内容来源：https://www.quantamagazine.org/how-many-elementary-particles-are-there-really-20260615/

内容总结：

标准模型下的基础粒子到底有多少个？答案远比你想象的复杂

当人们走进中学物理教室，墙上的标准模型海报通常会展示17种基本粒子：12种物质粒子（包括电子、μ子、τ子、三种中微子和六种夸克）、4种力的载体（光子、W和Z玻色子、胶子），以及赋予其他粒子质量的希格斯玻色子。哈佛大学粒子物理学教授梅丽莎·富兰克林明确表示：“我认为17就是正确答案。”

然而，这个看似简单的数字背后隐藏着巨大的复杂性。事实上，物理学界对此远未达成共识。

从17到37：反物质与色荷的加入

首先，为了满足狭义相对论的要求，每种物质粒子都有对应的反粒子。这意味着12种物质粒子实际上有24种。加上W+和W-两种带电玻色子（电中性的Z玻色子、光子和胶子没有反粒子），粒子总数跃升至30。

但还有更多。传递强力的胶子其实有8种，每种携带不同的“色荷”组合。夸克同样具有三种色荷（红、绿、蓝），反夸克则有相应的反色荷。这样算下来，六种夸克及其反夸克实际上有36种。如果把这些都计入，粒子总数达到了61种。

螺旋性与极化：从61到118

更细致的分类涉及“手性”——粒子可分为左旋和右旋两种状态。力的载体粒子也有类似的极化状态：光子和胶子有左、右两种极化，而W±和Z玻色子还多出一种“纵向”极化状态。如果逐一计算每种手性和极化状态，粒子总数将达到118种。

奇怪的物理学：非整数自由度

但物理学家们并未止步于此。他们用“自由度”这一更精确的数学概念来计数。2011年，物理学家亚当·施维默和佐哈尔·科马戈德斯基完成了一项引人注目的计算，证明在四维时空的量子场论中，每个标量场（如希格斯场）有1个自由度，每个物质场有5.5个自由度，每个力场有62个自由度。将这些数字代入标准模型，最终得出的自由度总数是——995.5个。

科马戈德斯基坦言：“1、5.5、62——这些数字就这么从定理中蹦出来了。我完全不知道大自然为什么选择了这些数字。”

结论：答案不是整数

剑桥大学物理学家、教科书作者戴维·通在一开始就给出了最诚实的回答：“我认为这个问题的真正答案不是整数！”他解释说，随着能量尺度的变化，可观测的粒子数量也在改变。在极高能量的早期宇宙中，可能存在许多现今无法产生的高能粒子；而在极低能量下，可能只剩下光子。

正如粒子物理学家克里斯·奎格所说：“我坚持区分左旋和右旋粒子。”但每个人对“基本粒子”的定义都不同。从富兰克林坚持的17种，到最大主义者心目中的118种，再到纯粹数学概念的995.5个自由度——这个看似简单的问题，实际上将我们带到了粒子物理学已知世界的边缘。“潜台词是：量子场论极其困难，我们并不擅长它，”通总结道，“我们还有很多不明白的地方。”

中文翻译：

究竟有多少种基本粒子？
导言
每当我撰写关于粒子物理学的文章时，总会对一个初看似乎明确的问题产生不确定感：我究竟应该说有多少种基本粒子？
在欧洲大型强子对撞机的实验中，物理学家将质子束相互撞击，将其分解成所有可能的基本碎片。与此同时，他们拥有一套极其精确的数学方程组，用以描述这些基本构件及其所有组合方式。因此，既然自然界已知粒子既可以被经验观测到，也可以用理论来描述，你可能会认为它们也能被数清。但可惜并非如此。我知道，由于某些我们即将探讨的原因，这份“粒子人口普查”并不像看上去那么简单。
于是，我最近给几位物理学家发了邮件，询问他们各自是如何统计自然界基本组分的。第一个显示问题复杂程度的迹象，来自剑桥大学物理学家、教科书作者戴维·唐（David Tong）在安排视频通话时的回复：“附注：我认为你问题的真正答案不是一个整数！”
我们稍后会谈到这一点（它源自2011年一项神秘的推算），不过让我们先从最表层开始进入这个“兔子洞”。
已知的基本粒子及其相互作用遵循一套被称为粒子物理标准模型的方程组。标准模型是一种“量子场论”，它用数学描述现实，认为一种称为“量子场”的实体遍布宇宙。在这些场中传播的涟漪就是我们所说的基本粒子；有些表现得像物质，而另一些则传递力。标准模型中的量子场及相关粒子构成了除引力、暗物质和暗能量（所有这些在基本层面上都以未知形式存在）之外所有已知物理现象的基础。
在教室墙上的海报中，标准模型展示了17种粒子。其中有12种物质粒子，或称费米子：电子、μ子、τ子；三种中微子；以及六种夸克。每种粒子对各种力都有不同的敏感度。还有四种传递力的粒子，或称“玻色子”：光子（传递电磁力）、W和Z玻色子（传递弱力）以及胶子（传递强力）。最后，还有希格斯玻色子，它是一种所谓的标量粒子，既非物质也非力；相反，它通过与其它粒子的相互作用赋予它们质量。
事情可能就这么简单。“我认为17是正确答案，”哈佛大学粒子物理学教授梅丽莎·富兰克林（Melissa Franklin）告诉我。
但每一位粒子物理学家，包括富兰克林在内，都承认存在一些保留意见。
从17开始，你可以继续数下去。你在哪里停止，取决于你对复杂性和神秘性的偏好。有多少种粒子这个问题，将我们带到了关于物质最基本层面已知知识的边缘。
17这个数字有一个明显的问题。为了满足狭义相对论，标准模型中的每一个物质场都同时支持一个粒子和一个“反粒子”，后者除了电荷相反外，与粒子完全相同。这就是我们通常所说的反物质。因此，实际上不是12种物质粒子，而是24种。同样，W玻色子也有带相反电荷的类型，称为W+和W−。（而Z玻色子、光子或胶子则不是这样；它们是电中性的。）
富兰克林表示，她在统计中排除了反粒子，因为在数学上它们或多或少是其粒子版本的镜像。（奇特的是，反粒子相当于在时间中逆向运动的粒子，反之亦然。）两者互为存在前提，因此不应重复计数。
但我认为这个理由缺乏说服力。粒子和反粒子无疑是不同的，即使它们是秘密的双胞胎。它们不能相互转化（中微子可能是个例外，它可能是也可能不是自身的反粒子），而且远非功能对等，它们在现实中扮演着完全不同的角色。在我们的宇宙中，物质占绝对主导地位，任何反物质通常都会迅速与物质相遇并湮灭。宇宙中这种物质-反物质不对称的原因，是物理学的一个重大谜团。
将反粒子算在内，总数达到了30。
但认为只有一种胶子的观点是另一种过度简化。实际上，强力是由八种胶子（及其相关场）传递的，每种胶子都拥有独特的“颜色”和“反颜色”电荷组合。不同的胶子在实验上无法区分，因此当我就是否应该逐一统计所有八种胶子提问时，身为实验学家的富兰克林嗤之以鼻并摇了摇头。然而，在定义标准模型的数学方程中，八种胶子彼此不同，其差异方式与W和Z玻色子之间的不同类似。为了保持一致性，我们可能不得不数上所有八种。这样一来，我们现在有37种了。
夸克也有颜色——三种可能性被称为红、绿、蓝——而反夸克则有反颜色，称为反红、反绿、反蓝。（不要太费劲去想象反红色；这些并非我们熟悉的光学颜色，尽管它们在数学上的组合方式是类似的。）这些颜色反映了胶子和夸克如何相互作用。
为了能够稳定孤立地存在，物质必须是颜色中性的。因此，正如红光、绿光和蓝光混合成白光一样，红、蓝、绿夸克也形成颜色中性的质子和中子（原子的基本构件）。
所以，不是六种夸克和六种反夸克，而是总共有36种。这就使得基本粒子的数量变成了61种。但还不止于此。
物质粒子还分为左旋和右旋两种类型，这种性质被称为手性——可以说是一个关键的区别。“我坚持认为有左旋和右旋粒子，”费米国家加速器实验室的资深粒子理论家克里斯·奎格（Chris Quigg）告诉我。“我无法解释这一点。怪我父母吧。”（更独特的是，奎格将传递力的粒子从他的列表中剔除，因为他认为它们是物质粒子的变换形式，而非粒子本身。）
手性是化学家在分子中看到的或我们在手臂末端看到的“手性”的量子版本。它不像那些是几何排列，但在数学上，这两种状态互为镜像；你不能通过旋转将一个变成另一个，就像你不能把左手变成右手一样。传递力的粒子也有类似区别，称为偏振态。光子和胶子可以是左偏振或右偏振，而W+、W−和Z玻色子还有第三种“纵向”偏振态。（这额外的状态有一个复杂的起源，与希格斯场以及大爆炸期间的事件有关。）
并非每个人都将这些不同的手性和偏振态视为不同的粒子类型。但这样做是合乎逻辑的，因为它们影响粒子的行为和相互作用方式。例如，弱力只影响左旋物质粒子。出于相关原因，中微子在标准模型中仅以左旋形式出现。这些是物理上不同的状态，在自然界中扮演着不同的角色。单独计算每种手性和偏振态，我们会得到118种粒子——从右旋、反红、反粲夸克，到绿-反蓝、左偏振胶子，再到纵向W−玻色子。
“现在，”唐说，“奇怪的部分来了。”
物理学家将粒子可以变化的所有方式称为“自由度”——粒子能拥有的每个状态对应一个不同的自由度。例如，颜色包含三个自由度：红、绿、蓝。但这些差异超出了我们已描述的状态。我们可以认为，对所有自由度的统计，是“究竟有多少种基本粒子”这个问题的一个更精确、更数学化的版本。
物理学家们早已注意到自由度中的一个规律：其数量取决于你计数的尺度。在我们日常现实的尺度上，描述一个物体所需的变量比描述其所有微观组成成分状态所需的变量要少。当你放大观察，比如说一个质子，揭示其组成夸克及其颜色和其他各种属性时，你会观察到更多的运动或变化方式——即更多的自由度。这就是难以确定粒子总数的主要原因之一。你越深入观察，它们的类别就越分化。
此外，大爆炸初期可能充满了额外的高能粒子，这些粒子无法在我们当前的低能宇宙中形成，也不属于标准模型。例如，许多针对高能早期宇宙的模型扩展都假定存在重右旋中微子，但这些中微子现在永远不会产生。“随着能量尺度的降低，”唐说，“你在这个过程中不断失去粒子，因为它们太重了”，因此只在更高能量下才有可能存在。“随着能量尺度的降低，你失去了对这些粒子的了解。”如果我们继续沿着这个思路，在极低能量下，就只剩下一种粒子：光子。因为光子没有质量，它们可以趋近于零能量。
人们自然会想，是否有可能进行全面核算。包括所有那些在最高能量和最小距离尺度上我们无法探测的自由度在内，究竟有多少基本自由度？这就引出了唐提到的由亚当·施维默（Adam Schwimmer）和佐哈尔·科马戈德斯基（Zohar Komargodski）在2011年完成的那项引人入胜的计算。
石溪大学的理论物理学家科马戈德斯基向我解释了这一点。我刚才提到一个趋势，即当我们从宇宙尺度上“拉远视角”时，能够探测到的有效自由度会减少。1989年，物理学家约翰·卡迪（John Cardy）猜想这是一条任何量子场论都必须遵循的不可违反的规则。该规则在数学上已被证明适用于描述沿直线运动的粒子的一维空间加一维时间的量子场论。但像标准模型这样涉及三维空间加时间（称为3+1D）的理论又如何呢？
魏茨曼科学研究所的物理学名誉教授施维默和科马戈德斯基证明了卡迪的猜想。他们的“a定理”在量子场论学家中备受赞誉，该定理指出，在3+1D量子场论中，当你拉远视角时，有效自由度的数量必须始终减少。他们通过探索量子场在四个不同位置受引力拉扯时如何响应，证明了这是普遍成立的。
他们的证明还得出一个关于在标准模型这样的3+1D量子场论中必须有多少基本自由度的奇怪结论。证明显示，量子场的变异数量不能是任意的。相反，只允许特定的值：像希格斯场这样的标量场只有一个自由度。物质场必须各有5.5个自由度。而力场各有62个自由度。这些数字是数学上得出的，与我们迄今为止讨论的具体粒子状态无关。“其他数值都不行，”科马戈德斯基说。
“1，5½，62——它们是从定理中‘蹦’出来的，”他补充道。“我完全不知道为什么自然界选择了这些数字。”
唐解释说，分数自由度（比如物质场多出来的那半个自由度）是那些并非完全独立于其他场自由度的变化。一个粒子可能的状态可能取决于另一个粒子的状态。“你往那边一踢，突然就乱套了，场到处都在振荡，”他说。
那么，假设标准模型中每个标量场、物质场和力场分别拥有上述的自由度数，总数是多少呢？科马戈德斯基暂停了我们的谈话，去问了ChatGPT，提供了相关数字，然后复核了它的计算。答案是：995.5。这显然就是标准模型中自由度的数量。
我不禁感到困惑。而且这似乎是普遍反应。
“这一切的背后，都说明了量子场论极其困难，而我们在这方面还不太擅长，”唐说。“我们还有很多不理解的地方。”
就我个人而言，在有多少种粒子这个问题上，我发现自己是个“最大化主义者”，即使（或者说正因为）这是一条通往谜团之路。但我也能理解17这个数字的魅力。

英文来源：

How Many Elementary Particles Are There, Really?
Introduction
Every time I write about particle physics, I encounter a moment of uncertainty about a quantity that, at first glance, ought to be clear. How many kinds of elementary particles should I say there are?
In experiments at the Large Hadron Collider, physicists smash together beams of protons, breaking them up into all possible elementary bits and pieces. Meanwhile, they have an incredibly accurate set of mathematical equations for describing these building blocks and all the ways they fit together. So, since the known particles of nature can be both empirically observed and theoretically described, you would think they could also be counted. But alas not. I knew that, for reasons we’ll see, the census is not so easy as it seems.
So I recently emailed a few physicists to ask how each of them personally tallies nature’s fundamental constituents. The first indicator of just how complicated the issue is came in a reply from David Tong, the University of Cambridge physicist and textbook author, when we were scheduling a video call: “P.S. I think the true answer to your question is not an integer!”
We’ll get to that (it comes from a mysterious calculation from 2011), but let’s enter this rabbit hole from the top.
The known elementary particles and their interactions obey a set of equations called the Standard Model of particle physics. The Standard Model is a “quantum field theory,” a mathematical description of reality in which entities called quantum fields permeate the universe. Ripples moving through these fields are what we call elementary particles; some behave like matter, while others impart forces. The quantum fields and associated particles in the Standard Model underlie all known physical phenomena other than gravity, dark matter, and dark energy (all of which take unknown forms at a fundamental level).
In posters on classroom walls, the Standard Model displays 17 particles. There are 12 matter particles, or fermions: the electron, muon, and tau; three neutrinos; and six quarks. Each of them has a distinct set of sensitivities to various forces. There are also four force-carrying particles, or “bosons”: the photon (which imparts the electromagnetic force), the W and Z bosons (the weak force), and the gluon (the strong force). Finally, there’s the Higgs boson, a so-called scalar particle that’s neither matter nor force; rather, it imbues other particles with mass through its interactions with them.
It may just be this simple. “I think 17 is the right answer,” Melissa Franklin, a professor of particle physics at Harvard University, told me.
But every particle physicist, Franklin included, recognizes that there are caveats.
From 17, you can keep counting. Where you stop depends on your taste for complexity and mystery. The question of how many particles there are brings us to the edge of what’s known about the most basic levels of stuff.
There is one glaring problem with 17. To satisfy special relativity, each of the Standard Model’s matter fields supports both a particle and an “antiparticle,” which is identical to the particle except for having the opposite electric charge. This is what we popularly know as antimatter. So instead of 12 matter particles, there are really 24. Likewise, W bosons come in oppositely charged types known as W+ and W−. (This doesn’t happen to the Z bosons, photons, or gluons; they’re electrically neutral.)
Franklin excludes antiparticles from her census, she said, because mathematically they more or less mirror their particle versions. (Bizarrely, antiparticles are equivalent to particles moving backward in time, and vice versa.) Neither is possible without the other, so they shouldn’t be counted twice.
But I find that rationale unconvincing. Particles and antiparticles are undeniably distinct, even if they are secret twins. They can’t transform into each other (with the possible exception of neutrinos, which may or may not be their own antiparticles), and far from being functionally equivalent, they play totally different roles in reality. Matter is so dominant in our universe that any antimatter typically encounters matter quickly and annihilates. The reason for the cosmos’s matter-antimatter asymmetry is a major physics mystery.
Antiparticles bring the total up to 30.
But the notion that there’s only one gluon is another oversimplification. Really, the strong force is conveyed by eight gluons (and their associated fields), each possessing a distinct blend of charges known as “colors” and “anticolors.” The different gluons are impossible to distinguish experimentally, so Franklin, being an experimentalist, scoffed and shook her head when I asked if all eight should be tallied individually. Yet in the mathematical equations that define the Standard Model, the eight gluons are distinct from one another in the same way that the W and Z bosons differ. For consistency’s sake, we probably have to count all eight. So now we’re at 37.
Quarks come in colors, too — the three possibilities are dubbed red, green, and blue — and antiquarks have anticolors, called anti-red, anti-green, and anti-blue. (Don’t try too hard to picture anti-red; these aren’t our familiar optical colors, though they combine in a manner that’s analogous mathematically.) The colors reflect how gluons and quarks interact with each other.
For matter to exist in stable isolation, it must be color-neutral. So, just as red light, green light, and blue light blend to make white, so do red, blue, and green quarks form color-neutral protons and neutrons (the building blocks of atoms).
So there aren’t six quarks and six antiquarks but rather 36 in total. And that makes 61 elementary particles. But there’s more.
Matter particles also come in left-handed and right-handed varieties, a quality known as chirality — arguably a crucial distinction. “I insist on left- and right-handed particles,” Chris Quigg, a senior particle theorist at the Fermi National Accelerator Laboratory, told me. “I can’t account for this. Blame my parents.” (Far more idiosyncratically, Quigg leaves the force-carrying particles off his list, as he considers them to be transformations of matter particles rather than particles themselves.)
Chirality is a quantum version of the handedness that chemists see in molecules or that we see at the ends of our arms. It is not a geometric arrangement like those, but mathematically the two states are mirror images of one another; you can’t rotate one to turn it into the other, any more than you can with left and right hands. The force-carrying particles have an analogous distinction, known as a polarization state. Photons and gluons can be either left- or right-polarized, while the W+, W−, and Z bosons have a third, “longitudinal” polarization state as well. (That extra state has a complicated origin connected to the Higgs field and events during the Big Bang.)
Not everyone counts these different chiral and polarization states as distinct particle types. Yet it’s logical to do so, because they affect how particles behave and interact. The weak force, for example, affects only left-handed matter particles. For related reasons, neutrinos appear only in a left-handed form in the Standard Model. These are physically distinct states with different roles in nature. Counting each chirality and polarization state separately gets us to 118 particles — from a right-handed, anti-red, anti-charm quark to a green–anti-blue, left-polarized gluon, to a longitudinal W− boson.
“Now,” Tong said, “comes the weird stuff.”
Physicists call all the ways that particles can vary “degrees of freedom” — with a different degree of freedom for each state a particle can hold. Color, for example, comprises three degrees of freedom: red, green, and blue. But those differences go beyond the states we have already described. We might consider the tally of all these degrees of freedom as a more precise, mathematical version of the question of how many elementary particles there can be.
Physicists have long noticed a pattern in the degrees of freedom: The number of them depends on the scale at which you count them. On the scale of our everyday reality, objects are describable with fewer variables than it takes to specify the states of all the microscopic constituents. When you zoom in on, say, a proton, and reveal its constituent quarks with their colors and various other properties, you’ll observe more ways of moving or varying — more degrees of freedom. This is one of the main reasons it’s so difficult to pin down the particle population. The closer you get, the more their categories splinter.
Furthermore, the beginning of the Big Bang might have abounded with additional, high-energy particles that can’t form in our current, low-energy universe and aren’t part of the Standard Model. For instance, many extensions of the model to the high-energy early universe posit the existence of heavy right-handed neutrinos, but these would never arise now. “As you go down in energy scale,” Tong said, “you’re losing particles as you go, because they’re so heavy,” and therefore only possible at much higher energies. “As you go down in energy scale you lose knowledge of those particles.” If we continue to follow this idea, at very low energies only one particle is left: the photon. Because they’re massless, photons can approach zero energy.
It’s natural to wonder if a full accounting is possible. How many fundamental degrees of freedom are there, including all of those at the very highest energies and most microscopic distances that we can’t possibly detect? This brings us to the fascinating 2011 calculation Tong told me about, by Adam Schwimmer and Zohar Komargodski.
Komargodski, a theoretical physicist at Stony Brook University, walked me through it. I just mentioned the trend in which, as we zoom out in the universe, we’re able to detect fewer effective degrees of freedom. In 1989, the physicist John Cardy conjectured that this is an inviolable rule that any quantum field theory must follow. The rule had already been mathematically proved true of quantum field theories with one space and one time dimension, which describe particles moving along lines. But what about theories like the Standard Model, which involves three spatial dimensions plus time (called 3 + 1D)?
Schwimmer, an emeritus professor of physics at the Weizmann Institute of Science, and Komargodski proved Cardy’s conjecture. Their “a theorem,” acclaimed among quantum field theorists, says that in 3 + 1D quantum field theories, the number of effective degrees of freedom must always decrease as you zoom out. They showed that this is universally true by exploring how quantum fields must respond to gravity tugging on them in four different places.
Their proof also yielded a strange conclusion about how many fundamental degrees of freedom there must be in 3 + 1D quantum field theories such as the Standard Model. Quantum fields, the proof showed, cannot have just any number of variations. To the contrary, only specific values are allowed: Scalar fields such as the Higgs field have just one degree of freedom. Matter fields must each have 5.5 degrees of freedom. And force fields each have 62 degrees of freedom. These figures emerge mathematically, without regard to the specific particle states we’ve been discussing to this point. “And nothing else works,” Komargodski said.
“One, 5½, 62 — they pop out of the theorem,” he added. “I have no idea why this is what nature chose.”
Tong explained that fractional degrees of freedom (like that extra half degree possessed by matter fields) are variations that aren’t fully independent from those of other fields. What’s possible with one particle might depend on the state of another. “You kick that way, and suddenly all hell breaks loose, and the field is oscillating all over the place,” he said.
So assuming the respective number of degrees of freedom for each scalar, matter, and force field in the Standard Model, how many does that make? Komargodski paused our conversation to ask ChatGPT, providing the relevant numbers, and then checked its work. The answer: 995.5. That’s apparently how many degrees of freedom there are in the Standard Model.
I can’t help but feel flummoxed. And apparently that’s the general reaction.
“Underlying all of this is the statement that quantum field theory is unbelievably hard and we’re not very good at it,” Tong said. “There’s still a lot we don’t understand.”
Personally, I find myself to be a maximalist on the question of how many particles there are, even though (or because) it is a path to mystery. But I also see the appeal of 17.