ELPH The Origin of Flavor SU3 Symmetry Breaking

ELPH研究会 The Origin of Flavor SU(3) Symmetry Breaking in Bag Model Yudai Morita Daisuke Jido Tokyo Institute of Technology

Motivation • 2 [1] T. De. Grant, R. F. Jaffe, K. Johnson, J, Kiskis(1975)

1. MIT Bag Model 2. Flavor SU(3) Symmetry Breaking 3. Cloudy Bag Model 4. Summary and future work 3

MIT Bag Model Pressure Inside Bag Perturbative Vacuum B R Outside Bag Nonperturbative Vacuum One Gluon exchange 4

Mass of Baryon –MIT Bag Model • Energy of free quarks Energy of pressure One gluon exchange spin-spin force Zero point Energy 5

Calculation –MIT Bag Model • 0(Me. V) 94(Me. V) 938(Me. V) 1236(Me. V) 738(Me. V) 145(Me. V) 0. 55 1. 84 Calculate other baryon masses with these parameters 6

Result – MIT Bag Model is not enough to reproduce Baryon mass. 7

1. MIT Bag Model 2. Flavor SU(3) Symmetry Breaking 1. Cloudy Bag Model 2. Summary and future work 8

Flavor SU(3) symmetry breaking u and d quark mass Current quark mass Constituent quark mass 0 Me. V 300 Me. V s quark mass difference 500 Me. V 100 Me. V 200 Me. V • In the current quark mass, the mass difference between u and d quarks and s quark is 100 Me. V. • In the constituent quark mass, the mass difference is about 200 Me. V. • the flavor SU(3) symmetry breaking can be divided into 2 parts: breaking in the current quark mass and breaking in the mass obtained by spontaneous breaking of chiral symmetry. 9

Flavor SU(3) symmetry breaking in Bag Model • [2] F. Myhrer, Z. Xu (1982) 10

1. MIT Bag Model 2. Flavor SU(3) symmetry Breaking 3. Cloudy Bag Model 4. Summary and future work 11

Cloudy Bag Model Inside Bag Perturbative Vacuum Ch-sym Restored Outside Bag Nonperturbative Vacuum NG Boson Cloud R Bag Surface Ch-sym is Broken Quarks and Mesons interact 12

Cloudy Bag Model • 13

Loop Correction 14

Calculation –Cloudy Bag Model 0 Me. V 94 Me. V 135 Me. V 497 Me. V 547 Me. V 938 Me. V 1236 Me. V 0. 093 • 145 Me. V 15

Result – Cloudy Bag Model • CBM improves MIT Bag Model • CBM is insufficient 16

Result • In MIT Bag Model, only about 1/3 of the actual mass difference appeared • In Cloudy Bag Model, about 2/3 • Breaking in the current quark mass and breaking in the mass obtained by spontaneous breaking of chiral symmetry is about same 17

1. MIT Bag Model 2. Flavor SU(3) Symmetry Breaking 3. Cloudy Bag Model 4. Summary and Future work 18

Summary • In Bag Model， Breaking in the current quark mass and breaking in the mass obtained by spontaneous breaking of chiral symmetry is about same • It is necessary to incorporate the latter contribution • This method is insufficient to fully reproduce the effect of flavor SU (3) symmetry breaking 19

Future Work • It is necessary to consider the influence on quarks by the interaction with Meson • At first, consider the effect on Bag radius 20

Bag Radius -Cloudy Bag Model • 5. 42 5. 41 5. 70 5. 69 5. 68 21

Required Bag Radius 22

Back up 23

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ゴミ捨て場 7. 72 6. 68 (Me. V) 94(Me. V) 8(Me. V) 1236(Me. V) 5(Me. V) 4. 18 0. 55 7. 77 4. 37 738(Me. V) 7. 85 1. 84 [2] F. Myhrer, Z. Xu (1982) 7. 50 8. 13 7. 72 4. 18 6. 675 4. 374 7. 771 7. 502 7. 85 8. 13 28 [1] T. De. Grant, R. F. Jaffe, K. Johnson, J, Kiskis(1975)c