Questions tagged [pions]

Pions, or pi mesons, are particles that consist of a quark and an antiquark of either up or down flavour. The exchange of virtual pions provides an explanation for the residual strong force between nucleons.

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Quark condensate and VEV of $\pi^0$

In David Tong's lectures on the Standard Model I saw that there is a quark condensate, which is just a Vacuum Expectation Value (VEV) of the $\bar{q}_{Li}\, q_{Ri}$ operator, $$ \left< \bar{q}_{Li}...
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How does pion exchange cause protons and neutrons to be attracted to each other? [duplicate]

I read that neutron and protons are attracted through exchanging pions between each other. However, as far as I understand, they are just exchanging a meson, not any force carriers. What causes them ...
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How are $\pi$ Mesons Created in the Residual Strong Interaction?

Watching this episode of PBS Space Time, they run an animation of how pi mesons are exchanged by nucleons as the residual strong interaction to overcome proton electromagnetic repulsion. https://youtu....
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Does most of the Universe's mass come from pions (or 'virtual' pions) rather than gluons and quarks?

After the discovery of the Higgs boson, we were all told that most of a proton's or neutron's mass does not actually come from their three main ('valence') quarks and their interaction with the Higgs, ...
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Kinematics in the pion decay

If a charged pion decays via a charged current $W$, the $W$ boson is much heavier than the pions. How is this not a problem? Could the processes be off-shell in such a drastic manner? It is tempting ...
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Why is Pionless Effective Field Theory Preferred in Modeling Nuclei for Fermion Scattering Processes?

There's a recurring preference for pionless effective field theory in recent papers modeling nuclei for fermion scattering processes (e.g., here). Why is pionless effective field theory commonly ...
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How to obtain the amplitude for the leptonic pion decay?

Consider the leptonic decay of the pion $$\pi^{+}\rightarrow l^{+}\nu_{l}$$ In my notes there's written that in order to compute the associated rate we can use the effective Lagrangian $$\mathcal{L}^{\...
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No gluon interaction between nucleons

Given the spatial overlap of nucleon wave functions within the nucleus, why is the bonding of nucleons only the result of pion exchange and not of gluon interactions between quarks in different ...
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Why do the nucleons interact via strong force even though they are color neutral?

Particles that transform non-trivially under color $SU(3)$ interact via strong nuclear force. However, neutrons and protons, despite being color singlets, interact via the strong force. How do we ...
Solidification's user avatar
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How is this equation about pion decay derived?

I'm reading Peskin's Concepts of Elementary Particle Physics and these equations confuse me. What are the $\pi^1$ and $\pi^2$ in (15.49) and why $\pi^-$ equals to this? I don't understand the ...
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How is the pion related to spontaneous symmetry breaking in QCD?

In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by $$\...
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Phase Space Contributions to Decays with Fixed Momentum

Neglecting helicity, consider the decays $π^-\rightarrow e^-\bar{ν_e}$ and$π^-\rightarrow μ^-\bar{ν}_μ$. I understand that from Fermi's golden rule, the decay probability should be proportional to the ...
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ELi5- How do pions hold nuclei together if they are so short-lived?

I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist ...
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Can a $\phi$ meson decay into a pair of charged pions ($\pi^-$ and $\pi^+$)?

I understand that $\phi^0 \to \pi^+ \pi^- \pi^0$ is OZI suppressed. But how about $\phi^0 \to \pi^+ \pi^-$? Wikipedia doesn't list this decay path but $\phi^0 \to K^+ K^-$. Why? $\phi^0$ is a mixing ...
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Intrinsic Parity of the $𝐾^+$ Meson

Why it is not possible to determine intrinsic parity of the $𝐾^+$ mesons from the $𝐾^+ → 𝜋^+ 𝜋^0$ decay?
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Consistency of One-Pion Exchange with Selection Rules for NN Pion Production (in Chiral EFT, e.g.)

Hope you're ready for a long question, but I think quite an interesting one! One-pion exchange is an established nucleon-nucleon potential which is well-defined for any joint angular momentum state of ...
Graham Van Goffrier's user avatar
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Why the long lived Kaon can not decay into two pions?

The short-lived and long-lived states of kaon $|K_1>$ and $|K_2>$ respectively have the following compositions if they are the eigen states of CP parity: $|K_1> = \frac{|K^0>\:-\:|\bar{K^0}...
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Why did Yukawa theorize a neutral pion? Was it necessary or a guess?

At the time, neutrons had just been discovered, but were only needed to explain the extra mass inside nuclei... We now know that the strong force isn't strong enough to hold positive protons together ...
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Energy distribution of photon from neutral pion ($\pi^0$) decay

The laboratory-frame energy $E_\gamma$ of either photon is uniformly distributed between $E_{min} = \frac{1}{2}E_{\pi}(1-\beta)$ and $E_{max} = \frac{1}{2}E_{\pi}(1+\beta)$, where $E_\pi$ is the ...
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Pion $SU(2)$ representation with two light flavors of quark

I am working through Srednicki's Quantum Field Theory. I'm in chapter 94 and, perhaps I missed something, but I'm wondering how he arrived at a result. He has the pion fields in his Lagrangian ...
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Why $\pi^+$ meson possible combinations of quarks is only three?

I am a starter at nuclear and particles physics. I am reading particles and nuclei an introduction to the physical concepts. There was a paragraph about Colour-neutral particles and how only ...
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Deriving the charged pion decay matrix element

From M Schwarz's QFT (p 570), Goldstone's theorem indicates that pions are created from the vacuum by the chiral ${\rm SU}(2)$ current $J_\mu^{5a}$, $$ \langle \Omega| J_\mu^{5a}(x)|\pi^b(p) \rangle =...
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Why does the trace of the pion operator vanish?

I am working my way through Srednicki's QFT book. Currently I'm in chapter 94. Between equations 94.20 and 94.21, Srednicki says that the following expression vanishes in the case of two light ...
Cory's user avatar
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Method of Neutral Particle Mass Calculations from Bubble Chamber Images

I am looking into events within bubble chamber images and have come across a stumbling block. It relates to finding masses of neutral particles within bubble chamber images, specifically the mass of ...
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What is the actual carrier of the strong force? [duplicate]

I have been digging into the particle physics recently and I have found two different answers for this question. First of all, according to Wikipedia the Pion is a meson that acts as the carrier ...
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Are Kaons and Pions (mesons) made up of quarks?

I have tried to reasearch this and google says yes. But i learnt that pions decay into muons and netrinos (and the antiparticle versions) which are basically electrons and neutrinos Which are ...
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Understanding depiction of gluons in the nuclear force Feynman diagram

In this Feynman diagram for the nuclear force, it labels this exchange as a pion. However, I was under the impression that this force was mediated by gluons. In the caption for this picture, it says ...
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Do pions not interact with other pions via the strong force?

Imagine a positive and negative pion, their only interaction between each other would be due to electromagnetism and the weak force, right? It is not like these two pions can form neutral pions due to ...
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The isospin of pions

In the thesis(Page:53), the author defined three pion bases, namely, $$ |\pi^{1}\rangle = |1, 1\rangle, \quad |\pi^{0}\rangle=|1,0\rangle, \quad |\pi^{-1}\rangle=|1, -1\rangle. $$ Here, the first ...
quantum's user avatar
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Hadrons as partons? e.g. hadron distribution function inside another hadron

Parton distribution functions (PDFs) are typically seen as describing the probability that a parton, e.g. a quark or gluon, can be found in a hadron with particular momentum fraction $x$. They can be ...
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On neutral Kaon mixing

Kaons are not eigenstates of $CP$: $$ CP|K\rangle =|\overline K\rangle\\ $$ Why do we need to mix them? One answer I read is "since they both decay into $2$ or $3$ pions". Couldn't they ...
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Opposite helicities of $e^-$ and $\bar{\nu}_e$ from angular momentum conservation in pion decay

Consider the decay $\pi^-\to e^-+\bar{\nu}_e$ in the rest frame of the pion so that $L_\pi=0$. Since the pion is a spin-$0$ particle, $S_\pi=0$. Therefore, the total initial angular momentum $J_i\...
Solidification's user avatar
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Deriving isospin factors in phenomenological pion nucleon nucleon interactions

Preface One commonly finds this interaction Lagrangian in phenomenology (ignoring constants): $$\mathscr{L} \propto \bar\psi \gamma^5\gamma^\mu \vec\tau\psi \cdot \partial_\mu \vec\pi \tag{1}$$ ...
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Unfamiliar notations about $\pi\pi\rightarrow\pi\pi$ scattering amplitudes in Weinberg’s QFT?

I’m reading section 19.5 of Weinberg’s second volume of QFT, and confused about some notations. In that chapter, he introduce the non linear sigma model as an low energy effective theory of 2-flavor ...
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Matrix elements of vector current in $\pi^-$ decay

In positive pion decay $\pi^- \rightarrow \mu^- + \overline{\nu}_\mu$, the matrix element contains the following factor: $$<0|\overline{u}(0)\gamma^\mu d(0)|\pi^-(p)>$$ On the book by Nachtmann, ...
Antonio19932806's user avatar
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Confused about helicity suppression in the decay $\pi^- \rightarrow \mu^- \overline{\nu}_\mu$

I know this question has been asked a few times before here in various ways, but I haven't found answers which helped me a lot. For one, the class I am in is not using any of the underlying math, so ...
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Why can't neutral pion decay to two neutrino's

I know neutral pions mostly decay electromagnetically to two photons, but I don't understand why the decay to two neutrino's is not possible. Perhaps they violate parity, but someone at the link https:...
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On $\Delta^{+}$ particle decay

Using isospin notation $$ \Delta^+=\left|\frac 3 2,\frac 1 2\right\rangle=\frac{1}{\!\sqrt{3}}\bigg(|duu\rangle+|udu\rangle+|uud\rangle\!\bigg) $$ It is known all of the $\Delta$ baryons with mass ...
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Identifying mesons with Goldstone modes

In QCD, due to the work of ‘t Hooft and Vafa-Witten, we know that confinement implies chiral symmetry breaking (David Tong’s gauge theory notes have a clear discussion of this). It is then said that ...
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Decay and Invariant mass [closed]

Consider the following decay : \begin{equation} K^+\longrightarrow \pi^0 + e^+ + l^0 \end{equation} where $l^0$ is a neutral lepton. What kind of particle is $l^0$? For $K^+$ , if it's at rest, ...
Shanks Tyler Red's user avatar
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Source of a problem on pion-proton interaction in elementary particles

What book is this picture taken from? It is page 383 of the book in question.
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Feynman diagrams for neutral pion decay into electron-positron pair

The main Feynman diagram I've seen corresponding to this decay is the following: What I don't understand is why is it not possible for the up-antiup quarks that form the pion to annihilate into a ...
Andreas C's user avatar
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PCAC - Ward Identity for non-conserved currents - Derivative and $T$-Order Commutation

I'm currently studying Goldberger-Treiman relation from the book by S. Coleman (Aspects of Symmetry, chapter 2) in which, working in the framework of a not better precised "weak interaction ...
Boreanaz's user avatar
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Kaon decay parity if pion parity is redefined as +1

I am reading in Neeman’s book, The particle hunter, second edition, page 169, about the “theta-tau riddle.” He writes that You might suggest that we define the parity of the pion as $+1$, but this ...
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Where do pions get angular momentum from?

If a neutral meson carrying intrinsic spin equal to 1 decays into a pair of charged pions, how can they possibly conserve angular momentum? Pions have no spin and if they originate from the same point ...
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How did Ernest Sternglass’ phenomenologically incorrect model of the neutral pion predict its mass and lifetime so accurately?

In 1961, Ernest Sternglass published a paper where, using what seems to be to be a combination of relativistic kinematics and Bohr’s old quantisation procedure, he looked at the energy levels of a set ...
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$C$-parity in $\pi^0\pi^+\pi^-$ system

I'm studying the conservation of the quantum number in the decay $\omega^0\rightarrow\pi^0\pi^+\pi^-$. Since $P(\omega^0)=-1$ and $P(\pi^0\pi^+\pi^-)=P(\pi^0)P(\pi^+)P(\pi^-)(-1)^{L_{+-}}(-1)^{L_{(+-)...
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Is the pion valence PDF symmetric?

The positive-pion $\pi^+$ is comprised of 1 valence up-quark and 1 valence anti-down-quark. Assuming isospin symmetry, the parton distribution functions (PDFs) for these two valence quarks should be ...
Arturo don Juan's user avatar
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Identification of physical pion states in chiral perturbation theory

In chiral perturbation theory, we introduce the parametrization of the Goldstone manifold $$ U = \exp\left( i \frac{1}{f_\pi} \pi_a \sigma_a\right), $$ where $\sigma_a$ are the Pauli matrices. Most ...
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About Pion decaying into two photons

Pion decays to 2 photons. If 1000 such pions with their energies ranging from 1 MeV to 1 GeV, decay, then, how can we plot the graph between the angle with which photons get emitted in different ...
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