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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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Link between photon helicity and polarization of $A^\mu$ electromagnetic potential

From Wigner theorem we know that the irreducible unitary representation of the Poincarè group for massless and spin 1 particle is labelled by the momentum $p_\mu$ and the two possible helicity $+1,-1$ ...
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3-Particle Kinematics and Parity of Operators

Recall that if the momentum of scattering amplitudes is taken to be complex and from little group scaling that the 3-particle interaction for massless particles of any spin is given as \begin{equation}...
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Elastic scattering and conservation of spin

I am trying to understand conservation of spin in QED elastic scattering in these nice notes (VJ Martin, Particle Physics, Spring 2012, University of Edinburgh): https://www2.ph.ed.ac.uk/~vjm/Lectures/...
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Scalar QED amplitudes with BCFW Recursion Relation

(This question comes from exercise 3.5 of Elvang's and Huang's "Scattering amplitudes in Gauge Theory and Gravity" book. This is not for a class, this is to learn a new technique; albeit I ...
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Helicity operator in spinor-helicity variables

How do I prove that the helicity operator is $$ H = \frac{1}{2} (\tilde{\lambda}_\dot{\alpha} \frac{\partial}{\partial \tilde{\lambda}_\dot{\alpha}} - \lambda_\alpha \frac{\partial}{\partial \lambda_\...
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How to derive this form of helicity spinor (massless/high energy limit)

Srednicki 50.7 says that in the massless limit, we can express $$u_-(\textbf{p})\bar{u}_-(\textbf{p}) = \begin{pmatrix} 0&-p_{a\dot{a}}\\0&0\end{pmatrix}$$ This comes from a previously ...
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If helicity of photons is +1 then the light is right- or left-circularly polarized?

In particle physics, we say: a particle has +1 helicity (right-handed) if its momentum and spin are parallel, or it has -1 helicity (left-handed) if its momentum and spin are antiparellel. Now, if we ...
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Yukawa Theory with Spinor-Helicity Formalism

I am trying to learn spinor-helicity formalism, and I am attempting to calculate the all-minus amplitude of 4-fermion scattering at tree level in Yukawa theory, but I have no way to check if my ...
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How many photons exist in another dimension spaces?

As I understand, there are 2 types of photons in our (3+1) space with photon helicity $\pm 1$. How many photons exist in another spaces like (2 + 1) or (1 + 1)? Can we apply the same for gravitons?
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Derivation of hypercharge neglecting squared amplitude for WZ helicities in paper

I am trying to get from equations (20) and (21) in this paper to equations (13) in this one. I will start with my attempt at deriving this for the LL case. (With $F$ from equation (4), $g_2-g_1$ from (...
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Can not follow derivation of $WZ(0, 0)$ amplitude in paper

i am re-reading this paper and trying to follow the derivation of equation (21) from equation (15). Maybe someone can tell me where i am going wrong. So the original equation 15 is: $$M(0,0) = F\frac{\...
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Confusion on the helicity formalism

I'm studying group representation theory from a more mathematical point of view but I don't understand the link between helicity formalism and the "classical one". They should be both ...
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Spin/Helicity-Density Matrices in Particle Physics

I am searching for literature explaining the Spin/Helicity-Density Matrix formalism in order to compute "spin-dependent" matrix elements and cross-sections in particle physics. I would ...
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Questions on Lorentz generators in Spinor-Helicity formalism

I have read the following PSE posts on Lorentz generators in Spinor-Helicity formalism: Total Angular Momentum Operator in Spinor-Helicity formalism Derivation of conformal generators in spinor ...
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Questions on Britto-Cachazo-Feng-Witten (BCFW) recursion method

I am reading about amplitude techniques, such as the spinor-helicity formalism: more specifically, the BCFW recursion relations. The lecture notes I am reading are titled as Scattering Amplitudes, and ...
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How to show that Helicity projectors are Lorentz covariant?

Consider the Helicity projectors $$\Pi_{\pm}:=\frac{\mathbb{1}\pm\gamma^{5}\gamma_{\nu}n^{\nu}}{2}$$ where I define the versor $n^{\mu}\equiv(\frac{|\stackrel{\rightarrow}{p}|}{m},\frac{ω_{p}}{m}\frac{...
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Difference between classical fields and wavefunctions? Relation between QM and Classical field theory

We all know that Dirac equation comes up naturally by trying to build a relativistic generalization of the Schrödinger equation $$(i\gamma^{\nu}∂_{\nu}-m)\psi=0$$ and that the associated solutions are ...
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Decay rate with specific helicity in rest frame and lab frame

Consider a two-body decay, such as the pion decay: $\pi^+\to \mu^+ + \nu_\mu^{}$. In the Standard Model, as there only exits left-handed massless neutrinos, the helicities of final particles are known....
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Can we determine the polarization of a neutrino?

I recently read that neutrinos have a polarization property---their polarization is opposite to antineutrinos. Is it possible to determine the polarization of a neutrino? For example, we can determine ...
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How is the chirality for the weak interaction conserved for non-relativistic neutrinos?

In this article, one can read that the neutrinos in the cosmic neutrino background have a speed of about 1/50 of the speed of light, which is clearly non-relativistic. From the viewpoint of, say, ...
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How many degrees of freedom does a photon have in 2+1D?

Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
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What is Helicity in High Harmonic Generation?

The harmonic spectra are calculated as $|FT(\frac{d}{dt}\mathcal{J}(t))|^2$, where $FT$ si the Fourier Transform and $\mathcal{J}(t)$ is the current. We need to identify which multiple of incident ...
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Checking eigenstates of the helicity operator

In Peskin & Schroeder's book, the helicity operator is defined as $$ h = \hat{p} \cdot \mathbf{S} = \dfrac{1}{2} \hat{p}_i \left(\begin{array}{cc} \sigma^i & 0 \\ 0 & \sigma^i \end{array}\...
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Is there a general argument for why non-dynamical degrees of freedom show up in the propagation of massless gauge bosons?

In both spin-1 and spin-2 gauge theories, the gauge bosons (e.g. the photon & gluon and the graviton respectively) have two physical degrees of freedom, which can be observed quantum mechanically ...
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Helicity of cosmic neutrinos

If neutrino has mass, then it can change it's helicity. But all registered neutrinos have negative helicity while all anti-neutrinos have positive. Does it stands for all registered neutrinos ...
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Mass as generator of two distinct sets of phenomena

We know that mass, which is a continous parameter, generates two classes of different phenomena: the ones where $m=0$ and the ones with $m \neq 0$. When a particle has $m=0$ we have phenomena which ...
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${\cal N}=2$ SUSY Multiplet

In https://www.physics.uci.edu/~tanedo/files/notes/SUSYXD.pdf, on page 47, I found that for ${\cal N}=2$ SUSY (massless representation), we start with a state $|\Omega\rangle$ with helicity $\...
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Are the massive spinors (left and right Weyl spinors) helicity eigenstates?

For massless spinor, with the help of Dirac equation, I can show that both left-handed and right-handed Weyl spinors are helicity eigenstates with eigenvalues +1 and -1 (respectively). I am unsure ...
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Spin 1 particle, vector and photon

In the statement: "The rotation of the spin of a photon through 360 degrees brings it back to its originial state, and hence it is a spin 1 particle, in other words its spin is a vector" ...
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Accounting for photon spin angular momentum in general relativity for two (anti-)parallel photons

General Relativity tells us that the paths of parallel photons propagating in free space should be unaffected by each other, while the paths of anti-parallel photons should bend towards each other. I'...
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Spinor-helicity variables and gauge transformations of the polarization vector

I am reading Clifford Cheung's 2017 TASI Lectures on Scattering Amplitudes. In section 2, "Crash Course in Kinematics", the spinor-helicity variables are introduced and discussed. In terms ...
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Spin quantum states and spin observables of photons (spin 1 particles with 0 rest mass)

I was reading Goldbring's article on the implications of $\text{MIP}^\ast=\text{RE}$ which contains a crash course-like overview of (classical, non-relativistic, non-QFT) quantum mechanics. This made ...
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3-Point Amplitude with Complex Momenta

The following is from Schwartz's Quantum Field Theory and the Standard Model. Next, consider the MHV amplitude. Again, there are only two possibilities allowed by little-group scaling. Since $\frac{\...
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On the simplicity of the three-particle amplitude in holomorphic configuration

I am reading Clifford Cheung's 2017 TASI Lectures on Scattering Amplitudes. In section 3, "Bootstrapping Amplitudes", the procedure for bootstrapping the three-particle amplitude for ...
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How to identify fermion (ie. $e^-$, $\mu^-$)'s spin direction with its momentum direction?

Spin doesn't has classical corresponding concept. In QFT, we use Poincare group to systematically classify particles, from where we use spin. (ie. scalar, spin-$0$, fermion, spin-$\frac{1}{2}$) So how ...
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Explaining "Left" and "Right" to an Alien using Chirality and Helicity

my professor told us that we could hypothetically explain the concept of "Left" and "Right" to a Martian (an alien, etc.) using the fact that Helicity is invariant under parity. ...
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Lorentz invariance of Quantum Electrodynamics [closed]

In chapter 5 of Weinberg QFT (Vol.$1$), in section 5.9, Weinberg demonstrated through an explicit calculation that there cannot be a massless vector field with helicities $\pm 1$. In fact, Weinberg ...
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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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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 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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