Decay coupling constants sum for
dibaryon octet into two baryon
octets with λ8 first order SU(3)
symmetry breaking
TA L L ER D E A LTA S E N ERG Í A S 2 0 1 6
E L Í A S N ATA N A E L P O L A N C O E UÁ N
C I N V E S TAV M É R I D A | A P P L I E D P H Y S I C S D E PA R T M E N T
1. Introduction
•Quarks (confined by color force): 𝑞 and 𝑞ത
•Nature (color singlets): Baryons 𝑞1 𝑞2 𝑞3 ≡ 𝐵
Mesons 𝑞1 𝑞2 ≡ 𝑀
Multiquark states
M
M’
•Multiquark states: Tetraquarks 𝑞1 𝑞2 𝑞3 𝑞4
B
M
Pentaquarks 𝑞1 𝑞2 𝑞3 𝑞4 𝑞5
Hexaquarks
Etc.
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Baryon number = 0
•Hexaquarks:
B
B’
𝑞1 𝑞2 𝑞3 𝑞ത4 𝑞ത5 𝑞ത6 ≡ 𝐵6
M M’ M’’
𝑞1 𝑞ത2 𝑞3 𝑞ത4 𝑞5 𝑞ത6 ≡ 𝑀6
B
Baryon number = 2
B
𝑞1 𝑞2 𝑞3 𝑞4 𝑞5 𝑞6 ≡ 𝐵6
(a stable dibaryon already exists in nature: deuteron (𝑝𝑛)).
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•Dibaryons 𝑆𝑈(3) [1-5]
1 ۩ 8𝑆 ۩ 8𝐴 ۩10۩10 ۩27
dibaryon multiplets
=
8⨂8
baryon octet + baryon octec
•(deuteron belongs to the dibaryon 10 multiplet 𝐷10 [1]).
[1] R. J. Oakes, Phys. Rev. 131, 2239 (1963).
[2] R. L. Jaffe, Phys. Rev. Lett. 38, 195 (1977).
[3] S-Q Xie and Q-R. Zhang, Phys. Lett. 143B, 441 (1984).
[4] M. Oka, Phys. Rev. D 38, 298 (1988).
[5] S. D. Paganis, et al., Phys. Rev. C 62, 024906 (2000).
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2. Notation
Sum rules for strong decay coupling constants of dibaryon octets into two
ordinary baryon octets 8𝑆,A → 8۩8 with first order SU(3) symmetry breaking
are determined (recently, sum rules for strong decays of dibaryon decuplets into
two baryon octets 10, 10 → 8۩8 were determined in Ref. [6])
[6] V. Gupta and G. Sánchez-Colón, Mod. Phys. Lett. A 30, 1550010 (2015).
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Notation [7]
Ordinary octet baryon:
Dibaryon octet:
the (𝑌,𝐼, 𝐼3) states of 𝐷8 are denoted by 𝐷8(𝑌,𝐼,𝐼3) with 𝑌 hypercharge, 𝐼 Isospin, and 𝐼3 isospin third component.
[7] P. A. Carruthers, Introduction to Unitary Symmetry (Interscience, USA 1966).
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3. Strong decay coupling constants
3.1. SU(3) SYMMETRY LIMIT
Interaction Hamiltonian for Yukawa couplings [8]:
ഥ8 𝐵8 𝐵8′ + 𝐵8′ 𝐵8
𝐻0𝑖𝑛𝑡 ≡ 𝑔80 Tr 𝐷
ഥ8 𝐵8 𝐵8′ − 𝐵8′ 𝐵8
+ 𝑔80′ Tr 𝐷
⇒ 2 parameters: 𝑔80 and 𝑔80′ for symmetric and antisymmetric final state, respectively.
[8] M. Muraskin and S. L. Glashow, Phys. Rev. 132, 482 (1963).
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3.2. FIRST ORDER SU(3) SYMMETRY BREAKING
SU(3) symmetry breaking interaction transforms like the hypercharge 𝑌 [7]:
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•Symmetric final state [8]:
ഥ8 𝜆8 𝐵8 𝐵8′ + 𝐵8′ 𝐵8 + 𝑔2′ Tr 𝐷
ഥ8 𝜆8 𝐵8 𝐵8′ + 𝐵8′ 𝐵8 λ8 +
𝐻𝑆𝑖𝑛𝑡 ≡ 𝑔1′ Tr 𝐷
ഥ8 𝐵8 Tr 𝐵8′ 𝜆8 + Tr 𝐷
ഥ8 𝐵8′ Tr 𝐵8 𝜆8 + 𝑔4′ Tr 𝐷
ഥ8 𝜆8 Tr 𝐵8 𝐵8′
𝑔3′ Tr 𝐷
⟹ 5 parameters in total: 𝑔80 and 𝑔𝑘′ , 𝑘=1,2,3,4.
•Antisymmetric final state [8]:
ഥ8 𝜆8 𝐵8 𝐵8′ − 𝐵8′ 𝐵8 + 𝑔2 Tr 𝐷
ഥ8 𝜆8 𝐵8 𝐵8′ − 𝐵8′ 𝐵8 λ8 +
𝐻𝑆𝑖𝑛𝑡 ≡ 𝑔1 Tr 𝐷
ഥ8 𝐵8 𝐵8′ − 𝐵8′ 𝐵8 𝜆8 + 𝑔4 Tr 𝐷
ഥ8 𝐵8 Tr 𝐵8′ 𝜆8 − Tr 𝐷
ഥ8 𝐵8 Tr 𝐵8′ 𝜆8
𝑔3 Tr 𝐷
⟹ 5 parameters in total: 𝑔80 and 𝑔𝑘 , 𝑘=1,2,3,4.
[8] M. Muraskin and S. L. Glashow, Phys. Rev. 132, 482 (1963).
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4. Sum rules
4.1. SYMMETRIC FINAL STATE
9 independent strong decay coupling constants described in terms of 5 parameters (𝑔80′ and
𝑔𝑘 ′ ) ⟹ 4 sum rules:
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With identical relationships for 𝐺[𝐷8(𝑌,𝐼,𝐼3⟶𝐵′𝐵)]=+ 𝐺[𝐷8(𝑌,𝐼,𝐼3⟶𝐵′𝐵)] .
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4.2. ANTISYMMETRIC FINAL STATE
8 independent strong decay coupling constants described in terms of 5 parameters (𝑔80 and 𝑔𝑘 )
⟹ 3 sum rules:
With identical relationships for 𝐺[𝐷8(𝑌,𝐼,𝐼3⟶𝐵′𝐵)]=− 𝐺[𝐷8(𝑌,𝐼,𝐼3⟶𝐵′𝐵)] .
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5. Concluding remarks
Hexaquarks states with baryon number 2, dibaryons, were considered.
 Earlier, sum rules for strong decays of dibaryon decuplets into two ordinary baryon octets have
been calculated [6].
 In this work sum rules for strong decay coupling constants of dibaryon octet into two ordinary
baryon octets with first order SU(3) symmetry breaking were determined.
 Next steps: experimental data input, sum rules for strong decays of the dibaryon 27-plet into
two baryons, extension to SU(4) symmetry, … .
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