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16 votes
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Why can a neutral pion decay into 2 photons but not one?

The pion has a rest frame where it has 0 momentum. Photons do not have rest frames, so if the pion decays into one photon, that photon will have momentum in every frame. So momentum cannot be ...
Brick's user avatar
  • 4,850
13 votes

Physical meaning of the chiral condensate in QCD

It's actually the other way around. That axial rotation of the pions ensures that, given its non-vanishing v.e.v., given by the condensate (assumed to be produced by QCD: a fact!), they therefore must ...
Cosmas Zachos's user avatar
11 votes
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What is the symmetry of the pion triplet ($\pi^{-}, \pi^{0}, \pi^{+}$)?

$\newcommand{\BK}[3]{\left|{#1},{#2}\right\rangle_{#3}} \newcommand{\BKB}[3]{\mathbf{\left|{#1},{#2}\right\rangle_{\boldsymbol{#3}}}} \newcommand{\FR}[2]{{\textstyle \frac{#1}{#2}}} \...
Frobenius's user avatar
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11 votes
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Is proton + antiproton $\rightarrow$ $\pi^0$ meson allowed?

In the center-of-mass frame of the collision, the total momentum is zero. Therefore, the neutral pion must be produced at rest in this frame, or else the interaction violates momentum conservation. ...
probably_someone's user avatar
10 votes
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Why $\pi^+$ meson possible combinations of quarks is only three?

In quantum mechanics the operation of swapping the charge is called charge conjugation and this operation swaps a particle for its antiparticle. So for example if we take an electron and swap the ...
John Rennie's user avatar
9 votes
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Why is $\pi^0 \rightarrow \gamma \rightarrow e^-e^+$ forbidden but $\pi^+\rightarrow W^+ \rightarrow e^+ \nu_e$ allowed?

The QCD and QED themselves conserve parity. The conclusion of this statement is that all corresponding effective vertices must conserve the parity. The only coupling of $\pi^{0}$ to $\gamma$ ...
Name YYY's user avatar
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9 votes
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Where do pions get angular momentum from?

Let’s see a concrete example: $ρ_0 \rightarrow π^+π^-$ This is an indicative first-order Feynman diagram for this decay . Pions have no spin and if they originate from the same point then their ...
anna v's user avatar
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8 votes
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Are virtual pions necessary to mediate the residual strong interaction?

You seem to be misunderstanding what the effective theory with the residual nuclear force between hadrons mediated by pions is: It is an effective theory which is a good approximation of the ...
ACuriousMind's user avatar
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8 votes
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Neutron-Antineutron Annihilation

Within a few MeV, from isospin symmetry of the strong interaction, it is similar to the antiproton proton annihilation which happens even at rest: Role of Delta exchange for proton-antiproton ...
anna v's user avatar
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7 votes
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Question about the linear sigma-model

You might consider 241162 and 102575. This is actually a history of science question, on a half-century old landmark in the intellectual history of 20th century physics, whose importance cannot be ...
Cosmas Zachos's user avatar
7 votes
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Why can the pion decay into two photons?

The photons have intrinsic spin (or, better, helicity) one, so the pair can have odd orbital angular momentum, still conserving total angular momentum (which has to be zero, as the pion is spinless). ...
pppqqq's user avatar
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7 votes
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How is the pion related to spontaneous symmetry breaking in QCD?

In a world without EW SSB, pions would, indeed, be perfect massless! Pion masses reflect two different SSBs. There are two SSB scales involved in the SM: the electroweak spontaneous breaking of $SU(2)...
Cosmas Zachos's user avatar
6 votes

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

In the pion reference frame the two outgoing leptons are very boosted, hence helicity and chirality almost coincide. The angular momentum conservation forces them to have opposite spins, since the ...
user126528's user avatar
6 votes

Questions about subnuclear decay: helicity and parity.

The pion is a pseudoscalar, with spin-parity $J^\pi=0^-$. In decay of a pion at rest the two decay products have equal and opposite momentum. Choose a coordinate system so that the electron goes to ...
rob's user avatar
  • 89.9k
6 votes

Why are charged pions are heavier than neutral pions?

Look at this illustration of the proton to get an idea of how complicated a hadron is. There are the valence quarks that define the quantum numbers of the particles but the greatest effect on the ...
anna v's user avatar
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5 votes
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QCD pion and electroweak symmetry breaking

This is a cluster of questions, with a very good one in the end, which is, in fact, the very question that inspired Susskind to introduce technicolor for EW SSB in the late 70s. I'll be very schematic ...
Cosmas Zachos's user avatar
5 votes
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Forbidden reaction from symmetries and conservation laws

You've concluded that, to conserve parity, $L$ must be odd. By the two pions are identical bosons, and so the wavefunction must by symmetric under exchange. If $L$ is odd, the wavefunction is anti-...
Chris's user avatar
  • 17.2k
5 votes

Why are charged pions are heavier than neutral pions?

As anna v says, hadrons are really complicated and you're not going to be able to do a full calculation without a lot of computer time. But you can get at least an idea by thinking about the quark ...
ragnar's user avatar
  • 1,122
5 votes
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Derivation of PCAC Condition $\langle 0|J^5_{\mu,a}(x)|\pi_b(p)\rangle=-if_{\pi}\delta_{ab}e^{-ipx}p_{\mu}$?

Two more key references in this answer: the Itzykson & Zuber discussion for the σ-model alluded to is peerless, if one really wishes to get to the bottom of it; summarized here. The chiral model ...
Cosmas Zachos's user avatar
5 votes

If virtual particles aren't real, then why do their masses correspond to those of real particles?

If I understand you correctly, I think there are actually two points being asked about here, and so it will be beneficial to try and separate them. First there is a question about the relation of the ...
Richard Myers's user avatar
5 votes
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How did Ernest Sternglass’ phenomenologically incorrect model of the neutral pion predict its mass and lifetime so accurately?

It is a coincidence. The claim in the article can be summarized as $$ \frac{\alpha}{2}\frac{m_\pi}{m_e}=0.96 $$ which is close to $1$. This relation doesn't have a deep origin, it is just a ...
AccidentalFourierTransform's user avatar
5 votes
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Why can't neutral pion decay to two neutrino's

Pion decay to two photons is electromagnetic (the original flavor chiral anomaly). But decay to two neutrinos could only go through a box diagram involving two Ws of opposite charge: the quarks or ...
Cosmas Zachos's user avatar
5 votes

How is the pion related to spontaneous symmetry breaking in QCD?

As you say, $SU(2)_A$ is a symmetry of the Lagrangian before Electroweak symmetry breaking. But, what we call 'particles', (in particular pions) are always to be understood as excitations on top of ...
QCD_IS_GOOD's user avatar
  • 6,795
5 votes

No gluon interaction between nucleons

Long-range nucleon-nucleon interactions are dominated by pion exchange, but at short enough distances the quark-gluon structure of the nucleons is important. As shown in this plot from Wikipedia, one-...
David Bailey's user avatar
  • 11.3k
5 votes
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Quark condensate and VEV of $\pi^0$

Nonono! You've made a bad hash of standard notation. The interpolating operator for the neutral pion you wrote is far too schematic/complacent, and lacks an all-important $\gamma^5$. You might ...
Cosmas Zachos's user avatar
4 votes

Applying ladder operators to Isospin states for quarks

The antiquarks are in the "antifundamental representation." If a quark in the fundamental representation transforms as $q_i\rightarrow U_{ij}q_j$, an antiquark transforms as $\bar{q}_i\rightarrow \bar{...
octonion's user avatar
  • 8,720
4 votes
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What is the force carrier for neutrons in fission?

The short answer is that the force carriers are mostly pions, but the details get quite complicated. In physics we know about four fundamental interactions: the strong force, the electromagnetic ...
rob's user avatar
  • 89.9k
4 votes

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 the pion lives in a representation of isospin SU(2) Sure, it is well described as a part of the meson octet. That is how the quarks were discovered. Do not forget that SU(2) is a subgroup of an ...
anna v's user avatar
  • 234k
4 votes
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Embedding of $SU(2)_L \times U(1)_Y$ into $SU(2)_L \times SU(2)_R$ in electroweak chiral effective theories

No, no evidence of nonsense, but they are a bit pedagogically smug and do not want to make it easy for readers who don't speak the language. You looked at the wrong equations in ref [3]. They ...
Cosmas Zachos's user avatar
4 votes
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$K\to \pi \gamma$ decay

Go to the PDG listing, detailing the decays of the charged K, and the exclusion limits of disallowed ones. You see that $K^+\to \pi^+ \gamma$ is excluded by angular momentum, an exact conservation ...
Cosmas Zachos's user avatar

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