I have seen some articles talking about the role of sigma meson in nuclear force, but more articles omit it and only mention pion, rho and omega (e.g., Wikipedia). What is this sigma meson?
At one point, I decided to make friends with the low-lying spectrum of QCD. By this I do not mean the symmetry numbers (the "quark content"), but the actual dynamics, some insight.  The pions are the sloshing of the up-down condensate, and the other pseudoscalars by extending to strangeness. Their couplings are by soft-particle theorems. The eta-prime is their frustrated friend, weighed down by the instanton fluid. The rho and omega are the gauge fields for flavor SU(2), and A1(1260) gauges the axial SU(2), and they have KaluzaKlein-like echoes at higher energies, these can decay into the appropriate "charged" hadrons with couplings that depend on the flavor symmetry multiplet. The proton and the neutron are the topological defects. That accounts for everything up to 1300 but a few scalars and the b1.  There are scalars starting at around 1300 MeV which are probably some combination of glue-condensate sloshing around and quark-condensate sloshing around, some kind of sound in the vacuum glue. Their mass is large, their lifetime is not that big, they have sharp decay properties.  On the other hand, there is nothing in AdS/QCD which should correspond to the sigma/f0(600), or (what seems to be) its strange counterpart f0(980). While looking around, I found this discussion: . The literature that it pointed to suggests that the sigma is a very unstable bound state of pions (or, if you like, tetraquarks).   gives strong evidence for an actual pole;  gives a more cursory review. The location of the pole is far away from the real axis, the width is larger than the mass by 20% or so, and the mass is about 400MeV. The authors though are confident that it is real because they tell me that the interpolation the interactions of pions is safe in this region because their goldstone properties dominate the interactions. I want to believe it, but how can you be sure?  I know this particle was controversial. I want to understand what kind of picture this is giving. The dispersion subtraction process is hard for me to visualize in terms of effective fields, and the result is saying that there is an unstable bound state.  Is there a physical picture of the sigma which is more field theoretical, perhaps even just an effective potential for pions? Did anyone who convinced himself of the reality of the sigma have a way of understanding the bound state properties? Is there an analog unstable bound state for other goldstone bosons? Any insight would be welcome.
I have 2 1tb hard drives on my computer with Windows 8 on the first hard drive and nothing on the other.  I want to install Ubuntu 14 on the second hard drive. I've looked up some guides and they all say to install Ubuntu on the sdb partition when booting off a usb stick. I have also seen some say to unplug the Windows HDD and then install Ubuntu onto the second HDD, and Ubuntu will automatically detect Windows and ask what you want to boot into upon boot.   I am really concerned about this - Will it ask me to choose what OS I want to boot into? Is there something like rEFInd(Mac) for Windows? Can anyone please give me a guide on how to do it without ruining my computer?  Thanks GUI for watching logs (tail and grep) Could you recommend a GUI application with powerful log watching capabilities?  Generally it would work as tail -f in GUI, but on top of that following features would be very useful:   filtering out some lines based on (regular) expressions  coloring some lines based on (regular) expressions interactive search saveable configuration easily applicable to different files notifications based on (regular) expressions   A similar tool on Windows is  and its paid version - Plotting recursive function using pgfplots \addplot Is it possible to plot a recursive function using pgfplots \addplot command?  I tried like this;  \documentclass{article} \usepackage{pgfplots}  \pgfmathdeclarefunction{fac}{1}{   \pgfmathparse{(#1&lt;=1)+                 (#1&gt;1)*#1*fac(#1-1)   } }  \begin{document} fac(5) is \pgfmathparse{fac(5)}\pgfmathresult  \end{document}   But the result seems to be an infinite recursion, as the entire function is being evaluated. Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$ Let $p_n$ be the $n$th prime number in its natural order. We want to show that  $$p_{n+1} \leq p_1\dotsc p_n + 1 \tag{1}$$  I know $p_1\dotsc p_n + 1 &gt; 1$, so it has at least one prime divisor, but the text says that $p_{n+1}$ cannot exceed the smallest of these divisors, but I cannot understand why, especially when I imagine $p_{n+1}$ being very large. Although some examples confirm that this statement is true, I cannot make a connection as to why the $n+1$ prime number cannot exceed the smallest prime divisor. Once this has been shown to be true, $(1)$ immediately follows. Why isn't .profile sourced when opening a terminal? Just installed Ubuntu 14.04.1 LTS.  According to .profile,  # ~/.profile: executed by the command interpreter for login shells.  # This file is not read by bash, if ~/.bash_profile or ~/.bash_login exists.   There is no ~/.bash_profile or ~/.bash_login.  It does not seem to source .profile when opening a terminal.   Why doesn't it source .profile when opening a terminal? Why is .profile there if it is not sourced? How do I know/control what is sourced when a new terminal is opened? When a new terminal is opened, does it do a "login"? Where is a good place to add $HOME/bin to my path? .bashrc? Will that cause a problem because .profile has the same code? Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set I'm mainly trying to prove that      If $0\not \in S\subseteq R$ is a multiplicative subset of a   commutative ring $R$ with identity. Then $R-S$ contains a prime ideal.   Now, by using Zorn's lemma, one can show that $R-S$ contains a maximal ideal I. In fact, I is a prime ideal as well, so we need to show this.To do that, I assumed the opposite, i.e $\exists a,b \in R$ s.t $ab\in I$, but $a,b \not \in I$. Then looked each case. However, I stuck when $a,b \in R-[S\cup I]$. The following is what I've done for this case;  Proof:  In this case, our assumptions are $a,b\in R-[S\cup I]$ and $I + (a) = J$, where $J$ is an ideal in $R$ and $J \cap S \not = \emptyset$.   These imply that; $S^{-1}(I + (a)) = S^{-1} J$, but since $J \cap S \not = \emptyset$, by a theorem that we proved in the class, $S^{-1} J = S^{-1}R$.Therefore, it must be true that $\exists (i\in I, r\in R, s_1,s \in S)$ s.t  $$\frac{i+ra}{s_1} =\frac{1}{s}$$ but this implies $\exists s_2 \in S$ s.t  $$ s_2(is + sra -1 s_1) = 0 \quad \Rightarrow \quad (s_1 s )i + (s_1 s r) a = (s_1 s )1,$$ ,so $$(b s_1 s )i + (s_1 s r) ab = (s_1 s )b.$$ Observe that by our assumption $ab\in I$, so $(s_1 s)b \in I$.  Now, at the point, I don't know how to proceed, so I would appreciate any help or hint because I stuck at this point for over a week now.  Edit  Thanks for the great answers; however, but I'm specifically interested in how to continue from the point where I stuck. How to remap an existing keybinding in Zathura For about 2 days I'm trying to configure Ubuntu so that I can send an email, but when I type in:  echo "Subject: sendmail test" | sendmail -v my@email.com   I'll get:  postdrop: warning: unable to look up public/pickup: No such file or directory Mail Delivery Status Report will be mailed to &lt;andreigbr&gt;.   Even if I change my@email with mine, the inbox will be empty. Can somebody help me, please? I watched about 5 tutorial about how to send an email fom the command line but still doesn't work. Random matrix theory impact on covariance matrix analysis Ubuntu 12.04 on Amilo LA1703 after istalling graphics doesn't start? GET and POST methods with the same Action name in the same Controller I have a question:     Suppose $f$ is continuous and even on $[-a,a]$, $a&gt;0$ then prove that   $$\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$$   How can I do this? Don't know how to start. A topological space $X$ is said to be irreducible if it cannot be written as a union $X = A∪B$, where $A$ and $B$ are proper closed subspaces of $X$  I want to try the following:  Show:  $(i)$ That every set with the indiscrete topology is irreducible, and every infinite set with the finite complement topology is irreducible.  $(ii)$ That an irreducible Hausdorff space contains at most one point.  Can you give me any suggestions on how to try this? Application is "Ready to Sale" but not reflected on iTunes Store I can't use the terminal while gedit command is running What is object slicing? Someone mentioned it in the IRC as the slicing problem. I know, it's been asked before but I couldn't really get a satisfying answer for some details/backgrounds and I guess it's an important question for many.    Some application seem only to be running with Adobe Flash 15 (or at least I know it does, because I have that version on my Windows Partition).  The official Adobe website says:     NOTE: Adobe Flash Player 11.2 will be the last version to target Linux as a supported platform. Adobe will continue to provide security backports to Flash Player 11.2 for Linux.   Some search on the web like "Ubuntu Adobe Flash 15" or similar does not return any good websites.  I found something that says   (using a "pepper-based version"), and  .   Is it impossible to use this for Firefox too? Would it be a privacy risk?  Are there no alternative projects (I know it's closed source but there are so many so very bright people out there using something similar to wine but just for the plugin....)?  How about the Mac-Version? Shouldn't someone be able to port that one to Linux? Number of subrings of a Field Getting Started with Unit Testing Unit testing is, roughly speaking, testing bits of your code in isolation with test code. The immediate advantages that come to mind are:  Running the tests becomes automate-able and repeatable You can test at a much more granular level than point-and-click testing via a GUI    My question is, what are the current &quot;best practices&quot; in terms of tools as well as when and where to use unit testing as part of your daily coding? Lets try to be somewhat language agnostic and cover all the bases. how to extend a basis