New Interpretation of the ABC Effect New Interpretation of the ABC Effect in Two-Pion Production in in Two-Pion Production in NNNN collisions collisions

Maria PlatonovaLomonosov Moscow State University

The 22nd European Conference on Few-Body Problems in Physics

9–13 September 2013, Cracow, Poland

• In 1960 A. Abashian, N.E. Booth & K.M. Crowe [PRL 5, 258 (1960); 7, 35 (1961)] reported an observation of a strange enhancement in p+d fusion to 3He, located near the 2π threshold.

22

3He , 743 MeVppd X T

What is ABC Effect?

• Later on the similar enhancements were observed in the reactions np → dX and dd → 4HeX.

ABC anomaly: I(JP) = 0(0+), mX ≈ 300 MeV

Phase space

pd → 3HeX, I = 0

33

• Strong ππ final state attraction in the scalar-isoscalar channel. Possibility of a 0(0+) resonance (σ-meson) formation. Good fit of ABC data with ππ scattering length as0 ≈ 2–3 mπ

-1. However:

Actual ππ scattering length: as0 ≈ 0.2 mπ-1;

No ABC effect in free ππ scattering and πN→ππN reaction.

• Prediction of a low-Mππ enhancement due to parallel decays of two ∆’s. Qualitative description of some inclusive data.

Contradicted by recent exclusive experiments!

We must look for some new interpretation.

1. Resonance formation in ππ FSI (K.M. Watson & A.B.C, 1961)

Previous Interpretations of the ABC Effect

2. The t-channel ΔΔ model (T. Risser & M.D. Shuster, 1973)

p

n

Δ

Δ

d

π

π

• The experimental data clearly show the formation of isoscalar dibaryonresonance D03 with parameters:

• … and distinct correlation between the np resonance and ABC enhancement:

4

2370 MeV=2M 90MeV

70 MeV 2

( ) 0(3 )PI J

M

t-channel ΔΔ

The first exclusive high-statistics experiments in full 4π-geometry 0 0

spectator , 1.0 1.4 GeVpp d p d T

New Exclusive Experiments of the CELSIUS-WASA and WASA@COSY Collaborations

D03: E = 2.38 GeV ABC: M

ππ =

290 M

eVABC peak

[P. A

dlars

on e

t al.,

 PRL 

106,

242

302,

 201

1]

55

The s-channel Resonance Ansatz

Δ

Δd

π

πD03

p

n2

2 2( ) , 0.15 GeV/F q c

q

• Interpretation of the new experimental results in terms of a Δ-Δ deeply bound state (M. Bashkanov et al.): a very soft form factor in D03→ΔΔ vertex is needed to reproduce the ABC enhancement.

• Such a low value of Λ means that D03 is a deuteron-like object.

This is incompatible with the observed large Δ-Δ binding in the D03 state: εB(D03) ≈ 90 MeV.

• The value of Λ should be 2 times softer to reproduce ABC peak in dd → 4He+(ππ)0 with the same model.

• Microscopic quark model calculations predict a radius for the 0(3+) Δ-Δ bound state r(D03) ≈ 0.7–0.9 fm, i.e., of the order of the nucleon size.

• The D03 resonance appears to be the truly dibaryon state in which the quark cores of two Δ’s are almost fully overlapped with each other.

66

First Prediction of Dibaryon States• By using SU(6)-symmetry, Dyson and Xuong predicted six zero-strangeness

low-lying dibaryons [F.J. Dyson and N.-H. Xuong, PRL 13, 815 (1964)]:

• From the simple SU(6) mass formula M = A+B[T(T+1)+J(J+1)-2], A being the deuteron mass and B = 47 MeV, the masses of NΔ and ΔΔ S-

wave resonances were predicted to be

M(D12) ≈ 2160 MeV;

M(D03) ≈ 2350 MeV.

• The deuteron D01 was positioned as NN S-wave dibaryon from the same

SU(3) multiplet as D03.

77

Indications of D12 and other Isovector Dibaryons• Isovector dibaryons were discovered in late 70ies in pp scattering

experiments and then confirmed in partial wave analyses of pp and π+d elastic scattering and especially π+d → pp reaction [R.A. Arndt et al., PRC 48, 1926 (1993)].

• All features of the dominant partial wave amplitude 1D2P are consistent with production of dibaryon resonance D12 with quantum numbers I(JP ) = 1(2+), mass M(D12) ≈ 2150 MeV and total width Γ(D12) ≈ Γ(Δ) = 120 MeV.

Argand plot of dominant partial-wave amplitudes in π+d → pp

Contributions of dominant 1D2P, 3F3D and 3P2D amplitudes

to the total X-section of π+d → pp

• From solving exact Faddeev equations for πNN and πNΔ systems the robust dibaryon poles corresponding to D12 and D03 were found.

• The pole positions are:

• These parameters are in full agreement with Dyson and Xuong predictions as well as with experimental findings.

• Thus, the D12 pole is located ≈20 MeV below the NΔ threshold (2170 MeV) and the D03 pole lies ≈100 MeV below the ΔΔ threshold (2460 MeV). The deuteron, i.e., the NN S-wave dibaryon D01, is located near the NN threshold.

• Let’s see what happens at short distances, when quark d.o.f. come into play.

88

A New Confirmation of Dibaryon Resonances D12 and D03

03 03( ) 2363 20 MeV, ( ) 65 17 MeVM D D

[A. Gal, H. Garcilazo, arXiv:1308.2112]

12 12( ) 2151 2 MeV, ( ) 120 6 MeVM D D

99

• In dibaryon model, an intermediate dibaryon production is assumed to be responsible for the basic NN attraction, i.e., for the short-range nuclear force.

• The basic meson field surrounding the 6q bag in dibaryon model is a scalar (σ) field. It arises in a 6q transition from a mixed-symmetry 6q configuration s4p2 to a fully symmetric s6 (in even NN partial waves): s4p2 → s6 + σ (Lσ = 0,2).

• The σ field stabilizes the quark bag and leads to a strong attraction between quarks; this results in effective attraction between nucleons at rNN~0.7–0.8 fm.

• Within the dibaryon model, a very good description of NN-scattering phase shifts up to EN = 1 GeV and of lightest nuclei properties was achieved with only a few basic parameters.

Dibaryon Model of NN Interaction

(very briefly… see talk by V.I. Kukulin)

t-channel meson exchange at short distances

production of s-channel dibaryon (6q bag dressed with meson fields)

is replaced by

The Deuteron in Dibaryon Model • The deuteron wave function (d.w.f.) in dibaryon model is a two-component

Fock column:

• The second component of the d.w.f. Ψ6q+σ is a fully symmetric 6q bag surrounded by σ-meson cloud, as well as the nucleon is a 3q bag dressed with pion cloud. However, closeness to NN threshold makes this “elementary deuteron” to be strongly coupled to NN channel.

• As a result, the quark-meson component Ψ6q+σ gives just a small contribution ( 2–3%) to the total d.w.f., however it is still dominant at ∼short NN distances, i.e., when two nucleons are overlapped with each other.

• Analogously, the D12 and D03 dibaryons at short distances may be considered as dressed six-quark bags strongly coupled to NΔ and ΔΔ channels, respectively.

10

6

NN

dq

• So, the dibaryon resonances D12 and D03 may be treated as excited states of the deuteron D01, in a similar way that baryon resonances Δ, N*(1440), etc., are treated as excited nucleon states.

• Besides the above mentioned decay mode we propose two alternative routes for the D03 resonance decay which can

lead to dππ final state:

• The mechanisms 1’) and 2’) resemble the respective routes for the Roper resonance decay N*(1440) → Δ + π and N*(1440) → N + σ.

• NOTE. The mechanisms 1) and 1’) lead to very similar results in pn→D03→dππ invariant mass and angular distributions. However, we consider the last mechanism 1’) to be the dominant one close to D03 peak energy (~2.38 GeV), since two Δ’s in D03

are deeply bound and almost fully overlapped with each other, so the dibaryon configuration should be more probable here.

11

503 12 3

303 01 3

1 ) ( ),

2 ) ( )

D D P

D D D

Decay Routes of the D03 Resonance

703 31) ( ),D S

12

• We took the above decay routes 1’) and 2’) for D03 resonance as a basis for our model of p + n → d + (ππ)0 reaction in the ABC region (Tp = 1.0–1.4 GeV) [M.N. Platonova, V.I. Kukulin, PRC 87, 025202 (2013)].

• The D03 (I(JP) = 0(3+)) dibaryon produced in p+n collision decays subsequently into the final deuteron (i.e., D01 (I(JP) = 0(1+)) and isoscalar ππ pair via two interfering processes:

(a) emission of a d-wave σ meson, which then decays into s-wave ππ pair; (b) sequential emission of two p-wave pions via an intermediate isovector dibaryon D12 (I(JP) = 1(2+)) production.

• 3 model parameters: σ-meson mass and width (presently known with a large uncertainty) and the relative weight of the amplitudes (a) and (b).

12

Dibaryon Model for the Basic 2π Fusion Reaction in the ABC Region

p

n d (D01)

ππ

D03

σ p

n d (D01)

π π

D03 D12

(a) (b)

1313

Results of the Model Calculations.I. Total Cross Section

Comparison with the WASA@COSY Experimental Data

1414

ABC peak

Each of two mechanisms proposedgives a resonance enhancement in the respective invariant-mass spectrum:• ABC enhancement is a consequence of σ-meson production;

• The peak in Mdπ spectrum reflects the isovector dibaryon D12 production.

Results of the Model Calculations.II. Invariant-mass spectra at E=2.38 GeV

Comparison with the WASA@COSY Experimental Data

1515

• The description of deuteron and pion angular distributions is not perfect, but still reasonable.

• Additional mechanisms, such as two uncorrelated pions production, other intermediate resonances and non-resonance contributions, should be considered for better description.

Results of the Model Calculations.III. Angular Distributions at E=2.38 GeV

Comparison with the WASA@COSY Experimental Data

1616

Results of the Model Calculations.IV. Energy Dependence of Mππ Spectrum

Comparison with the WASA@COSY Experimental Data

• When approaching the ΔΔ threshold (E=2.46 GeV), the Mππ spectrum gets closer to pp→dπ+π0 data (scaled to I=0 by isospin relations), described well by the ΔΔ model.

• The low-mass enhancement almost fully disappears.

New data from P. Adlarson et al., Phys. Lett. B721, 229 (2013):renormalized to σtot;

not fitted

2/5(pp→dπ+π0)

1717

• As extracted from our model fit to the ABC peak

• As found from dispersion analysis of ππ-scattering amplitude:

Is there any contradiction?

Parameters of σ-meson

300 MeV, 100 MeV.m

16 188 25441 MeV, 544 MeV.m

[I. Caprini, G. Colangelo, H. Leutwyler, PRL 96, 132001 (2006)]

[M.N. Platonova, V.I. Kukulin, PRC 87, 025202 (2013)]

1818

Chiral Symmetry Restoration• Numerous theoretical investigations (T. Kunihiro, M. Volkov, and others) show that the mass and

width of the σ meson produced in hot and/or dense nuclear matter may be significantly shifted downwards in comparison with its free-space parameters due to the partial Chiral Symmetry Restoration (CSR) effect.

• Partial CSR was demonstrated (L. Glozman et al.) to take place also in highly excited states of isolated hadrons (baryons and mesons). Thus, the appearance of approximately degenerate parity doublets in the spectra of highly excited baryons may be considered as a manifestation of partial CSR.

Temperature dependence of Mπ, Mσ and Γσ.[D. Blaschke et al., arXiv:0508264]

1919

In fact, the rise of baryon density or nuclear matter temperature as well as a high hadron excitation energy lead to an increase of quark kinetic energy, which results in suppression of the chiral condensate in QCD vacuum. This means the reduction of the σ-meson mass and width for the σ → ππ decay.

So, the σ meson, being a broad resonance in free space, may become a sharp resonance in dense/hot nuclear medium or highly excited hadronic states.

ρB

T Eh*

Eqkin qq m

chiral condensate – order parameter of a chiral phase transition

Γ(σ → ππ) mπ ≈ const!

quark kinetic energy baryonic density

and/or temperature

or hadron excitation energy

Chiral Symmetry Restoration

2020

• The D03 resonance:

1) dense quark matter (r(D03) ≈ 0.8 fm ↔ ~ 6 times normal nuclear density); 2) excitation energy of 500 MeV (above the deuteron).

• Dibaryon model of NN interaction predicts strong CSR effects even in a deuteron, i.e., its quark-meson component (due to 2ħω excitation of a mixed-symmetry 6q configuration s4p2 above a fully symmetric s6).

Thus, the CSR phenomenon is likely to occur in the D03 state and also in other dibaryons.

• If so, the σ meson produced from the D03 decay should have the lower mass and width than those for the free σ meson.

One can suggest that the low values for the σ-meson parameters extracted from the ABC peak indicate the partial CSR effect in excited dibaryon states.

Chiral Symmetry Restoration in Dibaryons

2121

Conclusions Within the σ-dressed dibaryon model, we succeeded in

description of numerous exclusive data on the basic two-pion production reaction p + n → d + (ππ)0.

The ABC effect, i.e., the low-Mππ enhancement, is interpreted as a consequence of the light scalar meson production, provided the chiral symmetry is partially restored in an excited dibaryon state.

This means the possibility to study the fundamental phenomenon of chiral symmetry restoration in few-body sector, through the production of light scalar mesons in N+N, N+d, etc., collisions at intermediate energies E ~ 1 GeV/u.

22

TThank hank YYou ou FFor or YYour our AAttention!ttention!