2016
Decay coupling constants sum rules for
dibaryon octet into two baryon octets with
first order SU(3) symmetry breaking
HUGS 2016
ELÍAS NATANAEL POLANCO EUÁN
CINVESTAV MÉRIDA | Applied Physics Department
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1. Introduction
● Quarks (confined by color force):
● Nature (color singlets):
𝑞 and 𝑞̅
Baryons (𝑞1 𝑞2 𝑞3 ) ≡ 𝐵
Mesons (𝑞1 𝑞̅2 ) ≡ 𝑀
Multiquark states
𝑀′
𝑀
● Multiquark states:
Tetraquarks (𝑞⏞
̅2 𝑞⏞
̅4 )
1𝑞
3𝑞
𝐵
𝑀
⏞1 𝑞2 𝑞3 𝑞⏞
Pentaquarks (𝑞
̅5 )
4𝑞
Hexaquarks
Etc.
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̅
𝐵
𝐵
′
⏞ 𝑞 𝑞 ⏞
̅ ̅ ̅
(𝑞
1 2 3 𝑞4 𝑞5 𝑞6 ) ≡ 𝐵6
Baryon number = 0
𝑀
𝑀′
𝑀′′
⏞𝑞
̅ ⏞ ̅ ⏞ ̅
(𝑞
1 2 𝑞3 𝑞4 𝑞5 𝑞6 ) ≡ 𝑀 6
● Hexaquarks:
{
𝐵
Baryon number = 2
{
𝐵′
⏞ 𝑞 𝑞 ⏞
{(𝑞
1 2 3 𝑞4 𝑞5 𝑞6 ) ≡ 𝐷
𝐃𝐢𝐛𝐚𝐫𝐲𝐨𝐧
(a stable dibaryon already exists in nature: deuteron (𝑝𝑛)).
● Dibaryons 𝑆𝑈(3) [1-5]:
̅̅̅̅⨁27 =
1⨁8
⏟ 𝑆 ⨁8𝐴 ⨁10⨁10
8⏟⊗ 8
baryon octet + baryon octet
dibaryon multiplets
̅̅̅ multiplet 𝐷̅̅̅̅
(deuteron belongs to the dibaryon ̅10
10 [1]).
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2. Abstract and 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,
̅̅̅̅, 10 ⟶ 8 ⊕ 8 )
sum rules for strong decays of dibaryon decuplets into two baryon octets (10
were determined in Ref. [6]):
● 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.
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3. Strong decay coupling constants
3.1.
SU(3) SYMMETRY LIMIT
Interaction Hamiltonian for Yukawa couplings [8]:
̅̅̅8 (𝐵8 𝐵8′ + 𝐵8′ 𝐵8 )] + 𝑔0′ Tr[𝐷
̅̅̅8 (𝐵8 𝐵8′ − 𝐵8′ 𝐵8 )]
𝐻0int ≡ 𝑔80 Tr[𝐷
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⇒ 2 parameters: 𝑔80 and 𝑔80′ for symmetric and antisymmetric final state, respectively.
3.2.
FIRST ORDER SU(3) SYMMETRY BREAKING
SU(3) symmetry breaking interaction transforms like the hypercharge 𝑌 [7]:
1 1 0 0
𝜆8 =
(0 1 0 )
√3 0 0 −2
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● Symmetric final state [8]:
̅̅̅8 𝜆8 (𝐵8 𝐵8′ + 𝐵8′ 𝐵8 )] + 𝑔2′ Tr[𝐷
̅̅̅8 (𝐵8 𝐵8′ + 𝐵8′ 𝐵8 )𝜆8 ]
𝐻Sint ≡ 𝑔1′ Tr[𝐷
̅̅̅8 𝐵8′ ]Tr[𝐵8 𝜆8 ]) + 𝑔4′ Tr[̅̅̅
+ 𝑔3′ (Tr[̅̅̅
𝐷8 𝐵8 ]Tr[𝐵8′ 𝜆8 ] + Tr[𝐷
𝐷8 𝜆8 ]Tr[𝐵8 𝐵8′ ]
⟹ 5 parameters in total: 𝑔80 and 𝑔𝑘′ , 𝑘 = 1,2,3,4 .
● Antisymmetric final state [8]:
̅̅̅8 𝜆8 (𝐵8 𝐵8′ − 𝐵8′ 𝐵8 )] + 𝑔2 Tr[𝐷
̅̅̅8 (𝐵8 𝜆8 𝐵8′ − 𝐵8′ 𝜆8 𝐵)]
𝐻Aint ≡ 𝑔1 Tr[𝐷
̅̅̅8 (𝐵8 𝐵8′ − 𝐵8′ 𝐵8 )𝜆8 ] + 𝑔4 (Tr[̅̅̅
̅̅̅8 𝐵8′ ]Tr[𝐵8 𝜆8 ])
+𝑔3 Tr[𝐷
𝐷8 𝐵8 ]Tr[𝐵8′ 𝜆8 ] − Tr[𝐷
⟹ 5 parameters in total: 𝑔80 and 𝑔𝑘 , 𝑘 = 1,2,3,4 .
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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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6. References
[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).
[6] V. Gupta and G. Sánchez-Colón, Mod. Phys. Lett. A 30, 1550010 (2015).
[7] P. A. Carruthers, Introduction to Unitary Symmetry (Interscience, USA 1966).
[8] M. Muraskin and S. L. Glashow, Phys. Rev. 132, 482 (1963).
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