# Questions tagged [charge-conjugation]

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### In this example, how can we have CP conservation with C violation?

Consider a simple two-body decay process $X\to Y+Z$ where $X$ is a boson, and $Y,Z$ are fermions. If $C$ is violated, $$\Gamma(X\to Y+Z)\neq \bar{\Gamma}(\bar{X}\to\bar{Y}+\bar{Z}).\tag{1}$$ However, ...
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### C, P and T transformations of $\phi$ that preserves symmetry

I have a series of exercises regarding C, P and T symmetry but I am not really sure how to start with the problems. If anyone could help me with one of the problems, or show me a few example problems ...
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### Does the $U(1)$ charge of a scalar particle flip under charge conjugation?

Consider a complex scalar particle $\phi$ coupled to an electromagnetic field. The Lagrangian is given by $$\mathcal{L} =(D_\mu \phi)^* D^\mu \phi - m^2 \phi^2 - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$...
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### Why do we need two gluons for the decay $ϕ \to 2K$?

The Feynman diagram for the decay $\phi \to K^+K^-$ usually depicts two gluons. (This can be seen e.g. on Wikipedia). Why do we need two gluons, instead of just one?
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### Why is the Higgs $CP$ even?

Why was it always assumed that the Higgs boson is a CP even particle? I understand that experimentally, it just is so but I am under the impression that before its discovery people took it to be CP ...
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### Invariance of Yang-Mills Lagrangian under charge conjugation

The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as $${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$ (Sum over $i$ implicit) This Lagrangian ...
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### The Majorana condition and C violation

Is the Majorana condition $$\psi = \psi^c = C \overline{\psi}^T,$$ general? The point is often made that Majorana particles should be defined by CPT symmetry and not C as generally theories do not ...
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### Physically, what is a pseudoreal representation?

There are three kinds of representations: real, complex, and pseudoreal. A complex representation is not equivalent to its conjugate, and a real one is, which is pretty straightforward. A pseudoreal ...
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### Antiparticle solution of the Dirac Equation

I'm really confused by the antiparticle solution of the Dirac equation. I follow Chapter 11 of Schwartz's book "Quantum Field Theory and the Standard Model" and find a couple of problems. In ...
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### How are parity and charge conjugation eigenvalues related to angular momentum?

I have seen many equations where $P$ and $C$ (eigenvalues of parity and charge conjugation, resp.) are related to $J$, $L$, $S$ and $I$ (eigenvalues of total angular momentum, angular momentum, spin, ...
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### Spin state of two distinguishable bosons

I was reading about the $C$-parity of a particle-antiparticle pair. Since charge conjugation has the effect of swapping the particle and antiparticle, the $C$-parity can be found from the symmetry of ...
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### Why is $|\bar{K}^0\rangle=\mathscr{CP}|K^0\rangle$ and not $|\bar{K}^0\rangle=\mathscr{C}|K^0\rangle$?

If the charge conjugation operator $\mathscr{C}$ changes a particle state into the corresponding anti-particle state then we must write $|\bar{K}^0\rangle=\mathscr{C}|K^0\rangle$. But instead, we ...
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### Charge conjugation in chiral representation

I'm reading Maggiore's book and I got to the part of charge conjugation symmetry for Dirac spinor. I get that the definition of charge conjugation is representation-dependent, however I couldn't find ...
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### Charge conjugation operator in second quantization

How can we write charge conjugation operator's action in second quantization's formalism? I don't know if I am explaining it correctly or not but I am interested in finding how can we write fermionic ...
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### Property of Charge Conjugation Operator

In class, we have defined the Charge Conjugation Operator ($C$) such that: \begin{equation} C \left(\gamma^\mu\right)^T C^{-1} = - \gamma ^\mu , \end{equation} \begin{equation} \psi^C \equiv C\,\...
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### If electrons were positive and protons were negative, would life be different? [duplicate]

This was a question on a worksheet during my first week in a class on Electromagnetism. The answer is essentially: No. Life would be no different if electrons were positively charged and protons ...
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### Questions about Five Dimensional SUSY Gauge Theories

I am studying the paper "Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces" by Intriligator, Morrison and Seiberg (arXiv:hep-th/9702198), and have a few questions ...
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### CP-violating coupling

In this paper, after equation (38), there is the statement that the term $$\bar{t}\sigma^{\mu\nu}q_\nu\gamma_5tZ_\mu$$ is CP-violating. How exactly do we see this? Can anyone make explicit how we ...
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### Charge Conjugation of massive Dirac spinor in 3 dimensions with Euclidean signature

In 2+1 dimensional massive Dirac equation (Minkowski signature), we can define the charge conjugation operator so that the equation can be symmetric under it. However, the charge conjugation does not ...
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### Is $N_R$ a Majorana field in the Seesaw Lagrangian?

Consider the Lagrangian for the type-I seesaw given by $$-\mathcal{L}=\bar{\nu}_{L}m_DN_{R}+\frac{1}{2}\overline{(N_{R})^c}M_R N_{R}+\text{h.c.}.$$ $\bullet$ In this Lagrangian, what is the nature ...
### Can a Majorana field $\psi$ be charged under some $U(1)$ with a charge other than zero?
I know Majorana particles have to be electrically neutral because electric charged is conserved. My question, however, is whether at all a Majorana field $\psi$ be charged under any $U(1)$ (other ...
The gamma matrices are defined by their anticommutation relations, which are symmetrical in permutations of $\gamma_1, \gamma_2, \gamma_3$. Given this symmetry, why is the change conjugation operator \$...