Qcd Definition and 155 Threads

One of the first particles predicted by quantum chromodynamics (QCD), which consists of the laws of physics related to the strong force, whose properties have been calculated for almost fifty years, is the glueball. The glueball is a strong force bound composite particle made up of gluons, but...

Question: Is it meaningful to think of the repulsion of mutual color charge and the attraction of three different color charge in QCD as being indicative of the classical concept of work taking place? Exactly, how is this explained in the context of three charges needed to elicit the...

At low energies, color is confined because attempting to remove a quark from a hadron will cause a response in the glue field that is often described as "snapping", or more formally, quark-antiquark pair production. However, how does this work at ultrahigh energies, let's say around 10^21 or...

A pair of new papers (here and here) make precision determinations of the quark masses and the strong force coupling constant using the renormalization group summed perturbation theory (RGSPT). For comparison purposes, I have followed each value with the Particle Data Group (PDG) value, and then...

What is the meaning of the expansion at first order in ##\delta_2## and ##\delta_3## at the second step in the last line? These quantities are not "small" - on the contrary, the entire point is to then take the ##\epsilon \to 0## limit and the counterterms blow up

The experimentally measured properties of protons and neutrons are known with exquisite detail. Our data is not quite as extremely precise, but still very good more other baryons and mesons with light quarks (u, d, and s) as valence quarks, such as pions and kaons. Yet, on a percentage basis...

On page 210, it's written the following paragraph: What has changed since then? have we found a different theoretical approach to explain exclusive phenomena?

I have calculated $Z$s as $$ \begin{aligned} Z_1 & = 1 + \frac{3g^2}{16\pi^2} \left[ 2 C(R) - \frac12 T(A) \right] \frac1{\epsilon} + \cdots, \\ Z_2 &= 1 + \frac{3g^2}{8\pi^2} C(R) \frac1{\epsilon} + \cdots, \\ Z_3 &= 1 + \frac{g^2}{24\pi^2} \left[ 5 T(A) - T(R) \right] \frac1{\epsilon} +...

In "CP violation" book by Bigi and Sanda (section 8.2.1. QCD), I read that "the QCD Lagrangian is invariant under CP transformations" and wanted to prove it. The QCD Lagrangian is given by \begin{equation} \mathscr{L}_{QCD} = \bar \Psi^f [i \gamma^{\mu}D_{\mu} -m_f] \Psi^f - \frac 1 4 G_{i...

Have a look at O5 & O6 in Eqtns(5.4) . Why is there a (V+A) ? (V+A) contains the projection operator which projects out the right Weyl from a Dirac spinor. As per the Feynman rules of electroweak theory, there is a (V-A) assigned to each (Dirac) spinor-W boson vertex because W only couple to...

First let's define as on page 13 of the book the perturbative coefficients of the hard scattering cross section ##H_{ab}## by: $$(22) \ \ \ \ H_{ab}=H_{ab}^{0}+\frac{\alpha_s}{\pi}H_{ab}^{(1)}+\mathcal{O}(\alpha_s^2)$$ Now, on page 16 it's written that the RG equation for ##H_{ab}## is: $$(31)...

This is a kind of continuation of the dispute I had with @A. Neumaier. According to one view, QFT of the Standard Model should fundamentally be viewed as a continuous theory, while the UV cutoff is just an auxiliary tool that eventually should be put to infinity. According to another view, the...

Hello everybody! I have to write the Feynman diagrams for the process ##\pi^- + p \rightarrow \Lambda_c^+ + D^-##. It is a strong process since all the quantum numbers are conserved. I have attached my attempt, is it correct? Thank you all in advance!

I was studying Particle Physics by Palash B. Pal. It is a good book, but after some chapters, I felt it is becoming incomprehensible, and I need some other book(s) to learn from a different perspective. I believe this a very common thing with students, and everyone knows that no single book is...

The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space): $$\beta=\beta'=0.813(9)$$ $$\nu_\perp=0.584(5)$$ $$\nu_\parallel=1.110(10)$$ The latter two numbers are in close agreement with the (soft)...

The term which is relevant for the calculus is: $$ \bar u(p) \gamma^\alpha \frac{1}{\displaystyle{\not}p+\not k} \gamma^\nu \frac{1}{\displaystyle{\not}p'-\not k} \gamma^\beta v(p') \frac{k_\alpha k_\beta}{k^2} $$ $$ \bar u(p) \displaystyle{\not}k \frac{1}{\displaystyle{\not}p+\not k}...

Below I refer to the following article: The Weight of the World Is Quantum Chromodynamics Andreas S. Kronfeld Science 21 November 2008 Vol.: 322, Issue 5905 - pp. 1198-1199 I've been trying to find more information on the subject but it's been hard for a Google peasant like myself. Just the...

I guess my question is really: is there redundancy in QCD. In particular, is it possible to use so(4)=su(2)xsu(2) as the gauge group for QCD instead of su(3). I only have a couple of qualitative observations to suggest this speculation. The first is the relationship between su(3) and so(4). If...

I'm given to understand that perturbation methods don't work in QCD because the coupling constant is too large. So they use supercomputers to calculate equations at various points on a lattice. Does this lattice method still take into account the virtual gluons that we might see in perturbation...

I am looking for articles or books that would clearly and succinctly state the open problem of and issues with computing hadron masses and spins in QCD from first principles, preferably in relation to the open problem of confinement and the general open problem of non-perturbative QCD. Any...

Is there a good introduction textbook or pdf for quantum chromodynamics?

I think the title sums up pretty well my doubts. I learned QFT from Peskin and Schroeder and other common sources, all implicitly defined QFT at zero temperature. Then I started learning about lattice QCD, how to define the action, how to find continuum limits, the importance of the dependence...

A proton is made of quarks and gluons bound by the strong force in a confined system. Further, all protons are basically interchangeable parts for the purposes of this question. Each one is identical in all material respects. Scientists know a lot about gluon energy density in protons. We have...

It is very difficult for me to understand that a theory based only in "very logical" and "common sense" assumptions (S-Matrix theory, prestring era) makes (some) valid predictions in non-p QCD, while lattice QCD does not. Could the experts comment on this subjet? P.S.: Not interested in string...

1-As you know classical electrodynamics has conformal symmetry. But does this symmetry survive renormalization? if not, can anyone give an explanation on why? 2-What is the situation with QCD? Does it have conformal symmetry at a classical level? If yes, does it survive renormalization? Thanks

I'm trying to show that the theta term in the QCD Lagrangian, ##\alpha G^a_{\mu\nu} \widetilde{G^a_{\mu\nu}}##, can be written as a total derivative, where ##\begin{equation} G^a_{\mu\nu} = \partial_{\mu} G^a_{\nu} - \partial_{\nu}G^a_{\mu}-gf_{bca}G^b_{\mu}G^c_{\nu} \end{equation} ##...

The QCD Lagrangian is ##\mathcal{L}=-\frac{1}{4}G^{a}_{\mu\nu}G^{a\mu\nu}+\sum\limits_{j=1}^n \left[\bar{q}_j\gamma^{\mu}iD_{\mu}q_j - (m_jq^{\dagger}_{Lj}q_{Rj}+h.c.)\right]+\frac{\theta g^2}{32\pi^2}G^{a}_{\mu\nu}\widetilde{G}^{a\mu\nu}## Why is it so often quoted as just...

"The strong coupling from a nonperturbative determination of the Λ parameter in three-flavor QCD" https://arxiv.org/pdf/1706.03821.pdf Their calculation gives strong coupling constant g^2/4pi ~= 0.08523 at 1.508 TeV. Small, but not tending to zero. Lattice calculations seem to converge on...

I'm reading about extensions of standard model and this pops up frequently but it's not very clear. I understand it's a region in parameters space so renormalization group naturally becomes relevant and that's about it for my understanding. I can't connect any of this to the beta function of the...

I have a very simple question. Let's consider the theta term of Lagrangian: $$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$ Investigate parity of this term: $$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$ $$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$ It is obvious. But what about...

In ordinary mechanics, adding 1 particle to a system of 1000000 doesn't change a lot. I know about the sign problem in QCD, so when temperature is cold the amount of calculation diverges. My question is: when we add yet another quark to a system of 1000000 quarks, the amount of calculation...

I. Background The magnetic moment of the muon, g, is predicted by the Standard Model, to be equal to 2 and a bit more, with the quantity that we look at being g-2. We have both experimental measurements and theoretical predictions that are close to each other to many significant digits, but...

hello all, I'm looking for a good and reasonably priced book on quantum chromodynamics any suggestions would be greatly appreciated. many thanks in advance

Hi, I'm trying to compute the cross section of a gluon emission from quarks in a electron-positron annihilation at first order (I attach the diagrams below). Applying the Feynman rules the matrix element should be: My problem is that I have no idea where this minus sign comes from. (I obtain...

Hi everyone, I have a question that, when came to me, sounded a bit silly to me as well, but then I realized, I myself maybe don't understand the logic behind this 100%, so why not discussing with you about it. So my question is the following. Usually we are used to do quantum field theory...

Hi. I'm reading an article about QCD phase diagram. https://arxiv.org/abs/1005.4814. I want to derive eq(20), but I don't know how. Does anyone know how to derive this?

Hello, I know QED and QCD as isolated theories but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically. As I understood my Feynman diagrams are nothing more like pictures for the...

The beta function for the strong coupling ##g_3## is given by ##\displaystyle{\mu \frac{\partial g_{3}}{\partial\mu}(\mu) = - \frac{23}{3} \frac{g_{3}^{3}(\mu)}{16\pi^{2}},}## with ##\alpha_{3}(\mu = M_{Z}) = 0.118.## We can use separation of variables to solve the beta function equation...

I was watching some new lectures on QCD from Colorado and I have a few questions from what I heard - --The ##\lambda^a_{ij}## are generators of SU(3) in the fundamental representation so are 3x3 matrices. That is because the ij indices are colour indices and they act on a 3x1 vector in colour...

I have a question about the use of trace in QFT in general - more specifically the use of trace in the lagrangian in the effective theory concerning chiral symmetry in QCD. I am slowly trying to get a hang of everything, and most things i am able to calculate, but i still have som very specific...

I am trying to learn about the various SU groups related to QCD. I have about 5 QFT and Particle physics books from my student library and written down about 20 pages of handwritten notes about specific parts of say generators, matrices, group properties etc. - but i don't really feel that I...

I read that hadrons are in colour singlet state and that gluons are not and that the colour singlet gluon is forbidden for the reason of making strong force a long range force otherwise (and that SU(3) has 8 generators and thus 8 gluons) but my question is: are mesons in a colour singlet state...

I know there is more than one approach in studying strong interaction, a geometric one based on gauge theories and one based on quantum field theory. In both of them I would like to know which topics I have to study in order to understand this theory, for example my knowledge of quantum physics...

Homework Statement So I am self-studying the book of Peskin&Schroeder, and there is something I don't understand on page 616. In eq. 18.80, there is a numerical factor of ½ and going from e2 to α will introduce a factor 4π when proceeding to eq. 18.84. But then there should be a numerical...

Hello! Could anybody help me? My wondering seems so trivial, but I can't skip it. They say that since u and d quarks are much lighter than QCD scale(~200MeV), in reality we can consider the QCD Lagrangian has an approximate global chiral symmetry with respect to these two flavors. At first, it...

The pole masses of the heavy quarks (c, b and t) are relatively well defined in QCD (i.e. the solution of m²(p²) = p² extrapolated using the beta function and the available data from other values of µ usually obtained based upon model dependent decompositions of hadron masses that include these...

I will soon start a Master thesis in Lattice QCD. There I will spends lots of time developing C++ code and running it on different supercomputers. After that I consider doing a PhD if the Master thesis runs well. For the experimentalists I can see a lot of almost-engineering jobs where they...

Homework Statement I want to diagonalize the quadratic form $$ m_0((m_u+m_d)\pi^3\pi^3+\frac{2}{\sqrt{3}}(m_u-m_d)\pi^3\pi^8+\frac{1}{3}(m_u+m_d+4m_s)\pi^8\pi^8)$$ which can be found under equation 5.47, in order to get the mass of the η and ##\pi^0## pions. This quadratic form is produced by...

Hello all, I hope you can give me a hand with a QFT homework I'm working on. We are to compute the beta equation of a Non-abelian SU(N) theory with: Complex scalars (massless), bosons, ghosts. My question is referring to the Boson self-energy scalar loop correction. 1. Homework Statement We...

I have the opportunity to pursue a research project in either lattice QCD or QED. In the case of QED, I'd be writing the code myself, will be able to understand the whole thing, et cetera. There shouldn't be any mystery in this. It almost seems like a long exercise, and there isn't anything I'd...