# Congratulation to Ashoke Sen !!

Indians must be proud of string theorist Ashoke Sen for being among the 9 winners of the first Yuri Milner Fundamental Physics Prize. Yuri Milner, a Russian internet investor, has announced the prize money to be $3 million, which beats the Nobel prize ($1.2 million). Apart from Sen, other winners are

Andrei Linde (Stanford),  Alexei Kitaev (Caltech), Maxim Kontsevich (IHES),  Nima Arkani-Hamed (IAS, Princeton),  Juan Maldacena (IAS, Princeton), Nathan Seiberg (IAS, Princeton), Edward Witten (IAS, Princeton), Alan Guth (MIT).

PS. If I am not wrong, Sen is the youngest FRS from India.

Sources:

http://www.nytimes.com/2012/07/31/science/9-scientists-win-yuri-milners-fundamental-physics-prize.html

http://www.fundamentalphysicsprize.org/laureates.html

# Brilliant billiard balls ! Pi from the pool.

We all know that mathematics helps us to understand physics or many natural phenomena. But what about using physics to understanding mathematics, specifically a mathematical constant, say the most famous one: $\pi$?

Well, before I start I must acknowledge my friend Devdatta and give him the full credit for sharing the youtube video that I am posting here right now.

Now you probably have understood what the video tells about. It’s just about exploiting the momentum conservation principle of our everyday physics and the energy conservation property of an elastic collision. What will be the easy pieces to realize the property of an elastic collision? The billiard balls, I guess, come in your mind first. If you hit a billiard motionless ball with another one, you often see that after hitting the ball stops, whereas the motionless ball starts moving. In an ideal situation (perfectly elastic collision) the moving ball transfers its all kinetic energy to the standing one and hence the latter starts moving with the same speed that the first ball initially had.

Now how do we get all the digits $\pi$ has (Note that it was a long chased effort by many mathematicians including the Indian genius Srinivas Ramanujan)? The idea was published in a paper by G. Galperin of the Dept. of Mathematics, Easter Illinois University, USA, with an interesting title : PLAYING POOL WITH $\pi$ (THE NUMBER $\pi$ FROM A BILLIARD POINT OF VIEW).

The paper briefly states the experimental setup, that you might have already seen in the video above, i.e. we hit a billiard ball of mass $m$ with another ball of larger mass $M=100^N\, m$ with a speed fast enough that the heavier ball hits the lighter ball and sends it to the wall. Then the lighter ball gets reflected by the wall and collides the heavier ball again and gets reflected back towards the wall. Under the assumption that all the collisions are elastic (between the balls and between the ball and the wall), there arises a situation when the heavier ball starts moving in the opposite direction (i.e. the last ball-to-ball collision). The paper proves that the number of hits will be always finite and it will be first $N+1$ digits of $\pi$ ignoring the decimal point.

The way the paper derives the proof is using a configuration space representation for the positions of the two balls: say, if the lighter and heavier balls are at positions $x(t)$ and $y(t)$ respectively at time $t$, then we can denote the configuration by a point $P(t)=(x(t),y(t))$ or a position vector $\vec P(t)=x(t)\hat x+y(t) \hat y$. We also note that collisions happen only when $x=y$, and $y>x\ge 0$ at all time before the final hit, if we consider the wall position to be at the origin.

Thus it turns out that we can plot the trajectory of $P(t)$ as multiple reflections inside an angle $\alpha=AOB$, and we can count the number of hits by counting the number of hits on the line OA and OB.

Galperin showed the number is the nearest integer equal or above $\pi/\alpha-1$, denoted as the ceiling function: $\lceil{ \pi/\alpha}-1\rceil$. Galperin showed that $\alpha=\arctan \sqrt{m/M}=\arctan\sqrt{10^{-N}}$. So the number of hits becomes

$\lceil\pi/\text{arctan}\sqrt{10^{-N}}\rceil-1(\simeq 10^N \pi$ when $\gg 1)$.

One initial check of the formula could be considering the $N=0$ case, i.e. when
the two balls have the same mass. So we can recall the example of elastic collision that I mentioned in the beginning, an extra piece comes due to hitting the wall. So (i) ball 1 hits the standing ball 2 and stops , (ii) ball 2 hits the wall and reflects back, (iii) ball 2 hits the ball 1 and stops where ball 1 starts moving in the opposite direction: number of hits is 3 and we can verify that indeed $\lceil \pi/\text{arctan}-1\rceil=4-1=3$.

However, in the video, Prof. Ed Copeland reaches to a similar conclusion after deriving an expression
for the speed of the heavier ball, starting with an initial speed $U_0$, after $n$ collisions:
$U_n =(1+m/M)\sqrt{m/M}U_0 \cos(n\theta)$, where $\cos\theta=(M-m)/(M+m)$. Now after the last collision (say, when $n=p$), the heavier ball (see Copeland’s notes)
moves in the opposite direction, $U_n$ changes its sign. But before it changes sign it has to pass through zero, which happens when $n\theta=\pi/2$ so that $\cos(n\theta)=0$, thus $\pi/2 > p\theta$ and $(p+1)\theta > \pi/2$.

However, I couldn’t figure out any published reference of Copeland’s derivation. But do you see any mismatch or difference between Galperin and Copeland? There’s an extra factor 16 in $M$ in Copeland’s work and he also needed the $M \gg m$ assumption too. (I’ll probably try to attach a note in future if I can make a connection between the two approaches successfully).

So if this sounds cool, then you may be ready to say, physics is not all about physics only!

Galperin’s paper.

Galperin’s homepage.

# A Higgs or The Higgs? : CERN’s Higgs quest – Part II

Well, now I must come to the point. I shall not pose self-opinions much here (since I’m not at all an expert). Rather I shall mention some quotes, that may help us to understand that whether it’s a right time to say: We have found the Higgs.

I think, the whole controversy started from CERN’s director general, Rolf-Dieter Heuer’s comment on the day of announcement:

As a layman I would say, I think we have it! You agree?

Definitely many people agreed or had to agree. Now when Heuer was asked for a clear message in the press confo, he made it
more elusive:

As a layman I would say we have it, but as a scientist I have to say, ’what do we have?’

So what do we have? Guess, we don’t know yet!

OK, let me just put a few more quotes:

Peter Higgs:
There’s almost definitely a particle there.
They aren’t absolutely sure this particle is the Higgs but it has some key Higgs-like properties.

(Source: http://www.philly.com/philly/blogs/evolution/162362446.html, interviewed by Faye Flam).

Joe Incandela (CMS spokesperson):
As an experimentalist, when we work we have no bias in what we’re seeing. We really want to observe nature. The theory of Higgs led us to look for this particle. We have no prejudgments of nature. We know that the story is not complete …

Fabiola Gianotti (ATLAS spokesperson):
The Standard Model is not complete. It is not the ultimate theory of particle physics and the dream is to find the ultimate theory and we are seeking that.

Fabiola Gianotti (ATLAS spokesperson):
I think we need to be a little patient.

Rolf Heuer:
Well, I think you have to define for me what is “the Higgs boson. If you mean the standard model Higgs boson, then we can’t answer that question at some stage. That will take time because as I said, you have to investigate the properties.”

John Ellis:
Extraordinary claims require extraordinary levels of proof.

Matthew Chalmers:
LHC data confirm discovery, but not identity, of Higgs-like entity.
(Source: http://www.nature.com/news/physicists-find-new-particle-but-is-it-the-higgs-1.10932)

Lily Asquith
Some people started blogging rumours of a discovery this week. This is bizarre – we only stopped taking data on Monday, and that data (basically just electrical signals) has to pass through a long series of steps to analysis, with each step providing ample opportunity for human error.
(Source: http://www.guardian.co.uk/science/life-and-physics/2012/jun/22/higgs-boson-particlephysics)

Jon Butterworth
Now, it looks like the Higgs boson. Or a Higgs boson. But it might not be.
(Source: http://www.guardian.co.uk/science/life-and-physics/2012/jul/04/higgs-like-discovery-inside )

I believe, the 5 $\sigma$ standard just give you confidence, but doesn’t tell anything about the property. If the boson is the standard model Higgs boson, then it must
be a spin-zero scalar. And there are other Higgs boson candidates which may have spin 2, 3, or something
else (spin-1 possibility has been denied for some reason).

That’s why Bill Murray said, We probably shouldn’t call it the Higgs…’A Higgs’ is the word we strictly use.
(Source: http://www.nature.com/news/physicists-declare-victory-in-higgs-hunt-1.10940)

Probably because of other possibilities, a recent paper came up on the arxiv by
Ian Lowa,b, Joseph Lykkenc, and Gabe Shaughnessy with the title Have We Observed the Higgs (Imposter)?. In the abstract they have said,

We show that current LHC data already strongly disfavor both the dilatonic and non-dilatonic singlet imposters. On the other hand, a generic Higgs doublet and a triplet imposter give equally good fits to the measured event rates of the newly observed scalar resonance, although a Standard Model Higgs boson gives a slightly better overall fit. … We emphasize that more precise measurements of the ratio of event rates in the $WW$ over $ZZ$ channels, as well as the event rates in $b\bar{b}$ and $\tau\tau$ channels, are needed to distinguish the Higgs doublet from the triplet imposter.

So we need to wait to know what kind of Higgs boson it is. But I believe, if it is not
the standard model Higgs, then it’s not the Peter Higgs’ Higgs or the Higgs.

Fine. Now what’s the connection between the Higgs boson and the comic sans?

Courtesy: http://www.quantumdiaries.org/

For more details, see

Cern press release:

Press conference full video: CERN, youtube.

# Is it Higgs or Higgs-like? : CERN’s Higgs quest- Part I

I know, the question may annoy many of my particle-physicist friends. Maybe this is because
the question can sound a bit disrespecting the discovery of a new boson announced (with online broadcast) by CERN on 4th of this month. But that is merely a prejudice. And I promise, I’ll try hard to clarify
my intention here.

Though I am a condensed matter theorist by profession, I was alert about the announcement program from
and also placed my ears on the webcast. As anticipated, I did not understand any of the slides that have been presented. But what I came to know that many results fit quite close to the behavior that was anticipated from the standard model theory, which demands the presence of Higgs bosons and they were quite definite that it must be a new kind of a boson. Also I heard something called 4.9 sigma confidence.

Before I realize anything or start thinking or do a google-search, many social network pages went flooded with the message that the God-particle (Higgs boson’s pop name) has been found finally. This sort of reaction and circulation totally blew me up. The next day or maybe the second next day, I started seeing announcements of seminars in Indian Institute of Science (IISc) and National Centre for Biological
Sciences (NCBS) in Bangalore on the “Discovery of Higgs particle”.

So it sounded to me that the verdict has been given: It was the Higgs! I personally never mind if the newly discovered particle becomes “the long-sought Higgs” and rather will gladly admire the beauty of the standard model.

However, my question was: Is the announcement of the discovery clear to the commonplace people? Note that
I said, the announcement, not the physics.

At least to me, it was very unclear until I attended Prof. B. Ananthanarayan‘s talk in IISc on 12th July.
He briefly explained the theory of the Higgs mechanism, which is also known as Englert-Brout-Higgs-Guralnik-Hagen-Kibble (EBHGHK) mechanism, emerges during a spontaneous symmetry breaking (SSB) of a local gauge symmetry (or in other words, presence of a finite vacuum expectation value). To construct a unified theory of the electromagnetic field and the weak force (responsible for the beta-decay) Abdus Salam, Sheldon Glashow and Steven Weinberg (GSW) came up with a SU(2)xU(1) gauge theory, where they introduced gauge bosons namely the $W^\pm$ and $Z$, with an equal footing to the photons for the electromagnetic gauge theory (U(1)). However, due to short-range nature of the weak interaction, the gauge bosons had to have masses in contrast to the massless photons
and to do they cleverly used the idea of Higgs mechanism by introducing an extra spinless scalar field:
the Higgs field. The particle excitations of the Higgs field is the so called Higgs particle or the Higgs boson or the God (damn) particle. As an additional benefit, due to the presence of Higgs field the leptons in the beta decay (even the Higgs boson itself) also acquire masses if we start with massless particles in absence of the field. This unification theory remained an important part of the standard model (SM) and GSW won nobel in 1979 for their contribution.

Birth of the Higgs boson: paper display at CERN museum
(Courtesy: Mou Bhattacharya).

Well, let’s come back to the title: Is the new boson the Higgs boson? Ananthanarayn showed two important
results from the Large Hadron Collider (LHC) experiments to us: one from the CMS and the other from the ATLAS.

The Higgs particles are supposed to be very short-lived. They easily decay to other stable particles.
The CMS data shows distribution of mass of the diphoton decay (Higgs converting into two photons).

Feynman diagram of a typical diphoton decay.

One can easily see a significant bump arises at the mass around 125 GeV, which signifies excess photon
production as one can expect that to happen due to Higgs’ decay. However, the confidence level
(the background significance) for the diphoton channel is 4.1 $\sigma$.
Nevertheless, the CMS spokesperson Joe Incadella summarized on 4th July: “We have observed a new boson with a mass of $125.3\pm0.6$ GeV at 4.9 $\sigma$ significance.”

Ananthanarayan showed the ATLAS data as well. Similar to the CMS one again bumps have been observed
around 126 GeV, this time in two photon channels. Though in the upper channel the bumps are quite obvious,
some of the audience objected saying that it’s a very highly fluctuating data and so they can draw bumps
in other places in principle.

Mass distribution data in the two photon channels of the ATLAS.

Then Anantha showed the probability plot, which shows that the probability of background signal excess is
minimum and is above 5 $\sigma$ (However, I didn’t understand the last line of the caption in
the last figure here.)

The probability of background to produce a signal-like excess for all energies in the ATLAS data.

Now what is this sigma business? Certainly people at CERN know it. So better you should not ask them.
Just because it’s so trivial to them. Let me explain. $\sigma$ is generally used to denote a standard
deviation of a statistical data and for a normal (Gaussian) distribution, which is probably a
typical assumption for the distribution of a large number of independent random variables (see Central Limit Theorem). Now $\sigma$ also indicates the central width of such Gaussian distribution. Therefore higher $\sigma$ should mean towards the tail part of the Gaussian, i.e. the lesser chance
to find a variable there. And 5 $\sigma$ is the particle physicists’ strategy to make a standard
for claiming discoveries, i.e. 99.9999426697% no-chance of background contribution (Likewise 6 $\sigma$ is the businessmen’s strategy). I must acknowledge Gaurav from the CHEP, IISc for helping me to understand this tiny concept.

As sigma increases, the probability decreases in a normal (Gaussian) distribution.

I know, the following questions still remain in your mind:

Well, now what about the title topic? It seems to fit to the Higgs story. So it must be “the Higgs”. Why did you say Higgs-like?

I think, I spoke a lot here. And we need a break too. I’ll make an effort to justify myself in my next post.

PS. I gave a small LHC_Talk in a science show called Dhwani, when LHC just started running.

( Please don’t miss the part -II above. )

Useful references:

4th July webcast –