Quarkonium

In particle physics , quarkonium (plural: quarkonia) denotes the bound states of a quark and its anti- quark. In other words, these are mesons without an electrical charge or flavor .

Bound states of heavy quarks ( ) have their own names: bound states (i.e. charm quark and antiquark) are called Charmonium , and bound states are called Bottomonium . A proof of the hypothetical system toponium is extremely difficult if not impossible, since its formation time is probably longer than the lifetime of the top quark , which is extremely short-lived due to its high mass. ${\ displaystyle c, b, t \! \,}$ ${\ displaystyle c {\ bar {c}}}$ ${\ displaystyle b {\ bar {b}}}$ ${\ displaystyle t {\ bar {t}}}$ ${\ displaystyle t \! \,}$

Bound quark-antiquark states of the light quarks ( ) mix quantum-mechanically due to the small mass difference - especially with each other . Therefore, the mesons formed from them cannot be assigned to a single type of quark. ${\ displaystyle u, d, s \! \,}$ ${\ displaystyle u {\ bar {u}}}$ ${\ displaystyle d {\ bar {d}}}$

nomenclature

Quantum Numbers and Spectroscopic States

The name quarkonium is analogous to positronium , in which an electron and a positron are bound to. As with positronium, Quarkonia is characterized by the following quantum numbers : ${\ displaystyle e ^ {+} e ^ {-} \! \,}$

Principal quantum number

{\ displaystyle \, n = 1, \, 2 \ ,, 3 \, \ ldots}

Coupling of quark spins (numerical value or ) or multiplicity (numerical value or ) ${\ displaystyle S \! \,}$ ${\ displaystyle 0 \! \,}$ ${\ displaystyle 1 \! \,}$ ${\ displaystyle 2S + 1 \! \,}$ ${\ displaystyle 1 \! \,}$ ${\ displaystyle 3 \! \,}$

Orbital angular momentum and

{\ displaystyle L \! \,}

Total angular momentum (possible values due to the spin-orbit coupling ) ${\ displaystyle J \! \,}$ ${\ displaystyle J = L + S, L + S-1, \ dots, | LS | \! \,}$ ${\ displaystyle {\ hat {J}} = {\ hat {L}} + {\ hat {S}}}$

orbital angular pulse ${\ displaystyle L \! \,}$	Code letter
0	S.
1	P
2	D.
3	F.
4th	G
5	H
6th	I.
7th	K
...	...

in the nomenclature ( term symbol ) or (spectroscopic designation), whereby the orbital angular momentum is indicated by a capital letter (see table). ${\ displaystyle n ^ {2S + 1} L_ {J} \! \,}$ ${\ displaystyle nL \! \,}$ ${\ displaystyle L \! \,}$

Note the following difference in the naming: While positronium the nomenclature of nuclear physics applies to the principal quantum number ( for the number of nodes of the radial wave function , small for the orbital momentum ), using the nomenclature of at Quarkonium nuclear physics with . A 2 ³ P ₁ positronium therefore corresponds to a 1 ³ P ₁ harmonium. ${\ displaystyle n = N + 1 + l \! \,}$ ${\ displaystyle N \! \,}$ ${\ displaystyle l \! \,}$ ${\ displaystyle n = N + 1 \! \,}$

In addition to the total angular momentum, only: ${\ displaystyle J \! \,}$

the parity and ${\ displaystyle P = (- 1) ^ {L + 1} \! \,}$
the charge conjugation . ${\ displaystyle C = (- 1) ^ {L + S} \! \,}$

Orbital angular momentum and quark spin coupling can be derived from this. ${\ displaystyle L \! \,}$ ${\ displaystyle S \! \,}$

Mesons

The following nomenclature applies to the mesons formed from these states

observed: ${\ displaystyle J ^ {PC} \! \,}$	Orbital angular momentum ${\ displaystyle L \! \,}$	coupled spin ${\ displaystyle S \! \,}$	Total angular momentum ${\ displaystyle J \! \,}$	Basic state ( ) ${\ displaystyle n ^ {2S + 1} L_ {J} \! \,}$	Mixture of and Isospin = 1 ${\ displaystyle u {\ bar {u}}}$ ${\ displaystyle d {\ bar {d}}}$	Mixture of , , isospin = 0 ${\ displaystyle u {\ bar {u}}}$ ${\ displaystyle d {\ bar {d}}}$ ${\ displaystyle s {\ bar {s}}}$	Charmonium ${\ displaystyle c {\ bar {c}}}$	Bottomonium ${\ displaystyle b {\ bar {b}}}$
${\ displaystyle J ^ {- +} \! \,}$	straight S, D, G, ... ${\ displaystyle \ Rightarrow}$	just 0 ${\ displaystyle \ Rightarrow}$	0, 2, 4, ...	1 ¹ S ₀	Pion ${\ displaystyle \ pi \! \,}$	η meson ${\ displaystyle \ eta, \ eta '\! \,}$	${\ displaystyle \ eta _ {c} \! \,}$	${\ displaystyle \ eta _ {b} \! \,}$
${\ displaystyle J ^ {-} \! \,}$	straight S, D, G, ... ${\ displaystyle \ Rightarrow}$	odd 1 ${\ displaystyle \ Rightarrow}$	1, 2, 3, ...	1 ³ S ₁	Rho meson ${\ displaystyle \ rho \! \,}$	Omega meson , phi meson ${\ displaystyle \ omega \! \,}$ ${\ displaystyle \ phi \! \,}$	${\ displaystyle \ psi \! \,}$	Y meson ${\ displaystyle \ Upsilon \! \,}$
${\ displaystyle J ^ {+ -} \! \,}$	odd P, F, H, ... ${\ displaystyle \ Rightarrow}$	just 0 ${\ displaystyle \ Rightarrow}$	1, 3, 5, ...	1 ¹ P ₁	${\ displaystyle b \! \,}$	${\ displaystyle h, h '\! \,}$	${\ displaystyle h_ {c} \! \,}$	${\ displaystyle h_ {b} \! \,}$
${\ displaystyle J ^ {++} \! \,}$	odd P, F, H, ... ${\ displaystyle \ Rightarrow}$	odd 1 ${\ displaystyle \ Rightarrow}$	0, 1, 2, ...	1 ³ P ₀	${\ displaystyle a \! \,}$	${\ displaystyle f, f '\! \,}$	${\ displaystyle \ chi _ {c} \! \,}$	${\ displaystyle \ chi _ {b} \! \,}$

↑ historical reasons the 1 ^- ground state as J / ψ meson called

For the mesons formed from heavy quarks ( ), the spectroscopic designation ( ) is given, if known - e.g. B. , as well as another index - z. B. . The latter is not necessary with d. H. at , because then . If a spectroscopic assignment is not possible due to a lack of data, the mass is given in MeV / c ² for a more detailed description , e.g. B. . ${\ displaystyle c, b \! \,}$ ${\ displaystyle nL \! \,}$ ${\ displaystyle \ psi (2S) \! \,}$ ${\ displaystyle J \! \,}$ ${\ displaystyle \ chi _ {c1} (1P) \! \,}$ ${\ displaystyle S = 0 \! \,}$ ${\ displaystyle 2S + 1 = 1 \! \,}$ ${\ displaystyle J = L \! \,}$ ${\ displaystyle \ psi (3770) \! \,}$

The spectroscopic designation is not used for the mesons formed from light quarks ( ); instead, the mass is given in MeV / c ² for a more detailed description . ${\ displaystyle u, d, s \! \,}$

This information can be omitted for the lowest states - so and .

{\ displaystyle \ eta _ {c} (1S) = \ eta _ {c} \! \,}

{\ displaystyle \ phi (1020) = \ phi \! \,}

Charmonia and Bottomonia

The quantum numbers of the X (3872) particle are the subject of current studies, its identity has not been fully clarified. It can be:

a candidate for the 1 ¹ D ₂ state;
a hybrid Charmonium state;
a molecule. ${\ displaystyle D ^ {0} {\ bar {D}} ^ {* 0}}$

In 2005 the BaBar experiment published the discovery of the new state Y (4260). The observations were confirmed by the CLEO and Belle experiments . At first the new particle was mistaken for a charmonium, but now the observations suggest more exotic explanations, such as a D “molecule”, a tetraquark, or a hybrid meson.

J ^PC	Term symbol n ^{2 S + 1}L _J	Charmonium ${\ displaystyle c {\ bar {c}}}$		Bottomonium ${\ displaystyle b {\ bar {b}}}$
J ^PC	Term symbol n ^{2 S + 1}L _J	Particles	Mass (MeV / c ² )	Particles	Mass (MeV / c ² )
0 ^{- +}	1 ¹ S ₀	η _c (1 S ) = η _c	2983.9 ± 0.5	η _b (1 S ) = η _b	9399.0 ± 2.3
0 ^{- +}	2 ¹ S ₀	η _c (2 S ) = η _c^'	3637.6 ± 1.2	η _b (2 S )
2 ^{- +}	1 ¹ D ₂	η _c (1 D ) ^†		η _b (1 D ) ^†
1 ⁻⁻	1 ³ S ₁	J / ψ (1 S ) = J / ψ	3096.900 ± 0.006	Υ (1 S ) = Υ	9460.30 ± 0.26
1 ⁻⁻	2 ³ S ₁	ψ (2 S ) = ψ (3686)	3686.097 ± 0.025	Υ (2 S )	10,023.26 ± 0.31
1 ⁻⁻	3 ³ S ₁			Υ (3 S )	10,355.2 ± 0.5
1 ⁻⁻	4 ³ S ₁			Υ (4 S ) = Υ (10580)	10,579.4 ± 1.2
1 ⁻⁻	5 ³ S ₁			Υ (5 S ) = Υ (10860)	10,889.9 ± 3.2
1 ⁻⁻	6 ³ S ₁			Υ (6 S ) = Υ (11020)	10,992.9 ± 10
1 ⁻⁻	1 ³ D ₁	ψ (3770)	3773.13 ± 0.35
2 ⁻⁻	1 ³ D ₂	ψ ₂ (1 D ) = ψ ₂ (3823)	3822.2 ± 1.2	Υ ₂ (1 D )	10,163.7 ± 1.4
3 ⁻⁻	1 ³ D ₃	ψ ₃ (1 D ) ^†		Υ ₃ (1 D ) ^†
1 ⁻⁻	? ^?? _?	ψ (4260) = Y (4260)	4230 ± 8
1 ^{+ -}	1 ¹ P ₁	h _c (1 P ) = h _c	3525.38 ± 0.11	h _b (1 P ) = h _b	9899.3 ± 0.8
1 ^{+ -}	2 ¹ P ₁	h _c (2 P ) ^†		h _b (2 P )
0 ⁺⁺	1 ³ P ₀	χ _{c 0} (1 P ) = χ _{c 0}	3414.71 ± 0.30	χ _{b 0} (1 P ) = χ _{b 0}	9859.44 ± 0.52
0 ⁺⁺	2 ³ P ₀	χ _{c 0} (2 P ) ^†		χ _{b 0} (2 P )	10,232.5 ± 0.6
1 ⁺⁺	1 ³ P ₁	χ _{c 1} (1 P )	3510.67 ± 0.05	χ _{b 1} (1 P )	9892.78 ± 0.40
1 ⁺⁺	2 ³ P ₁	χ _{c 1} (2 P ) ^†		χ _{b 1} (2 P )	10,255.46 ± 0.55
1 ⁺⁺	3 ³ P ₁			χ _{b 1} (3 P )	10,512.1 ± 2.3
2 ⁺⁺	1 ³ P ₂	χ _{c 2} (1 P )	3556.17 ± 0.07	χ _{b 2} (1 P )	9912.21 ± 0.40
2 ⁺⁺	2 ³ P ₂	χ _{c 2} (2 P )	3927.2 ± 2.6	χ _{b 2} (2 P )	10,268.65 ± 0.55
1 ⁺⁺	? ^?? ₁	χ _{c 1} (3872) = X (3872)	3871.69 ± 0.17

Remarks:

^* yet to be confirmed
^† predicted but not yet identified.

literature

Bogdan Povh et al: Particles and Cores. 6th edition. Springer, 2004, ISBN 3-540-21065-2 .

Individual evidence

↑ Particle Data Group: Naming scheme for hadrons (Revised in 2017). (PDF; 86 KB) Accessed February 17, 2018 (English).

^ LHCb collaboration: Determination of the X (3872) meson quantum numbers . In: Physical Review Letters . tape 110 , no. May 22 , 2013, doi : 10.1103 / PhysRevLett.110.222001 , arxiv : 1302.6269v1 .

↑ A new particle discovered by BaBar experiment. Istituto Nazionale di Fisica Nucleare , July 6, 2005, accessed March 6, 2010 .

↑ B. Aubert et al. (BaBar Collaboration): Observation of a broad structure in the π ⁺ π ^- J / ψ mass spectrum around 4.26 GeV / c ² . In: Physical Review Letters . tape 95 , no. 14 , 2005, pp. 142001 , doi : 10.1103 / PhysRevLett.95.142001 , arxiv : hep-ex / 0506081 .

↑ M. Tanabashi et al . (Particle Data Group), 2018: cc̅ Mesons

↑ M. Tanabashi et al . (Particle Data Group), 2018: bb̅ Mesons

[2] storical reasons the 1 ^- ground state as J / ψ meson called

[1] Particle Data Group: Naming scheme for hadrons (Revised in 2017). (PDF; 86 KB) Accessed February 17, 2018 (English).