# What is Yukawa: Definition and 50 Discussions

In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is a scalar field (or pseudoscalar field) ϕ and a Dirac field ψ of the type

V

g

ψ
¯

ϕ

ψ

{\displaystyle ~V\approx g\,{\bar {\psi }}\,\phi \,\psi \quad }
(scalar)

or

g

ψ
¯

i

γ

5

ϕ

ψ

(pseudoscalar).The Yukawa interaction was developed to model the strong force between hadrons. A Yukawa interaction is thus used to describe the nuclear force between nucleons mediated by pions (which are pseudoscalar mesons).
A Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark and lepton fields (i.e., the fundamental fermion particles). Through spontaneous symmetry breaking, these fermions acquire a mass proportional to the vacuum expectation value of the Higgs field. This Higgs-fermion coupling was first described by Steven Weinberg in 1967.

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1. ### A Scalar decay to one-loop in Yukawa interaction

I am trying to calculate the amplitude for a decay ##\phi \to e^+e^-## under a Yukawa interaction ##\mathcal{L}_I = -g\phi \bar{\psi}\psi## to one-loop order (with massless fermions for simplicity). If I'm not wrong, there are 4 diagrams that contribute to 1 loop, three diagrams involving...
2. ### Is the function v(r) = (e^(-mr))/r a solution to the Yukawa PDE equation?

(1) From "Radial solutions to Laplace's equation", we know that $$\Delta u(x) = v(r)''+\frac{n-1}{r}v(r)'$$ we re-write the PDE $$- \Delta u+m^2u=0$$ in terms of ##v(r)## $$- v(r)''-\frac{n-1}{r}v(r)'+m^2v(r)=0$$ to give a linear second order ODE with...
3. ### A Boundary conditions of eigenfunctions with Yukawa potential

Hello, I was going to solve numerically the eigenfunctions and eigenvalues problem of the schrödinger equation with Yukawa Potential. I thought that the Boundary condition of the eigenfunctions could be the same as in the case of Coulomb potential. Am I wrong? In that case, do you know some...
4. ### Initial condition of Wave functions with Yukawa Potential

Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1...
5. ### I Form of the Standard Model: Higgs-Fermion Yukawa Coupling

Hey there, I was looking at the Higgs sector of the standard model, particularly its coupling to the fermions: ##\mathscr{L}_{ yukawa }=-\sum _{ a,b=1 }^{ 3 }{ \left( { Y }_{ ab }^{ u }{ \bar { Q } }_{ a }{ \hat { \varepsilon } }_{ 2 }{ H }^{ \dagger }{ u }_{ b }+{ Y }_{ ab }^{ d }{ \bar { Q }...
6. ### Yukawa Potential: Find Value of Parameter 'a

So this is the problem: My only point of confusion right now is in what the value of a is... I'm having trouble finding it anywhere, and online stuff about the yukawa potential just states that it's a parameter. Thanks for any help! Edit: It might be worth noting that gamma equals kq1q2.
7. ### I Estimate of ground state energy for the Yukawa potential

I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
8. ### I Phenomenological potentials and exchange of force carriers

Consider a proton-neutron system. Phenomenlogical nucleon-nucleon potentials contain exchange forces terms (Majorana, Bartlett and Heisenberg terms), which are linked to the symmetry of the state w.r.t. (for example) the exchange of isospin (i.e. charge). On the other hand proton and neutron...
9. ### Perturbation for Yukawa Potential

Homework Statement The photon is normally assumed to have zero rest mass. If the photon did have a tiny mass, this would alter the potential energy the electron feels in the hydrogen atom (due to the Coulomb interaction with the proton). The potential then becomes yukawa potential...
10. ### B Yukawa interaction vs gauge interaction

The Higgs boson can be thought of as mediating a "fifth force" that is not a gauge force but a Yukawa interaction. What is the main difference between Yukawa and gauge interaction?
11. ### A Spinor indices on Yukawa coupling terms in electroweak sector

In the electroweak sector, we define the left-handed Weyl fields ##l## and ##\bar{e}## in the representations ##(2,-1/2)## and ##(1,+1)## of ##SU(2) \times U(1)##. Here, ##l## is an ##SU(2)## doublet: ##l = \begin{pmatrix} \nu\\ e \end{pmatrix}.## The Yukawa coupling in the electroweak sector...
12. ### Rayleigh–Ritz method - Yukawa coulomb potential

Hello everyone Homework Statement I have been given the testfunction \phi(\alpha, r)=\sqrt{(\frac{\alpha^3}{\pi})}exp(-\alpha r) , and the potential V(r,\theta, \phi)=V(r)=-\frac{e^2}{r}exp(\frac{-r}{a}) Given that I have to write down the hamiltonian (in spherical coordinates I assume), and...
13. ### Yes, your working is correct so far. Keep going with the rest of the problem!

Homework Statement (a) Calculate the equations of motion for a massive vector ##A_{\mu}## from the Lagrangian ##\mathcal{L}=-\frac{1}{4}F_{\mu\nu}^{2}+\frac{1}{2}m^{2}A_{\mu}^{2}-A_{\mu}J_{\mu},## where ##F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}##. Assuming...
14. ### Top quark mass mt at energy scales μ<mt?

Does it make sense to talk about the top mass at energies below mt, although in all processes the corresponding energy scale is above mt because of the rest mass energy of the top quark? Using an effective field theory approach, the top quark decouples at energies below the top quark mass and...
15. ### Decay into electron-positron pair in Yukawa theory

Homework Statement I have a question regarding exercise 48.4-b in Srednicki's QFT book (the chapter is related to Yukawa theories). I have the official solution + explanation to the problem but I still do not fully understand the reasoning used in it, so perhaps you can help me. In the...
16. ### Yukawa interaction and chirality.

i still can't figure out how the higgs vev couples opposite chiral fermions(spinor components) to compose a physical electron/positron. (and actually in kurros 's thread it says that the yukawa interaction does not flip chirality nor helicity. what the hell does it mean for the yukawa...
17. ### Yukawa Interaction: What Is It & Why Not Part of Standard Model?

Hello There I may have some mistakes so correct me when I wrote something wrong.My question is:what's the yukawa's interaction and why it is not part of standard model?
18. ### Trouble Finding Renormalization Conditions in Yukawa Theory

I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...
19. ### Problem with Fourier bessel transform of Yukawa potential

Hello, I am trying to find Fourier Bessel Transform (i.e. Hankel transform of order zero) for Yukuwa potential of the form f(r) = - e1*e2*exp(-kappa*r)/(r) (e1, e2 and kappa are constants). I am using the discrete sine transform routine from FFTW ( with dst routine). For this potential...
20. ### Feynman rules for Yukawa theory

Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, and maybe an example of application to decay of fermion?
21. ### Derivatives in 3D and Dirac Delta

For a research project, I have to take multiple derivatives of a Yukawa potential, e.g. ## \partial_i \partial_j ( \frac{e^{-m r}}{r} ) ## or another example is ## \partial_i \partial_j \partial_k \partial_\ell ( e^{-mr} ) ## I know that, at least in the first example above, there will be a...
22. ### Yukawa potential and the Klein Gordon

Homework Statement a)Show that the yukawa potential is a valid static-field euation b)Show this solution also works Homework EquationsThe Attempt at a Solution Part (a) Using the relation given, I got LHS = \frac{e^{-\mu r}}{r} \left[ (m^2 - \mu^2) - \frac{2\mu}{r} - \frac{2}{r^2}...
23. ### Integrating the Yukawa Potential: Understanding the 3rd Step

Please, can anyone explain me the steps made in the resolution of this integral? http://en.wikipedia.org/wiki/Common_integrals_in_quantum_field_theory#Yukawa_Potential:_The_Coulomb_potential_with_mass
24. ### Why Does Yukawa Scattering Focus on 2-to-2 Particle Processes?

Im currently reading these lectures notes on yukawa scattering (charged scalars and real scalars). http://www.damtp.cam.ac.uk/user/tong/qft.html In the interaction part he focuses strictly on 2 particle to 2 particle scattering, is there a reason other types are not discussed? For example a 2...
25. ### Yang-Mills, QED, QCD and Yukawa theories

What is the difference between Yang-Mills and QED theories? Yukawa and QCD? specially in terms of the lagrangians. I really want to get into this subject with a previously first sight.
26. ### Vertex corrections 1-loop order Yukawa theory

Consider the Yukawa theory ##\mathcal{L}_0 = \bar{\psi}_0(i\not \partial - m_0 - g\phi_0)\psi_0 + \frac{1}{2}(\partial \phi_0)^2 - \frac{1}{2}M_0^2 \phi_0^2 - \frac{1}{4!}\lambda_0 \phi_0^4## with cutoff ##\Lambda_0##; a lower cutoff ##\Lambda < \Lambda_0## is then introduced with an effective...
27. ### Amplitude for fermion-fermion Yukawa scattering

Suppose that we have that: \mathcal{M} = c \bar{u}^{s'}(p') u^s(p) \bar{u}^{r'}(k') u^r(k) For a fermion fermion scattering: f(k,r)+ f(p,s) \rightarrow f(k',r')+ f(p',s') Now if I want to calculate the polarization summed and averaged squared amplitude: \frac{|c|^2}{4} \sum_{r,r',s,s'}...
28. ### Derivating a Yukawa theory loop-integral

Hello fellow physicists, during some calculations for a project regarding Renormalization, I had a difficulty in computing a derivative of a loop integral in Yukawa theory. The thing I'm reffering to can be found in Peskin and Schroeder's book, Introduction to QFT , in Chapter 10 page...
29. ### QFT: Scattering Amplitudes in Yukawa Theory

Homework Statement I'm working with the Yukawa theory, where the interaction term in the Lagrangian density is g\varphi\overline{\psi}\psi. As an exercise for getting used to using the Feynman rules for the theory, I'm asked to show explicitly (i.e. I'm not allowed to invoke charge...
30. ### Why does the integral of the Yukawa potential converge for q/alpha >= 1?

While preparing for an exam I came across an integral of the form \int_0^\infty dx\;e^{-\alpha x}\sin{q x} with q,\alpha>0. My question will be regarding my solution to the integral which I present as follows: I expand the sine function as a Taylor series and differentiate with respect to...
31. ### Two Questions: Yukawa Potential and Weak Force

1. Yukawa Potential So reading about the yukawa potential I notice that the constant k is related to the inverse of the effective distance of the force from what I've been reading. Thing is everything I read about the strong force states it has infinite range but simply has a maximum potential...
32. ### Yukawa [3 Dirac - 8 scalar] interaction lagrangian

Homework Statement Given an interaction lagrangian L = i \, g \, \bar \psi(x)_i (\lambda^a)_{ij} \gamma_5 \, \psi(x)_j \phi(x)_a where \psi_i are three Dirac fermions with mass M and \phi_a are eight real scalar fields of mass m and \lambda_a are the generators of SU(3). I have to find...
33. ### Which symmetry protects the yukawa couplings?

I asked this in a thread on string theory, but the answer could well be in the standard model, so here I ask the same from the traditional point of view. Naturalness tells us, roughly, that if there is a quantity near zero, it is because a slightly broken symmetry protects it. Of the 24...
34. ### Dark Matter as a Yukawa Like 5th force?

Just an idea: Suppose dark matter has a repulsive force towards matter and dark matter which follows a yukawa potential. It would be consistent with the lack of it in globular clusters, galactic center besides its clustering in galaxies. In case it touches matter, it would just cause an...
35. ### Yukawa potential energy function

Homework Statement This is not yet an attempt at solving a problem. I just need confirmation on that I'm on the right track. So, I am supposed to derive an expression for the radial force function from the given Yukawa-function. Homework Equations U(r) = -(r/r0)U0 exp-(-r/r0) The...
36. ### Yukawa force versus scattering amplitude

When does the Yukawa potential apply and when does the scattering matrix apply? Take QED for example. When calculating a scattering amplitude, you have an expansion in powers of the fine structure constant, 1/137. Where does Coulomb's law F=e^2/r^2 come in? As far as I can tell, all...
37. ### Yukawa Potential Homework: Sketch, Schrodinger Eq & Perturbation Theory

Homework Statement The Yukawa potential is given by: V_{\gamma}(r) = -\frac{q^{2}}{4\pi \epsilon_{0}r}e^{-\gamma r} Where \gamma is a constant. This describes a screened Coulomb potential. I. Sketch the radial dependence of this potential. II. State the radial Schodinger...
38. ### Bound states of Yukawa potential

Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...
39. ### Understanding Yukawa Matrices and Particle Masses

Hi, did I understand this correct: The Yukawa matrices are the couplings of the particles to the Higgs filed. They are in general not diagonal, but could be diagonalized by proper unitary matrices. The physical masses of the particles are the eigenvalues of that diagonal matrix .
40. ### Estimating the Value of Yukawa Coupling g for Neutron-Proton Scattering

I can't find the value of the Yukawa coupling g, for neutron-proton scattering for example, where the Yukawa potential reads - g^2 exp(-m*r) / r. Can some1 tell me at least an approximate value?
41. ### Generating Functional for Yukawa Interactions

Hello, I want to derive the connected two point function for the interacting boson-fermion theory. I know that the generating functional is Z(J, \overline{\eta}, \eta) = N \; exp \left( \int d^4 z \; L_{int} \left(-i \frac{\delta}{\delta J(z)} \right) \left(-i \frac{\delta}{\delta...
42. ### Explanation of Yukawa potential

I would appreciate an explanation of Yukawa potential
43. ### Yukawa Potential Homework: Calculating Meson Energy Levels

Homework Statement I have been given the following assignment: "The meson moves within the nucleus under the influence of a screened Coulomb potential known as the Yukawa potential. Given that the mass of a meson is about 270 times the mass ot the electron and that the effective extent of...
44. ### Exploring Yukawa Potential with Coupling Constant 0.3

If I had was given a yukawa potential of the form: \text{YL}[\text{r$\_$}]=\left(\left.g_L{}^{\wedge}2\right/r\right) \text{Exp}\left[-\mu _Lr (c/\hbar )\right] I put the c/h in the exponent to make it unitless, but what do I do about the outside? i'm given the coupling constant is 0.3. Just...
45. ### Derivation of Yukawa potential: quandry

Can someone provide some help with a derivation in Peskin and Schroeder (equation 4.126, p.122): V(\bold{x}) = \int \frac{d^3q}{(2\pi)^3} \frac{-g^2}{|\bold{q}|^2+m^2}e^{i\bold{q}\cdot\bold{r}} = \frac{-g^2}{4\pi^2}\int_0^\infty dq\; q^2\; \frac{e^{iqr}-e^{-iqr}}{iqr}}...
46. ### Can GUTs Explain Yukawa Couplings?

I don't know that much about GUT's, but am interested in them. My question is can they be used to explain the Yukawa coupling constants like G_e which appear in terms like: L_{\phi e} = - G_e \left( {\begin{array}{*{20}c} {\bar \upsilon _e } \\ {\bar e} \\ \end{array} }...
47. ### Yukawa Potential: Analyzing Shapes & Angular Momentum

Homework Statement A particle moves under the Yukawa Potential of (-alpha)*exp(-kr)/r where k is real. Discuss all possible shapes of the effective potential. At what values of angular momentum L can the particle move in the potential with finite/bounded motion The Attempt at a Solution The...
48. ### Yukawa potential ,confused

could anyone help me also with this question as i am very confused,i have read my notes but i really have a problem with this stuff making anysense, any help would be appreciated thanks:redface: question 6)) The Yukawa potential is given by V°(gamma)(r) = (q)^2/{ 4(pi)(eo)0r...
49. ### Yukawa Interaction: Constraints and Transformations

I have been trying to independently learn quantum field theory, and I've been stumped on a few points... Suppose I had an interacting Lagrangian with the following form: L = H(x) PsiBar(x) (a + i b gamma5) Psi(x) where: H(x) is a field in which the Hermiticity condition is imposed...
50. ### Yukawa predicted the existence of the pi-meson

In 1935 Yukawa predicted the existence of the pi-meson. In which year was it finally discovered?