Scientists recently announced that the latest experimental results on the mass of the W boson deviated from the theoretical prediction by one thousandth of a percent, causing widespread concern. what is the W boson? What does its mass deviation mean?

By Zhang Hao (Associate Researcher, Department of Theoretical Physics, Institute of High Energy Physics, Chinese Academy of Sciences)

Editor/Ding Lin Li Yunfeng

Recently, the CDF experimental group at Fermi National Laboratory has published the latest analysis of the mass measurements of the Standard Model W boson. The results have attracted the attention of physicists because of the difference of more than 7 times the standard deviation from the theoretical expectation of the Standard Model of particle physics (Standard Model).

What is the W boson? How was its mass measured? What does this deviation found by the new study imply? This paper attempts to briefly introduce these questions to the reader.

1

Who is W?

In 1896, the French physicist Henri Becquerel discovered the phenomenon of natural radioactivity. It was soon discovered that there are three types of rays with different penetrating abilities in natural radioactive phenomena - alpha rays, beta rays and gamma rays.

▲ By studying the deflection of radiation in a magnetic field, physicists found that radiation includes positively charged, negatively charged and uncharged three kinds, and named them α-rays, β-rays and γ-rays. The process of emitting β-rays is a decay process, so it is called β-decay. (Image source: Human Education Textbook)

For the "classical" physicists of the late 19th century, this was a completely new phenomenon, and many of its properties were puzzling. Its study initiated the history of human understanding of various elementary particles and their interactions over the next century or so.

Today, physicists who have mastered the tools of relativistic quantum field theory are well able to understand natural radioactivity, especially the origin of beta rays in it. The production of beta rays is the result of a completely new type of interaction - a weak interaction - distinct from gravity and electromagnetism.

Similar to the electromagnetic force that exists between "charged" particles, there is a "weak force" between certain particles if they have a so-called "weak charge". Beta rays in natural radioactivity are simply the result of the "decay" of a neutron in the nucleus into a proton, an electron and an (anti-electron) neutrino under the action of a weak force.

▲ Schematic diagram of neutron decay (image source: science.org)

One thing that tends to confuse people (and, indeed, physicists have been confused about this for some time in history) is that this decay does not mean that the neutrons are made up of these three particles. It is like an electron turning in an electromagnetic field, although it radiates electromagnetic waves (photons), it does not mean that the original electron is composed of the later electron and the radiated photons. Similarly, we should not think of neutrons as a "mini-solar system" of protons, electrons and neutrinos circling each other.

The (uncritical) analogy above is perfectly fine to continue. Now physicists know that neutrons, protons, electrons and neutrinos all have a weak charge. We can imagine, without being strict, that the neutron "radiates" the electron and neutrino and turns itself into another weakly charged particle, the proton.

Unfortunately, such a simple description is not allowed in a "well-behaved" quantum field theory. Physicists spent decades understanding the difficulties and finally realized that neutrons can only "throw" one particle at a time, so in the process of neutron decay, there must be a new particle, which is called the W boson. The capital letter W comes from the word "weak" (Weak) for weak interaction.

2

W's "theoretical weight"

Speaking of the latest results from Fermilab that don't match theoretical expectations, how heavy should the theory predict the W boson to be? It's more than 85 times the mass of a neutron!

Wasn't the W "thrown" by the neutron? How can it be heavier than a neutron?

The study on the "overweight" of the W boson was published as the cover article of Science in early April.

In fact, this is precisely the result of the "inability to measure principle" of quantum physics. Under the action of the weak force, a neutron can "throw out" a W boson and become a proton, and a W boson can "throw out" an anti-electron neutrino and become an electron. Although it is against the law of energy conservation for a neutron to "eject" a much heavier W boson, according to the "energy-time uncertainty relation" in quantum physics, as long as the process occurs in a short enough time, it will not As long as the process occurs in a short enough time, it will not "exhibit" any effect that breaks the conservation of energy. Physicists estimate the mass of the W boson by calculating the rate of neutron decay - this is the earliest information we have about the mass of the W boson.

Today, various particles from the Standard Model of particle physics have been experimentally observed, and particle physicists have made numerous measurements of the interaction properties of these particles, not the least of which are some very precise measurements. There are no direct measurements of W boson masses in these observations, but they depend in principle on only a few (at most a dozen) physical parameters. Physicists can invert the mass of the W boson by calculating these observed quantities. That is, if the Standard Model is correct, the mass of the W boson should be this large to explain the experimental data on particle physics described above - this is the origin of the Standard Model's expectation of the mass of the W boson. Today this expectation is 80,357 MeV, which is 85.644 times the mass of the proton. The accuracy of this estimate is as high as 0.75 parts per million!

The Collider Detector (CDF) at Fermi National Accelerator Laboratory collected a large amount of high-energy particle collision data between 1985-2011, pictured during the dismantling of the CDF (Photo credit: Fermilab)

3

How to measure the mass of W "directly"?

Although the Standard Model has predicted the mass of the W boson with great accuracy, particle physicists still need to make "direct" measurements of it as an important physical quantity. If this measurement is consistent with theoretical expectations, it will be a great success for the Standard Model, and if not, it may be a signal from "new physics" beyond the Standard Model.

Measuring the masses of elementary particles is very difficult; they are too small and light compared to macroscopic objects to be weighed directly on a balance. On the other hand, many of the elementary particles decay rapidly. The good thing is that for such decaying particles (including the W boson), physicists can record the motion information of other particles produced by their decay in particle detectors, and then recombine the energy and momentum of these particles to restore the information of the particles before decaying, so as to calculate their masses. In principle, this method of measuring the mass of unstable particles is somewhat similar to the method suggested by Xu Chu in the story "Cao Chong Weighs the Elephant": remove the elephant in eight pieces, weigh each piece and then add them up.

▲This computer image shows the event of the W boson decaying into positrons (magenta block, bottom left) and undetected neutrinos (yellow arrows) in the CDF detector (image source: nature.com)

Another difficulty faced in measuring the mass of the W boson is that one of the two particles of its decay products is a neutrino, a particle that cannot be captured and recorded by the collider's detectors. Therefore, we cannot get information about every piece of "meat" of the "elephant". The good thing is that physicists can still infer the mass of the W boson by using the statistical distribution of the motion of the other decay product, the electron (or muon).

Based on the above principle, the experimentalists of the CDF experiment team analyzed very carefully the "huge amount" of experimental data left in the Tevatron collider of Fermi National Laboratory, which was shut down more than ten years ago, and finally obtained the most accurate direct measurement of the W boson mass in the world: 80433.5 MeV, which is an amazing precision of 1.17 parts per million!

4

How can the anomalous results be explained?

We will find by a simple calculation that there is a difference of about one thousandth (76.5 MeV) between the theoretical expectation of the W boson mass (80,357 MeV), and the latest experimental result (80,433.5 MeV). This difference may seem insignificant, but both the theoretical expectation and the experimental measurement have a claimed error of about one ten thousandth of one percent.

The results are based on data from trillions of CDF "proton-antiproton" collision experiments (image credit: Baylor University)

The measurement deviates from the Standard Model prediction by a factor of "seven standard deviations," to use the customary expression in particle physics.

What does 7 times the standard deviation mean? It means that assuming that there are no errors in the theoretical calculations and measurements, no new physics beyond the existing theory, and both error estimates are reasonable, the probability of such a result resulting purely from statistical ups and downs and random experimental bias falls in a region outside the 7 times standard deviation of the central value of the normal distribution. The reader familiar with statistics can obtain with a simple calculation tool that this probability is only 0.00000000000256 (if the calculator is not accurate enough, it will simply report a 0). This probability can also be interpreted in the reverse direction: the probability that the experimental observation is wrong, that there is new physics, or that the error estimate is faulty is as high as 99.999999999999999754%.

▲ In a normal distribution, the larger the standard deviation of the data from the middle value (μ), the smaller the probability of occurrence. For example, the probability of occurrence of data with standard deviation other than 3σ is only about 0.27% (image source: mit.edu)

In the particle physics community, the standard of deviation required to overturn the results of established theories is typically 5 times the standard deviation. That is, physicists will say "new physics has been discovered" when the deviation between observations and theory is 5 times the standard deviation (or higher), otherwise it is classified as a "potential" problem. The choice of the "5-fold" threshold involves various considerations, including industry practices, historical experience, and so on. However, it is enough to realize that such a high deviation means that something must be wrong, and that it is unlikely to be a statistical rise or fall.

So what went wrong? There are several possibilities as follows.

(1) The existence of new physics: This is certainly the most exciting explanation. In fact, within just a few days of the experimental article being published online, there have been dozens of theoretical articles that attempt to explain this deviation in terms of new physics effects beyond those of the standard model. Among them are successful examples that also show some of the challenges such deviations pose to the new physical model. Of course, since other experimental measurements of the W boson mass to date (within the error tolerance) are consistent with the theoretical expectations of the Standard Model, all of these "new physics" models still need to answer the question of why only the CDF experimental results show such mass deviations.

▲CDF's newly released measurement results are extremely accurate. In contrast, the measurements from earlier experiments are closer to the theoretical predictions of the Standard Model (Photo credit: Science)

(2) Errors in calculations or experimental measurements of Standard Model expectations: Historically, there have been bizarre results such as the "superluminal neutrino" that reached six times the standard deviation and turned out to be low-level experimental errors. However, the probability of either of these two scenarios is extremely low in this case.

(3) The error of the result is underestimated: As mentioned above, the measurement result of the CDF experiment does not give the mass of W boson directly, but needs to compare the distribution of certain properties of the decay product particles collected by the detector with the distribution given by the theory under different W boson mass parameters, and the W mass is the measurement result when the two are in the best agreement. Is there an underestimated error in this process? This is currently a major concern for theorists. After all, this is a result with an accuracy of the order of one ten thousandth of a percent, and any error that is not significant at the level of one hundredth or one thousandth of a percent accuracy may show up to have a significant impact.

The results of this measurement by the CDF experimental group are another important advance in particle physics precision measurement experiments. In the future, the interpretation of the final results, either of the above, will deepen the scientific community's understanding of the physics behind them. On the other hand, more precise experiments are expected to make independent measurements of the W boson mass with higher precision and less uncertainty. This task can only be left to future leptonic colliders such as CEPC and FCC-ee.

Producer: Beijing Science and Technology News | North Tech Media

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