Baryons are made of three quarks which are spin-1/2 particles. According to the rule of addition of angular momentum, baryons can have either spin-1/2 or spin-3/2. It is intriguing to note that light baryons have spin-1/2 and heavy baryons have spin-3/2. Does this suggest any connection between their mass and spin?
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asked Jun 14, 2021 at 17:05
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1$\begingroup$ Your text should be discussing Chew-Frautschi plots. Of course there is a systematic Regge trajectory picture relating mass and spin. Take a look at Tang, A., & Norbury, J. W. (2000). Properties of Regge trajectories. Physical Review D, 62(1), 016006. $\endgroup$– Cosmas ZachosCommented Jun 14, 2021 at 17:44
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$\begingroup$ High spin ground state baryons are always heavier than lower spin ground state baryons with the same valence quark composition (as we know from a more or less exhaustive set of measurements of possible baryons with the same valence quarks but different spins except in the very heaviest cases). $\endgroup$– ohwillekeCommented Jun 14, 2021 at 22:35
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$\begingroup$ @ohwilleke But why? $\endgroup$– SolidificationCommented Aug 20, 2021 at 17:50
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$\begingroup$ @mithusengupta123 Heuristically, because it takes a strong QCD binding force to hold together a hadron that has quarks with aligned spins than it does to hold together quarks with complementary and opposite spins. $\endgroup$– ohwillekeCommented Aug 20, 2021 at 18:07
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1 Answer
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The same phenomenon is observable in the hydrogen atom. The total spin (proton plus electron) quantum number $F\in(0,1)$ increases with total mass; however, the spin-spin coupling is on the order of micro eV (the famous 21 cm line), so it's just called "hyperfine structure", not "mass", since the total mass is around 939 MeV, or 1 trillion times larger.
Meanwhile, in the hadronic sector, aligning the quark spins in the nucleon ($M_{\frac 1 2} \approx 939\,$MeV) leads to the $\Delta$-baryon ($M_{\frac 3 2} \approx 1232\,$MeV), so the QCD hyperfine splitting is on the order of $\frac 1 3$ the mass (and the name "hyperfine" is not justified).
