The boson, the spin and the graviton

Some days ago, ATLAS has been released a draft about the spin of the new boson. The decay channels studied are the fab four: $H \rightarrow \gamma \gamma$, $H \rightarrow WW^*$, $H \rightarrow l\nu l\nu$, $H \rightarrow ZZ^* \rightarrow 4l$. The idea is combining data from the four channels in order to understand the spin of the new boson, in detail to distinguish between two cases: spin 0 ($J^P = 0^+$), and so a boson compatible with the Standard Model, and spin 2 ($J^P = 2^+$), that it could be connected with a model (arXiv) that represents a light coupling between the Standard Model's fields and the hypothetical graviton.
These the ATLAS' conclusions:

The data are in good agreement with the expected distributions of a $J^P=0^+$ particle while the graviton-inspired $J^P=2^+$ model, that is expected to be produced dominantly via the gluon fusion process, is excluded at more than 99.9% confidence level.

We could say that it starting the elimination process of the models that would lead the research of the new physics beyond the Standard Model for the next years. A good luck to all of them, but we don't forget the key role of the Standard Model, that is in some sense confirmed by this last draft from ATLAS.

Turmoil in the heavens

This one-page comic story published on Race to the Moon #2, that is now in public domain, is referred to an old theory proposed by Heinrich Wilhelm Matthäus Olbers, a german astronomer:

His bold hypothesis of their origin by the disruption of a primitive large planet, although now discarded, received countenance from the finding of Juno by Harding, and of Vesta by himself, in the precise regions of Cetus and Virgo where the nodes of such supposed planetary fragments should be situated.

The hypothetical planet, instead of Polis like suggested in the comic, was named Phaeton by Yevgeny Leonidovich Krinov. Olbers' model is today substituted by the accretion model.

Ted Turner Interviews Carl Sagan

Carl Sagan and Ted Turner discuss the issues that are vital to the survival of our species on earth. Sagan explains the benefits of our space program, the fascinating possibility of time travel, and our search for life on other worlds.

Play the game with the Higgs boson

In the mid-March at Moriond 2013 ATLAS and CMS presented the last results about the research of the Higgs' boson. While CMS reduced the excess for the $H \rightarrow \gamma \gamma$ decay channell, ATLAS continued to observe it. This result could be a clue that the boson discovered and announced last year is only the first of a series of Higgs' bosons. Indeed, following Albert De Roeck of CSM, the photon decay could be connected with...

new physics and there are a great deal of models that can come with such a number

In order to resolve the question (is the new boson the only Higgs' boson or simply a Higgs' boson?) we have to wait the end of the maintenance work of LHC, but in the meantime we could play with the Quark Matter Card Game, in particular the variant named Higgs Boson - on Your Own!

Object of the game: to win, by detecting a decay of a Higgs boson. If this does not happen in a given game, one can win by statistics, by collecting the largest number of particle cards.

The proposed game is a variation of Memory

Pierre Deligne and the Weil conjectures

posted by @ulaulaman about #PierreDeligne #AndreWeil #AbelPrize2013 #mathematics

Pierre Deligne, a belgian mathematician, wins the Abel Prize 2013

for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields

One of the most famous contribution by Deligne was the proof of one of the three Weil conjectures. These conjectures was stated by Andre Weil, the mathematician who proofed the Fermat's last theorem, in 1949 (Numbers of solutions of equations in finite fields) in order to solve the following problem:

how to count the number of solutions to systems of polynomial equations over finite fields⁽¹⁾

In particular

Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by Dwork (1960), the functional equation by Grothendieck (1965), and the analogue of the Riemann hypothesis was proved by Deligne (1974)

How to drawn with Sappo: portrait and numbers

via Matteo Stefanelli

A very brief story of the Pi

posted by @ulaulaman about #PiDay #Archimedes #SrinivasaRamanujan and other mathematical curiosities

Warped by Mike Cavna via Bamdad's Math Comics

As you know, the $\pi$ is defined as the ratio of the circumference to its diameter. This number, which is transcendental, was, apparently, known since ancient times. There are, in fact, some Egyptologists who believe that $\pi$, or perhaps $\tau = 2 \pi$, was known to them since the age og the Giza's pyramid, built between 2589 and 2566 BC, because the relationship between the perimeter and the height is 6.2857.
There are no explicit proof of the fact that, at the time, Egyptian mathematics became aware of a number such as $\pi$, however, between 600 and 1000 years later on a Babylonian tablet it is geometrically established the first value of $\pi$: $25/8 = 3.1250$. From documents written more or less in the same period it can be deduced that also the Egyptians calculated the value of $\pi$, obtaining $(16/9)^2 \simeq 3.1605$.
Indian mathematics, however, seems a little late: in 600 BC on Shulba Sutras, it is calculated for the $\pi$ value like $(9785/5568)^2 \simeq 3.088$, which will be updated later in 150 BC as $\sqrt{10} \simeq 3.1622$, which is a value much closer to the value calculated by the Egyptians.
A good approximation of $\pi$ value is in Mishnat ha-Middot, a geometric treatise by Rabbi Nehemiah: $3 + 1/7 \simeq 3.14286$.
The approximation, however, the most amazing not only for accuracy but also for the method is that proposed by Archimedes, the italo-greek mathematician who invented the method of polygons in order to calculate $\pi$, a costant that for a millennium became known simply as the Archimedes' constant.
He simply calculated the perimeter of polygons inscribed and circumscribed in a circle, thus obtaining a lower and an upper estimate of the value of the constant: \[223/71 < \pi < 22/7\] or \[3.1408 < \pi < 3.1429\] It's clear that his method of calculation is very modern and above suggests that Archimedes was well aware of the transcendental nature of the constant, which could be known only through approximations.
Today $\pi$ is known to 5 trillion digits and if you try to type the symbol $\pi$ on modern scientific calculators, the value they give you is, to the first decimal place, 3.14159265...