Ds prediction of novel exotic charmed N Λ resonances ... · Introduction Formalism: The VV...

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Introduction Formalism: The VV interaction Results Conclusions A new interpretation for the D s2 (2573), the prediction of novel exotic charmed mesons and narrow N , Λ resonances around 4.3 GeV R. Molina 1 , T. Branz 2 , Jia-Jun Wu 3 , B. S. Zou 3 and E. Oset 1 1 Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071 Valencia, Spain 2 Institut für Theoretische Physik, Universität Tübingen, Kepler Center for Astro and Particle Physics, Auf der Morgenstelle 14, D-72076 Tübingen, Germany 3 Theoretical Physics Center for Science Facilities, CAS, Beijing 100049, China

Transcript of Ds prediction of novel exotic charmed N Λ resonances ... · Introduction Formalism: The VV...

Page 1: Ds prediction of novel exotic charmed N Λ resonances ... · Introduction Formalism: The VV interaction Results Conclusions A new interpretation for the D∗ s2(2573), the prediction

Introduction Formalism: The VV interaction Results Conclusions

A new interpretation for the D∗s2(2573), the

prediction of novel exotic charmedmesons and narrow N∗, Λ∗ resonances

around 4.3 GeV

R. Molina1, T. Branz2, Jia-Jun Wu3, B. S. Zou3 and E. Oset1

1Departamento de Física Teórica and IFIC, Centro Mixto Universidad deValencia-CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071

Valencia, Spain2Institut für Theoretische Physik, Universität Tübingen, Kepler Center for Astro and

Particle Physics, Auf der Morgenstelle 14, D-72076 Tübingen, Germany3Theoretical Physics Center for Science Facilities, CAS, Beijing 100049, China

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Outline

Introduction

Formalism: The VV interactionThe PP decay mode

ResultsVV resonancesPrediction of narrow N∗ and Λ∗ resonances above 4.2 GeV

Conclusions

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Introduction Formalism: The VV interaction Results Conclusions

Introduction

• Heavy quark symmetry framework (HQS): with l = 1 twodoublets of Ds states are generated:

- light quark → jl = 3/2, total angular momentum:JP = 1+, 2+

- light quark → jl = 1/2, total angular momentum:JP = 0+, 1+

• The doublet with JP = 1+,2+ is identified with theDs1(2536) and Ds2(2573) in HQS

• However, the doublet with JP = 0+,1+ and very broadstates cannot be identified with the narrow statesdiscovered: the D∗

s0(2317) and the Ds1(2460) (100 MeVlower in mass than the predictions)

• D∗s0(2317): strong s-wave Coupling to DK , E. van Beveren and G. Rupp, PRL

(2003); Couple Channels: D∗s0(2317) ∼ DK , D. Gamermann, E. Oset, D.

Strottmann, M. J. Vicente Vacas , PRD (2007); Ds1(2460) ∼ KD∗(ηD∗s ),

Ds1(2536) ∼ DK ∗(Dsω)) D. Gamermann and E. Oset, EPJA (2007)

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The hidden gauge formalism

Lagrangian

L = L(2) + LIII (1)

L(2) =14

f 2〈DµUDµU† + χU† + χ†U〉 (2)

LIII = −14〈VµνV µν〉 +

12

M2V 〈[Vµ − i

gΓµ]2〉

DµU = ∂µU − ieQAµU + ieUQAµ, U = ei√

2P/f (3)

P ≡0

B

B

@

1√2π0 + 1√

6η8 π+ K+

π− − 1√2π0 + 1√

6η8 K 0

K− K 0 − 2√6η8

1

C

C

A

,

Vµ ≡0

B

B

@

1√2ρ0 + 1√

2ω ρ+ K∗+

ρ− − 1√2ρ0 + 1√

2ω K∗0

K∗− K∗0 φ

1

C

C

A

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Introduction Formalism: The VV interaction Results Conclusions

Inclusion of spin-1 fields

Vµν = ∂µVν − ∂ν Vµ − ig[Vµ, Vν ]

Γµ =1

2[u†

(∂µ − ieQAµ)u + u(∂µ − ieQAµ)u†] u2

= U (4)

FV

MV=

1√

2g,

GV

MV=

1

2√

2g, FV =

√2f , GV =

f√

2, g =

MV

2f(5)

Upon expansion of [Vµ − ig Γµ ]2

L′s

LVγ = −M2V

eg

Aµ〈V µQ〉

LVγPP = egAµ〈V µ(QP2 + P2Q − 2PQP)〉LVPP = −ig〈V µ[P, ∂µP]〉LγPP = ieAµ〈Q[P, ∂µP]〉

LPPPP = − 18f 2 〈[P, ∂µP]2〉. (6)

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The VV interaction Bando, Kugo, Yamawaki

LIII = −14〈VµνV µν〉 L(3V )

III = ig〈(∂µVν − ∂νVµ)V µV ν〉

L(c)III = g2

2 〈VµVνV µV ν − VνVµV µV ν〉

Vµν , g

Vµν = ∂µVν − ∂νVµ − ig[Vµ,Vν ]

g = MV2f

Vµ0

B

B

B

B

B

@

ρ0√

2+ ω√

2ρ+ K∗+ D∗0

ρ− − ρ0√

2+ ω√

2K∗0 D∗−

K∗− K∗0 φ D∗−s

D∗0 D∗+ D∗+s J/ψ

1

C

C

C

C

C

A

µ

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The VV interaction

VV

V V

−→

a) b) c) d)

V V

V

+

• The VV interaction comes from 1. a) and c)• 1. d):

- p-wave repulsive for equal masses (R. Molina, 2008)- minor component of s-wave for different masses (L. S.

Geng, 2009)

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Formalism: The VV interaction

Approximation

ǫµ1 = (0, 1, 0, 0)ǫµ2 = (0, 0, 1, 0)

ǫµ3 = (|~k |, 0, 0, k0)/m

kµ = (k0, 0, 0, |~k |)~k/m ≃ 0,kµ

j ǫ(l)µ ≃ 0

ǫµ1 = (0, 1, 0, 0)ǫµ2 = (0, 0, 1, 0)ǫµ3 = (0, 0, 0, 1)

Spin projectors

P(0) =13ǫµǫ

µǫνǫν

P(1) =12

(ǫµǫνǫµǫν − ǫµǫνǫ

νǫµ)

P(2) = {12(ǫµǫνǫ

µǫν + ǫµǫνǫνǫµ) − 1

3ǫαǫ

αǫβǫβ}

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Formalism: The VV interaction

+

+

(c)

(a) (b)

(d)

+

• (a) and (b)→ Polemass and width

• (c) → p-waverepulsive (notincluded)

• (d)→ Pole width

Bethe equation

T = [I − VG]−1V G =∫ qmax

0q2dq(2π)2

ω1+ω2

ω1ω2[(P0)2−(ω1+ω2)2+iǫ]

+ + + ...

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Introduction Formalism: The VV interaction Results Conclusions

The VV interaction

1. f0(1370), f2(1270) ∼ ρρR. Molina, D. Nicmorus and E. Oset, Phys. Rev. D 78,114018 (2008)

2. f0(1370), f0(1710), f2(1270), f ′2(1525) ∼ ρρ, K ∗K ∗...K ∗

2 (1430) ∼ ρK ∗, ωK ∗...L. S. Geng and E. Oset, Phys. Rev. D 79, 074009 (2009)

3. D∗(2640), D∗

2(2460) ∼ ρ(ω)D∗

R. Molina, H. Nagahiro, A. Hosaka and E. Oset, Phys. Rev.D 80, 014025 (2009)

4. Y(3940), Z(3930), X(4160) ∼ D∗D∗, D∗

sD∗

sR. Molina and E. Oset, Phys. Rev. D 80, 114013 (2009)

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The VV interaction

• C = 0; S = 1; I = 1/2(hidden charm):

D∗

sD∗, J/ψK ∗

• C = 1; S = −1; I = 0, 1:

D∗K ∗

• C = 1; S = 1; I = 0:

D∗K ∗, D∗

sω, D∗

• C = 1; S = 1; I = 1:

D∗K ∗, D∗

• C = 1; S = 2; I = 1/2:

D∗

sK ∗

• C = 2; S = 0; I = 0, 1:

D∗D∗

• C = 2; S = 1; I = 1/2:

D∗

sD∗

• C = 2; S = 2; I = 0:

D∗

sD∗

s

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The PP decay mode

• The PP box diagram has only JP = 0+ and JP = 2+

quantum numbers• We only find atractive interaction in the sectors:

- C = 1; S = −1; I = 0: D∗K ∗

- C = 1; S = 1; I = 0: D∗K ∗, D∗sφ,

D∗sω

- C = 1; S = 1; I = 1: D∗K ∗, D∗s ρ

- C = 2; S = 0; I = 0; J = 1: D∗D∗

- C = 2; S = 1; I = 1/2; J = 1:D∗

s D∗

K∗(k4)K∗(k2)

K(P − q)

D(q)

D∗(k3)D∗(k1) D∗

K∗

D∗s

K

D

φ

π(k1 − q) ππ(k3 − q) K

φ φ

D∗sD∗

s

D

K

KK

D∗

K∗ K∗

D∗

D

K

ππ

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The VV interaction

• Model A:

F1(q2) =Λ2

b − m21

Λ2b − (k0

1 − q0)2 + |~q|2 ,

F3(q2) =Λ2

b − m23

Λ2b − (k0

3 − q0)2 + |~q|2 ,

with q0 =s+m2

2−m24

2√

s, ~q running variable, Λb = 1.4, 1.5 GeV and

g = Mρ/2 fπ

• Model B:

F (q2) = e((q0)2−|~q|2)/Λ2,

with Λ = 1, 1.2 GeV, q0 =s+m2

2−m24

2√

s, g = Mρ/2 fπ,

gDs = MD∗s/2 fDs = 5.47 and gD = gexp

D∗Dπ = 8.95 (experimentalvalue)

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Couplings ( ga) in units of MeV

Tab =gagb

s − sp

C = 1; S = −1; I = 0

I[JP ]√

spole gD∗K∗

0[0+ ] 2848 12227

0[1+ ] 2839 13184

0[2+ ] 2733 17379

C = 1; S = 1; I = 0

I[JP ]√

s gD∗K∗ gD∗s ω gD∗

s φ

0[0+] 2683 15635 −4035 6074

0[1+] 2707 14902 −5047 4788

0[2+] 2572 18252 −7597 7257

C = 1; S = 1; I = 1

IG [JPC ]√

spole gD∗K∗ gD∗s ρ

1[2+] 2786 11041 11092

C = 2; S = 0; I = 0

I[JP ]√

spole gD∗D∗

0[1+] 3969 16825

C = 2; S = 1; I = 1/2

I[JP ]√

spole gD∗s D∗

1/2[1+] 4101 13429

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Summary

C, S I[JP ]√

s ΓA(Λ = 1400) ΓB(Λ = 1000) State√

sexp Γexp

1,−1 0[0+ ] 2848 23 25

0[1+ ] 2839 3 3

0[2+ ] 2733 11 22

1, 1 0[0+ ] 2683 20 44

0[1+ ] 2707 4 × 10−3 4 × 10−3

0[2+ ] 2572 7 18 Ds2(2573) 2572.6 ± 0.9 20 ± 5

1[2+ ] 2786 8 9

2, 0, 0[1+ ] 3969 0 0

2, 1 1/2[1+] 4101 0 0

Table: Summary of the nine states obtained. The width is given forthe model A, ΓA, and B, ΓB. All the quantities here are in MeV. Twovalues of α are used: −1.6 and −1.4.

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PB and VB resonances in the hidden charm sector

• I = 1/2,S = 0. Channels: DΣc , DΛ+c , ηcN, πN, ηN, η′N,

KΣ, KΛ

• I = 0,S = −1. Channels: DsΛ+c , DΞc , DΞ

′c, ηcΛ, πΣ, ηΛ,

η′Λ, KN, KΞ

B1

V*V*

(a) (b)

P1 P2 V1

B2 B1B2

V2

LBBV = g(〈Bγµ[Vµ, B]〉 + 〈BγµB〉〈Vµ〉)

tB1B2V = {g151C151

(20′ ⊗ 20′) + g152C152

(20′ ⊗ 20′) + g1 C1(20′ ⊗ 20′)}ur′ (p2)γ · ǫ ur (p1)

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T = [I − VG]−1V Tab =gagb√s − zR

PB resonances

(I,S) zR (MeV) ga

(1/2, 0) DΣc DΛ+c

4269 2.85 0(0,−1) DsΛ

+c DΞc DΞ′

c

4213 1.37 3.25 04403 0 0 2.64

VB resonances

(I,S) zR (MeV) ga

(1/2, 0) D∗Σc D∗Λ+c

4418 2.75 0(0,−1) D∗

s Λ+c D∗Ξc D∗Ξ′

c

4370 1.23 3.14 04550 0 0 2.53

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Prediction of narrow N∗ and Λ∗ resonances above 4.2 GeV

PB resonances (units in MeV)(I,S) M Γ Γi

(1/2,0) πN ηN η′N KΣ ηcN4261 56.9 3.8 8.1 3.9 17.0 23.4

(0,−1) K N πΣ ηΛ η′Λ KΞ ηcΛ4209 32.4 15.8 2.9 3.2 1.7 2.4 5.84394 43.3 0 10.6 7.1 3.3 5.8 16.3

VB resonances

(I,S) M Γ Γi

(1/2,0) ρN ωN K ∗Σ J/ψN4412 47.3 3.2 10.4 13.7 19.2

(0,−1) K ∗N ρΣ ωΛ φΛ K ∗Ξ J/ψΛ4368 28.0 13.9 3.1 0.3 4.0 1.8 5.44544 36.6 0 8.8 9.1 0 5.0 13.8

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Production cross section of the N∗ resonances at FAIR

p

p

π0

N*+cc

p

p

ηc

p

p p

p

ηc

π0N*+

cc

p

p

π0

p ηcp

p

(b)(a)

(c)

p

p

π0

p

p

p

ηc(d)

• p beam of 15 GeV/c,√

s = 5470 MeV → MX ≃ 4538 MeV.dσpp→N∗+

cc (4265)p→ηcppdcosθdM2

I= 0.3µb/GeV 2 at peak, σ ≃ 0.07µb.

• σ(pp → N∗+cc (4418)p → ηcpp) ≃ 0.002µb.

This corresponds to an event production rate of 80000 and1700 events per day for the N∗+

cc (4265) and N∗+cc (4418)

respectively for a Luminosity of 1031cm−2s−1.

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Conclusions

• We studied dynamically generated resonances fromvector-vector interaction in the charm-strange, hidden-charmand flavor exotic sectors and meson-baryon resonances withhidden charm

• In the present work we can assign one resonance to anexperimental counterpart, which is the D∗

2(2573)

• We have found flavor exotic resonances with double charm,double charm-strangeness and new N∗, Λ∗ states around 4.3GeV that if observed cannot be accomodated in terms of qq

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References

M. Bando, T. Kugo, S. Uehara, K. Yamawaki andT. Yanagida, Phys. Rev. Lett. 54 (1985) 1215

M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164(1988) 217

M. Harada and K. Yamawaki, Phys. Rept. 381 (2003) 1

R. Molina, D. Nicmorus and E. Oset, Phys. Rev. D78 (2008)114018

L. S. Geng and E. Oset, Phys. Rev. D79 (2009) 074009

F. S. Navarra, M. Nielsen and M. E. Bracco, Phys. Rev. D65 (2002) 037502