In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.
QCD exhibits three salient properties:
Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although analytically unproven, color confinement is well established from lattice QCD calculations and decades of experiments.
Asymptotic freedom, a steady reduction in the strength of interactions between quarks and gluons as the energy scale of those interactions increases (and the corresponding length scale decreases). The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. For this work, all three shared the 2004 Nobel Prize in Physics.
Chiral symmetry breaking, the spontaneous symmetry breaking of an important global symmetry of quarks, detailed below, with the result of generating masses for hadrons far above the masses of the quarks, and making pseudoscalar mesons exceptionally light. Yoichiro Nambu was awarded the 2008 Nobel Prize in Physics for elucidating the phenomenon, a dozen years before the advent of QCD. Lattice simulations have confirmed all his generic predictions.
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?
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:
$$(31)...
This is a kind of continuation of the dispute I had with @A. Neumaier. According to one view, QFT of the Standard Model should fundamentally be viewed as a continuous theory, while the UV cutoff is just an auxiliary tool that eventually should be put to infinity. According to another view, the...
I want to calculate transition amplitudes in QCD for processes like ##q(k)q^\prime(p)\rightarrow q(k^\prime)q^\prime(p^\prime)##, where ##q,q^\prime## are quarks. However, I am unsure what to do with the colour indices of the quark spinors upon squaring the matrix element. For the sake of...
Hello everybody!
I have to write the Feynman diagrams for the process ##\pi^- + p \rightarrow \Lambda_c^+ + D^-##. It is a strong process since all the quantum numbers are conserved.
I have attached my attempt, is it correct?
Thank you all in advance!
I was studying Particle Physics by Palash B. Pal. It is a good book, but after some chapters, I felt it is becoming incomprehensible, and I need some other book(s) to learn from a different perspective. I believe this a very common thing with students, and everyone knows that no single book is...
The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space):
$$\beta=\beta'=0.813(9)$$
$$\nu_\perp=0.584(5)$$
$$\nu_\parallel=1.110(10)$$
The latter two numbers are in close agreement with the (soft)...
The exchange of soft Pomerons (and Reggeons) (##\alpha_R(0)=0.55## and ##\alpha_P(0)=1.08##) seem to describe total hadron-hadron cross sections pretty well in the Regge limit. See, for example:
https://arxiv.org/abs/hep-ph/9209205
In this limit, QCD is of very little use since the exchanged...
The term which is relevant for the calculus is:
$$ \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...
When I calculate light-cone PDF by taking pz in quasiPDF to infinity before one-loop integration, I will encounter all the integrations vanish. Such as this integral below:
https://imgur.com/8DbDzsV
This is from one of one-loop quasiPDF diagram, the sail diagram.
The definition is above...
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
Hi PhysicsForums,
I have a pretty basic question about extracting physical parameters from lattice QCD simulations. As described in "Quantum Chromodynamics on the Lattice" by Gattringer and Lang, it seems we should be able to extract the static quark/anti-quark potential by considering the...
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...
It is my understanding that the task of enumerating all of the divergent diagrams in a quantum field theory can be reduced to analyzing a hand full of diagrams (well, at the moment I know that this is at least true for QED and phi^4 theory), and that all other divergent diagrams are divergent...
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...
Archeology and evolution of QCD
https://arxiv.org/abs/1610.07466
a ""few of the points which...illustrate well the QCD evolution (in time), both from a scientific and a sociological point of view.'
I felt much of that energy expressed in that paper because as an undergrad and grad student, I...
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...