Hyperon and charmed baryon productions with an instanton interaction

Transcription

1 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Hyperon and charmed baryon productions with an instanton interaction Sang-In Shim RCNP, Osaka University 16 March 2018 Collaborated with Prof. Atsushi Hosaka and Prof. Hyun-Chul Kim

2 List of contents Background and Motivation - Diuarks and heavy baryons - Researches on heavy baryon productions Methods for heavy baryon productions - One- and Two-body processes - Transition amplitudes Results Summary and Outlook Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March

3 Sang-In Shim ( RCNP, Osaka University ) Workshop on Structures of Heavy Quark and Exotic Hadrons J-PARC. Tokai, Ibaraki, 6 March /28 Diuarks and heavy baryons Baryon excitations can be expressed as ρ- and λ-modes

4 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Diuarks and heavy baryons Baryon excitations can be expressed as ρ- and λ-modes ρ- and λ-modes show distinct difference in heavy baryons

5 Researches on heavy baryon productions Early theoretical studies 1,2 - The cross sections and production rates of heavy baryons were predicted - Only λ-modes are considered Experimental plan 3 - Experiment for charmed baryon productions are planed at J-PARC In J-PARC plan 1 S.-H.Kim, A.Hosaka, H.-Ch.Kim, H.Noumi and K.Shirotori, PTEP(2014)no.10, 103D01. 2 S.-H.Kim, A.Hosaka, H.-Ch.Kim, H.Noumi, PRD92(2014)no.9, Charmed baryon spectroscopy via the () reaction (2012). J-PARC P50 proposal.,d () reaction (2012). J-PARC P50 proposal. Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March

6 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Researches on heavy baryon Charm productions spectrum Similarity with hypernucleus productions π + p π + p D * + B c* (J P ) D (Kim, Hosaka, Kim, Noumi, 2015) Ground state Ground state Excited states Excited states(only λ-modes) Excited states HQ doublet J = j l + s H = j l ±1/ 2 p J = j l + s H = j l ±1/ 2 s l = 0 l = 1 l = 2 1/ 2 + 1/ 2 3 / 2 l = 25 / 2 + l = 0 l = 1 HQ doublet 1/ / 2 5 / 2 1/2 + 1/2-3/2-5/ /2 + d 3 / : 2 3 / : 3 1 : 2 2 : 3 π Y π Y K ΛY(J P ) K + s p d

7 Motivation ρ- and λ-modes can be clarified in heavy baryons ( They are hard to distinguish in light baryons ) Diuark properties can be studied by identifying ρ- and λ-modes of heavy baryons Observables such as cross sections can be obtained from proper description of processes and heavy baryon structures can be studied Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March

8 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March One- and two-body processes One-body process Two-body process _ Q Q _ One-body Two-body Q λ-modes Q λ-modes ρ-modes One-body process - One uark in the baryon is involved in the reaction - The heavy baryon can be excited only to λ-modes Two-body process - Both ρ- and λ-modes can be found - Need to consider 3-uark interactions

9 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Quark interactions in the instanton model ( t Hooft interaction ) Quarks interact with each others via instantons Hyperon productions can be described by using t Hooft interactions

10 Sang-In Shim ( RCNP, Osaka University ) Workshop on Structures of Heavy Quark and Exotic Hadrons J-PARC. Tokai, Ibaraki, 6 March /28 Quark interactions in the instanton model ( t Hooft interaction ) Two-body process d u _ d _ s u d u Two-body s d u λ-modes ρ-modes Quarks interact with each others via instantons Hyperon productions can be described by using t Hooft interactions

11 Baryon wave functions ( m1 = m2 = m ) ~ = ~r 2 ~r 1 ~ = 1 2 ( ~r 1 +~r 2 ) ~r 3 ~p 1, ~p 2, ~p 3 ~P B, ~p, ~p H = X i ~p 2 i 2m i + X i<j X k 2 ~r i ~r j 2 X ~ ~ 3D Harmonic oscillators of and ~p = 1 2 (~p 2 ~p 1 ), ~p = m 3 2m + m 3 (~p 1 + ~p 2 ) 2m 2m + m 3 ~p 3 Sang-In Shim ( RCNP, Osaka University ) Workshop on Structures of Heavy Quark and Exotic Hadrons J-PARC. Tokai, Ibaraki, 6 March /28

12 Baryon wave functions ( m1 = m2 = m ) ~ = ~r 2 ~r 1 ~ = 1 2 ( ~r 1 +~r 2 ) ~r 3 ~p 1, ~p 2, ~p 3 ~P B, ~p, ~p H = X i ~p 2 i 2m i + X i<j X k 2 ~r i ~r j 2 X m = m 2 m = 2m m 3 2m + m 3 = ~ P 2 B 2M B + ~p2 2m + ~p2 2m m! 2 ~ m!2 ~ 2 3D Harmonic oscillators of ~p = 1 2 (~p 2 ~p 1 ), ~p = m 3 2m + m 3 (~p 1 + ~p 2 )! 2 = 3k 2m! 2 = 2k m ~ and ~ 2m 2m + m 3 ~p 3 Sang-In Shim ( RCNP, Osaka University ) Workshop on Structures of Heavy Quark and Exotic Hadrons J-PARC. Tokai, Ibaraki, 6 March /28

13 Baryon wave functions ( m1 = m2 = m ) ~ = ~r 2 ~r 1 ~ = 1 2 ( ~r 1 +~r 2 ) ~r 3 ~p 1, ~p 2, ~p 3 ~P B, ~p, ~p H = X i ~p 2 i 2m i + X i<j X k 2 ~r i ~r j 2 X m = m 2 m = 2m m 3 2m + m 3 = ~ P 2 B 2M B + ~p2 2m + ~p2 2m m! 2 ~ m!2 ~ 2 3D Harmonic oscillators of ~p = 1 2 (~p 2 ~p 1 ), ~p = m 3 2m + m 3 (~p 1 + ~p 2 )! 2 = 3k 2m! 2 = 2k m ~ and ~ 2m 2m + m 3 ~p 3 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March

14 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Transition amplitudes for two-body processes h L i Z ~P N ~ ~P Y Z _ 3 2 Two-body process ~p 3 ~p 2 Z 1 2 ~p 1 ~p 0 3 = ~p 3 + ~ 3 ~p 0 2 = ~p 2 + ~ 2 ~p 0 1 = ~p 1 h L i (3) Z L i Z Z ~p Y ~p p ~ d 3 2 d 3 (3) hy (Y c ), K(D) L th p, i Z Z 3 ~ ~ 2 ~ 3 Z (3) ~p Y ~p p ~ d 3 2 d 3 (3) CY(Yc)K(D) 3 ~ ~ 2 ~ 3 Z Z Z Z d 3 e i ~ ~ l (~ ) 0 (~ ) d 3 e i ~ ~ 0 l ( ~ ) 0 ( ~ ) Z ~ e :E ectivemomentum Z transfer, Z ~ e = 2 3 ~p p 2m Z +m Q ~p Y (Yc ) L th : Interaction Lagrangian for the 3-uark interaction or ( ) l : Wave function for - or - modes of the initial(final) state baryon Q _ Q 3 1 ~ = ~ 2 + ~ eff ~ = 1 2 ~ 2 2m

15 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Summary and Outlook Productions of hyperon are being studied and the results show some similarities with one-body processes Not only λ- but also ρ-mode transition amplitudes are found by using two-body processes (it cannot be done with one-body processes) Calculations of production rates and extension for charmed baryons are planed

16 Sang-In Shim ( RCNP, Osaka University ) Workshop during IPC SPring-8 Field Trip RIKEN SPring-8 Center, 16 March Thank you for your attention!