Questions tagged [helicity]

In particle physics, helicity is the projection of the angular momentum onto the direction of momentum. For massless spin-1⁄2 particles, helicity is equivalent to the chirality operator multiplied by $\hbar/2$, so may be used for related chirality questions as well.

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When we talk about the helicity of a particle, why are we (apparently) ruling out the cases of the spin being perpendicular to the motion direction?

If I assume the (linear) momentum is in the direction of the X-axis, could I NOT find the spin-up in the positive Y-(or Z-) axis and the spin-down in the negative Y-(or Z-) axis?
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A question for "Scattering amplitudes for all masses and any spins" : What is the exact two-component expression of the high spin wave function?

Now I'm studying the spinor helicity formalism with several liturature. I could understand roughly how to calculate the $n$-point on-shell amplitudes for massless particles very efficiently and ...
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Parity transformation of spinor helicity brackets

I'm trying to figure out why a parity transformation $P: (E, \textbf{p} ) \rightarrow (E, - \textbf{p})$ implies $\langle i \ j \rangle \rightarrow - [i \ j]$ and $[i \ j]\rightarrow - \langle i \ j \...
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Charged fermions have both chiralities, with the same mass. Shouldn’t neutrinos, also massive, have both chiralities, though with different masses?

Thanks to answers a previous question, I have realised the difference between helicity, a non-Lorentz-invariant quantity, and the Lorentz invariant chirality. Let me summarise what I understand, ...
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A thought experiment about neutrinos

I don't understand all the details of Dirac mass, Majorana mass, and many other "deep" notions. I have in mind a very simple thought experiment. Because of neutrino oscillations we know ...
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Peskin & Schroeder's QFT on page 166

I have two points not clear in Peskin & Schroeder's QFT on page 166. On Figure 5.6, "Since helicity is conserved, a unit of spin angular momentum is converted to orbital angular momentum&...
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Helicity conservation during nuclear resonance in Goldhaber Experiment

Within the context of the Goldhaber Experiment. If a polarised photon of helicity $\pm 1$, is used to excite a $^{152}Sm$ Samarium nucleus to an excited state $^{152}Sm^*$, that then, by spontaneous ...
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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\...
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How to apply MHV rules to QED?

I've been working lately with scattering amplitudes using spinor helicity formalism. I understand how amplitudes with all positive (or negative) $A_n[\pm\pm\dots\pm]=0$ while working with gluons and ...
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How do massless particles have the same chirality and helicity when they are different properties?

I read this article about chirality and helicity. At some point it says For massless particles, chirality is the same as helicity. But as far as I know, helicity takes form in numbers, $(-1/2, +1/2)...
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$A(\phi\phi^*\gamma \gamma)$ with Spinor Helicity Formalism

I am calculating $A_4(\phi\phi^*\gamma\gamma)$ with the spinor helicity formalism (Exercise 2.16). I am following the conventions defined in Elvang's notes Such computation requires three diagrams, ...
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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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Regarding mass insertion and helicity (?) flip

I am reading Grozin's book "Lectures on QED and QCD: Practical Calculation and Renormalization of One- and Multi-loop Feynman Diagrams" and specifically, I want to understand a paragraph on ...
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Why is helicity in this context well-defined?

I am reading these notes on helicity. One of the definitions (see page 5) that is used is the following (here $J^{a}=\bar{\psi} \gamma^{a} \psi$ is the probability current and $K_{a}=\bar{\psi} \...
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Chirality vs Helicity in Top Quark Decay

I still have not had a good explanation of how a Right Handed Top Quark decays. As I understand it, helicity and chirality are both a part of spin. Does this mean that if either is left handed, the ...
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Noether Charge in ideal fluid

I'm having some problems with the definition of the action in Euler fluid and in the Bose-Einstein condensate. In particular in this article https://arxiv.org/abs/1708.01526 the author apply the ...
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Helicity for massless particles

The little group for massless particles is $ISO(2)$, with the following Lie algebra: $$[A,B]=0, \; [J^3,A]=iB, \; [J^3,B]=-iA,$$ where $A,B$ generate translations and $J^3$ generates rotations. To ...
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Physical meaning of the magnitudes of a spinor helicity variable

I wonder if the magnitude (or its square) of a spinor helicity variable has any physical meaning. Let us assume that the spinor helicity variables are defined as follows: \begin{equation} \lambda^\...
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Why does a gluon soft factor depend only on the adjacent legs?

The gluon soft factor can be obtained by taking the soft gluon limit in the $n$-point MHV amplitude $$A(1,2,\cdots, n)=\frac{\langle i,j\rangle^4}{\langle 1,2\rangle\cdots\langle n, 1\rangle},$$ to be ...
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How do we show that for massless fermions, Helcity and Chirality align?

The Helicity operator of a representation of the Lorentz group is given by $$h = \varepsilon_{ijk}S^{jk}\frac{P^i}{|P|}$$ where $S^{\mu\nu}$ are the generators of the Lorentz group. In the $(\frac{1}{...
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What are the real Electromagnetic fields of Circularly Polarized Light?

It is my understanding that the $\vec{E}$ and $\vec{B}$ fields of a circularly polarized photon sit purely in the $(1,0)$ or $(0,1)$ representation of the (complexified) Lorentz Group, and have ...
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How to convert a singlet current in electroweak theory to a doublet current?

I am referring to an aspect of Glashow-Salam-Weinberg theory of leptons. More specifically a step in the book 'Gauge Theory of Weak Interactions' by Walter Greiner page 147. We can write the ...
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Quantization of Helicity for massless particles [duplicate]

My understanding is that the quantization of Helicity for little group of massive particles comes from the fact that rotation in space leaves the 4-momentum $P^\mu=(m,0,0,0)$ invariant; we know that $...
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$\omega$ vs $\rho ^0$ meson decay into $e^+e^-$

The decay $\omega \rightarrow e^+e^-$ has a partial width that is around 10 times smaller than the partial width for the decay $\rho \rightarrow e^+e^-$. Why is this the case? The only difference I ...
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Spin sign for antiparticle

I have this problem with the sign of the spinor for the antiparticle. In the chiral basis, a spinor is represented by $\psi =(\psi_{L},\psi_{R}$). Now, we consider a particle with mass = 0, so Dirac's ...
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How to prove the helicity operator is a Casimir operator for massless particles?

I am reading the classification of irreducible unitary Poincaré group representations. It seems that for massless particles, the momentum operator and the Pauli-Lubanski operator get aligned so the ...
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Find operator that produce a given amplitude

While I was studying spinor helicity formalism, in many articles, it gives the operators that produce a given amplitude. Is there a generic method of finding operators that produce a given amplitude? ...
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Chirality/helicity of anti-particles (again)

Questions (very) closely related to this one have been posted dozens of times, but the joint information (including even lecture notes and books) is incredibly contradictory, so I state my specific ...
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Is an Anti-positron actually only a relativistic effect on the observed helicity of an electron?

I have read quite recently this article here: https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/ in which it is explained that an Anti-positron is actually a different ...
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Identity in spinors

How to write the following contracted spinor expression in terms of Mandelstam variables? The expression is: $$ [p|m\circ n\circ(1+2+... m)|q\rangle $$ where the notation means: $$p^{B'}m_{AB'}n^{AC'}(...
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Definition of the helicity operator

While studying the Dirac equation my professor defined the helicity operator as $$\hat{\lambda}=\dfrac{\vec S \cdot \vec{p}}{|\vec p|}$$ where $\vec S$ is the spin matrix and $\vec{p}$ is the momentum ...
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Distinguishing right/left hand by aliens

If we are in some way contacting aliens, and we want to tell them how to use nuclear $\beta$ -decay to tell clockwise from counterclockwise. For this, we will need to figure out how to relate the L in ...
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Analog of spin VS helicity for internal symmetries

This might be more of a soft question, since I don't While learning about representations of the Lorentz group, I found in Maggiore's book (Chapter 2) that massive particles of spin $j$ have $2j+1$ ...
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Scattering right handed fermions

Assume we have a QED like vector exchange, and I scatter only right handed electron-positron pair- ${e}_ R^+ e_R^-\to e_R^+ e_R^-$. Am I correct that There is no s-channel amplitude-they cannot ...
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Are massless antineutrinos in the Standard Model right-handed or right-chiral?

For massless fermions, their chirality (determining under which representation of the Lorentz group they transform) and their helicity (projection of spin onto three-momentum) eigenvalues are the same....
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Feynman rules to spinor helicity

The following amplitudes of the 3-gluon vertex are obtained only from momentum conservation (shown in Quantum Field Theory and the Standard Model, Schwartz): $$M^{+++}=C^{abc}\frac{1}{\langle12\rangle\...
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Parke-Taylor formula and MHW-amplitudes

In Matthew Schwartz Quantum Field Theory and Standard Model the author presents the Parke-Taylor formula $\tilde{M}(1^+2^+...j^-...k^-...n^+) = \frac{\langle j k \rangle^4}{\langle 1 2 \rangle \...
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Has the “spin” of a photon anything to do with a rotation movement?

If not, where does this denomination come from?
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What are exactly the various polarisations of the photon and how many are there?

What are exactly the various polarisations of the photon and how many are there? Are there: left and right : this makes $2$ linear, circular, elliptic : this makes $3$ (incompatible with the ...
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Bhabha scattering in the spinor-helicity formalism

I am trying to calculate the square amplitude for Bhabha scattering $e^-(p_1)e^+(p_2)\rightarrow e^-(p_3)e^+(p_4)$ using the spinor-helicity formalism but one of the interference terms just will not ...
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What are the Feynman rules for the spinor-helicity formalism?

If we do not work with helicity amplitudes, there are Feynman rules for the external legs of a Feynman diagram, i.e. $u_s(k),\overline{v}_s(k),\epsilon_r(k)$ for an incoming fermion, antifermion and ...
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Weak interaction in a relativistic frame?

Particle is said to be right-handed (right-helicity) if the direction of particle's spin is in the same direction with it's motion and left-handed (left-helicity) if they are opposite. Picture below ...
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How does parity act on relativistic one-particle states?

Please allow me to set the context based on my understanding before I present the question. In quantum field theory, one-particle states are the basis states of the infinite-dimensional unitary ...
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Particle Physics: Decomposition of a Helicity Spinor

I would have a general question: If we consider the decay of the $W^{-}$ boson into $l^{-}\nu_{\bar{l}}$, how can we calculate the polarization of the $l^{-}$?For example, Mark Thomson has on page 299,...
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If you travel faster than a neutrino, will it appear right-handed?

Since neutrinos have mass they move slower than lightspeed. So it is possible to move faster. And if you move faster than the relative direction of the neutrino velocity is backwards. But the spin ...
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Why is helicity a good quantum number while spin isn't?

I'm studying the Dirac equation for free particles and read that spin doesn't commute with the hamiltonian and one has to define the helicity operator to find a third good quantum number. What's the ...
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What is the helicity of a stationary spin?

Spin nonzero. But linear momentum $\vec{p}=\vec{0}$ (all components are zero).
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The unit momentum operator $\hat{\textbf{p}} ={\textbf{p} \over |\textbf{p}|}$

In studying the Dirac equation, I often come across the unit momentum operator $\hat{\textbf{p}}$ which is defined as $$\hat{\textbf{p}} ={\textbf{p} \over |\textbf{p}|},$$where $\textbf{p}$ is ...
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Theories with only positive helicity particles have a trivial S-matrix

How to prove and explain statement from What is the Simplest Quantum Field Theory? (page 8): Theories with only positive helicity particles have a trivial S-matrix It isn't quite clear, because: In ...
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Finding helicity eigenstates

Question: Give the mode expansion of the $A_i$ in terms of plane wave \begin{equation} \epsilon^{\pm}_i(p)e^{-ip \cdot x} \ \ \ \ \ \text{ and } \ \ \ \ \ \epsilon^{*\pm}_i(p)e^{-ip \cdot x} \...