Parçacık Fiziği 1 Ders Notları

Parçacık Fiziği dersini verdiğim zamanlarda hazırladığım ders notları. David Griffiths'in Introduction to Particle Physics kitabı ile birlikte kullanmak üzere hazırladım. Oldukça kapsamlı ve ek bilgiler içermektedir. Parçacık fiziği öğrenmek isteyenler için yardımcı olacak bir kaynak. 

Bölüm 0  - Bu bölümde Parçacık Fiziği hakkında temel kavramları tanıtılmaktadır. PDF

Klasik Fiziğin sonu ve Modern Fiziğin başlangıcı neresidir, Parçacıklar nasıl üretilir ve nasıl gözlemlenir. Parçacık Fiziği alanında kullanılan birim sistemi nedir? CERN nedir? Büyük Hadron Hızlandırıcısı ve CMS Deneyi. Higgs neye benziyor sorularına cevap vermektedir.

Bölüm 1-1  - Bu bölüm temel parçacık fiziğinin bir çeşit tarihçesi anlatılmaktadır, kısım 1. PDF

Bölüm 1-2  - Bu bölüm temel parçacık fiziğinin bir çeşit tarihçesi anlatılmaktadır, kısım 2. PDF

Çeşitli parçacıkların tarihsel olarak nasıl keşfedildiği ve büyük resmin neresine oturdukları hakkında görüş vermektedir. Temel parçacık için kullanılan bazı temel kavramlar açıklanmaktadır. 

Bölüm 2  - Bu bölüm parçacıkların dinamiği anlatılmaktadır. PDF

Bu bölümde dört temel kuvvet, (Kuantum Elektrodinamiği, Kuantum Renk Dinamiği, Zayıf Etkileşmeler, Elektromanyetik Etkileşimler) Bozunumlar ve Korunum Yasaları ile Büyük Birleşme Senaryoları anlatılmaktadır.

Bölüm 3  - Bu bölüm parçacıkların göreli kinematiği anlatılmaktadır. PDF

Bu bölüm parçacıkların rölativistik çarpışmalarında enerji ve momentumun korunumunu ifade etmek için kullanılan dört vektör cebri ve bazı uygulamaları anlatılmaktadır. Klasik mekanik konularını yeni bir yaklaşım ile daha basit hesaplama yapılabilir.

Bölüm 4  - Bu bölüm parçacıkların etkileşimlerinde simetrinin önemi ve uygulaması anlatılmaktadır. Oldukça önemlidir. PDF

Simetriler, Gruplar ve Korunum Yasaları, Açısal Momentum, Çeşni Simetrileri ve Kesikli Simetriler anlatilmaktadır.

Bölüm 5  - Bu bölüm parçacıkların bağlı durumları incelenmektedir. PDF

Kuantum mekaniğinin önemli uygulamaları temel parçacıklardan oluşan bazı sistemlere uygulanmıştır. Hidrojenin spektrumunda görülen ince yapı ve bunun nasıl ortaya çıktığı anlatılmaktadır. Lamb kayması ve Aşırı ince yapı sabiti anlatılmıştır. Son olarak Pozitronyum ile Kuarkonyum incelenmiş ve kuark dalga fonksiyonlarının kendileri simetri ile birleşimi açıklanmıştır. (Eklenecektir)

Bölüm 6

Bölüm 7

Bölüm 8

Bölüm 9

Bölüm 10

Bölüm 11

Bölüm 12

#particle #physics

International Linear Collider

I think the reader of this blog might already know that the LHC is a powerful machine to discover new particles. However, there are some areas where it is blind. A new machine like a lepton collider is needed to complement all the LHC results. Experimental High Energy Physics community is working on the next project which is called International Linear Collider. ILC could be the next magnifying glass to solve the mysteries of the universe. A nice reading by H. Baer, V. Barger, and J. List.

http://www.scientificamerican.com/article/the-collider-that-could-save-physics/

Power of The Computation

Recently, I am working on a program which calculates the radiative correction and one loop level Feynman diagrams. For that, I am calculating a bunch of Feynman amplitudes of elementary particles. Just to see my program does well, I have calculated a very basic process like $e^+e^- \longrightarrow \mu^+\mu^-$ at one loop level.

Actually, I am working on charging and neutralino pair production in the context of MSSM and one loop level. I wanted to check my little program can calculate scattering processes at one loop level (hopefully radiative corrections too, very soon) so I have calculated a basic QED process and checked it against to available experimental results. After a little search, I have found data available from Novasibirsk in ($\sqrt{S}=980\; MeV \;-\; 1400\;MeV$) energy region. Below you will see two plots for the scattering process, the first one is just zoomed in according to exp. result and the second one is between $200\;MeV\; - \;2000\;MeV$. The blue dots represent the experimental data taken from HEPDATA, the green one is LO calculation and the red one is NLO level. The fitting between NLO result and experiment is amazing as you can see below. 

Comparison of hepdata and calculation at one loop level for $e^+e^-\rightarrow\mu^+\mu^-$ scattering.

UPDATE(1 March 2015): Well the computation is perfected and finally it produced a paper. You may have a look at the neutralino pair production in the context of supersymmetry at ILC. HERE In this work, I have looked at the neutralino pair production in the benchmark scenarios introduced after LHC7 and LHC8 data. The total integrated cross section and angular dependence are also presented.

Open Hardware Revolution (Arduino)

Well, time passes so fast, and you don't sense it after some time. After the great Higgs discovery at CERN, I haven't published anything not because I don't have something to tell, but due to many projects I run, and they need status report every 6-months or so.

Besides I also have a duty as an instructor in undergrad labs and sometimes I find myself thinking whether students could make these demonstrations at homes but not spending a considerable amount of $$$ to a couple of lab suppliers. Lately, I was wondering with an idea of Muon Telescope (using scintillator, PMT, and counter) and there are numerous source available on the web and looking for cheap and affordable Data Acquisition (DAQ) system possibilities. There are NIM and CAMAC crates available in the lab, but these are so-called old generation equipment. Since we are in the 21st century and many achievements have been done over the years on computing and technology, computer-driven, compact and DAQ systems (affordable compared to WME and PXE) could be built up, or I could build one. After spending some time on possible DAQ systems for scientific experiments, I noticed there are compact and cheap DAQ systems from National Instruments for small size experiments. One advantage is you could program your hardware using LabView (another product of NI) and interface it to your computer using USB connection. After doing another search on these, I discovered there are Open Hardware systems too which are almost free compared to NI-DAQ systems, and there are a massive amount of resources on the web for various project. That small gadget is called Arduino, it uses ATMEL micro-controller, it is interfaced with USB, and you could easily program it using C++ as a bonus LabView interface is also available. 

Arduino UNO Rev3.

Arduino has analog input channels as well as digital inputs/outputs, you could read voltages (10-bit resolution) from various sensors, it is possible to PWM, SPI interface, serial too, 16MHz clock and many specs I haven't mentioned here. You could check it here. You might be surprised when you learn how many sensor and shield there are available for Arduino.

I think students could build their own scientific experiments cheaply and quickly using Arduino. It is possible to read temperature, read pressure, connect a GPS module, connect an ethernet shield so you could control the device from the web, ultrasonic range finder, relay and many more. Besides of Muon Telescope, I am building a Geiger Muller detector too which will log the radiation on each location using GPS module, display the values on the screen and send the data to my computer as soon as it arrives home via Wi-Fi. Anyway, it is still progressing, and I will let the readers see the device as soon as build it.

I think Arduino makes a revolution on gadgets we pay a fortune, there is massive support on the web, and there are many possibilities. Just some of them are available here.

The video below is one of the core engineers of project Arduino - Massimo Banzi - gives a TED talk. 

So Long, Thanks for Higgs boson!

Yesterday, 4th of July was one of the remarkable achievement of the mankind has done over the century. I don't know how to describe the discovery of this particle. It was postulated to give mass to the SU(2) gauge bosons, and that mechanism also explained the mass of the fermions in the Standard Model via Yukawa couplings by a couple of Physicists in the 70s and took almost 40 years to find that particle. While studying (in fact I am still) QFT I always wonder if there could be another mechanism for electroweak symmetry breaking or let say not break the symmetry but somehow make them acquire mass by a different mechanism.  For those who seek more theoretical explanation could look at this link.

Let me say couple things about Higgs particle. To capture the Higgs particle or the particles which it decays to took around 50 years (Higgs mechanism proposed around 1964). The reason was due to high background comes from other SM decays which ends up the same particles at the end of the decay thus the Higgs particle couldn't be extracted. I should mention that the production rate is also low compared to other SM processes so it needs high statistics to extract the signal and claim a discovery. Thanks to the detectors which designed to let it seen in and the people who investigated extensively by Monte Carlo studies. In the picture below you can see a real picture of the collision event where Higgs decays to 2 photons. This is one of the channels which Higgs could be extracted at high efficiency from the background. Timestamp of the event is also seen at the top left corner of the picture. The bending lines represent the charged particle deflected due to 4 Tesla magnetic field. Green bars show the energy deposited in electromagnetic calorimeter (ECAL) by the two photons. Since there is not much activity in the barrel region besides these two photons, they are reconstructed at high efficiency. There is some activity at the end caps but could be ignored since new physics or resonances tend to decay at barrel region, and these bars are, most likely, from the underlying activity.

In this figure, you can see Higgs->2 Photon decay.

I think one of the beautiful plots from yesterday's talk was the one where you can see the diphoton invariant mass distribution and the very nice peak around $126GeV$ which indicates a resonance and a boson-like particle. This particle was one of the biggest pieces of the SM unresolved, and finally, it is found and fitted to the picture. But I am afraid this is not the end, in fact, this is just the beginning. There are still many open questions not answered by the SM but beyond the SM theories and these models and theories need to be tested as well. CMS and ATLAS will look at that those BSM signals with growing effort. One question asked by many at CERN is what kind of Higgs is that, for example, SUSY predicts there are 5 Higgs like particles at EW scale and could this resonance is one of these.

This figure shows the invariant Diphoton mass distribution for the selected events.

Another decay channel of higgs particle is 4 lepton channel. Higgs could be extracted from the background if you have a high efficient electron or muon identification. In the plot below you can see the invariant mass distribution from different channels like $Z+X \rightarrow 4 lepton$, Z$\gamma \rightarrow 4 lepton$ and $higgs \rightarrow 4lepton$. The red line shows a peak around $126GeV$, and it is the Higgs particle. 

This figure shows the invariant 4lepton mass distribution for the selected events.

This signal seen here is also recognized by ATLAS collaboration, and the significance of the discovery is around $5\sigma$ in both experiment which means it is likely to happen such a peak at one out of 1.744 Million by statistical fluctuation. In everyday words, it means it is almost impossible to be just a  statistical fluctuation and happen to be a peak at that energy.

I have just stumble upon on a good explanation of the Higgs Mechanism in PhDComics. You could even watch it.

Higgs Search in CMS and ATLAS

While we are coming to the end of this year, there were lots of rumors on Higgs last week. Today at CERN the two big experiment CMS and ATLAS which are explicitly designed to discover the so-called Higgs particle announced the last finding of Higgs.

Both experiments found some excess in $115-130 GeV/c^2$ (ATLAS $115-130GeV/c^2$, CMS $115-127GeV/c^2$) and that could be due to Higgs boson decay. The experimental scientists at CERN carefully analyzed the all known decays of all known particles, then did some Monte Carlo simulations for a particle behaves like Higgs and compared the results. Indeed there is excess both in ATLAS and CMS more importantly in a few different decay channels those channels have quite different backgrounds so seeing that excess is quite significant. If Higgs really exist and its mass is in that region today could be one of the days that will be remembered and mentioned in popular science physics textbooks.

A candidate event for H->Diphoton in CMS.

But in human history there are many false discovery claims, surely it could be false, and in time when we get enough data, the excess could be just a statistical fluctuation. In 2012 the LHC will continue to deliver proton beams and both experiments will continue to gather the data from the debris of proton collisions, possibly at the end of 2012 the data will be at least two folded and then we could certainly falsify the Higgs or celebrate the discovery.

Here you can find the famous excess both in CMS and ATLAS. I also attached statements and the presentations below.

In CMS a total of $~4.6fb^{-1}$ data is analyzed.

In ATLAS in total up to $~4.9fb^{-1}$ data is analyzed.

Scientist to find out whether an excess of the data is indeed a particle or just statistical fluctuations they use statistical techniques. So to claim a discovery, they use a parameter called $sigma$. Let me try to explain simply what the particle physicists mean when they say "we observed an excess with $sigma$ equals to something."

If Newton were sitting under his apple tree and making observations of falling apples, so he can claim the discovery of gravitation, and made 100 observations of falling apples and hitting him in the head and only ONE instance of those falling apples didn't hit him in the head, it is called $\sigma=2.5$. At $\sigma=3$ apples fell and didn't hit Newton in one out of every 370 times. That is not a scientific discovery either. If you observe the falling apples for a more than million times and only one of the apple doesn't hit in the head then we say $\sigma=5$. THAT is what we call a SCIENTIFIC DISCOVERY.

The CMS Statement

The ATLAS Statement

You may also check these links where you could watch the presentations held by ATLAS and CMS Spokesperson, 

http://cdsweb.cern.ch/record/1406052

http://cdsweb.cern.ch/record/1406051

Do the neutrinos break the speed of light?

Neutrinos have such small mass,

we couldn't even measure it but

constrain what it could be at most. 

Last week according to the result published by the OPERA experiment held between CERN (Geneve-Switzerland) and Gran Sasso (Italy) seems like neutrinos- created by electroweak interactions- appears like travel faster than the speed of light. The last report from that experiment suggest that neutrinos with an average energy 17GeV exceed the speed of light about 

$(v-c)/c=2.48\pm0.28(stat.)\pm0.30(sys.) \times 10^{-5}$

here $c=299\,\,\,792\,\,\,458m/s$ is the speed of light in vacuum. Neutrinos are created at CERN, and they travel to Gran Sasso about $730534.61m$ and according to the detailed analysis by OPERA experiment neutrinos exceed the speed of light by an amount of $~7435m$. That seems quite small compared to the speed of light but if it is true the implications on modern physics and the understanding of the laws of the universe are unthinkable. Therefore I would like to point out that since I see a lot of articles about Einstein implying that he was wrong or his theory just broke apart. In fact, in the article about special relativity, he never claimed that nothing could travel higher than the speed of light, contrary he claimed that nothing could accelerate and exceed the speed of light.

To be more clear I would like to write down the speed of light and the speed of neutrinos. 

speed of light         $299\,\,\,792\,\,\,458 \,m/s$

speed of neutrinos  $299\,\,\,799\,\,\,893 \,m/s$

Just notice the last four digits. If you would like to learn much about the experiment or the analysis you could read the report in arXiv.

Update: Recently the OPERA collaboration after more analysis on the data and new data, they analyzed systematic error sources and backed up their first result that neutrinos indeed travel exceeding the speed of light. Sure a lot of discussions and possible explanations for the phenomena emerge, here one of the blog pages where a lot of discussions still going on.

The Crackpot Index

Well, once in a while I indeed face an uneducated fella who claims that Einstein's energy-mass relation is wrong not knowing there is momentum as well in the equation or some other who just discovered a machine that could run forever or a way to produce energy but giving less. Anyway, I have found a way to index all these ideas thank John Baez for supplying this list. Here is some of them

A simple method for rating potentially revolutionary contributions to physics:

1. A -5 point starting credit.
2. 1 point for every statement that is widely agreed on to be false.
3. 2 points for every statement that is clearly vacuous.
4. 3 points for every statement that is logically inconsistent.
5. 5 points for each such statement that is adhered to despite careful correction.
6. 5 points for using a thought experiment that contradicts the results of a widely accepted real experiment.
7. 5 points for each word in all capital letters (except for those with defective keyboards).
8. 5 points for each mention of "Einstien", "Hawkins" or "Feynmann".
9. 10 points for each claim that quantum mechanics is fundamentally misguided (without good evidence).
10. 10 points for pointing out that you have gone to school as if this were evidence of sanity.

The rest of the list.

13.8 Billion Years Ago: All set, let's fire this COLLIDER

Couple of days ago I found a comic on one of the doors in Theory Division @ CERN. I took a photo. Whenever I  look at it still makes me laugh :) I congratulate whoever draw it. Sorry don't know who to credit.

TED Talks

I know a lot of people who watches TED talks, and most of the days I, indeed, try to watch at least one interesting talk I have found irresistible to watch. There are a lot of joy in the stories and also one the speakers. The talks are in wide broad from science, fascinating facts even on how to tie your shoe lashes. I strongly suggest to search or go to main page and look at already smartly labeled talks like

• ... persuasive
• ... courageous
• ... ingenious
• ... fascinating
• ... inspiring
• ... beautiful
• ... funny
• ... informative

The motto of TED is IDEAS WORTH SPREADING.

One talk I found interesting...