Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography
Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity — supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have int...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
5 July 2016
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| In: |
International journal of modern physics. A, Particles and fields, gravitation, cosmology
Year: 2016, Volume: 31, Issue: 19 |
| ISSN: | 1793-656X |
| DOI: | 10.1142/S0217751X16300295 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0217751X16300295 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S0217751X16300295 
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| Author Notes: | Stanley J. Brodsky, Guy F. de Téramond, Hans Günter Dosch, Cédric Lorcé |
| Summary: | Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity — supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons: LM=LB+1.LM=LB+1.<math display="inline" overflow="scroll" altimg="eq-00001.gif"><msub><mrow><mi>L</mi></mrow><mrow><mi>M</mi></mrow></msub><mo class="MathClass-rel">=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>B</mi></mrow></msub><mo stretchy="false" class="MathClass-bin">+</mo><mn>1</mn><mo class="MathClass-punc">.</mo></math> The dynamics of the superpartner hadrons also match; for example, the power-law fall-off of the form factors are the same for the mesonic and baryonic superpartners, in agreement with twist counting rules. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. This procedure also generates a spin-spin interaction between the hadronic constituents. A specific breaking of conformal symmetry inside the graded algebra determines a unique quark-confining light-front potential for light hadrons in agreement with the soft-wall AdS/QCD approach and light-front holography. Only one mass parameter λ−−√λ<math display="inline" overflow="scroll" altimg="eq-00002.gif"><msqrt><mrow><mi>λ</mi></mrow></msqrt></math> appears; it sets the confinement mass scale, a universal value for the slope of all Regge trajectories, the nonzero mass of the proton and other hadrons in the chiral limit, as well as the length scale which underlies their structure. The mass for the pion eigenstate vanishes in the chiral limit. When one includes the constituent quark masses using the Feynman-Hellman theorem, the predictions are consistent with the empirical features of the light-quark hadronic spectra. Our analysis can be consistently applied to the excitation spectra of the ππ<math display="inline" overflow="scroll" altimg="eq-00003.gif"><mi>π</mi></math>, ρρ<math display="inline" overflow="scroll" altimg="eq-00004.gif"><mi>ρ</mi></math>, KK<math display="inline" overflow="scroll" altimg="eq-00005.gif"><mi>K</mi></math>, K∗K∗<math display="inline" overflow="scroll" altimg="eq-00006.gif"><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false" class="MathClass-bin">∗</mo></mrow></msup></math> and ϕϕ<math display="inline" overflow="scroll" altimg="eq-00007.gif"><mi>ϕ</mi></math> meson families as well as to the NN<math display="inline" overflow="scroll" altimg="eq-00008.gif"><mi>N</mi></math>, ΔΔ<math display="inline" overflow="scroll" altimg="eq-00009.gif"><mi mathvariant="normal">Δ</mi></math>, ΛΛ<math display="inline" overflow="scroll" altimg="eq-00010.gif"><mi mathvariant="normal">Λ</mi></math>, ΣΣ<math display="inline" overflow="scroll" altimg="eq-00011.gif"><mi mathvariant="normal">Σ</mi></math>, Σ∗Σ∗<math display="inline" overflow="scroll" altimg="eq-00012.gif"><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false" class="MathClass-bin">∗</mo></mrow></msup></math>, ΞΞ<math display="inline" overflow="scroll" altimg="eq-00013.gif"><mi mathvariant="normal">Ξ</mi></math> and Ξ∗Ξ∗<math display="inline" overflow="scroll" altimg="eq-00014.gif"><msup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo stretchy="false" class="MathClass-bin">∗</mo></mrow></msup></math> baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass-squared of the light hadrons can be expressed in a universal and frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin-spin contributions. We also predict features of hadron dynamics, including hadronic light-front wave functions, distribution amplitudes, form factors, valence structure functions and vector meson electroproduction phenomenology. The mass scale λ−−√λ<math display="inline" overflow="scroll" altimg="eq-00015.gif"><msqrt><mrow><mi>λ</mi></mrow></msqrt></math> can be connected to the parameter ΛMS¯¯¯¯¯¯¯¯ΛMS¯<math display="inline" overflow="scroll" altimg="eq-00016.gif"><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mover accent="false" class="mml-overline"><mrow><mstyle><mtext class="textrm" mathvariant="normal">MS</mtext></mstyle></mrow><mo accent="true">¯</mo></mover></mrow></msub></math> in the QCD running coupling by matching the nonperturbative dynamics, as described by the light-front holographic approach to the perturbative QCD regime. The result is an effective coupling defined at all momenta. The matching of the high and low momentum-transfer regimes determines a scale Q0Q0<math display="inline" overflow="scroll" altimg="eq-00017.gif"><msub><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow></msub></math> proportional to λ−−√λ<math display="inline" overflow="scroll" altimg="eq-00018.gif"><msqrt><mrow><mi>λ</mi></mrow></msqrt></math> which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q0Q0<math display="inline" overflow="scroll" altimg="eq-00019.gif"><msub><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow></msub></math> to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the scheme-independent Principle of Maximal Conformality (PMC) procedure for setting renormalization scales, can greatly improve the precision of perturbative QCD predictions. |
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| Item Description: | Gesehen am 19.05.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1793-656X |
| DOI: | 10.1142/S0217751X16300295 |