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I have trouble understanding string breaking in QCD. I have read an article on arxiv (http://arxiv.org/abs/hep-lat/0505012), and I still don't understand what truly happens.

My understanding of string breaking (of a meson - let's say bottomonium) is as follows: We have a quark $b$ and an anti-quark $\bar b$ on distance of $R$ at temperature $T=0$ (this is probably to limit the effects of quark-gluon plasma?). As we "pull" them apart the potential energy increases. At some crytical distance $R_c$ it is more favourable that a pair of quark-antiquark is created from vacuum and thus the final state are two mesons.

For calculating the static potential between a quark and antiquark we use correlation function for creating a meson at $t=0$ and destroying it at $t=\tau$. We then use Wick rotation $t \rightarrow -it$ which then transforms oscilating functions into exponentially decaying ones: $$C(R,t)=a_0e^{-\frac{E_0}{\hbar}t}+a_1e^{-\frac{E_1}{\hbar}t}+\ldots \hspace{2 mm}.$$ We interpolate ground state with $e^{-\frac{E_0}{\hbar}t}$ which is just the static potential $V(R)$, since we neglect kinetic energy.

My first question is: Does the potential static potential $V(R)$ at temperature $T=0$ saturate or not. Many articles say it follows a Cornell potential, which is $$V(r)=-\frac{e}{r}+\sigma r\hspace{1mm},$$ which grows linearly with distance (and doesn't saturate and thus doesn't show string breaking). My second question is about the first excited state, which should be a final state of two mesons (in this case probably $B$ and $\bar B$ meson). Can we get the energy of this excited state with simple correlation function which I mentioned (energy $E_1$), or must we use the correlation function (which is a matrix) in the article (defined on the first page). They also calculate mixing of states which I don't understand fully. Where do they get the energy of eigenstates? The eigenstates they calculate are:$$|1\rangle=\cos(\theta)|b\bar b\rangle + \sin(\theta)|B\bar B\rangle \\ |2\rangle=-\sin(\theta)|b\bar b\rangle + \cos(\theta)|B\bar B\rangle\hspace{1 mm}.$$

PS The picture of string breaking is showed on page 19 in the article.

I would be extremely thankfull if someone showed me an article which explains (qualitatively and quantitatively) string breaking in simpler language.

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  • $\begingroup$ I don't understand your logic when you say that the Cornell potential "doesn't saturate and thus doesn't show string breaking." When you separate quarks to a distance of $R_c$, string breaking creates new quarks at a distance smaller than $R_c$. It also screens out the interaction between the original two quarks. Demonstrating saturation requires that it be possible to determine the potential for separations greater than $R_c$, when it is clear this cannot happen due to confinement, since this ensures that you will always have a separation less than $R_c$ at $T=0$. $\endgroup$ – probably_someone Sep 22 '18 at 21:32
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The paper You refer to is too technical...

You can imagine, two bb' quarks in Upsilon meson annihilate via gluons into u---u' (or d---d' or s---s') quark pair.

Light quarks move apart from each other with velocity v=0.998c.

Due to the confinement, the string of gluonic fields between them is created and it breaks via (qq') pairs creation, producing new mesons in this way.

Regards, Peter.

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