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Junpei Fujimoto | KEK | Japan

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アムステルダムにて(at Amsterdam)

Saturday, August 1st, 2009

私ども、GEACE開発チームの何人かが、今オランダのアムステルダムに来ています。アムステルダムにはNIKHEFというオランダの国立の高エネルギー研究所があり、そこの理論家と議論しています。GRACEシステムは加速器実験でおきる素粒子反応の確率を理論に沿って精密に計算して実験と比較することで、理論の正しさや、限界を探る計算プログラムシステムです。GRACE システムは主に2つのパーツからできていて、記号処理を行う部分と、それにより生成された公式を数値化する部分です。


GRACEシステムがはきだす公式はとても巨大です。ひとつの素粒子反応の反応確率を計算するコードは容易に数十ギガバイトを超えてしまいます。NIKHEFの理論家の数式処理プログラムはガンマ行列やレビ・チビタ テンソルといった数学対象の公式がたくさん教え込まれていて、そのためGRACEの吐き出す公式を飛躍的に短くする可能性があります。今回も、新しい公式を導入するために相談に来ました。


We, some of the GRACE team, are staying in Amsterdam to have a meeting with theorists from NIKHEF, National Institute for Subatomic Physics. The GRACE system consists from two parts, treatment of formula in symbolic way and numerical evaluation of the symbolic expression. 


A theorist from NIKHEF has developed the symbolic manipulation system, which is widely used in the particle physics. You may know the Mathematica, of which author is also a particle theorist. Physicists not only offer the new mathematical objects like the delta-function or the path integral, but also the symbolic manipulation systems to treat large scale formula.


The GRACE system produces the formula to calculate the probability of the particle reactions, of which output size becomes more than several ten GB for a reaction. The system developed in Amsterdam equips with a set of formula to treat the special mathematical objects like gamma matrices and Levi-Civita tensor. This feature has great possibility to shrink the output from the GRACE system.


Next week, French physicists and German physicists are also joining to Amsterdam and we have a meeting to discuss the issue about LHC physics. They are also heavy users of the symbolic system and we will exchange ideas to use the system  and problems for the LHC.


GRACE School 2009

Sunday, July 19th, 2009








We, GRACE group, have a plan to hold ‘GRACE school 2009’ at KEK from 31st of Aug. to 3rd of Sept. In this school, it is the purpose for young high energy physicists to calculate the necessary cross section in high energy physics and to be able to generate the simulated events of the particle reactions by themselves.

To investigate the higher order effects, the GRACE system, an automatic calculation system of Feynman amplitude, has been developed. In this school the GRACE system is introduced and you will learn treatment of the infrared divergence and the mass singularity of the photon or gluon radiation.

Unfortunately, this time, the school will be held in Japanese. If you have an idea with Japanese, please refer the following URL;


and take contact with me.


TV viewer rate

Sunday, June 21st, 2009

There are more than 15,000,000 families in Tokyo area. TV viewer survey is performed with 600 families as samples in this region. One wonders whether 600 families are enough as representative of Tokyo area

Statistics tells us the TV viewer survey should be understood with an error bar. The error bar can be calculated with the following equation;

error bar = ±1.96×( p×(1p)/n)^(0.5) with 95% confidence level(CL),


error bar = ±2.58×( p×(1p)/n)^(0.5) with 99% CL,

where n is a number of effective samples and p is the rate. If we put n=600 and p=0.2, then the rate should be understood (20±3.2)% with 95%CL, which means that the rate is located between 16.8% and 23.2% in the probability of 95%. It is interesting that the case of 50% rate has the largest error of ±4.0%.

Now one can understand that why 600 families are picked up. If one likes to have 10 times better accurate rate, number of sampled families should be increased 100 times, then 60,000 families have to be surveyed. It costs much.

Sampling of 600 families seems to be so tiny, but the result from 600 families has enough meaning with an error bar of 3% or 4%. Conversely, it is stupid to assign great value to the difference of the rate in a few-percent level.

TV viewer rate has another good example of the error bar has important role to read the data. One needs to pay attention to the error bar more. It even has an essential role for physicists to see the results from experiments.



誤差の大きさ= ±1.96×( p×(1-p)/n)^(0.5)  (ただし、95%の信頼度で) ,


誤差の大きさ= ±2.58×( p×(1-p)/n)^(0.5)  (ただし、99%の信頼度で),

ここで、nが有効回答数、あるいは視聴率の場合は調査対象となった世帯数に対応し、p はその調査の結果得られた視聴率を表します。もし視聴率が20%でしたという報告があったとき、上の式にしたがって計算すると、95%の信頼度で、視聴率は(20±3.2)%と誤差棒つきで考えることとなります。その意味するところは、600世帯のセットを変えて、100回の調査を実行したら、そのうちの95回の結果は16.8%から23.2%の間に入ってくるでしょう、という予測をしているということです。この式で面白い点は、視聴率が50%のときが4%と一番誤差棒が大きくなるということです。




History of measurement

Monday, June 8th, 2009
History of tau-mass measurement

History of tau-mass measurement

I picked up two figures from a PDF file delivered by PDG.

This plot shows a historical perspective of
measured values of mass of tau-lepton as a function of published data. The first measurement reported 1806± 20 MeV/c^2. The second one did 1784 ± 4 MeV/c^2.

The center values of the measurements seem drifted. One should, however, realize importance of error bars. The first measurement has 20 MeV as error for the center value, which means expected true value can be located between 1806-2*20=1766 MeV/c^2 and 1806+2*20=1846 MeV/c^2 in 95% of time. The most up-dated one, 1776.84 MeV/c^2 is actually located in this range. So whole measurements seem consistent.

History of neutron-lifetime measurement

History of neutron-lifetime measurement

On the other hand, the second plot, which shows another history of measured values of life time of neutron, is bit funny.

In 60’s, it was measured as 1110 +/- 30 sec. In the beginning of 70’s, one experiment reported the center of value was different from previous ones systematically as 920±15 sec. In 90’s, better
observations appeared and finally it is 885.7 ± 0.8 sec.

The difference between 1110 and 885.6 is around 225, which is 7 times larger than 30, the error of 1110. From the statistics consideration, it is very low probability to have such a shift. It seems the first cluster of experiments must have not only statistical error but also systematic error. No one knows, however,at this point what happend there.

These examples are quite instrutive in the following poit;

The center of values themselves from measurements has meaningless. Just the value with a bandwidth constructed by error bar is important.


最初の図は、τ粒子の質量の測定値が歴史的にどう変わってきたかを示すものです。最初の実験はその質量を1806± 20 MeV/c^2と報告しました。で、2番目以降はだいたい1784 ± 4 MeV/c^2.そして結局現時点でのベスト値は1776.84±0.17 MeV/c^2となっています。

この絵をみるとずいぶんと質量の値が変わってきているように見えます。でも、実は中央値の次の誤差の値に注目しなければいけません。最初の値には20MeVという誤差がついていますが、その意味は、τ粒子の質量の真の値は95%の確率で、1766 MeV/c^2(=1806-2*20)と1846 MeV/c^2(=1806+2*20)の間にあるだろうということです。最新の値、1776.84±0.17 MeV/c^2はその中に入っていますから、τの質量の測定は一貫して矛盾なく、そして精度がどんどんとよくなっていることを示しています。

一方、2つ目の図は、やはり測定値の歴史的推移を示していますが、今度は中性子の平均寿命の測定に関してです。60年代にはだいたいどの測定も1110 +/- 30秒ということでした。ところが70年代に入ってひとつの実験がそれまでの測定値とやや異なった値を発表すると、920±15秒あたりとなりました。現在は885.7 ± 0.8秒ということになっています。





Proton and electron

Thursday, May 28th, 2009

We still play with PDG site. Let’s see the property of proton. Please click “Baryon” after “Particle Listing” to enter the world of baryons, which are the family of three-quarks bound states. You will click “p” for proton from “N (Nucleon) baryons” to get a PDF file on proton.

Again, a lot of properties of proton are reported. Let’s focus on the value of the neutrality of matter;

(qp + qe )/ e < 1.0 x 10-21.

of which result was got from observation on neutrality of the sulfur hexafluoride, SF6 (Ref. Physical Review A (1973) 1224).

We can see the difference of absolute value of charges between proton and electron is less than 10-21! In other words, in such a precision, the absolute charges of proton and electron are identical. Of course, atoms should have neutrality, but interesting point is the size or level of neutrality.

Proton is constructed of 2 up-quarks and one down-quark .The standard theory assumes up-quark has +2/3 charge, down-quark has -1/3 charge in the unit of the absolute charge of electron. Of course electron is assumed to have -1 charge.

It is, however, just assumption,then ,as usual, experiments have been performed to check.

This assumption has no theoretical bases, the following becomes a question; why absolute values of electron and proton charges have the same value. This is one of reasons to go to the beyond the standard theory or the grand-unified theory (GUT), in which electron and quarks should have reason for their charge.

In addition, we have another necessity for the relation of -1, +2/3, -1/3 among electron, up-quark and down-quark. You may have heard about the word, ‘generation’. Usually it is explained that electron-neutrino, electron, up-quark and down-quark form the 1st generation, muon, muon-neutrino, muon, charm-quark and strange-quark do the 2nd one, and finally tau- neutrino, tau, top-quark and bottom-quark do the third one.

The predictable theory must have such a group. You can make summation of the total charge in each generation: electron-neutrino has 0, electron has -1, up-quark has +2/3, but there are three types up-quarks, red up-quark, green up-quark and blue up-quark, then the charge from up-quark in total is +2/3×3=+2. Also there are three types of down-quark, then -1/3×3=-1. As a result, the total charge of each generation is 0-1+2-1=0!!

I said “predictable theory”. If the sum of charge in each generation differs from 0, then that theory loses the predictability, i.e., it just gives us the infinite probability of the reaction, which has no meaning at all.

That’s why the result on the value of the neutrality of matter is important and this is unknow part of the structure of nature.

もう少しPDGで遊んでみます。今度は陽子について見てみましょう。”Particle Listing”から”Baryon”をクリックして3つのクォークからなるバリオン粒子の世界に入ってみます。で、”N (Nucleon) baryons”から陽子(proton)を意味する”p”をクリックすると、陽子に関する測定値が書いてあるPDFファイルが開きます。

ここでは、”the value of the neutrality of matter”(物質の電荷の中性さの度合い)に注目してみます。;

(qp + qe)/e < 1.0 x 10-21.

これは六フッ化硫黄ガスを使ってその中性度を測った実験からの結果です。(論文はPhysical Review A (1973) 1224です。)









Size of electron

Tuesday, May 19th, 2009

This is continuation of the previous blog. Electron has various nature. PDG is reporting the following values;
1) Electron mass:0.510998910 +/- 0.000000013 MeV/C2.
2) Mass difference between electron(e) and positro(e+) : (Me+–Me)/(Me++Me) < 8×10–9.
3) Charge difference between e+ and e : (qe+–qe)/e < 4×10–8.
4) Electron magnetic moment(g) anomaly: (g-2)/2=(1159.65218111 +/- 0.00000074)x10–6.
5) g anomaly difference between e+ and e: (g_e+-g_e/g(average) = (-0.5 +/- 2.1)x10–12.
6) Electron dipole moment(d): d = (0.069 +/- 0.074)x 10–26 ecm
7) Electron mean life from e to electron neutrino and photon : > 4.6×1026 yr .

You see electron is so stable more than 1024 years from 7) .

How about the size of electron? As a matter of fact, there is no direct report on it. Alternatively, there is a measurement on the compositeness of electron. In the framework of the standard theory, electron and positron are assumed as point-like particle, which means they have no spread and no structure in space, and they can be scattered just via photon.

But one can consider that we just can’t see the size of electron because we have poor accelerators. If electron has a structure, we must observe the reaction of direct scattering of electron and positron using enough magnification by the more powerful accelerator.

This effect can be introduced to put assumed compositeness scale into the equation of electron of which dimension should be the energy. Experiments have measured the angular distribution of electron or positron through the reaction: e+ e going to e+ e, so called Bhabha scattering, and have seen the difference from the distribution predicted by the standard theory. Up to now, the distribution is consistent well with the theory, then the statistical treatment tells us the lower limit of the compositeness.

In PDG, it is reported in “Other searches (SUSY, Compositeness, …)” after “Particle Listing”, the scale of contact interactions should be more than 8 TeV. Because the corresponding length is inverse of energy scale, it means that electron has no structure more than in 1/1018 m.


1) 電子の質量:0.510998910 +/- 0.000000013 MeV/C2.
2) 電子と陽電子の質量の差
:(Me+–Me)/(Me++Me) < 8×10–9.(つまり差は観測されていなし)
3) 電子と陽電子の電荷の差:(qe+–qe)/e < 4×10–8(やはり差は観測されていない)
4) 電子の異常磁気モーメント(2からのずれ): (g-2)/2=(1159.65218111 +/- 0.00000074)x10–6. (非常に精度よく測定されています。)
5) 電子と陽電子の異常磁気モーメントの差: (g_e+-g_e/g(average) = (-0.5 +/- 2.1)x10–12.(これも差はないということ)
6) 電子の2重極モーメント(d):d = (0.069 +/- 0.074)x 10–26 ecm
7) 電子がニュートリノと光子に崩壊する平均寿命: 4.6×1026 年以上(つまり崩壊は観測されていない)





PDGでは、”Particle Listing”で、”Other searches (SUSY, Compositeness, …)”をクリックすると実験結果が報告されており、それによると、そのエネルギースケールの下限値は8000GeVであることがわかります。このエネルギースケールの逆数が”長さ”に対応するので、結局電子の大きさは1/1018 m以下であると測定されていると言えるのです。



Monday, May 11th, 2009

A lot of experiments are under going and new improved values of measurements are going to be reported. Do you know where physicists pick up the most updated and reliable values? There is a PDG(Particle Data Group) site to have a great database on the measured properties of particles, which is funded by US DOE,US NSF, CERN,MEXT(Japan), INFN(Italy),MEC(Spain) and IHEP & RFBR (Russia).

http://ccwww.kek.jp/pdg/ is one of the mirror home pages of PDG.

Home page of PDG

From ‘Particle Listing’ please enter to the world of particles. You will find “electron” after “LEPTONS (e, mu, tau, neutrinos, heavy leptons …)” and see “J=1/2” in the headline which means electron is a spin-half particle. For example, the most updated value of the mass of electron in MeV/c^2 unit is 0.510998910±0.000000013 where c means the speed of light.

You may not be familiar with MeV unit. MeV means Mega electron Volts. If you like to check the conversion factor from ‘kg’ to ‘MeV’, please visit “Reviews, Tables, Plots” page from the top page. You soon find it in “Physical Constants (Rev.)” after “Constants, Units, Atomic and Nuclear Properties”, which tells us

1 eV/c^2 = 1.782 661 758(44) × 10^{-36} kg, then

the electron mass in kg unit should be 0.910938 x 10^{-30}kg !!

Please also notice the precision of the value of the electron mass has 7 effective digits. You must wonder how one can get such one. PDG also tells you about the reference of the experiments, too. The previous number was the averaged one of various experiments reported by Peter J. Mohr, Barry N. Taylor, and David B. Newel in arXiv:0801.0028(preprint server) entitled “CODATA Recommended Values of the Fundamental Physical Constants:2006.” Each experiment to measure the mass of electron can be seen, for example, in the paper of Physical Review Letters Vol. 88, 0011603 in 2001 by Thomas Beier, Hartmut Ha”ffner, Nikolaus Hermanspahn, Savely G. Karshenboim, H.-Ju”rgen Kluge, Wolfgang Quint, Stefan Stahl, Jose’ Verdu’, and Gu”nther Werth where they compared Larmor frequency of the electron bound in a 12C^{5+} ion with the cyclotron frequency of a single trapped 12C^{5+} ion.

Please enjoy PDG trek.



トップページの”Particle Listing”から、入って、”LEPTONS (e, mu, tau, neutrinos, heavy leptons …)”に入り、更に”electron”にたどり着けば、それが電子のいろいろな性質に関する測定値のページとなります。”electron”の見出しのすぐ横に”J=1/2″と書いてありますが、それは電子がスピン1/2の粒子であることを示すものです。ちょっと下の方を見ると、MeV/c^2という単位で計ったときの電子の質量の値、0.510998910±0.000000013を見つけることができるでしょう。

MeVというのは、100万電子ボルトのことです。アインシュタインの式、E=mc^2により、エネルギーの単位、電子ボルトを光の速度cの二乗で割れば、それば質量(m)になります。でも換算係数がないとピンとこないでしょう。その換算係数もこのサイトで探すことができます。トップページから”Reviews, Tables, Plots” に入り直して、”Constants, Units, Atomic and Nuclear Properties”の中の”Physical Constants (Rev.)”に行けば、

1 eV/c^2 = 1.782 661 758(44) × 10^{-36} kg

と載っています。ですので、電子の質量は0.910938 x 10^{-30}kgということになります。上記の電子の質量の桁数にご注目ください。なんと、7桁も有効数字があります。こんなに精度よくどうやって測定したのだろうと思われることでしょう。PDGは測定値のみではなく、その測定を行った実験の論文も紹介しています。先ほどの7桁の電子の質量は、Peter J. Mohr, Barry N. Taylor, and David B. Newelたちが、それまでに行われた電子の質量に関する測定値を平均して得た値で、プレプリントサーバーに投稿した”CODATA Recommended Values of the Fundamental Physical Constants:2006.”という題名の論文(arXiv:0801.0028)に掲載されていた値です。その平均値のもととなる個々の測定についても記述があります。たとえば、Thomas Beierらが行い、学術論文誌Physical Review Lettersの2001年の88巻の0011603に発表された、炭素イオン12C^{+5}に捕獲された電子のラーモア振動数とサイクロトロン振動数との比較から得られた値、0.510998901±0.000000020も載っています。




Monday, May 4th, 2009
S. Ramanujan

S. Ramanujan( from http://www.math.rochester.edu/u/faculty/doug/)

I was asked by a friend of mine to read the blog to give him an example that numbers are interesting. It reminds me a very famous episode of S. Ramanujan, who was an Indian mathematician in the early 20th cent. He found tremendous numbers of mathematical formulas or relationships among numbers. When he was in the bed of a hospital, an English mathematician, G.H. Hardy visited his room, and said that he took a taxi of which plate number was 1729, and that this number was quite trivial one. But Ramanujan immediately answered that 1729 was quite interesting one, because it was the minimum number which could be presented by the sum of two cubic numbers in two ways, as follows;

1729 = 12^3 + 1^3 = 10^3 + 9^3.

It is natural to have a question why Ramanujan so quickly remembered 12^3=1728. Those days, Fermat’s Last Theorem, relating to cubic numbers, was one of the center problems among mathematicians. So it is not so strange, in some sense.


R.P. Feynman( photo by Magnus Waller)

This question is, however, solved by R.P. Feynman who was an American physicist, establishing the theory of electron and photon, quantum electrodynamics(QED) in the middle of 20th cent. Almost the same number appears in the book, ‘Surely you are joking, Mr. Feynman!’ That number is 1729.03.

At a restaurant in Brazil, Feynman had to compete against a Japanese who was very good at counting on the abacus. The problem was to calculate cubic root of 1729.03. Feynman immediately remembered 1728 = 12^3 because a cubic foot is 1728 cubic inches. Then Feynman used Taylor expansion to get better accurate solution, 12.002, before the Japanese got a result with his abacus. We, Japanese, do not use inch-feet system. But we can learn from this story that 1 foot is 12 inches! I wonder a large fraction of Europeans or Americans must know well about 1728=12^3.

But it was just Ramanujan who realized 1729 had such an interesting nature. Especially it is not trivial to prove 1729 is the minimum one. In this context, it is natural to agree with another English mathematician, J.E. Littlewood to say “Every positive integer is one of Ramanujan’s personal friends”.








Public Lecture at TILC09

Wednesday, April 29th, 2009

TILC09, an international workshop was held in Tsukuba, Japan, from the 17th of to the 21st of April, which was the eleventh in the series of meetings on the physics and detector of the ILC organized by the Asian Committee for Future Accelerators (ACFA) joint Linear Collider Physics and Detector Working Group. It also represented the eleventh of the major meetings to host the ILC Global design effort (GDE) discussion which pursues the development of the design and project planning for the ILC accelerator systems. More than 200 physicists got together and discussed physics on ILC and the action plan toward construction of the ILC in the international framework. (http://tilc09.kek.jp/)


Posters of TILC09(illustrator Yuji Kaida) and of a public lecture

This workshop series has a tradition to have a public lecture as a satellite session. The date was also coincident with a week of science-technology outreaching set by theMinistry of Education, Culture, Sports, Science and Technology, then it was intended to invite families to the fun world of physics, of which title was Missing of anti-matters is the greatest magic of the universe with three presenters, Prof. Hitoshi Murayama from Institute for the Physics and Mathematics of the Universe (IPMU Tokyo Univ.), Dr. Takeo Higuchi from KEK as a member of Belle collaboration and Mr. Tomohiro Maeda, a Close Up Magician.

In the part 1, Prof. Murayama explained matter and anti-matter using Pikachu and anti-Pikachu, which was enough to pull children into the physics. He also explained the concept of energy, the kinetic energy and potential energy with short movies like http://www.youtube.com/watch?v=FdCJzO3w7_M.

After his presentation, three presenters were on the stage to make a panel discussion. Mr. Maeda played in total three magics which were related to the energy conservation, the prediction of the phenomena and the reaction of particles. Dr. Higuchi told people that anti-matter is other specialty goods of Tsukuba city in the sense that KEK leads the world in positron production.

Around 300 questionnaires were back among 500 audiences. One-fifth was young people less than 20 years old. Compared with the age distribution in usual event on physics or science-café, it was quite young. In the end, several children raised their hand to ask questions. I was personally afraid no questions by them, but it was needless fear. Even a 10 years old boy said he wished to be a physicist of KEK. More young Japanese are moving away from the sciences. It is important to attract them to the physics world with various way. It’s also important to remember that the questionnaires told us that two-thirds were the first-time participants to the event on the particle physics. They went back home with words, anti-matter, Higgs particle, accelerator and ILC in mind.Please also visit http://tmaeda.exblog.jp/9615443/ of Mr. Maeda’s web page (in Japanese) to see his followers’ opinion for this event.

It is told that the movie of this event is planned to be posted in near future.








Quantification 4 — not enough —

Friday, April 24th, 2009
Title page of “Discorsi e Dimostrazioni Mathematiche” in 1638

Title page of “Discorsi e Dimostrazioni Mathematiche” in 1638

Before closing a series of “Quantification”, I have to say the quantification is not enough to study physics, of course. A good example is Einstein’s theory of relativity. As often your reading the text book, there are Galilei’s relativity principle and Einstein’s relativity one. The latter is finite light-velocity version of the former.

In the book by Galilei, “Discorsi e Dimostrazioni Mathematiche” in 1638, he even proposed to measure the speed of light using the distance of two mountains, but light was too fast to get the value. Ole Christensen Romer, a Danish astronomer, in 1676 made the first quantitative measurements of the speed of light to use a satellite of Jupiter, of which value was 214300km/s. Romer’s result that the velocity of light was finite was not fully accepted until measurements of the aberration of light were made by James Bradley in 1727, of which value was 299042km/s. In 1849, Armand Hippolyte Louis Fizeau, a French physicist, got the value 315300±500km/s on the ground to use a special apparatus with gears.In 1862, Jean Bernard Leon Foucault, a French physicist, got 298000±500km/s with mirrors system.

We can see the quantification of the speed of light was already well done in the middle of 19th cent. Light was also identified as the electro-magnetic wave from its value of the speed. Nobody, however, realized it had a special meaning that light had finite speed. Maxwell’s equations of the electromagnetism obeys the version of the relativity principle with the finite speed of light, but Newton’s eq. of motion does not! This observation caused Einstein to postulate the speed of light in free space is the same for all observers. It was leap to the modern physics. So the quantification is indispensable but not enough to reach to physics.

The first part of the paper on the theory of special relativity by Einstein, Annalen der Physik, 17(1905)

The first part of the paper on the theory of special relativity by Einstein, Annalen der Physik, 17(1905)