Question

I am just now starting my particles education so forgive me if this is elementary...

Looking at interaction terms in a scalar field Lagrangian, I get:

L=12(∂φ)2+...+gχφ2
Where both χ
and φ
are scalar fields.

I've seen somewhere that the χφφ
coupling constant here is actually 2g
, since the proper interaction Lagrangian form for scalar fields is actually:
Lint=g∏knk!∏kϕnkk
And if that's the proper form, then I have:
Lint=12(2gχφ2)
The question is, is this correct? And if so, please provide a detailed reference to a book (i.e. at least which chapter)

For whomever is wondering, I am trying to justify the hZZ vertex factor to be
hZZ→2im2zgμνv
Got lost trying to read Peskin&Schroeder :(
Options:

A) Yes, the deduction is correct, referring to Chapter [XX] of Textbook Name.
B) No, the interpretation lacks accuracy based on the scalar field theory, described in Chapter [YY] of Reference Book.
C) The statement is partly accurate, explained in detail in Chapter [ZZ] of Physics Manual.
D) The deduction is correct but requires more comprehensive context, elaborated in Chapter [WW] of Specialized Physics Text.

Answer 1

C) The statement is partly accurate, explained in detail in Chapter [ZZ] of Physics Manual.

Step-by-step explanation:

The deduction presented in the question involves understanding the coupling constant for the χφφ interaction term in the scalar field Lagrangian. While the expression provided is on the right track, the correct interpretation requires a closer examination of the scalar field theory. In Chapter [ZZ] of the Physics Manual, a more comprehensive discussion on scalar field interactions sheds light on the correct form of the coupling constant.

The expression for the interaction Lagrangian, as mentioned in the question, involves a factor of 2g, but the correct interpretation involves a more nuanced understanding that is elaborated in the specified chapter.

Scalar field theories, as discussed in reputable physics manuals, often require a deep dive into the mathematical formulations. In this context, the accurate deduction involves considering the proper form of the interaction Lagrangian, as outlined in Chapter [ZZ]. The additional factor of 2g in the presented expression can be clarified through the detailed discussions provided in the manual.

The nuances of scalar field theory, including interaction terms, are critical to correctly interpret the coupling constants and derive meaningful results in theoretical physics.

Therefore, the correct option is: C) The statement is partly accurate, explained in detail in Chapter [ZZ] of Physics Manual.