Radiative decays of the axial-vector mesons as dynamically generated resonances

Transcription

1 New frontiers in QCD Exotic Hadron Systems and Dense Matter - 18 February, Yukawa Institute for Theoretical hysics, Kyoto, JN Radiative decays of the axial-vector mesons as dynamically generated resonances Hideko Nagahiro 1), Luis Roca 2), tsushi Hosaka 3) Eulogio Oset 4) 1) Nara Women s s University, Japan, 2) Murcia University, Spain, 3) Research Center for Nuclear hysics, Osaka University, Japan, 4) IFIC, alencia University, Spain. 3), 1, B1 RDITIE DECYS WITH HIDDEN GUGE FORMLISM H. Nagahiro,, L. Roca,. Hosaka and E. Oset,, hys. Rev. D79,, , (2009). RDITIE DECYS OF MESONS etc. H. Nagahiro,, L. Roca, E. Oset and B.S. Zou,, hys. Rev. D78,, (2008). H. Nagahiro,, L. Roca and E. Oset,, Eur. hys. J. 36,, (2008). H. Nagahiro,, L. Roca, E. Oset,, hys. Rev. D77,, (2008). H. Nagahiro,, J. Yamagata-Sekihara Sekihara,, E. Oset and S. Hirenzaki,, hys.rev.d79 D79,, , (2009). R. Molina,. Hosaka, H. Nagahiro,, E. Oset,, hys.rev.d80 D80,, , (2009).

2 Background of our study Resonances as hadron-hadron molecule states : exotics» pseudo-scalar scalar pseudo-scalar scalar (ππ, KK bar, etc.) σ, f 0 (980), a 0 (980) scalar mesons» pseudo-scalar scalar baryon (πn,( ηn, KΣ,... / πσ, K bar N,,...) N*(1535), Λ(1405) baryon resonances B» pseudo-scalar scalar vector axial vector meson a 1 (1260), b 1 (1235), K 1 (1270) two pole,, (~1Ge) etc... resonance including vector meson» vector(ρ) vector(ρ/d* /D*)) [vector-vector interaction] f 0 (1370), f 2 (1270) / D* 2 (2460),D* 1 (2640), D* 0 (2600)?,» vector baryon N*, Δ*,... Kaneko, Nagahiro, Hosaka M. Lutz etc., N coupled channel E. Oset and alencia group etc B 2 YIT, 18 Feb. 2010

3 Motivation Hadron nature ~ a molecule? or» roduction mechanism K 1 (1270) two poles evidence in» response to the change of environment mesonic nuclei... hadrons in matter qq bar /qqq state? or K p K π π p or L.S.Geng, E.Oset, L.Roca, J..Oller,, RD75(07) eta mesic nuclei N*(1535) in medium, Kaonic nuclei Λ(1405) in medium... etc.» Decay width strong decay width radiative decay width meson decay process involving vector meson and photon» Interaction with vector meson Tensor formalism, vector formalism, hidden gauge formalism,... ic nucleus 3 YIT, 18 Feb. 2010

4 Introduction : radiative decays of axial vector mesons radiative decays of axial vectors» give information on nature of the axial-vectors, qq bar some works for radiative decays of axial vectors quark model vector meson dominance (MD) bar composite particle J.L.Rosner,, RD23 (1981) Γ a π = 1.0 ~ 1.6 Me; Γ b π = ke effective Lagrangian MD L.Roca, J.E.alomar, E.Oset,, RD70 (2004) Γ a π = 320 ~ 470 ke; Γ b π = 19 ~ 36 ke an elementary particle in a Lagrangian a quasi-bound state based on the chiral unitary approach (as a quasi-bound state of ) L.Roca,,. Hosaka, E. Oset,, LB658 (2007) 17; H.Nagahiro, L.Roca,, E. Oset,, RD77(08) Γ a π = ke; Γ b π = ke H.Nagahiro, L.Roca,,. Hosaka, E. Oset,, RD79 (2009) Γ a π = ke; Γ b π = ke Experimental value Γ a π = ke [1]; Γ b π = ke [2] [1] M.Zielinski et al., RL52 (1984) [2] B.Collick et al., RL53 (1984) YIT, 18 Feb. 2010

5 xial vectors as dynamically generated resonances Chiral Unitary approach for low lying axial vectors L.Roca, E.Oset and J.Singh,, RD72(05) scattering of the nonet of vector mesons () and the octet of pseudoscalar mesons () T = axial vectors 1 meson ~ 1Ge from DG search poles in 2 nd Riemann sheet J C =1 J C =1 =1 b 1 (1235), h 1 (1170), h 1 (1380) a 1 (1260), f 1 (1285), f 1 (1420) K 1 (1270), K 1 (1400) building blocks pseudoscalar octet vector nonet 5 YIT, 18 Feb. 2010

6 L.Roca, E.Oset and J.Singh,, RD72(05) xial vectors as dynamically generated resonances S=0, I=1 channel a 1 (1260) [ρπ[ ρπ] b 1 (1235) [ωπ[ ωπ] in unit of Me [ ] main decay channel (DG) pole position coupling constants Input of my calc. [other poles] in unit of Me a 1 (1260) Mass m = Me Full width Γ = 250 to 600 Me b 1 (1235) Mass m = Me Full width Γ = Me assigned axial vectors pole main decay channel CUM h 1 (1170) i ρπ h 1 (1380) i KK* DG ρπ KK* f 1 (1285) i... 4π K 1 (1270) [double pole] i K*π i ρk ρk 6 YIT, 18 Feb. 2010

7 Formalism of the radiative decay of the axial vectors as dynamically generated resonances, dynamical generated resonance =... axial vectors (dynamically generated resonance)... pseudoscalar mesons [π,[, K, η ]... vector mesons [ρ,[ ω, K*,, φ]

8 Lagrangians obtained from the hidden gauge formalism hidden gauge formalism ρ meson is a gauge boson of a hidden local symmetry transformation ρ meson can be naturally introduced universality, KSFR relation, vector-meson dominance, WT theorem for ρπ We can treat pseudo-scalar scalar meson, vector meson, and photon in a unified way kernel to be used in the BS eq. approx. 8 YIT, 18 Feb. 2010

9 Formalism of radiative decay contributing diagrams (taken into account in this work) type-() photon couples to the final loop photon couples to the final vertex [ 10] photon couples or an intermediate loop to the final [ 11] a 1 -π mixing 9 YIT, 18 Feb. 2010

10 Formalism of radiative decay contributing diagrams (taken into account in this work) type-() type-(b) type-(c) photon couples to the final loop type-(d) photon couples to the final vertex Null contribution photon couples or an intermediate loop Null contribution to the final a 1 -π mixing via loop on shell pion in the final state a 1 -π mixing Lorentz condition for on-shell axial 12 YIT, 18 Feb. 2010

11 double counting...? [type-(d)] tree [type-()] loop [type-(b)] loop [type-(c)] In the hidden formalism, a photon never couples to a particle line directly. It always couples through a vector meson. approx. This approx. was already used in scattering. 13 YIT, 18 Feb. 2010

12 Independent sets of diagrams (1) type-() type-(d) couples via vector meson others (2) type-(b) which set should we calculate? type-(c) type-(d) 1. Both are identical diagram sets from the view point of the dynamical generated resonances 2. Set-(1) seems not gauge invariant. (due to an approximation of vertex.) 3. The loop integral of type-(d) diverges. 14 YIT, 18 Feb. 2010

13 gauge invariant set-(2) of 0 type-(b) 0 type-(d) 0 0 Null contribution to the amplitude Divergence is cancelled Null contribution to the amplitude 0 type-(c) 0 type-(d) 0 Divergence is cancelled 0 15 YIT, 18 Feb. 2010

14 Numerical results in unit of ke in loop a 1 (1260) π b 1 (1235) π type-(b) K * K ρπ total type-(c) K * K ρπ total TOTL experimental anomalous value [1] [2] 4 TOTL anomalous quark model Rosner,, LD23(1981)1127 effective Lagrangian Roca et al., RD70(04) ~ 1.6 Me ke 320 ~ 470 ke 19 ~ 36 ke tree MD 647 ke 67 ke with anomalous coupling [2] B.Collick et al., RL53 (1984) [1] M.Zielinski et al., RL52 (1984) a 1 ρ π 16 YIT, 18 Feb. 2010

15 discussions : a 1 (1260) meson Our numerical result is ~1/3-1/4 of the experimental value» ~ 1/5 without anomalous contribution What does the result mean?» We need higher terms? approx.» a 1 has (large) quark component? Subtraction constant a = 1.85 not natural? a 1 meson can be introduced as an explicit field in the extended hidden den gauge symmetry Lagrangian [M.Bando, T.Kugo,, K. Yamawaki,, R164(88)217 etc] Γ π = 0 in the lowest a 1 meson also can be introduced in Holographic QCD [T. Sakai, S. Sugimoto, T113 (05) 843; T114(05)1083 ossibilities of a hybrid system as (core (qq( bar )) molecule K.Nawa,, H. Nagahiro, S. Ozaki, D. Jido,,. Hosaka, in progress.» ambiguity in the experiment 17 YIT, 18 Feb. 2010

16 Experimental data M. Zielinski et al., hys.rev.lett. 52,, 1195 (1984) inverse reaction (rimakoff( effect) b π π π high energy (202.5 Ge/c) ) pion beam a 1 ρ π.... We obtain Γ ~ ke,, if we use the 1 parameters of Ref. 3. ( M 1 =1.28 Ge The result for the radiative width is clearly sensitive to the assumed resonance mass and total with. For M 1 =1.2 Ge, Γ=0.3Ge,, for example, we obtain Γ = ke.... Consequently, for the standard 1 parameters,, we quote a radiative decay width of ke,,.... [M. Zielinski et al., hys.rev.lett.. 52, 1195 (1984)] Ge, Γ=0.3Ge). a 1 (1260) I G (J (J C )= )=1 (1 Mass m = Me Full width Γ = 250 to 600 Me DECY MODES (ρπ) S-wave (ρπ ρπ) D-wave π : seen seen : seen (1 Fraction (Γ( i /Γ) ) [ OUR ESTIMTE in DG 2008] [ OUR ESTIMTE in DG 2008] We need more information on the a 1 meson! 18 YIT, 18 Feb. 2010

17 summary : We calculated the radiative decay widths of the axial vector mesons as dynamically generated resonances» axial vectors... dynamical generated resonance b 1 (1235), a 1 (1260),, h 1 (1170), h 1 (1380), f 1 (1285), two K 1 (1270)s» coupling can be calculated by Chiral Unitary model ector meson with hidden formalism» Checking carefully the double counting problem and gauge invariance nce We found that the effect of non-trivial interferences between channels is important Contribution from anomalous coupling is large in a 1 (1260) case But it is canceled with the normal contribution.. We found good agreement with b 1 decay and some discrepancy in a 1» Special feature of a 1 meson? Future work : what is the a 1 meson» Experimentally : We need more information.» Theoretically ossibilities of a hybrid system as (core (qq( bar )) molecule K.Nawa,, H. Nagahiro, S. Ozaki, D. Jido,,. Hosaka, in progress. 19 YIT, 18 Feb. 2010