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2answers
73 views

How are pions created?

I have listened to a lecture explaining the strong force which is actually nuclear force and colour force. And the pions are the force carrier of the nuclear force. And basically pions are created ...
3
votes
1answer
32 views

Do AGN produce protons that are relativistic enough to collide with the CMB and make pions?

AGN (Active Galactic Nuclei) produce protons in their jets and they are relativistic. I was reading about photo-pion production, where a proton and photon annihilate to produce a pion. Could this ...
0
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0answers
24 views

Pion decay from chiral anomaly

I have to compute the decay rate of the process: $$ \pi^{0} \rightarrow \gamma \gamma $$ with 4-momenta $P \rightarrow K_{1}+K_{2},$ by the means of the following effective Lagrangian, coming from ...
3
votes
1answer
56 views

Pion decay: why is the positron electron neutrino decay suppressed?

I'm reading through M. Thomson's Modern Particle Physics to better understand why the positron electron neutrino decay channel is suppressed relative to the muon and muon neutrino decay route. I know ...
0
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0answers
65 views

Pion-pion scattering amplitude with an effective Lagrangian

I have to compute the scattering amplitude at tree level for the process $$ \pi^{a}\pi^{b} \rightarrow \pi^{c}\pi^{d} $$ with an interaction given by what is written in the square brackets of the ...
0
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0answers
18 views

Neutral pion mass correction from electroweak instantons

It is stated that the virtual process $$ \pi^{0}\to 2W \to \pi^{0}, $$ where $\pi^{0}$ is neutral pion and $W$ denotes $W-$boson, generates the small correction to the pion mass, namely $$ \delta m_{\...
2
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0answers
47 views

Are the pions really all that light?

I'm studying the sigma model where the pions are identified as the (pseudo) Nambu-Goldstone bosons of chiral symmetry breaking ("pseudo" from mild isospin symmetry violation). This argument usually ...
1
vote
0answers
128 views

Feynman diagram; $\pi^0+\pi^0\rightarrow \pi^++\pi^-$

For the reaction below draw three Feynman diagrams, one that proceeds through exchange of a gluon, one through a photon and one exchanging a weak W-Boson. $\pi^0+\pi^0\rightarrow \pi^++\pi^-$ Which ...
1
vote
1answer
266 views

Why is the decay of a neutral pion $\to$ electron-positron loop suppressed?

To my understanding the decay of a neutral pion into an electron-positron pair can only happen by the electromagnetic force and the mediation of two virtual photons in a triangle-diagram, so it is ...
3
votes
2answers
124 views

Quark composition of the neutral pion

I wonder why the neutral pi meson is $$ | \pi^0\rangle = \frac{1}{\sqrt{2}}\left(\vert u\overline {u}\rangle - \vert d \overline{d} \rangle \right) $$ and not $$ | \pi^0\rangle = \frac{1}{\sqrt{2}}...
1
vote
2answers
115 views

How do protons and neutrons interchange?

I recently read in a book that a nucleon with +1/2 isospin is a proton and if the isospin is changed to -1/2, it is a neutron, so it is the same particle in different states. If a proton has a ...
3
votes
1answer
186 views

How can we calculate pion decay constant in Chiral Perturbation Theory ?

Above diagram is an one-loop contribution to the Pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not ...
2
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0answers
115 views

Isospin In Kaon Decay

The decay $ K \to \pi \pi $ at zero-strong interaction level is calculated by considering the matrix element of the operator $ Q_2 = (\bar{s}u)_{V-A} (\bar{u}d)_{V-A} $ for two kinds of processes: ...
2
votes
2answers
293 views

Selection rule of Kaon decay to pions

in Peskin QFT page 611, he said the isospin change for $${K^0} \to {\pi ^ + }{\pi ^ - }$$ is 1/2, while isospin change for $${K^ + } \to {\pi ^ + }{\pi ^0}$$ is 3/2. Why? If ${I_3}({K^ + }) = 1/2$,$...
1
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2answers
1k views

Photon energies after neutral pion decay

I am trying to find the photon energies of the decay $\pi_0 \rightarrow \gamma\gamma$ and their dependence on the pion energy $E_{\pi}$, its initial velocity $\beta$ and the scattering angle between ...
1
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0answers
70 views

Weinberg Chapter 19.5, pion scattering amplitude derivations

I've been reading through Weinberg's Chapter 19, and am somewhat confused about how he manages to derive equations 19.5.25 and 19.5.29, which read: $$\mathcal{M}_{abcd}^{(v=2)}=4F^{-2}\left[\delta_{...
4
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1answer
167 views

Pion decay: V-A vs. V coupling

For the Decay $$ \pi^- \to \mu^- \bar{\nu}_\mu $$ the Feynman rules for this tell us that the vertex couples with $\gamma^\mu (1-\gamma^5) / \sqrt{2} $. This gives me the reduced amplitude of $$ M = \...
0
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1answer
340 views

Energy of resultant photons from meson decay

I am a little unsure how to answer the following question, Find the energies of two photons emitted in opposite directions along the pion's original line of motion if the pion has a r.m.e of 500MEV ...
0
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1answer
276 views

Why is rho to two pions not allowed? [duplicate]

Why is the $\rho^0 \rightarrow \pi^0 + \pi^0$ decay not allowed? I have seen this question but I am not satisfied with the answers. The $J^{PC}$ of the $\rho$ and $\pi$ are $1^{--}$ and $0^{-+}$ ...
2
votes
3answers
228 views

Pions, parity, spin

Pions have odd parity ($P=-1$) which means their wavefunction is anti-symmetric $\psi(x)=-\psi(-x)$. According to Spin-Statistics theorem fermions (spin 1/2 particles) have anti-symmetric ...
1
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1answer
209 views

Pions as a superposition of quark states

in Isospin space there are two fundamental states called up and down quarks, which satisfy the following eigenvalue equations: $I u = (1/2) u$, $I d = (1/2) d$ and $I_3 u = (1/2) u, I_3 d = (-1/2) d$....
9
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2answers
662 views

How do we measure meson decay constants?

I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay ...
11
votes
3answers
399 views

Is the neutral pion a singlet?

In Griffiths' Introduction to Elementary Particles, it is mentioned p. 179 that the $\pi^0$ is a singlet under $SU(2)$ isospin. But it is also part of the $\pi^-,\pi^0,\pi^+$ isospin triplet. How can ...
1
vote
0answers
30 views

How can a pion with neutral charge exist? [duplicate]

A $\pi^0$ consists of an up and anti-up quark. However, I also learned that when a particle and its anti-particle meet, energy is produced. So, my question is that how can $\pi^0$ exist? Won't it ...
5
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1answer
414 views

Pion decay in particle physics

I'm taking a particle physics course and we're using Perkins Introduction to High Energy Physics as the text. I am looking at problem 1.7. It asks whether $$\pi^0\rightarrow e^- + e^+$$ is allowed or ...
2
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1answer
178 views

Interaction muons with Iron

I would like to know why $\mu^+$ muons can easily penetrate a solid metal such as Fe with negligible interactions while $\pi^+$ mesons lose their energy a lot faster when traveling through the metal. ...
3
votes
4answers
2k views

Angular momentum conservation in pion decay?

I have seen the charged pion decay $$\pi^{-}~\to~ \bar{\nu}_{\ell} +\ell^{-}$$ represented with diagrams containing a $W^-$ in the $s$-channel. The $\pi^-$ and $W^-$ have angular momentum $0$ and $1$ ...
7
votes
3answers
3k views

Why is the decay of a neutral rho meson into two neutral pions forbidden?

Why is the decay of a neutral rho meson into two neutral pions forbidden? (Other modes of decay are possible though.) Is it something with conservation of isospin symmetry or something else? Please ...
7
votes
2answers
247 views

What's the heuristic reasoning for Chiral Symmetry breaking

In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not ...
2
votes
1answer
750 views

What is the speed of a neutral pion and how is it measured?

Alvager et al 1964 purportedly disproved Ritz's emitter theory in an experiment that generated neutral pions with a vellocity of $v =B.c$ where B is slightly smaller than one. How is the velocity of ...
4
votes
1answer
346 views

Why does the pion half-life differ between the charged and uncharged species?

Why does the uncharged pion have much shorter half-life than the charged pion despite the fact that the uncharged pion has a little bit less mass than the charged one, so that according to the ...
2
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0answers
566 views

Charged pion decay and spin conservation [duplicate]

Charged pions $\pi^\pm$ decay via an intermediate $W$ to (e.g.) a lepton-neutrino pair. The pions being scalar (spin-0) particles and the intermediate $W$ having spin 1, how is spin conserved in ...
-1
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1answer
309 views

Is the neutral pi meson a relativistic electron positron pair?

Is the neutral pi meson a relativistic electron positron pair? An electron position pair orbiting at relativistic speeds is proposed as a model of a neutral pi meson by Ernest Sternglass. However, ...
7
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1answer
1k views

Pion production in proton-proton collision

Why is $\pi^0$ created in the high-energy collision $p+p\to p+p+\pi^0$?
4
votes
1answer
433 views

Why is a pion so light compared to a neutron or proton?

A pion is made out of a pair of up and/or down quarks. A neutron or proton is three up or down quarks. So naively I'd expect a pion to be about 2/3 the mass of a nucleon. In fact it's less than 1/6 ...
3
votes
1answer
359 views

Decay of a particle

Would someone please explain the following found on P. 125 of these notes? On the other hand, two $π^0$’s cannot be in an $l = 1$ state. The reason for this is that pions are bosons and so the ...
1
vote
1answer
130 views

Which pion is mediator in nucleon-nucleon interaction

In nucleon-nucleon interactions of n-n, p-p, n-p how do you determine which pion is the mediator?
0
votes
1answer
413 views

What process could produce two neutral pions only?

Any examples? $$? \rightarrow \pi^0 \pi^0$$ If such a process exist, could there be nonzero total orbital angular momentum in the final states of the two neutral pions? But then how to understand ...
1
vote
2answers
894 views

Quark compositions in $\pi^+$ to $\pi^0$ pion decay

Pions can undergo a rare beta-like decay into leptons: Pion beta decay (with probability of about $10^{−8}$) into a neutral pion plus an electron and electron antineutrino (or for positive ...
4
votes
2answers
261 views

How can a pion have a mass, given it's a “field mediator” and created/destroyed continuously?

Maybe some of my assumptions here are basically wrong, but isn't it true that pion is the "mediator" for the strong force field. the quantum field theory basically says that there are no fields, ...
4
votes
1answer
673 views

Why the pion does not get mass under Spontaneus breaking of chiral symmetry, but the quarks do?

Some sources state that when the mass of a quark goes to zero, it allows for Spontaneous Breaking of Chiral Symmetry and gets a constituent mass of about $200\, \mathrm{MeV}$. Other sources state ...
5
votes
1answer
2k views

Chiral anomaly and decay of the pion

I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of ...
1
vote
1answer
910 views

Neutral Pion Decay

While studying C-symmetry, a question about neutral pion decay came up. The most probable channels in which neutral pion $\pi^0$ decays are: $\pi^0\longrightarrow\gamma+\gamma$ (98%) $\pi^0\...
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votes
3answers
4k views

What does it mean that the neutral pion is a mixture of quarks?

The quark composition of the neutral pion ($\pi^0$) is $\frac{u\bar{u} - d\bar{d}}{\sqrt{2}}$. What does this actually mean? I think it's bizarre that a particle doesn't have a definite composition. ...
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4answers
7k views

Is it pions or gluons that mediate the strong force between nucleons?

From my recent experience teaching high school students I've found that they are taught that the strong force between nucleons is mediated by virtual-pion exchange, whereas between quarks it's gluons. ...
3
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2answers
2k views

What Quark and Anti-quark are electrically neutral Pions made out of?

A positive pion is an up and an anti-down. A negative pion is a down and an anti-up. What's a pion with an electrical charge of 0?
21
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3answers
6k views

The exchange of photons gives rise to the electromagnetic force

Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing. If EM force is caused by the exchange of photons, does that mean only when ...