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Questions tagged [pions]

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4
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1answer
41 views

CP-symmetery conservation

How can one show that for a given decay, say $\pi^+ \rightarrow \nu_\mu + \mu^+$, CP-symmetry is conserved or violated? Is there a visual way of doing such?
2
votes
1answer
96 views

Why can the pion decay into two photons?

The neutral pion belongs to the pseudoscalar meson octet, so it has, in the ground state ($L=0$): \begin{align} P_{\pi^0}&=-1 \\ C_{\pi^0}&=+1. \end{align} And the photon has \begin{align} ...
0
votes
2answers
63 views

Why is the relative angular momentum of quark+antiquark in a pion equal to zero?

In a set of lecture notes provided by my lecturer, it says that a pion consists of a quark ($q$) and an antiquark ($\bar{q_2}$) with relative $L=0$. The negative parity and the fact that $S=0$ makes ...
0
votes
2answers
88 views

Why does the pion live in a representation of isospin SU(2) and is the mediator of the strong force generated by color SU(3)?

Why does the pion live in a representation of isospin $\rm SU(2)$ and is the mediator of the strong force generated by color $\rm SU(3)$? I somehow find strange that this is the case. Given that $\rm ...
1
vote
1answer
85 views

A question about isospin of pion and kaon

In Ch.18 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.611 when discussing QCD renormalization of the weak interaction, two operators ${\cal O}^{1/2}$ and ${\...
0
votes
0answers
33 views

Transformation of opening angle in different frame of rerefence in special relativity

I have to find the minimum opening angle for the decay $\pi^0 \rightarrow \gamma \gamma$ given the energy and rest mass of the $\pi^0$. My question is that: since the center-of-mass frame's opening ...
2
votes
2answers
110 views

How does the exchange of pions result in the strong force?

I understand that the residual strong force is a result of an exchange of pions. But I fail to understand how this exchange results in a force that holds nuclei together! May this query please be ...
0
votes
1answer
64 views

Pion decay constant: How to know which convention to follow?

As summarized by Wikipedia, different sources use different choices for the (pion) decay constant. This means that the numerical value can vary between $$ \sqrt 2\ f_\pi \quad\leftrightarrow\quad f_\...
1
vote
3answers
72 views

Why would gamma spectroscopy be a tool for nuclei?

I am very much familiar with Atomic spectroscopy, not much with nuclear spectroscopy. In atoms (electronic cloud), we have electromagnetic interaction that plays the leading role, whose exchange ...
0
votes
1answer
78 views

What is direct interaction, if exist, between gluons and pions?

Gluons mediate the strong force between quarks. Pions mediate the nuclear force or nucleon-nucleon interaction or residual strong force. I had thought of some scalar bosons for my idea because if I'm ...
0
votes
1answer
30 views

High spin for $Δ^{++}$ resulting from angular momentum of pion in relation to proton

When a pion (Spin 0) collides with a proton (Spin 1/2) the result can be a Δ++ (Spin 3/2). When I tried to look up how the resulting Spin is possible, I came about an answer I do not understand. It ...
1
vote
1answer
60 views

Parity conservation in electromagnetic decays

When a $\pi^0$ decays into photons, the only possible number of photons to which it can decay is 2$\times n$, with $n$ a natural number. This is because in electromagnetic decays charge conjugation is ...
0
votes
0answers
52 views

Pion and quark mass

I would like to know why $$m^2_{\pi} \sim m_q$$ where $m_q = (m_u + m_d)/2$? Which values should I use to see that? I have used values from PDG and I do not see this equivalence. Could someone help me ...
8
votes
3answers
441 views

What is the symmetry of the pion triplet ($\pi^{-}, \pi^{0}, \pi^{+}$)?

Under the entry "Isospin" in Wikipedia, it is written: The pions are assigned to the triplet (the spin-1, $\mathbf{3}$, or adjoint representation) of $SU(2)$ Why is the symmetry not $SU(3)$ since ...
1
vote
1answer
216 views

Most trivial neutral pion decay

Literature states neutral pion decay by QED cannot occur directly because the pion is uncharged. However, I cannot see why Photons are not allowed to interact with the Quarks directly. Please ...
0
votes
1answer
55 views

Is the process $\pi^0 \to \gamma\gamma\gamma$ kinematically possible?

The process$$ \pi^0 \to \gamma\gamma\gamma $$is forbidden because of charge conjugation violation, but I was wondering whether, regardless of charge conjugation violation, this process could be ...
1
vote
1answer
70 views

What is the product of a proton interacting with the CMB?

Assuming the CMB is at 2.7 K, if a proton interacts with it, what would be the particles resulting of this collision? I read that at the GZK cut-off (~$10^{21}$ eV), there is photo-pion production, ...
1
vote
1answer
57 views

Does the decay of $\rho^0$ meson imply that charged pions have non-integer orbital angular momentum?

In the decay $\rho_0\rightarrow \pi^+ + \pi^-$ the $\rho_0$ has total angular momentum 1 and the $\pi^\pm$ both have spin zero. In order to conserve total angular momentum, the pions must therefore ...
2
votes
1answer
69 views

Scattering amplitude with a change in basis of fields

Suppose I know the Feynman rules for the scattering process $\pi^j \pi^k \rightarrow \pi^l \pi^m$ where $j,k,l,m$ can be $1, 2$ or $3$. Define the charged pion fields as $\pi^\pm=\frac{1}{\sqrt{2}}(\...
0
votes
1answer
57 views

Is it possible for the reaction $\pi^+ \, \pi^- \rightarrow \nu_e \, \bar{\nu}_e$ to occur? If so, how would this happen?

The reaction doesn't violate any conservation laws that came to my mind - however I am having trouble thinking of how it might occur.
0
votes
1answer
42 views

Special Relativity: Which is the correct time taken for a pion travelling between two detectors?

I'm struggling to ascertain which reference frame (pion or detectors) has the 'longer time taken' in the following example: Consider a pion which is travelling at 0.95c. It passes two detectors 34m ...
1
vote
1answer
76 views

What is the force carrier for neutrons in fission?

Say I have a neutron capture event, leading to a fission reaction in which a few neutrons are expelled. These neutrons inherit a certain momentum from this fission reaction. How do these neutrons ...
1
vote
1answer
89 views

Forbidden reaction from symmetries and conservation laws

If $\rm p\bar p$ (proton-antiproton) annihilation at rest proceeds via the $S$ state ($L=0$), why is it that the reaction: $\rm p\bar p\to \pi^0 +\pi^0$ is forbidden as strong interaction (i.e. parity ...
2
votes
1answer
203 views

Old-fashioned approach to neutral pion’s decay rate

I am uncomfy with the calculation of the neutral pion’s decay rate via the triangle anomaly diagram, which gets touted as evidence of three colors. The calculation invokes PCAC in the guise of the ...
2
votes
1answer
266 views

Rho meson decay to three neutral pions

In my assignment, I am asked to show whether $\rho^0\to3\pi^0$ is allowed. From the particle data group, I cannot find the decay mode; hence, I am guessing it is not allowed. Based on the knowledge ...
-1
votes
1answer
75 views

About electron and proton

Can electron stick ''glue'' with proton if they collide with each other? What will happen if electron collide with pion? Can it glue with it or not?
7
votes
0answers
149 views

Up and down quark content of neutral pion

If isospin were a perfect symmetry, then the neutral pion would have equal $u\bar u$ and $d\bar d$ content, but since up quarks are slightly lighter than down quarks, the neutral pion, being the ...
1
vote
2answers
804 views

What is the isospin of the neutral pion?

The neutral pion, π0, should have an isospin of 0. To be certain, I am referring to the third component of isospin, $I_3$. The reason for this is very simple: I3 is an additive quantum number. The ...
1
vote
1answer
187 views

$\rho$ meson decay rate

In page 10 of this talk by Boris Kayser (http://www.pha.jhu.edu/groups/particle-theory/seminars/talks/S10/talk.kayser.pdf) it is said that although the final state of the decay $\rho^0 \to \pi^+ \pi^-$...
5
votes
1answer
167 views

QCD pion and electroweak symmetry breaking

Equation (28.33) in Matthew Schwartz's QFT text book $$ \mathcal{M}(\pi^+ \rightarrow \mu^+ \nu_\mu) = \frac{G_F}{\sqrt{2}}F_\pi p^\mu \bar{\psi}_{\nu_\mu}\gamma^\mu(1-\gamma^5)\psi_\mu \tag{28.33} $$ ...
1
vote
1answer
150 views

Scattering amplitude calculation using first order Chiral Perturbation Theory Lagrangian

Consider the Chiral Perturbation Lagrangian to first order(quark masses set to zero): $$L = L^{(2)} = \frac{f^2}{4}tr[\partial_{\mu} U \partial^{\mu} U^{\dagger}] ,$$ where U is a $2 \times 2 $ ...
2
votes
1answer
202 views

How is pion decay compatible with conservation of angular momentum?

A pion is a spin-zero composite particle, so $S = S^z = 0$. A $\pi^-$ pion can decay into an antineutrino $\bar{\nu}$ and a negatively charged lepton $l$, each with spin-$1/2$. Let the direction of ...
0
votes
1answer
80 views

Orbital angular momentum in weak interaction

I am bit confused with a statement in Griffiths where he talks about the decay of pions by weak interaction to muons and neutrino. Here, he says that if angular momentum of muon and neutrino is ...
-1
votes
1answer
306 views

Relativistic kinematics - decay [closed]

I'm struggling to solve this problem in relativistic kinematics: $D$ meson decays to $\pi$ and $K$. After a while, the kaon decays to $\pi^0$ and $\pi^-$. If the $\pi^0$ moves vertecally to $K^-$ ...
0
votes
1answer
467 views

Isospin, cross section

I need to find the ration of cross sections for the following two reactions: $$\rm p + d\rightarrow He^3 + \pi^0$$ and $$\rm p+d\rightarrow H^3 + \pi ^+.$$ Since the cross section for a reaction $\...
4
votes
1answer
237 views

Are virtual pions necessary to mediate the residual strong interaction?

In relation to another question I asked recently, I was wondering if the forces between the up and down quarks of the protons and neutrons in nuclei would be sufficient to keep the nuclei bound ...
1
vote
1answer
151 views

Conservation of angular momentum, pion-deuteron reaction

If I have the following reaction : $\pi^- + d \rightarrow n + n$, it's said that the two neutrons are in a state with s=1 and l=1, so that $j_f =l+s$$\space \rightarrow$ $j_f =0,1,2$ . And that the ...
0
votes
1answer
185 views

Applying ladder operators to Isospin states for quarks

I'm having trouble finding the isospin representation of the meson isospin triplet $|\rho\rangle$. Starting from the $|\rho^+\rangle$ meson $|u^\uparrow\bar d^\uparrow\rangle$ (where the arrows ...
6
votes
1answer
387 views

Why is $\pi^0 \rightarrow \gamma \rightarrow e^-e^+$ forbidden but $\pi^+\rightarrow W^+ \rightarrow e^+ \nu_e$ allowed?

I am slightly confused why the decay $\pi^0 \rightarrow \gamma \rightarrow e^-e^+$ is forbidden. A naive guess would say that the intemediate photon $\gamma$ has a spin 1, the initial pion has a spin $...
3
votes
1answer
182 views

Experimental proof pions are pseudoscalar particles

In nuclear physics lessons I've been taught that pions are pseudoscalar particles and thus their intrinsic parity is odd. The professor said that an experimental proof of this can be derived observing ...
1
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0answers
429 views

Feynman Diagrams for pion production in proton-proton collisions

I have a conceptual question about the Feynman Diagrams representing pion production at the LHC. When trying to draw the FD for this process, I have drawn two possibilities, and I'm not sure which is ...
-1
votes
2answers
524 views

$\rho\to \pi\pi$ parity

I'm having some difficulty understanding why the $\rho^0$$\rightarrow$$\pi^+ \pi^-$ decay conserves parity. By my understanding, the parity of a meson is given by $P_aP_b(-1)^{L+1}$ and the parity of ...
0
votes
1answer
156 views

Form of the one-pion exchange potential

Part of the one pion exchange potential (OPEP) contains the following term $$V(r) \propto (\vec{\sigma}^{(1)} . \nabla)(\vec{\sigma}^{(2)} . \nabla) \frac{\exp\left(- \frac{r}{R}\right)}{r} $$ And I ...
0
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0answers
235 views

Tree Order Feynman Diagram with neutral pion

I am trying to draw the tree-order Feynman diagram for the process $\gamma + p \rightarrow \pi^0 + p$. My question regards the quark content (thus the quark lines of the diagram) for the neutral pion....
0
votes
1answer
66 views

What does it mean to subtract these quantum states?

For example, in particle physics the neutral pion $π^0$ exists in two quantum states $u\bar{u}$, and $d\bar{d}$; and is displayed in the form: $$\frac{u\bar{u}-d\bar{d}}{\sqrt2}$$ I understand that ...
0
votes
2answers
105 views

Pion interaction in vacuum [closed]

Does pion zero particle $\pi^0$ (zero charge and null spin) experience casimir force? If i wonder how pion particle with quantum electrodynamic field.
1
vote
1answer
103 views

Neutral meson weak interaction

Suppose the quark neutral current weak interaction lagrangian: $$ \tag 1 L = \bar{q}\gamma_{\mu}(g_{V}+g_{A}\gamma_{5})qZ^{\mu}, \quad q = u,d $$ How to derive from this Lagrangian the neutral ...
3
votes
1answer
655 views

Electromagnetic decay of a neutral pion

Why do neutral pions decay electromagnetically? Other neutral particles such as the neutron decay weakly, and charged pions decay weakly.
0
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1answer
267 views

Isospin of pions

Suppose that I have two pions with zero relative angular momentum. I want to find possible total isospin values. What I'm thinking is that their state should be symmetric since they are bosons. Each ...
1
vote
1answer
164 views

Unitary matrix of pionic fields and pions as coordinate vectors

I am currently studding theory for Chiral Perturbation Theory( ChPT) and I have stumbled at two point, having a difficulty at understanding. I will present the problem at first and then phrase the ...