Electromagnetic and transition form factors of the Baryon Decuplet Hyun-Chul Kim Department of Physics, Inha University Incheon, Korea
Modern Understanding of Hadron structures
Traditional way of a hadron structure Traditional way of studying structures of hadrons H 0 ( p 0 ) Possible probes: photons, W , Z bosons, mesons, nucleons...... γ , W ± , Z 0 , · · · Understanding the internal structures of hadrons H in terms of form factors H ( p )
Modern understanding of a baryon structure 5D 3D 1D Today’s topic to discuss State of the art of the nucleon tomography Figure taken from Eur. Phys. J. A (2016) 52: 268
� � Modern understanding of a baryon structure 3D Nucleon Tomography b y b y b y 1 1 ∼ ∼ Q 2 Q 2 b ⊥ b ⊥ xp xp b x b x b x x x x Momentum fraction R d x ∆ → 0 ρ ( b ⊥ ) q ( x, b ⊥ ) q ( x ) 0 0 b ⊥ b ⊥ x x Transverse densities Structure functions GPDs of Form factors Parton distributions Nucleon Tomography
<latexit sha1_base64="BldTm6GFDZ24b+srZpMog+Ydt/E=">AB+HicdVBNSwMxEJ31s9avqkcvwSJ4KrtasN5KvXhswX5Au5Rsm1Dk+ySZIW69Bd41bs38eq/8eovMW1XqEUfDzem2FmXhBzpo3rfjpr6xubW9u5nfzu3v7BYeHouKWjRBHaJBGPVCfAmnImadMw2knVhSLgN2ML6d+e0HqjSL5L2ZxNQXeChZyAg2VmrU+oWiW3LnQEvkplwpe1fIy5QiZKj3C1+9QUQSQaUhHGvd9dzY+ClWhFOp/leomMyRgPadSiQXVfjo/dIrOrTJAYaRsSYPm6vJEioXWExHYToHNSK96M/FPLxArm01Y8VMm48RQSRaLw4QjE6FZCmjAFCWGTyzBRDF7OyIjrDAxNqu8DeXnc/Q/aV2WPLfkNcrFai2LJwencAYX4ME1VOEO6tAEAhSe4BlenEfn1Xlz3heta042cwK/4Hx8A/QCk4k=</latexit> <latexit sha1_base64="BldTm6GFDZ24b+srZpMog+Ydt/E=">AB+HicdVBNSwMxEJ31s9avqkcvwSJ4KrtasN5KvXhswX5Au5Rsm1Dk+ySZIW69Bd41bs38eq/8eovMW1XqEUfDzem2FmXhBzpo3rfjpr6xubW9u5nfzu3v7BYeHouKWjRBHaJBGPVCfAmnImadMw2knVhSLgN2ML6d+e0HqjSL5L2ZxNQXeChZyAg2VmrU+oWiW3LnQEvkplwpe1fIy5QiZKj3C1+9QUQSQaUhHGvd9dzY+ClWhFOp/leomMyRgPadSiQXVfjo/dIrOrTJAYaRsSYPm6vJEioXWExHYToHNSK96M/FPLxArm01Y8VMm48RQSRaLw4QjE6FZCmjAFCWGTyzBRDF7OyIjrDAxNqu8DeXnc/Q/aV2WPLfkNcrFai2LJwencAYX4ME1VOEO6tAEAhSe4BlenEfn1Xlz3heta042cwK/4Hx8A/QCk4k=</latexit> <latexit sha1_base64="BldTm6GFDZ24b+srZpMog+Ydt/E=">AB+HicdVBNSwMxEJ31s9avqkcvwSJ4KrtasN5KvXhswX5Au5Rsm1Dk+ySZIW69Bd41bs38eq/8eovMW1XqEUfDzem2FmXhBzpo3rfjpr6xubW9u5nfzu3v7BYeHouKWjRBHaJBGPVCfAmnImadMw2knVhSLgN2ML6d+e0HqjSL5L2ZxNQXeChZyAg2VmrU+oWiW3LnQEvkplwpe1fIy5QiZKj3C1+9QUQSQaUhHGvd9dzY+ClWhFOp/leomMyRgPadSiQXVfjo/dIrOrTJAYaRsSYPm6vJEioXWExHYToHNSK96M/FPLxArm01Y8VMm48RQSRaLw4QjE6FZCmjAFCWGTyzBRDF7OyIjrDAxNqu8DeXnc/Q/aV2WPLfkNcrFai2LJwencAYX4ME1VOEO6tAEAhSe4BlenEfn1Xlz3heta042cwK/4Hx8A/QCk4k=</latexit> <latexit sha1_base64="BldTm6GFDZ24b+srZpMog+Ydt/E=">AB+HicdVBNSwMxEJ31s9avqkcvwSJ4KrtasN5KvXhswX5Au5Rsm1Dk+ySZIW69Bd41bs38eq/8eovMW1XqEUfDzem2FmXhBzpo3rfjpr6xubW9u5nfzu3v7BYeHouKWjRBHaJBGPVCfAmnImadMw2knVhSLgN2ML6d+e0HqjSL5L2ZxNQXeChZyAg2VmrU+oWiW3LnQEvkplwpe1fIy5QiZKj3C1+9QUQSQaUhHGvd9dzY+ClWhFOp/leomMyRgPadSiQXVfjo/dIrOrTJAYaRsSYPm6vJEioXWExHYToHNSK96M/FPLxArm01Y8VMm48RQSRaLw4QjE6FZCmjAFCWGTyzBRDF7OyIjrDAxNqu8DeXnc/Q/aV2WPLfkNcrFai2LJwencAYX4ME1VOEO6tAEAhSe4BlenEfn1Xlz3heta042cwK/4Hx8A/QCk4k=</latexit> <latexit sha1_base64="M54t5qyn6Bw3lH9jhczDE6roU6Y=">AB+XicdVBNSwMxEJ31s9avqkcvwSJ6KrtasN5KvXisYj+gXUo2zbahSXZJskJZ+g+86t2bePXePWXmLYr1KIPBh7vzTAzL4g508Z1P52V1bX1jc3cVn57Z3dv3Bw2NRoghtkIhHqh1gTmTtGY4bQdK4pFwGkrGN1M/dYjVZpF8sGMY+oLPJAsZAQbK93XznqFoltyZ0AL5LpcKXuXyMuUImSo9wpf3X5EkGlIRxr3fHc2PgpVoYRTif5bqJpjMkID2jHUokF1X46u3SCTq3SR2GkbEmDZuriRIqF1mMR2E6BzVAve1PxTy8QS5tNWPFTJuPEUEnmi8OEIxOhaQyozxQlho8twUQxezsiQ6wMTasvA3l53P0P2lelDy35N2Vi9VaFk8OjuEzsGDK6jCLdShAQRCeIJneHFS59V5c97nrStONnMEv+B8fANW05O6</latexit> <latexit sha1_base64="M54t5qyn6Bw3lH9jhczDE6roU6Y=">AB+XicdVBNSwMxEJ31s9avqkcvwSJ6KrtasN5KvXisYj+gXUo2zbahSXZJskJZ+g+86t2bePXePWXmLYr1KIPBh7vzTAzL4g508Z1P52V1bX1jc3cVn57Z3dv3Bw2NRoghtkIhHqh1gTmTtGY4bQdK4pFwGkrGN1M/dYjVZpF8sGMY+oLPJAsZAQbK93XznqFoltyZ0AL5LpcKXuXyMuUImSo9wpf3X5EkGlIRxr3fHc2PgpVoYRTif5bqJpjMkID2jHUokF1X46u3SCTq3SR2GkbEmDZuriRIqF1mMR2E6BzVAve1PxTy8QS5tNWPFTJuPEUEnmi8OEIxOhaQyozxQlho8twUQxezsiQ6wMTasvA3l53P0P2lelDy35N2Vi9VaFk8OjuEzsGDK6jCLdShAQRCeIJneHFS59V5c97nrStONnMEv+B8fANW05O6</latexit> <latexit sha1_base64="M54t5qyn6Bw3lH9jhczDE6roU6Y=">AB+XicdVBNSwMxEJ31s9avqkcvwSJ6KrtasN5KvXisYj+gXUo2zbahSXZJskJZ+g+86t2bePXePWXmLYr1KIPBh7vzTAzL4g508Z1P52V1bX1jc3cVn57Z3dv3Bw2NRoghtkIhHqh1gTmTtGY4bQdK4pFwGkrGN1M/dYjVZpF8sGMY+oLPJAsZAQbK93XznqFoltyZ0AL5LpcKXuXyMuUImSo9wpf3X5EkGlIRxr3fHc2PgpVoYRTif5bqJpjMkID2jHUokF1X46u3SCTq3SR2GkbEmDZuriRIqF1mMR2E6BzVAve1PxTy8QS5tNWPFTJuPEUEnmi8OEIxOhaQyozxQlho8twUQxezsiQ6wMTasvA3l53P0P2lelDy35N2Vi9VaFk8OjuEzsGDK6jCLdShAQRCeIJneHFS59V5c97nrStONnMEv+B8fANW05O6</latexit> <latexit sha1_base64="M54t5qyn6Bw3lH9jhczDE6roU6Y=">AB+XicdVBNSwMxEJ31s9avqkcvwSJ6KrtasN5KvXisYj+gXUo2zbahSXZJskJZ+g+86t2bePXePWXmLYr1KIPBh7vzTAzL4g508Z1P52V1bX1jc3cVn57Z3dv3Bw2NRoghtkIhHqh1gTmTtGY4bQdK4pFwGkrGN1M/dYjVZpF8sGMY+oLPJAsZAQbK93XznqFoltyZ0AL5LpcKXuXyMuUImSo9wpf3X5EkGlIRxr3fHc2PgpVoYRTif5bqJpjMkID2jHUokF1X46u3SCTq3SR2GkbEmDZuriRIqF1mMR2E6BzVAve1PxTy8QS5tNWPFTJuPEUEnmi8OEIxOhaQyozxQlho8twUQxezsiQ6wMTasvA3l53P0P2lelDy35N2Vi9VaFk8OjuEzsGDK6jCLdShAQRCeIJneHFS59V5c97nrStONnMEv+B8fANW05O6</latexit> Modern understanding of a baryon structure Probes are unknown for Tensor form factors and the Energy-Momentum Tensor form factors! B 0 Form factors as Mellin moments of the GPDs B
Baryon as Nc quarks bound by the pion mean fields
Mean-Field Approximation Simple picture of a mean-field approximation Mean-field potential that is produced by all other particles. Nuclear shell models Ginzburg-Landau theory for superconductivity Quark potential models for baryons
Mean-Field Approximation More theoretically defined mean fields S [ φ ] Given action, � δ S φ 0 � = 0 : Solution of this saddle-point equation � δφ � φ = φ 0 Key point: Ignore the quantum fluctuation. How to understand the structure of Baryons, based on this pion mean field approach.
<latexit sha1_base64="wHq128HwlK0rSarg7i8ulBfjtk8=">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</latexit> <latexit sha1_base64="wHq128HwlK0rSarg7i8ulBfjtk8=">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</latexit> <latexit sha1_base64="wHq128HwlK0rSarg7i8ulBfjtk8=">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</latexit> <latexit sha1_base64="wHq128HwlK0rSarg7i8ulBfjtk8=">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</latexit> Baryon in pion mean fields A baryon can be viewed as a state of Nc quarks bound by mesonic mean fields (E. Witten, NPB, 1979 & 1983). Its mass is proportional to Nc , while its width is of order O(1) . Mesons are weakly interacting (Quantum fluctuations are suppressed by 1/Nc: O(1/Nc) . Meson mean-field approach (Chiral Quark-Soliton Model) Baryons as a state of Nc quarks bound by mesonic mean fields. ∂ + iMU γ 5 + i ˆ S e ff = − N c Tr ln ( i / m ) Key point: Hedgehog Ansatz ⇢ n a F ( r ) , n a = x a /r, a = 1 , 2 , 3 π a ( r ) = 0 , a = 4 , 5 , 6 , 7 , 8 . It breaks spontaneously SU(3) flavor ⊗ O(3) space → SU(2) isospin+space
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