Chiral dynamics and in-mediummodification of particles

E. Oset, University of Valencia

The Λ(1520) in the nuclear mediumThe hidden local gauge theory and vector baryon interactionThe K*- in nucleiCharmed and hidden charm mesons in nucleiMultimeson “nuclei”???η‘ N interaction and η‘ in nuclei.

One takes chiral Lagrangians for the interaction of pseudoscalar mesonswith baryons of the Δ decuplet. In S=-1 we have πΣ* , K Ξ*

The first two channels fixed by chiral Lagrangian, the last two channels are fitted to the data

The T matrix is obtained withunitary Bethe Salpeterequations in coupled channels

T=(1-VG)-1 V

One finds a pole for theΛ(1520) with largest couplingto πΣ*(1385), qualitativelylike a bound state of πΣ*(1385)

The Λ(1520) (3/2-) in chiral dynamics.

Roca, Sarkar, Magas, E. O. PRC2006

The Λ(1520) in the nuclear medium

In free space there in no phase space for decay intoπΣ*. In the medium the πbecomes a ph and there isabout 140 MeV phasespace The width in themedium becomes verylarge.

Recall analogy withmesonic and nonmesonicΛ(1015) decay in hypernuclei, with themesonic decay forbiddenby Pauli blocking.

Kaskulov, E. O, PRC 2006

The width of the Λ(1520) as a function of the nuclear density

Large increase of thewidth. Could be testedin Λ(1520) productionIn nuclei : TransparencyRatio.

Hidden gauge formalism for vector mesons, pseudoscalars and photonsBando et al. PRL, 112 (85); Phys. Rep. 164, 217 (88)

Extension to the baryon sector

q

In the approximation q2/MV2= 0 one recovers the chiral Lagrangians

Weinberg-Tomozawa term. For consistency, for vectors we take q/MV=0

Vector propagator 1/(q2-MV2)

> 200 works

Kolomeitsev et alSarkar et al

New: A. Ramos, E. O.,Eur. Phys J. A, 2010

New: J. Vijande, P. Gonzalez. E.OPRC,2009Sarkar, Vicente Vacas, B.X.Sun, E.OEur. Phys. J. A, 2010

Vector octet – baryon octet interaction

Vν cannot correspond to an external vector.Indeed, external vectors have only spatial components in the approximation of neglecting three momenta, ε0= k/M for longitudinal vectors, ε0=0 for transversevectors. Then ∂ν becomes three momentum which is neglected. Vv corresponds to the exchanged vector. complete analogy to VPPExtra εμεμ = -εiεi but the interaction is formally identical to the case of PBPBIn the same approximation only γ0 is kept for the baryons the spin

dependence is only εiεi and the states are degenerate in spin 1/2 and 3/2

K0 energy of vector mesons

We solve the Bethe Salpeter equation incoupled channels Vector-Baryon octet.

T= (1-GV) -1 V

with G the loop function of vector-baryon

Apart from the peaks, poles are searchedIn the second Riemann sheet and pole positions and residues are determined.

The G function takes into account the mass distribution of the vectors (width).Decay into pseudoscalar-baryon not yetconsidered.

T. Mibe et al, LEPS collaboration , Phys Rev Lett. 95, 2005

Titov and Kaempfer PRC 2207reproduce background with Pomeron and meson exchange

Kiswandhi, Jie Ju Jun, S. N. Yangsuggest that the peak around 2 GeV is a signal of a resonance.

Could it be the V-Boctet resonancefound around 2 GeV which couples to ΦN?

Improvements needed to account for the width:

J. Garzon

Kbar* in the nuclear medium Tolos, Molina, E. O. ,Ramos, PRC (2010)

The K* selfenergy is evaluated and inserted in the K* propagatordemanding selfconsistency.

….

Finitedensity

Kbar* spectral function

Kbar* spectral function

ρ

Peters, Post, Lenske, Leupold, Mosel, Nucl. Phys. A 1998

N*(1520) N-1

Charmed mesons in a nuclear medium

D,Dbar in the medium, Lutz, Korpa PLB(2006); Mizutani, Ramos PRC 2006;Tolos, Ramos Mizutani PRC2008

Work on dynamically generated mesons with charm from light-heavy mesonInteraction, Kolomeitsev, Lutz PLB 2004; Guo, Shen, Chiang, Ping PLB 2006;Gamermann, E. O, Strottman, Vicente Vacas, PRD 2007

The scalar Ds0(2317) is dynamically generated among other resonances

In Gamermann, E. O, Strottman, Vicente Vacas, a scalar hidden charm mesonis generated, X(3700) , in analogy to the f0(980) which is mostly K Kbar.

Gamermann et al.

Once we know the basic components of the resonances, then we can study againtheir dynamical generation inside a nuclear medium, taking into account theselfenergy of the components in the nuclear medium, D, Dbar, K, Kbar … which have been studied before.

This leads to new properties of the dynamically generatedresonances, which show large changes.

Molina, Gamermann, E. O, Tolos Eur. Phys. J. A 2009

X(3700)

These properties can be the objectof study at PANDA/FAIR

“Nuclei” with many mesons, instead of baryons?

The essence of stability of nuclei is baryon number conservation.

In mesons we do not have that. They can decay into systems with smallernumber of mesons. Very unstable systems expected……

Yet, …. succesful description of the X(2175) as a ф K Kbar system, A. Martinez, Khemchandani, Geng, Napsuciale, E.O. PRD 2008

Can one think of systems with more mesons??

Clue, strong binding, large spin to make decay difficult….

There is such a case !!!

Multi ρ states with their spins aligned

From the work of Molina, Nicmorus and E. O, PRD 2008 one generatesdynamically the f0(1370) and f2(1270).The interaction is calculated in the local hidden gauge approach.In Spin=2 it is huge.

The picture gets extra support from work of Yamagata et al in γγ decay,Geng et al in J/Psi decay into V f2 ….; Hanhart el al in J/psi -> γ f2 …..

Take a f2 and add a ρ -> ρ3

Take two f2 -> f4

Add a ρ -> ρ5

Take f2 and f4 -> f6

Looks good wish, but calculations done!

Luis Roca, E. O, arXiv:1005.0283

A description of the f2(1270), rho3(1690), f4(2050), rho5(2350) and f6(2510) resonances as multi-rho(770) states

Calculations done using theFixed Center ApproximationTo Faddeev equations

A. Ramos and E. Oset

Ф for the singlet is Does not contributebecause of the commutator

Mixing of singlet and octet in thephysical η‘ and η‘ states

Scattering lenghts in fm

In the Giessen experiment, M. Nanova et al. , the η‘ are producedwith an average momentum of 900 MeV/c, so, not at threshold, But our model would produce a width in the medium of about 3 MeVfrom Im Πη’ = t η’N ρ.

We have (experimental) reasons to think that there must be more to it.

I. Jaegle , Crystal Barrel-TAPS at ELSA

Resonance close to threshold?Threshold energy 1900 MeVvery close to Vector-Baryon resonances

One should allow the η’ couple to the Vector-Baryon channels and to these resonances

New developments,Results coming soon

Conclusions:

Many body effects are spectacular in some cases:They teach us about excitation mechanisms of the nucleus,but also about elementary properties of some resonances tiedto their composition.

Watch for multihadron states (not ordinary nuclei), they werealways there but only now are emerging…. BELLE, COMPASS, WASA/COSY, FAIR……

The time for η’ nuclear physics has arrived. Little is known and weshould be open to interesting surprises.