Helicity Definition and 62 Threads

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...

Hello everybody! I have a question regarding the process ##e^+ e^- \rightarrow Z/\gamma \rightarrow f \bar{f}##, where ##f## is a fermion and ##\bar{f}## is an antifermion. I am studying the process to understand LEP measurements. Supposing of being in ultrarelativistic regime, so helicity and...

Hello! The free Dirac hamiltonian doesn't commute with the z component of the spin operator ##S_z##, but it commutes with the helicity operator ##h=S\cdot\hat{p}##. This means one can know at the same time the energy and helicity of a particle, but not its spin along the z-axis. I am a bit...

It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g $$\Pi^{\mu \nu} = (g^{\mu \nu} - q^{\mu} q^{\nu}/q^2)T_T + q^{\mu} q^{\nu}T_L,$$ where mu and nu are polarisation indices. How do I relate...

Hi! I am kinda confused about what gets conserved in QED and what not. So the chirality is always conserved, I got that. So in the massless limit, helicity is too. Now in the massive limit. Are spin and helicity conserved? And if they are, are they at each interaction vertex, or just overall...

Hello! So Weyl spinors are 2 dimensional spinors which describe massless particles and have definite helicities. So if we have a right handed Weyl spinor going along the positive x-axis, it's spin will always point along the positive x-axis too. I am a bit confused how can an object have 2 spin...

So I heard on different occasions that chirality it's a very confusing concept and it is often mixed with helicity. I read some definitions and examples from a book and as far as I can tell (at least for QED), helicity it's an operator that gives the component of the spin along the direction of...

Homework Statement For massless particles, we can take as reference the vector ##p^{\mu}_R=(1,0,0,1)## and note that any vector ##p## can be written as ##p^{\mu}=L(p)^{\mu}_{\nu}p^{\nu}_R##, where ##L(p)## is the Lorentz transform of the form $$L(p)=exp(i\phi J^{(21)})exp(i\theta...

I am a bit confused about spin conservation at relativistic energies. I am reading a QFT book by Peskin and at a point he specifies that "In the nonrelativistic limit the total spin of the system is conserved". Later when we go to the relativistic limit (there is the interaction between a photon...

Hi, My question basically comes from this book called "Deep inelastic scattering" In the second chapter, it first made a similar argument for J = 1 Jz = -1, +1 which is pretty easy to get along with. However, immediately following from that there was this argument which confuses me a bit...

The helicity in non relativistic quantum mechanics is given by ##\sigma \cdot p / |p|## where ##\sigma## are the pauli matrices and ##p## the momentum. In spinor space, the ##\sigma## are 2x2 matrices, and thus, the helicity, if we calculate it, is a 2x2 quantity. But in 3d physical space, the...

Hello! I have some questions about helicity and chirality: So I understand how is helicity defined and that it has eigenvalues of 1 or -1. But can a particle (massless) have mixed helicity? Like the spin not to be along the direction of motion? (I assume it can but I want to make sure, because...

In trying to understand the Neutrino where it has mass and its chirality is the same as its helicity, I have always had trouble visualizing a particle. I recently ran into this particle. I believe the "the chirality is the same as helicity" as in one direction it would feed things through the...

Suppose a Fermion having left-handed helicity travels faster than light between points A and B. Some observers see it traveling from A to B. Some observers see it traveling from B to A (backwards in time). Some observers see it traveling instantaneously (infinite speed). Do any any of these...

Homework Statement Let ##V^{3}(t)## be a compact region moving with the fluid. Assume that at ##t=0## the vorticity ##2##-form ##\omega^{2}## vanishes when restricted to the boundary ##\partial V^{3}(0)##; that is, ##i^{*}\omega^{2}=0##, where ##i## is the inclusion of ##\partial V## in...

Can we use the Zig-Zag model of the electron to get an intuitive understanding of the difference between helicity and chirality? Suppose we have a long and narrow cylinder where the spin 1/2 massless zig and zag particles bounce between the top and bottom of the inside of the cylinder at the...

The drive shaft of a truck undergoing acceleration twists a small amount. That twist defines a helicity. If you just know the rotation of a drive shaft you can not tell which way power flows but if given rotation and the twist of the shaft that can determine the direction of power flow? Thanks!

Why helicity of phon is 1 but not 3 or higher?Is there any quantity relation between the circular polarization of light and spin of photon?Why spin of graviton is 2?Is there any relation with vector and tensor charater of electromagnetic and gravitation fields and of P symmetry?Why do the...

My lecture notes give an example of two decay modes of ##K^+##, namely ##K^+\rightarrow \mu^+ \nu_\mu## and ##K^+\rightarrow e^+ \nu_e##. Both of these decays are suppressed due to helicity considerations which I understand, and the suppression factors are ##\frac{m_\mu c^2}{E_\mu}## and...

Hi there, The question about the helicity operator ## h= S . \bf{p} ## ( where S is 2 by 2 matrix, with ##\sigma^i ## on the diagonal ), that as mentioned in a reference as [arXiv:1006.1718], it commutes with the Dirac Hamiltonian ## H = \gamma^0 ( \gamma^i p^i + m ) ## equ. (3.3), due to...

Could someone please help me to understand the difference between the concepts of Weak Isospin, Chirality and Helicity. In particular, I have the following questions to which I was unable to find answers so far: 1. Since both spin direction and momentum are vectors, would not their apparent...

Homework Statement Draw feynman diagrams for pi+ muon lepton decay and suggest which process is more likely.Homework EquationsThe Attempt at a Solution [/B] The feynman diagrams are: The lepton decays proceed via the weak interaction W+ boson. This implies that e+ should be...

A left handed neutrino (chirality) can be seen with a right helicity due to a lorentz boost. Can this neutrino interact ? Yes because it is still left-handed chirality ?

(Chiral Representation ##\gamma_5## is diagonal) According to An introduction to QFT - Peskin & Schroeder 3.3 : ##h=\hat{p}\cdot S## and ##h=+1/2## is right-handed while ##h=-1/2## is left-handed. It is quite easy for fermions. But I'm confused when it comes to anti-fermions. In Pestkin's...

First: a question about spin. When we say that an electron has spin 1/2, we mean that it can have the values ħ/2 or -ħ/2. So when we say that a photon has spin 1, I would expect this to mean that the measurement of a photon would give values either ħ or -ħ. But then I am confused by the...

As we know photon's helicity are \pm1. Helicity is the projection of the spin S onto the direction of momentum, p, which is considered as Sz. What about Sx and Sy? They are both ZERO?

why massless particle, such as photon, can only have two helicity states? Photon's helicity is 1,-1. Helicity zero is forbidden. why?

Hi all! So rumor has it, that the spin of a particle is preferably aligned opposite to the direction of the particle's momentum, whereas an antiparticle spins along the direction of motion. For the sake of simplicity let us assume that the (anti-)particle is massless and hence it is an...

Hi, Is there any good books which explain/calculate Wigner rotation, tensor operator, two-particle helicity state and related stuff in detail? Thanks.

The Z0 is a linear combination of W0 and B0 bosons, so unlike the charged current interaction it can interact with both handednesses (is that a word). In the search to quantify this mixing, people measured the cross section for muon (anti)neutrinos to scatter off electrons. This is a reaction...

Good morning everyone ! I've been reading discussions on PF for a long time, but here I'm stuck on a little problem that really annoys me and I couldn't find answer anywhere, so I guess it was time to register. :> I've been focusing on quantum electrodynamics for a couple of weeks now as part...

At the beginning of cpt 9, Griffiths states that massive bosons have three polarization states (m_s = 1, 0, -1), but massless ones have only two (m_s = 1, -1). Are these polarization states the same thing as helicity states? I.e. the W/Z would have 3 helicity states and the photon only 2?

1) Since Wigner it is well known that for massless particles of spin s the physical states are labelled by helicity h = ±s; other states are absent. So e.g. for photons the physical states are labelled by |kμ, h> with kμkμ = 0 and h = ±1 and we have two d.o.f. 2) For gauge theories with...

Dear everyone, I have a simple question about the helicity of photon. The helicity operator is defined as \hat{\mathbf{S}} \hat{\mathbf{p}}/|\mathbf{p}|. How to show the photon has +1/-1 helicity eigenvalue from this definition? Thank you ~~

Hi... I read somewhere that positron, in the massless, limit will have the same helicity as the antineutrino. This must be because they are in the same SU(2) doublet. So helicity operator must commute with the SU(2) generators. Please confirm.

Can someone please explain what is meant by "helicity flip suppression" and how this mechanism operates? (I'd like to see an explicit amplitude and/or cross section if possible.) I've been reading papers in which a Majorana fermion self-annihilates into some resonance (say, a Z)...

Apparently there are two helicities or "handednesses" of an electron: right and left. A right-handed electron spins in the same direction as its phase advances, whereas the left-handed electron spins opposite to its phase advance. This leads to many questions in my mind, some of which this...

I am having some conceptual difficulties here. Let's start with the electron-photon vertex piece of the QED Lagrangian: -e\overline{\psi}\gamma^\mu\psi A_\mu Now we can write this in the chiral representation as -e\overline{\psi}_L\sigma^\mu\psi_R A_\mu -...

In page 72, equation (2.5.39) gives J_3\Psi_{k,\sigma}=\sigma\Psi_{k,\sigma} (k is the standard momentum (0,0,1,1)) and he says \sigma will be the helicity. As he explains: However, J_3 is the generator of rotation along the 3-axis(the z-axis), then why isn't \sigma the angular momentum...

Hi, I have a problem involving helicity. Homework Statement In a scattering e^{+}+e^{-} \rightarrow \nu_{\mu}+\overline{\nu}_{\mu} I have to determine for which values of the helicity of initial particles the cross section is not 0. Homework Equations The Attempt at a Solution On a...

Hello all, This is something that has irked me for a while. The Li/Yang/Wu beta decay showed parity violation in the weak force, but from what I gather, it was the helicities of the electrons they measured, while it is the chiral states which are important. For a massive fermion, aren't the...

Can somenone check if my reasoning is correct. I would like to have deeper insight into the difference between spin and helicity. Let's consider two particles: (1) Particle with mass m in momentum-spin state \psi=|{p_1}^\mu=(\sqrt{p^2+m^2},0,0,p); s=1,s_{z}=1 \rangle (these informations...

Hi. I need some information about chirality and Helicity basic information it's application in Dirac equation and quantum field any notes or presentation good reference I'm still Beginner in these subject

Hi, I was reading a lecture of qft and I found that two equations: \begin{flalign*} i \gamma^\mu \partial_\mu\psi_R - m\psi_L=0 \\ i \gamma^\mu \partial_\mu\psi_L - m\psi_R=0 \end{flalign*} after splitting in two Dirac's equation with Weyl's projectors. I found that really interesting that the...

Hello, 1)Why does the number of helicity states depend on space-time dimension ? Masselss graviton in 4 dimensional space has 2 helicity states ( 2 degrees of freedom). In 5 dimensional space it has (still massless in 5 D) 5 helicity states (5 degrees of freedom) ... In 6 dimesional...

Does anyone has any idea how the spinors of the 3/2 particles look in the helicity basis? Basically, I'm trying to calculate a Feynman diagram for a nucleon Delta scattering, keeping the helicity inices explitly. I've had a look at this...

Weyl spinors are not eigenstates of the helicity operator when the mass is not zero. But they have well-defined chiralities no matter what the mass is. Yet, it seems to me that references keep talking of Weyl spinors as if they have well-defined helicities, regardless of the mass...

All neutrinos are left handed and all anti neutrinos are right handed.so,it should be lorentz invariant and travel at speed of light. if it travels at c,then it is massless. but, neutrino oscillation requires mass? why there is contradiction?

Hi... Consider a neutrino with a Dirac mass m_\nu and the weak interaction {\cal{L}}=\frac{g}{2 \sqrt{2}} \sum_l[{W_{\mu}^+ \cdot \bar{\psi}_{\nu_l} \gamma^{\mu}(1-\gamma_5)\psi_l + W_{\mu}^- \cdot \bar{\psi}_{l} \gamma^{\mu}(1-\gamma_5)\psi_{\nu_l} }\right{]} + \frac{g}{4...

I'm perplexed about something that Wikipedia says about photon helicity: (see http://en.wikipedia.org/wiki/Photon) But for a photon, doesn't the spin vector always point in the same direction as the momentum vector - and therefore, shouldn't the magnitude of a photon's helicity equal it's...