<p>You're correct that "$p$-wave" in this context means that the charmonium has orbital angular momentum $L=1$. The principal observable effect is that two-particle states with even $L$ have even <a href="https://en.wikipedia.org/wiki/Parity_%28physics%29" rel="nofollow">parity</a>, while those with odd $L$ change sign under parity.</p>

<p>If you were to skim the <a href="http://pdg.lbl.gov/2014/tables/rpp2014-tab-mesons-c-cbar.pdf" rel="nofollow">Particle Data Group's list of charmonia</a> (or the $c\bar c$ section of <a href="http://pdg.lbl.gov/2014/tables/rpp2014-qtab-mesons.pdf" rel="nofollow">the short list</a>) you would find that each particle has a value listed for spin, $J$, and parity, $P$. The lightest few states are</p>

<ul>
<li><p>$\eta_c(1S)$, with $J^P = 0^-$. This is a charm-anticharm bound state where the two quarks have opposite spins and the angular momentum $L=0$. (The total parity is negative because the intrinsic parities of the $c$ and $\bar c$ have opposite sign.)</p></li>
<li><p>$J/\psi(1S)$, with $J^P=1^-$. This has the same parity as the spinless $\eta_c$, but a unit of spin. So it must be that here the two quarks have the same spin and $L=0$.</p></li>
<li><p>$\chi_{c0}(1P)$, with $J^P=0^+$. The change in parity suggests that this state must have a different $L$ than the $\eta_c$ and $J/\psi$, and it's the first with a $P$ in its name. There's also a $\chi_{c1}$ and $\chi_{c2}$ with $J^P=1^+, 2^+$, respectively. That suggests these are the three spin combinations of a charm-anticharm pair with spin $S=1$ and orbital angular momentum $L=1$.</p></li>
</ul>

<p>There are also some charmonia with $(2S)$ and $(2P)$ in their names. There don't appear to be any definitively labeled $d$-wave charmonia.</p>

CC BY-SA 3.0
2014-09-12T19:46:06.873Z
2014-09-12T19:46:06.873Z
rob
<p>What exactly does p-wave mean when referring to particles, like charmonia states. </p>

<p>For example, see the following reference:</p>

<p><a href="http://arxiv.org/abs/hep-ph/9208254" rel="nofollow">http://arxiv.org/abs/hep-ph/9208254</a></p>

<p>My doubt is - p wave in scattering means l=1. But how is that used to label a particle state?</p>

<p>Thanks. </p>

<high-energy-astrophysics>
meaning of p-wave charmonia
Terence Tze
# meaning of p-wave charmonia

(Asked by: username_0 on 2014-09-03)

What exactly does p-wave mean when referring to particles, like charmonia states.

For example, see the following reference:

<http://arxiv.org/abs/hep-ph/9208254>

My doubt is - p wave in scattering means l=1. But how is that used to label a particle state?

Thanks.

**Tags:** high-energy-astrophysics

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## 1 answers

### Answer by username_1 on 2014-09-12. Score: 3

You're correct that "$p$-wave" in this context means that the charmonium has orbital angular momentum $L=1$. The principal observable effect is that two-particle states with even $L$ have even [parity](https://en.wikipedia.org/wiki/Parity_%28physics%29), while those with odd $L$ change sign under parity.

If you were to skim the [Particle Data Group's list of charmonia](http://pdg.lbl.gov/2014/tables/rpp2014-tab-mesons-c-cbar.pdf) (or the $c\bar c$ section of [the short list](http://pdg.lbl.gov/2014/tables/rpp2014-qtab-mesons.pdf)) you would find that each particle has a value listed for spin, $J$, and parity, $P$. The lightest few states are

* $\eta\_c(1S)$, with $J^P = 0^-$. This is a charm-anticharm bound state where the two quarks have opposite spins and the angular momentum $L=0$. (The total parity is negative because the intrinsic parities of the $c$ and $\bar c$ have opposite sign.)
* $J/\psi(1S)$, with $J^P=1^-$. This has the same parity as the spinless $\eta\_c$, but a unit of spin. So it must be that here the two quarks have the same spin and $L=0$.
* $\chi\_{c0}(1P)$, with $J^P=0^+$. The change in parity suggests that this state must have a different $L$ than the $\eta\_c$ and $J/\psi$, and it's the first with a $P$ in its name. There's also a $\chi\_{c1}$ and $\chi\_{c2}$ with $J^P=1^+, 2^+$, respectively. That suggests these are the three spin combinations of a charm-anticharm pair with spin $S=1$ and orbital angular momentum $L=1$.

There are also some charmonia with $(2S)$ and $(2P)$ in their names. There don't appear to be any definitively labeled $d$-wave charmonia.


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