quark can’t get away from other quarks without creating more quarks in the processes, and so a high-energy quark or gluon fleeing the proton collision “hadronizes” into a pack of hadronic particles. It’s important to therefore be able to identify *groups *of particles originating from the same quark or gluon, called jets. Here’s a nice candidate for a two-jet event:

The wireframe cylinder shows where the tracking detector is, with the yellow lines being tracks of charged particles from the collision. On top of that, red and blue bars show where the calorimeters (surrounding the tracking detector) registered energy. The tracks and calorimeter energy are clustered into two apparent jets, indicated by the yellow cones. This is as much of a quark or gluon as nature will ever allow us to see.

On Monday, the LHC gave the experiments a few hours of record-breaking 2.36 TeV collisions. At high collision energies, the production rate of more massive particles increases. One intriguing event from this run contains not just one muon, but two. Moreover, the invariant mass of this pair is 3.03 GeV, consistent with J/ψ→μμ, where the J/ψ mass is 3.097 GeV. This event alone is not a “J/ψ observation” because other processes yield muon pairs— imagine one of the invariant mass plots above with a single event in it. That event has the right mass to be in the peak of the distribution, though.

This display shows three views of the event, including the muon detector measurements that identify the two long, red tracks as muons. Of all the stable charged particles that originate in proton collisions, only muons pass through enough steel to reach the muon detectors. Thus, seeing anything at all in these detectors, matched to a track in the central detector, is a pretty clean muon identification.

Some of the (older) professors I worked with in grad school told stories about the November Revolution, the 1974 discovery of the J/ψ that changed particle physics overnight. Up to that point, all of the major ideas of the Standard Model had been expressed in one form or another, but had not jelled into the single picture we know today. One of these ideas was that the strange-flavored quark should have a charm-flavored counterpart— a patch on the quark theory to avoid neutral flavor-changing decays through Z bosons that were not observed (the GIM mechanism). The dramatic J/ψ resonance discovered months later (thousands of events with little background) could only be explained as a charm-anticharm bound state, which lent a lot of credibility to the quark model for making such a prediction, and made W and Z bosons concievable, as long as there’s also a Higgs boson to generate their masses— one by one, the pieces of the Standard Model fell into place. According to James Bjorken, the whole theory was complete by 1976, though people tell me that they weren’t convinced until the early 80’s when W, Z, and gluon jets were observed. It turned the field from a collection of puzzling observations into a Theory of Almost Everything, and a search for hints of physics beyond the Standard Model.

Hopefully, we’ll get back into the business of puzzling observations soon enough.

December 16, 2009 at 5:57 pm |

Jim, I want to thank you for this and all your other posts about the LHC and CMS. They are very informative, at a level much higher than that found on newspapers but still understandable to non-particle-experimentalists.

December 17, 2009 at 5:03 pm |

[…] The LHC shut down yesterday for an end-of-year break after a very successful initial period of beam commissioning at beam energies of 450 GeV and 1.18 TeV. Tomorrow at CERN there will be public reports about the state of the LHC and the initial results from the experiments. I gather that by now all sorts of particles have been rediscovered, including kaons and lambdas, here are some details from Jim Pivarski. […]

December 18, 2009 at 7:01 pm |

[…] The particle body-count […]

December 30, 2009 at 10:15 am |

Super post, many thanks. I’ve repreoduced some of it on my blog for my students, hope that’s ok! Cormac

December 30, 2009 at 10:49 am |

[…] is a really nice summary of what has been achieved so far, taken from Jim Pivarski’s blog The Everything Seminar – I think it gives a really good insight into how particle physics is done. Earlier today, the LHC […]

October 24, 2011 at 2:27 am |

Popular brands…[…]The particle body-count « The Everything Seminar[…]…

November 6, 2011 at 7:37 am |

White Page People Search…[…]The particle body-count « The Everything Seminar[…]…

November 7, 2011 at 5:48 am |

cook chicken nuggets…[…]The particle body-count « The Everything Seminar[…]…

April 6, 2013 at 2:43 pm |

Reblogged this on Le rayon vert.

August 5, 2013 at 1:54 am |

I love to disseminate understanding that I’ve accrued through the season to help improve group functionality.

August 5, 2013 at 4:44 pm |

I have a happy synthetic attention meant for

detail and may anticipate complications prior to they will take place.

February 16, 2014 at 7:21 am |

Your method of explaining all in this paragraph is actually nice, all can without difficulty

understand it, Thanks a lot.

May 31, 2014 at 7:19 pm |

Article writing is also a excitement, if you know then you can write if not it is complex

to write.

December 8, 2015 at 5:36 am |

recommend don’t e help cle can can to you orpo lesli bisnis a

April 12, 2019 at 10:47 am |

indeed this remarkable formula that is fundamental observed prof dr mircea orasanu and prof drd horia orasanu

May 12, 2019 at 10:50 am |

indeed must observed that are many consequences and considered by prof dr mircea orasanu and prof drd horia orasanu and followed with evaluate the virtual work done, we will need the virtual displacement which we may readily get from the kinematic approach since we already have the equation of velocity of the pin B. This way, the virtual work is:

And for the Lagrange equations we have,

where the constraints hold such that,

Green function for the classical Orr-Sommerfeld equations and derive sharp semigroup bounds for linearized Navier-Stokes equations around a boundary layer profile. This is part of the long program to understand the stability of classical Prandtl’s layers appearing in the inviscid limit of incompressible Navier-Stokes flows.

May 15, 2019 at 11:30 am |

these considerations have depth consequences in mathematics observed prof dr mircea orasanu and prof drd horia orasanu and followed for for LEGENDRE Formula and ordinary differential equations in connexion wih GALOIS Theory or Watson integral transforms with Hermite equations that implies some aspects of hyper geometric equations where prof dr mircea orasanu have many contributions that are connected with problem of entropy and other so most properties of transforms as Laplace ,or Lagrange lead to proved a significant result known as Watson’s lemma, that has many applications in the theory on the asymptotic behaviour of exponential integrals.[1]

June 22, 2019 at 10:46 am |

these indeed are most important forms for high school observed prof dr mircea orasanu and prof drd horia orasanu and so Together with the fact that

the last inequality yields

.

Therefore

,

Where

Then, by repeating the scheme of the proof of Theorem 4 [4], we obtain estimates (1). Lemma is proved.

Proof of Theorem. According to Lemma

, (2) . (3)

(2), (3) and the relations bottom follow from theorem

.

Theorem is proved.

Corollary. If , then .

REFERENCES

[1] Emelichev V., Podkapaev D. Quantitative stability analysis for vector problems of 0-1 programming // Discrete Opnimization . – 2010.- v.7.- p. 48-63. (in Russian)

[2] Devyaterikova M.V., Kolokolov A.A. Stability Analysis o Some Discrete Optimization Algorithms // Automation and Remote Control, 2004. № 3. pp. 48-54.

[3] Ramazanov A.B. On stability o the gradient algorithm in convex discrete optimization problems and related questions // J. Discrete Mathematics and Applications, 2011, vol. 21, Issue 4, pp. 465-476.

Camille Jordan’s father, Esprit-Alexandre Jordan (1800-1888), was an engineer who had been educated at the École Polytechnique. Camille’s mother, Joséphine Puvis de Chavannes, was the sister of the famous painter Pierre Puvis de Chavannes who was the foremost French mural painter of the second half of the 19th century. Camille’s father’s family were also quite well known; a grand-uncle also called Ennemond-Camille Jordan (1771-1821) achieved a high political position while a cousin Alexis Jordan (1814-1897) was a famous botanist.

Jordan studied at the Lycée de Lyon and at the Collège d’Oullins. He entered the École Polytechnique to study mathematics in 1855. This establishment provided training to be an engineer and Jordan, like many other French mathematicians of his time, qualified as an engineer and took up that profession. Cauchy in particular had been one to take this route and, like Cauchy, Jordan was able to work as an engineer and still devote considerable time to mathematical research. Jordan’s doctoral thesis was in two parts with the first part Sur le nombre des valeurs des fonctions Ⓣ being on algebra. The second part entitled Sur des periodes des fonctions inverses des intégrales des différentielles algebriques Ⓣ was on integrals of the form ∫ u dz where u is a function satisfying an algebraic equation f (u, z) = 0. Jordan was examined on 14 January 1861 by Duhamel, Serret and Puiseux. In fact the topic of the second part of Jordan’s thesis had been proposed by Puiseux and it was this second part which the examiners preferred. After the examination he continued to work as an engineer, first at Privas, then at Chalon-sur-Saône, and finally in Paris.

Jordan married Marie-Isabelle Munet, the daughter of the deputy mayor of Lyon, in 1862. They had eight children, two daughters and six sons.

From 1873 he was an examiner at the École Polytechnique where he became professor of analysis on 25 November 1876. He was also a professor at the Collège de France from 1883 although until 1885 he was at least theoretically still an engineer by profession. It is significant, however, that he found more time to undertake research when he was an engineer. Most of his original research dates from this period.

Jordan was a mathematician who worked in a wide variety of different areas essentially contributing to every mathematical topic which was studied at that time. The references [3], [4], [5], [6] are to the four volumes of his complete works and the range of topics is seen from the contents of these. Volumes 1 and 2 contain Jordan’s papers on finite groups, Volume 3 contains his papers on linear and multilinear algebra and on the theory of numbers, while Volume 4 contains papers on the topology of polyhedra, differential equations, and mechanics.

Topology (called analysis situs at that time) played a major role in some of his first publications which were a combinatorial approach to symmetries. He introduced important topological concepts in 1866 built on his knowledge of Riemann’s work in topology but not the work by Möbius for he was unaware of it. Jordan introduced the notion of homotopy of paths looking at the deformation of paths one into the other. He defined a homotopy group of a surface without explicitly using group terminology.

Jordan was particularly interested in the theory of finite groups. In fact this is not really an accurate statement, for it would be reasonable to argue that before Jordan began his research in this area there was no theory of finite groups. It was Jordan who was the first to develop a systematic approach to the topic. It was not until Liouville republished Galois’s original work in 1846 that its significance was noticed at all. Serret, Bertrand and Hermite had attended Liouville’s lectures on Galois theory and had begun to contribute to the topic but it was Jordan who was the first to formulate the direction the subject would take.

To Jordan a group was what we would call today a permutation group; the concept of an abstract group would only be studied later. To give an illustration of the way he tried to build up groups theory we will say a little about his contributions to finite soluble groups. The standard way to define such groups today would be to say that they are groups whose composition factors are abelian groups. Indeed Jordan introduced the concept of a composition series (a series of subgroups each normal in the preceding with the property that no further terms could be added to the series so that it retains that property). The composition factors of a group G are the groups obtained by computing the factor groups of adjacent groups in the composition series. Jordan proved the Jordan-Hölder theorem, namely that although groups can have different composition series, the set of composition factors is an invariant of the group.

Although the classification of finite abelian groups is straightforward, the classification of finite soluble groups is well beyond mathematicians today and for the foreseeable future. Jordan, however, clearly saw this as an aim of the subject, even if it was not one which might ever be solved. He made some remarkable contributions to how such a classification might proceed setting up a recursive method to determine all soluble groups of order n for a given n.

A second major piece of work on finite groups was the study of the general linear group over the field with p elements, p prime. He applied his work on classical groups to determine the structure of the Galois group of equations whose roots were chosen to be associated with certain geometrical configurations.

His work on group theory done between 1860 and 1870 was written up into a major text Traité des substitutions et des équations algebraic que