The top student must be diligent.

Chapter 164 The whole audience was shocked
Time passed quietly.

Soon, the news that Xiao Yi was going to give a report spread within the Institute of High Energy Physics. After all, it was arranged by Director Tang Yifang, so it spread quickly.

Various discussions immediately arose within the Institute of High Energy Physics.

"Xiao Yi actually came to our institute to hold a report meeting?"

"Xiao Yi actually came to our research institute?"

"Who is Xiao Yi?"

"The village doesn't have internet yet."

"It was arranged by Director Tang, and the director asked all the researchers and associate researchers in the institute to temporarily put down their work and attend. As for others, it is recommended that they attend."

"Ah? Why? Is his report so important that so many of us have to go?"

"Who knows? Doesn't he study mathematics? And now he has made achievements in our high-energy physics?"

"Ahem, after all, our high-energy physics and mathematical physics are closely related. Maybe they really have something very important."

"But what is the title of his lecture?"

"It seems to be called... Hmm, it feels a bit strange. It's called: Experimental Error Analysis and Data Processing?"

"What? Error analysis... and data processing? So it has a lot to do with mathematics?"

"Hiss...it seems to be true?"

"Ah!!! Why is it mathematics!"

For a moment, many people showed painful expressions.

Although experimental error analysis and data processing are very important in their field, the accuracy of many results is related to this.

However, for them, this kind of thing is too painful to learn!

However, there is no way out. The director has made a request, and all of them, researchers or associate researchers, must participate. What else can they do?

All we can do is wait for the report day to arrive.

……

The time came until the day before the report.

On that day, two banners were posted at the entrance of the Institute of High Energy Physics, one in Chinese and one in English.

The above means: [Welcome Professor George Parisi and his team from CERN to visit the Institute of High Energy Physics for exchanges and learning! ]

At ten o'clock in the morning, a bus stopped in front of the institute. As the door opened, foreign faces kept getting off the bus.

The leader was an old professor who looked very Italian.

This person is George Parisi, a giant in the field of theoretical physics and a candidate for the Nobel Prize in Physics. At the same time, he has also won almost all other awards in physics. In the first half of this year, he also won the Wolf Prize in Physics, which is second only to the Nobel Prize in terms of gold content.

According to some experience in previous years, the Wolf Prize is a barometer of the Nobel Prize. Maybe he will become the winner of the Nobel Prize in Physics in October this year.
It can be said that it is a very rare thing to be able to invite him to the Institute of High Energy Physics for exchanges and studies.

In front of the car door, Tang Yifang and all the leaders of the Institute of High Energy Physics were already standing there waiting. When they saw the big boss coming down, they all went to greet him.

"Professor Parisi, welcome!"

Tang Yifang walked up and shook hands with George Parisi.

George Parisi nodded and said, "Hello, Professor Tang. I am very happy to come to the Institute of High Energy Physics of China and communicate with you."

While talking, they introduced their people to each other, and finally, all the people from CERN were welcomed into the institute.

Tang Yifang began to explain the arrangements for the next exchange with George Parisi: "Today I will mainly introduce you to our Institute of Physics, and then BEPC, and then..."

Before he could finish his sentence, George Parisi interrupted him and said, "There's no need to go into details. The collision energy at BEPC is too low, and you can't do any experiments with high enough energy."

"I'm more interested in what you told me yesterday about the report tomorrow."

George Parisi asked, "That math genius Xiao Yi, tomorrow's report might involve a very important discovery?"

Tang Yifang was stunned, thinking that this was indeed the matter that concerned him the most.

Then he smiled and nodded and said, "Yes, Professor Parisi, you should also know that Xiao Yi is a mathematical genius, so he provided a new error analysis and processing method for our particle collision experimental errors."

"After processing a type of data using his new method, he discovered something that was inconsistent with current theoretical data."

George Parisi was immediately surprised: "It doesn't match the current theoretical data? Is this certain?"

Tang Yifang nodded and said, "According to Xiao Yi's calculations, this is the case."

George Parisi began to think.

If this is true, it would be a very significant discovery.

After a moment, he asked, "When will the presentation be tomorrow?"

When Tang Yifang heard him ask this, he laughed. It was obvious that the other party was interested.

"Ten o'clock tomorrow morning."

"Okay! Then I'm looking forward to tomorrow's report meeting." Parisi said, "But, which theoretical data do you mean is inconsistent?"

Tang Yifang smiled apologetically: "This... let me keep it a secret for now, you will know when I report tomorrow."

"Oh?" George Parisi raised his eyebrows, then smiled and said, "Okay."

……

The arrival of George Parisi and his team immediately made the Institute of High Energy Physics lively, but it did not have much impact on Xiao Yi.

There was less than a day left before the report was due, and during these days, in addition to further optimizing the error analysis and processing methods, he also used the optimized methods to process more experimental data.

Almost two thousand data have been processed.

All of these data show that the W boson is indeed very likely to be overweight. The difference in standard deviation basically reaches at least 5 σ, or even more than 5 σ. Quite a few exceed 6 to 7 σ, or even more.

Of course, the amount of data in 2000 is still relatively small, but it is enough to make the physics community begin to doubt the mass of the W boson in the standard model.

"Just wait for tomorrow's report."

According to the data calculated on the draft paper, Xiao Yi smiled slightly, then put the papers away.

At this moment, his peripheral vision caught sight of several other sheets of draft paper beside the corner of the table.

Take these draft papers and you will see a bunch of dazzling physics derivations written on them.

【L_YM=1/4FμνaFaμν……】

【Fμνa=μAνaνAμa+gf^abcAμbAνc……】

These things are all related to the Yang-Mills equations.

These days, he has also begun to study the quality gap problem.

Although the existence of the mass gap has been verified in many experiments, it has not yet been proven mathematically.

Only by proving it mathematically can physicists gain a deeper understanding of the strong interaction and ensure the internal consistency and rigor of the non-Abelian gauge theory. This will provide a solid theoretical foundation for the academic community, avoiding internal contradictions and inconsistencies when unifying different interactions at a higher level.

In particular, grand unified theories attempt to unify the strong and electroweak interactions into a single gauge group at high energy scales.

Therefore, it is obvious that once the mass gap problem is proven, it will indirectly help the unification of the three fundamental forces of strong, electric and weak forces.

"Hmm...how can I prove this?"

Looking at this question, Xiao Yi fell into deep thought.

Faced with this kind of mathematical proof in physics, he, who had previously been studying pure mathematical problems, felt a little uncomfortable.

However, this problem is not a big deal, after all, we still need to follow various mathematical methods.
In this way, time slowly passed, and many thoughts emerged in Xiao Yi's mind.

However, there is still a long way to go to solve this problem.

Just like that, another day passed.

……

The next day, 10 am.

The largest lecture hall at the Institute of High Energy Physics was almost full of people.

All the researchers and associate researchers of the Institute of High Energy Physics are already in it, and there are also some assistant researchers and intern researchers who came to participate because of their interest. Of course, there are also other postdoctoral fellows, graduate students, etc., a total of about 150 people.

In addition to these researchers from the Institute of High Energy Physics, there is also the team of Professor George Parisi from CERN.

At this time, Professor George Parisi and Director Tang Yifang were sitting in the middle of the first row. In the seat next to them, Xiao Yi was communicating with Professor Parisi because the report had not officially started yet.

"I heard from Professor Tang that your research results can find a result that is inconsistent with the predictions of the Standard Model, right?"

Parisi asked, smiling.

Xiao Yi nodded: "Yes, according to my calculations..."

But before he could finish, Parisi reached out to stop him: "Okay, let's talk about this matter when you report later."

He glanced at Tang Yifang beside him with a smile and said, "After all, Professor Tang told me yesterday to know it from your speech in today's report, so there is no need to rush to say it now."

"Professor Tang, isn't that right?"

Tang Yifang laughed: "Since Professor Parisi thinks so, then we naturally cannot let you down. Xiao Yi, it's up to you later."

"No problem at all."

Xiao Yi smiled and nodded.

At this time, the time for the speech had officially arrived. He stopped talking nonsense and walked directly to the stage.

The lecture hall quickly fell silent. Standing on the podium and facing the many physicists present, Xiao Yi bowed slightly, then smiled and said, "Hello everyone, I am very happy to be able to share my recent achievements with you at the Institute of High Energy Physics."

"First of all, I would like to thank Director Tang for arranging such a report for me. At the same time, I would also like to thank Professor Parisi for being willing to attend my report."

"To be honest, although I have made many reports, this is my first time making a physics report, so please forgive me if there are any mistakes later."

"Well, without further ado, let's get to the point."

Xiao Yi clicked on the multimedia, the PPT lit up, and the theme of the report appeared on the screen.

【Experimental error analysis and data processing】

"For any experiment, due to the limitations of technical means, various errors will inevitably occur when measuring data, and these errors will greatly affect our judgment of the results."

"This is especially true for high-energy physics. After all, what we are observing is the collision of particles at speeds reaching 99.99% of the speed of light, and the events that occur may even disappear in just a few microseconds, so the data obtained in the end becomes even more inaccurate."

"For this, we have to use more advanced error analysis methods to help us analyze which part of the experimental data is error and which part is real, and then use data processing methods to retain the real data."

Xiao Yi smiled: "It is said that the relationship between mathematics and physics can be described as close. I think this point can also prove it."

The people present laughed.

"In this report, I bring you a more sophisticated error analysis and processing method, which can help us further extract effective information from the data."

"Next, I will directly use a set of experimental data to give an example."

The PPT moved, and then a set of data appeared on it.

"This is a set of signal data about the lepton decay mode of the W boson."
"We all know that the W boson can decay into a lepton and a neutrino, where the lepton can be an electron, a muon, or a tau."

As he spoke, Xiao Yi also came to the blackboard next to him and wrote on it: [W±→±+ν].

"The data I chose is the combination of the W boson decaying into high-energy electrons and neutrinos, where the electrons are detected by the electromagnetic calorimeter in the detector, and the electron energy given here is 45.38 GeV."

"Since neutrinos cannot be detected directly, their presence is manifested by missing transverse momentum, which we obtained here is 35.31 GeV."

"Okay, now, let's use traditional methods to analyze the errors."

"First, we consider the energy resolution error of the detector and calculate the measurement error of the electron momentum and MET..."

"Then we calculate it through the error propagation formula."

【σM=√￣[(MσE/E)^2+(MσMET/MET)^2]】

……

"Finally, we calculated the partial derivatives and substituted the values. The final mass we got was 80.319±0.044GeV. According to the calculation of the standard model, the mass of the W boson should be 80.379, with an error within 2 standard deviations."

Xiao Yi turned his head and looked at the people present, and said: "Obviously, whether it is the 79.319 we calculated or the standard deviation of 0.044, the gap is quite large. Of course, this may also be because the confidence level of a single data point is too low."

"But please let me borrow this data and analyze it using my new method."

"First, we need to recalibrate the detector's data. Here, the method I use is maximum likelihood estimation. Of course, if we simply use maximum likelihood estimation, there will definitely still be a gap. So, I will need to introduce some new methods here..."

Xiao Yi's mouth curled up slightly, he turned around and started writing on the blackboard.

As he demonstrated a few simple steps, Tang Yifang and Parisi both narrowed their eyes in the audience.

This mathematical method...

It seems a little different?

Xiao Yi actually introduced a new algorithm to optimize the maximum likelihood estimation!

Among the others, some people also more or less noticed some of the mysteries and showed surprised expressions.

"… In this way, we calibrated the data of this detector, and the data we finally obtained was: electron momentum 45.84 GeV, missing transverse momentum 35.65 GeV."

After coming up with this result, Xiao Yi did not stop and continued to the next step: "Next, we will analyze the error."

"Using the error propagation formula in general here certainly cannot meet our requirements."

"Other existing systematic error analysis methods have limitations when dealing with complex data and cannot fully separate and quantify the impact of various error sources."

"For this, we need to introduce an Error Matrix first."

Error matrix.

Offstage, when Tang Yifang heard Xiao Yi mention this, he quickly recalled the method Xiao Yi introduced to him ten days ago. It must be said that the error matrix is ​​indeed a very ingenious method.

Parisi, who was sitting next to him, took out paper and pen at some point and started calculating with Xiao Yi.

Obviously he had been completely attracted by what Xiao Yi said.

When he heard the error matrix proposed by Xiao Yi, he looked up again and listened carefully.

In this way, time passed slowly, and Xiao Yi finally finished explaining the error analysis framework.

“…Finally, we combine all the individual error components and plug them into a new error propagation formula to calculate the total systematic error.”

"This new error propagation formula can help us to divide the nonlinear relationship and interaction between various error sources in more detail."

"That way, we can end up with a much cleaner data set."

"Now, let's plug in the initial data..."

"We can get the final result that the mass of this W boson is 80.471±0.027GeV!"

Seeing this result, Parisi narrowed his eyes immediately.

This result...

If we consider the range of 5 standard deviations, it would be [80.336, 80.606].

Compared to the 80.379 predicted by the standard model, this lower limit is already a bit dangerous!

That’s almost 4 standard deviations!

He suddenly realized why Xiao Yi used the W boson as an example.

Could it be...

"Of course, this result is relatively average."

"I don't see anything special. Perhaps the only thing worth noting is that the gap between its mass and the W boson mass predicted by the Standard Model is close to 4 standard deviations."

"But if we use this data method to process 2000 sets of data, what will the final result be?"

Xiao Yi smiled slightly and revealed the answer.

As the pages on the PPT turned, the results finally appeared.

【80.438±0.011GeV】

Just now, because Xiao Yi mentioned the standard deviation, when the people in the audience saw this result, they immediately calculated the lower limit of five standard deviations of this result.
80.383!

"What the hell?!"

"I bought it!"

All of a sudden, the audience below exclaimed.

"What's this?!"

"So, the mass of the W boson is higher than the value predicted by the Standard Model?"

"This value really exceeds 5 standard deviations!"

"Not really... it's only over 4MeV, right?"

"Isn't that enough? Even if the lower bound is only 4MeV, that's enough! Isn't that enough to publish a PRL?"

……

The entire lecture hall began to be filled with various low-pitched discussions, and the previous silence turned into noise.

How could they not be excited by a discovery beyond the Standard Model?
This means new discoveries in physics!

However, Xiao Yi did not stop them. After all, this was exactly the effect he wanted.

At this time, Professor Parisi in the first row suddenly asked, "You only have 1 pieces of data?"

Xiao Yi nodded: "Yes, and these data are all derived from the most recent collision results of BEPC."

"The amount of data is still a little small..." Parisi pondered for a moment, and finally said: "I must say that your report really gave me a big surprise."

"It's not just the problem of the W boson being overweight. We all know that the mass of the W boson is given by the Higgs mechanism. So once the mass of the W boson does not match the predicted value under the standard model, it is very likely that the Higgs mechanism has problems, or is imperfect."

“But, as I said, the amount of data is still too small.”

"If you can get results with more data, I think that would help prove your results."

After listening to Parisi's words, Xiao Yi nodded.

At this time, Tang Yifang said: "Professor Parisi, I need your help. The data from the LHC may help us get a more accurate result."

"This one……"

Parisi thought about it, and finally said: "It's possible, but you also know that the latest data of LHC will not be released in the first few years. Xiao Yi needs to come up with something that can convince CERN."

Then, he turned to look at Xiao Yi and said, "If you can write the contents of this report into a paper and publish it, I can convince CERN to provide this part of the data."

In response, Xiao Yi nodded naturally: "Of course no problem."

"Okay." Parisi smiled and said, "Then I'll wait for you to finish your paper."

……

(End of this chapter)