Charmed hadrons in Dense ma.er based on chiral models

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1 Charmed hadrons in Dense ma.er based on chiral models Masayasu Harada (Nagoya University) Hadron structure and interac>on in dense ma.er (November 11, 2018) Based on T. Yamazaki and M. Harada, arxiv: [hep-ph]. T. Yamazaki and M. Harada, work in progress. M. Harada, Y.L. Ma, D. Suenaga, Y. Takeda, PTEP2017, 113D01 (2017). See also Y. Motohiro, Y. Kim, M. Harada, Phys. Rev. C 92, (2015); Erratum: Phys. Rev. C 95, (2017). D.Suenaga, B.-R.He, Y.L.Ma, M.Harada, Phys. Rev. C 89, (2014) D.Suenga, B.-R.He, Y.L.Ma, M.Harada, Phys. Rev. D 91, (2015) D.Suenaga, M.Harada, Phys. Rev. D 93, (2016). D.Suenaga, S.Yasui, M.Harada, Phys. Rev. C 96, (2017) 2018/11/11 Hadron structure and interac>on in dense ma.er 1

2 Introduc)on 2018/11/11 Hadron structure and interac3on in dense ma5er 2

3 of Hadrons Origin of Mass? of Us = One of the Interes4ng problems of QCD 2018/11/11 Hadron structure and interac3on in dense ma5er 3

4 spontaneous chiral symmetry breaking chiral symmetry broken phase at vacuum chiral symmetric phase at high T and/or density qq 0 (chiral condensate) qq = 0 The spontaneous chiral symmetry breaking is expected to generate a part of hadron masses. It causes mass difference between chiral partners. Changing T and/or density will cause some change of hadron masses. 2018/11/11 Hadron structure and interacdon in dense maeer 4

5 Phase diagram of Quark-Gluon system high temperature 1 trillion kelvin Early Universe ChiralSymmetry Restra<on Deconfinementof Quarks Spontaneous ChiralSymmetry Breaking Confinement of Quarks RIBF RISP 100 million ton/cm 3 Neutron Star High density 2018/11/11 Hadron structure and interaction in dense matter 5

Dense nuclear ma,er by a Skyrme-crystal model Y. L. Ma, M. Harada, H.K. Lee, Y. Oh, B. Y. Park, M.

Rho, PRD90 (2014) 34105 There exists the half-skyrmion phase where the space-average of the chiral

Nucleon mass decreases with density in the normal phase, while it is stable In the half-skyrmion

6 Dense nuclear ma,er by a Skyrme-crystal model Y. L. Ma, M. Harada, H.K. Lee, Y. Oh, B. Y. Park, M. Rho, PRD88 (2013) Y. L. Ma, M. Harada, H.K. Lee, Y. Oh, B. Y. Park, M. Rho, PRD90 (2014) There exists the half-skyrmion phase where the space-average of the chiral condensate vanishes. Nucleon mass decreases with density in the normal phase, while it is stable In the half-skyrmion phase. Nucleon mass ~ 2 r 0 σ 0 z 0 z 0 y x x y 0 0 z 0 d 3 x qq 0 0 density normal hadron half-skyrmion Chiral invariant mass? phase phase 2018/11/11 Hadron structure and interacjon in dense ma,er 6

7 Chiral Invariant Mass of Hadrons? Parity doublet model for light baryons In [C.DeTar, T.Kunihiro, PRD39, 2805 (1989)], N*(1535) is regarded as the chiral partner to the N(939) having the chiral invariant mass. m B = m 0B + m qq chiral invariant mass spontaneous chiral symmetry breaking How much mass of nucleon is from the spontaneous chiral symmetry breaking? What is the value of the chiral invariant mass? 2018/11/11 Hadron structure and interacton in dense mauer 7

8 l l l We studied nuclear ma/er using models with parity doublet structure. Ø Y. Motohiro, Y. Kim, M. Harada, Phys. Rev. C 92, (2015); Erratum: Phys. Rev. C 95, (2017). Ø Y. Takeda, Y. Kim and M. Harada, Phys. Rev. C 97, no. 6, (2018). Ø Y. Takeda, H. Abuki and M. Harada, Phys. Rev. D 97, no. 9, Ø Ø (2018). T. Yamazaki and M. Harada, arxiv: [hep-ph]. T. Yamazaki and M. Harada, in preparayon. We showed that the chiral invariant mass is constrained by the saturayon properyes and neutron star properyes. We presented a density dependence of the nucleon mass, which changes reflecyng the paryal chiral symmetry restorayon. What happens to the masses of other hadrons in nuclear ma/er? 2018/11/11 Hadron structure and interacyon in dense ma/er 8

Medium modifica,on of charmed meson masses QCD sum rule One-loop in an effec,ve model One-loop in an effec,ve model at finite temperature K.Suzuki, P.Gubler, M.

9 Medium modifica,on of charmed meson masses QCD sum rule One-loop in an effec,ve model One-loop in an effec,ve model at finite temperature K.Suzuki, P.Gubler, M.Oka, PRC 93, (2016) D meson mass is increased at finite density S.Yasui, K.Sudoh, PRC 87, (2013) D meson mass is decreased at finite density C.Sasaki, PRD 90, (2014) D meson mass is stable at finite temperature 2018/11/11 Hadron structure and interac,on in dense ma9er 9

10 Medium modification of charmed meson masses 2 In a series of papers, we studied in-medium modifica7ons of charmed meson masses based on chiral models. D.Suenaga, B.-R.He, Y.L.Ma, M.Harada, Phys. Rev. C 89, (2014) D.Suenga, B.-R.He, Y.L.Ma, M.Harada, Phys. Rev. D 91, (2015) D.Suenaga, M.Harada, Phys. Rev. D 93, (2016). D.Suenaga, S.Yasui, M.Harada, Phys. Rev. C 96, (2017). M. Harada, Y.L. Ma, D. Suenaga, Y. Takeda, PTEP2017, 113D01 (2017). In Ref., based on the mean field approxima7on, we showed Increasing or decreasing of pseudo-scalar charmed meson mass only is not enough for measuring the par7al chiral symmetry restora7on. 200 In addi7on to study the mass difference of chiral partners, taking average of par7cle and an7-par7cle will give a clue for par7al chiral symmetry restora7on. In Ref., we studied a spectral func7on of scalar charmed meson, and showed that 3 peaks appears. Ø Talk by Daiki Suenaga D(+) D( ) r B /r 0 = /11/11 Hadron structure and interac7on in dense ma8er

11 In this talk, I will summarize our recent works. T. Yamazaki and M. Harada, arxiv: T. Yamazaki and M. Harada, in prepara5on. We study 4 nucleons, N(939), N(1440), N(1535), N(1650) based on the parity doublet structure. We construct nuclear ma7er using the model and study the density dependence of charmed meson masses. Outline 1. Introduc5on 2. An extended parity doublet model for nucleon 3. Nuclear ma7er from an extended parity doublet model 4. Density dependence of effec5ve masses of charmed mesons based on chiral partner structure 5. Summary 2018/11/11 Hadron structure and interac5on in dense ma7er 11

12 2. An Extended Parity Doublet model for Nucleons T. Yamazaki and M. Harada, arxiv: [hep-ph]. 2018/11/11 Hadron structure and interacpon in dense maqer 12

) 2,0 +, - ( 0, 1 + & chiral symmetry breaks. * ) 2 -/ % down and the,' isospin symmetry remains $ ( = 5 * 1 ) 2,0 +, - ( 0, 1 + &.

13 chiral representation of baryons representation of quark under SU( 2) R SU( 2) L q ~ q r + q l ~ ( 2,1) ( 1,2 ) or # 1 % $ 2,0 & ' ( # 0, 1 & % $ 2 ( ' representation of baryon under SU 2 ( ) ( 1,2 )& ' 3 ( ) ( 1,2 )& $ ( ) ( 2,3) ψ ~ q q q ~ $ % 2,1 = 5$ % 2,1 ' 3% 3,2 ( ) R SU( 2) L ( ) ( 1,4 ) & ' $ % 4,1 $ ( or ψ ~ q q q ~ * 1 ) 2,0 +, - ( 0, 1 + & chiral symmetry breaks. * ) 2 -/ % down and the,' isospin symmetry remains $ ( = 5 * 1 ) 2,0 +, - ( 0, 1 + &. * ) 2 - %,' / 3 $ ( 1, 1 + * ) 2, - ( * 1 ) 2,1 + &. - %,' / $ ( * 3 ) 2,0 +, - ( 0, 3 + &. * ) 2 -/ %,' I = 1 2 baryons 3 I = 3 2 baryons & ' 2018/11/11 Hadron structure and interac:on in dense ma<er 13

Parity Doublet models with 2,1 1,2 nucleons C.DeTar, T.

is regarded as the chiral partner to the N(939).

" #$ % & ' $ ( #$ ( & ' $ % Spontaneous chiral symmetry breaking generates the mass

14 Parity Doublet models with 2,1 1,2 nucleons C.DeTar, T.Kunihiro, PRD39, 2805 (1989) D.Jido, M.Oka, A.Hosaka, PTP106, 873 (2001) S. Gallas, F. Giacosa, D. Rischke, PRD82, (2010) An excited nucleon with nega1ve parity such as N(1535) is regarded as the chiral partner to the N(939). N(939) and N(1535) have a chiral invariant mass: Ø! " #$ % & ' $ ( #$ ( & ' $ % Spontaneous chiral symmetry breaking generates the mass difference between chiral partners. Ø * % #$ %+,$ %- + #$ %-, / $ %+ * ( #$ (-,$ (+ + #$ (+, / $ (- /, = transforms, * 8, * 9, = #1 0 causes the spontaneous chiral symmetry breaking. 2018/11/11 Hadron structure and interac1on in dense majer 14

15 A model with 1,2 2,1 and 2,3 3,2 representa1ons We include two representa1ons, & 1,2 2,1 and ( 2,3 3,2 to study N(939), N(1440), N(1535), N(1650). There are 2 chiral invariant masses. Ø * +, -&,. / & 0 -& 0. / &, * Yukawa Couplings T. Yamazaki and M.Harada, arxiv: [hep-ph]. (,. / ( 0 ( 0. / (, Ø A, -&,B C&,D + -&,D C F &,B A 0 G -& 0D C& 0B + -& 0B C F & 0D H etc. We also have 4 terms with one deriva1ve. Ø I, -&,B. J K J C& 0B -&,D. J K J C F & 0D etc 2018/11/11 Hadron structure and interac1on in dense maher 15

16 Physical inputs We use the following 10 physical inputs to determine 10 parameters (10 couplings) for fixed values of the chiral invariant masses! " ($) and!" (&). Masses Decay widths Axial charges (LaKce analysis [T.T.Takahashi, T.Kunihiro, PRD78 (2008)] ) 2018/11/11 Constraint (LaKce analysis [T.T.Takahashi, T.Kunihiro, PRD78 (2008)] shows ' ( ~*(0.1). Hadron structure and interaccon in dense mader 16

Chiral invariant masses & Chiral partner structure Group 5 5 Groups of solu:ons Group 4, 5 N(939) is dominated by 1,2 2,1 Chiral partner to N(939) = a mixture of N(1535) & N(1650) Group 3 Group 2

17 Chiral invariant masses & Chiral partner structure Group 5 5 Groups of solu:ons Group 4, 5 N(939) is dominated by 1,2 2,1 Chiral partner to N(939) = a mixture of N(1535) & N(1650) Group 3 Group 2 Group 1 Group 4 Group 3 Small % & (() : N(939) is dominated by 1,2 2,1. Large % & (() : N(939) is dominated by 2,3 3,2. Chiral Partner N(1535) Group 2 N(939) is dominated by (2,3)+(3,2) Chiral partner to N(939) = a mixture of 3 nucleons Group 1 N(939) is dominated by (2,3)+(3,2) representa:on. Chiral partner to n(939) = N(1440) 2018/11/11 Hadron structure and interac:on in dense ma;er 17

18 3. Nuclear Ma,er from an extended parity doublet model T. Yamazaki and M. Harada, work in progress 2018/11/11 Hadron structure and interacfon in dense ma,er 18

19 Construction of Nuclear Matter We include the omega and rho mesons into our model using the hidden local symmetry. We calculate the thermodynamic poten9al in the nuclear medium in our model, using the mean field approxima9on. Then, we adjust model parameters to reproduce the following physical inputs for given values of the chiral invariant masses! " ($) and!" (&). Nuclear satura9on density ' ( ) = 923MeV = ' " = 0.16fm 8 Binding energy at normal nuclear density 9 :!(939) < = = > <?!(939) Incompressibility < = = 16MeV & = 9' C 9 : BE " A = 9'? B< C " A = 240MeV < B< = <= Symmetry energy E sym (r 0 ) = 31 MeV 2018/11/11 Hadron structure and interac9on in dense ma;er 19

20 Constraint to model parameters Group 5 Group 3 Group 2 Group 1 Group 4 We checked whether the satura7on proper7es are sa7sfied for the parameter choices indicated by mark. We found that, for the parameter choices indicated by mark, the satura7on proper7es are NOT sa7sfied. So, these parameter choices are excluded. In par7cular, please note that the parameter choices in Group 1 are all excluded. 2018/11/11 Hadron structure and interac7on in dense ma8er 20

21 Constraint from Neutron Star Properties We are obtaining more constraints to the chiral invariant masses from the proper9es of Neutron Stars. Maximum mass of NS 2# Tidal deformability: %Λ 800 with # chirp = # So far, we found 3 solu9ons of chiral invariant masses: (5) (8) 2 3, 23 = 900,700, 705,790, (1155,765) 2018/11/11 Hadron structure and interac9on in dense majer 21

22 Mean fields & Effec.ve masses in symmetric ma5er (-) (0) * +, *+ = 900,700! (MeV) " = $ %&& ' % ( ) (MeV) Effec.ve Masses N(1650) N(1535) N(1440) N(939) 2018/11/11 Hadron structure and interaction in dense matter 22

23 4. Density dependence of effec1ve masses of charmed mesons based on chiral partner structure T.Yamazaki and M.Harada, work in progress. M. Harada, Y.L. Ma, D. Suenaga, Y. Takeda, PTEP 2017, 113D01 (2017) 2018/11/11 Hadron structure and interacgon in dense maher 23

24 Chiral partner structure for charmed mesons 2 heavy quark mul8plets with J l =1/2 are regarded as the chiral partner: "D(0 # ),D * (1 ) $ M.A.Nowak, M.Rho and I.Zahed, PRD48, 4370 (1993) W.A.Bardeen and C.T.Hill, PRD49, 409 (1994) (((( " # D * 0 (0 + ),D 1 (1 + ) $ % % chiral partner Mass difference is generated by the chiral condensate, and the value is roughly equal to the cons8tuent quark mass. Experimental value implies that the chiral partner structure seems to work: m ( 0 + ) m ( 0 ) m ( 1 + ) m ( 1 ) 0.43GeV 2018/11/11 Hadron structure and interac8on in dense mayer 24

25 Masses of charmed mesons in symmetric 2018/11/11 nuclear ma3er In this talk, I define effec:ve masses of nucleons by including effects of exchanging the sigma and omega mesons in the mean field approxima:on, following our recent work [M.Harada, Y.L.Ma, D.Suenaga, Y.Takeda, PTEP 2017, 113D01 (2017)]. Effec:ve masses for D(J P =0 - ), D(J P =0 + ) in symmetric nuclear ma3er (eff) * Ø! "($) =! +, (eff) * Ø! "(3) =! + +, "" 2 / "" 2 / Effec:ve masses for an:-charmed mesons (eff) * Ø!"($) 5 =! +, (eff) * Ø!"(3) 5 =! + +, -. / + 0 1"" 2 -. / + 0 1"" 2 Hadron structure and interac:on in dense ma3er D D D D s ω 25

26 Charmed meson masses in symmetric ma0er (eff) Δ +! "($) =! 2 (eff) Δ +! "(3) =! "" 2 / "" 2 / (eff) Δ +!"($) 5 =! 2 (eff) Δ +!"(3) 5 =! "" 2 / "" 2 / An example : 0 1"" = 3.7 ;! ; (<),!; (>) = 900,700 5A + 5A A + A( ) Increasing or decreasing of pseudo-scalar D(-) meson mass only is not enough for measuring the par8al chiral symmetry restora8on. 2018/11/11 Hadron structure and interac8on in dense ma0er 26

27 Partial chiral symmetry restoration 0 1"" = 3.7! 8 (9),!8 (;) = 900,700 (eff) Δ +! "($) =! 2 (eff) Δ +! "(3) =! / 0 1"" 2 -. / 0 1"" 2 (eff) Δ +! "($) =! 2 (eff) Δ +! "(3) =! / + 0 1"" 2 -. / + 0 1"" 2 D(+) D( ) D(+) + D(+) D( )+ D( ) In addi8on to study the mass difference of chiral partners, taking average of par8cle and an8-par8cle will give a clue for par8al chiral symmetry restora8on. Threshold energy for produc8on of D and an8-d meson pair in medium is larger than vacuum reflec8ng the par8al chiral symmetry restora8on. 2018/11/11 Hadron structure and interac8on in dense ma9er 27

28 5. Summary No.1 We include two representa9ons,! 1,2 2,1 and ' 2,3 3,2 to study N(939), N(1440), N(1535), N(1650). We use masses, decay widths and axial charges to determine the model parameters for fixed values of 2 chiral invariant masses. We constructed nuclear ma:er using a mean field approxima9on. we adjust model parameters to reproduce the following physical inputs for given values of the (,) (.) chiral invariant masses ) * and )*., and found that, for the parameter choices indicated by mark, the satura9on proper9es are NOT sa9sfied. We are obtaining more constraints to the chiral invariant mass from the proper9es of Neutron Stars. Heavy NS with 2/ can be realized Tidal deformability: 1Λ 800 with / chirp = / We found 3 pairs of chiral invariant masses: (,) (.) ) *, )* = 900,700, 705,790, (1155,765) 2018/11/11 Hadron structure and interac9on in dense ma:er Group 5 Group 3 Group 2 Group 1 Group 4 28

29 Summary No.2 We studied density dependence of charmed meson masses from the mean field contribu:ons of sigma and omega mesons in the nuclear medium. Increasing or decreasing of D(-) meson mass only is not enough for measure the chiral symmetry restora:on. In addi:on to study the mass difference of chiral partners, taking average of par:cle and an:-par:cle will give a clue for par:al chiral symmetry restora:on. D(+) D( ) D( )+ D( )!" +!"! +!( ) D(+) + D(+) 2018/11/11 Hadron structure and interaction in dense matter 29

30 2018/11/11 Hadron structure and interaction in dense matter 30

Charmed meson masses in medium based on effec1ve chiral models

Charmed meson masses in medium based on effec1ve chiral models Masayasu Harada (Nagoya University) @ KEK theory center workshop on Hadron and Nuclear Physics in 217 (KEK, JAPAN, January 9, 217) Based on