New Interpretation of the ABC Effect in Two-Pion Production in NN collisions Maria Platonova Lomonosov Moscow State University The 22 nd 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 3 He, located near the 2π threshold. 2 2 What is ABC Effect? Later on the similar enhancements were observed in the reactions np → dX and dd → 4 HeX. ABC anomaly: I(J P ) = 0(0 + ), m X ≈ 300 MeV Phase space pd → 3 HeX, I = 0

3 3 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 a s0 ≈ 2–3 m π -1. However: Actual ππ scattering length: a s0 ≈ 0.2 m π -1 ; No ABC effect in free ππ scattering and πN→ππN reaction. Prediction of a low-M ππ 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 dibaryon resonance D 03 with parameters: … and distinct correlation between the np resonance and ABC enhancement: 4 t-channel ΔΔ The first exclusive high-statistics experiments in full 4π-geometry New Exclusive Experiments of the CELSIUS-WASA and Collaborations D 03 : E = 2.38 GeV ABC: M ππ = 290 MeV ABC peak [P. Adlarson et al., PRL 106, , 2011]

5 5 The s-channel Resonance Ansatz Δ Δ d π π D 03 p n 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 D 03 →ΔΔ vertex is needed to reproduce the ABC enhancement. Such a low value of Λ means that D 03 is a deuteron-like object. This is incompatible with the observed large Δ-Δ binding in the D 03 state: ε B (D 03 ) ≈ 90 MeV. The value of Λ should be 2 times softer to reproduce ABC peak in dd → 4 He+(ππ) 0 with the same model. Microscopic quark model calculations predict a radius for the 0(3+) Δ-Δ bound state r(D 03 ) ≈ 0.7–0.9 fm, i.e., of the order of the nucleon size. The D 03 resonance appears to be the truly dibaryon state in which the quark cores of two Δ ’s are almost fully overlapped with each other.

6 6 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(D 12 ) ≈ 2160 MeV; M(D 03 ) ≈ 2350 MeV. The deuteron D 01 was positioned as NN S-wave dibaryon from the same SU(3) multiplet as D 03.

7 7 Indications of D 12 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 1 D 2 P are consistent with production of dibaryon resonance D 12 with quantum numbers I(J P ) = 1(2 + ), mass M(D 12 ) ≈ 2150 MeV and total width Γ(D 12 ) ≈ Γ(Δ) = 120 MeV. Argand plot of dominant partial-wave amplitudes in π + d → pp Contributions of dominant 1 D 2 P, 3 F 3 D and 3 P 2 D 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 D 12 and D 03 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 D 12 pole is located ≈ 20 MeV below the NΔ threshold ( 2170 MeV ) and the D 03 pole lies ≈ 100 MeV below the ΔΔ threshold ( 2460 MeV ). The deuteron, i.e., the NN S-wave dibaryon D 01, is located near the NN threshold. Let’s see what happens at short distances, when quark d.o.f. come into play. 8 8 A New Confirmation of Dibaryon Resonances D 12 and D 03 [A. Gal, H. Garcilazo, arXiv: ]

9 9 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 s 4 p 2 to a fully symmetric s 6 (in even NN partial waves): s 4 p 2 → s 6 + σ (L σ = 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 r NN ~0.7–0.8 fm. Within the dibaryon model, a very good description of NN-scattering phase shifts up to E N = 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. Ψ 6q+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 Ψ 6q+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 D 12 and D 03 dibaryons at short distances may be considered as dressed six-quark bags strongly coupled to NΔ and ΔΔ channels, respectively. 10

So, the dibaryon resonances D 12 and D 03 may be treated as excited states of the deuteron D 01, 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 D 03 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→D 03 →dππ invariant mass and angular distributions. However, we consider the last mechanism 1’) to be the dominant one close to D 03 peak energy (~2.38 GeV), since two Δ’s in D 03 are deeply bound and almost fully overlapped with each other, so the dibaryon configuration should be more probable here. 11 Decay Routes of the D 03 Resonance

12 We took the above decay routes 1’) and 2’) for D 03 resonance as a basis for our model of p + n → d + (ππ) 0 reaction in the ABC region (T p = 1.0–1.4 GeV) [M.N. Platonova, V.I. Kukulin, PRC 87, (2013)]. The D 03 (I(J P ) = 0(3 + )) dibaryon produced in p+n collision decays subsequently into the final deuteron (i.e., D 01 (I(J P ) = 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 D 12 (I(J P ) = 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 (D 01 ) π π D 03 σ p n d (D 01 ) ππ D 03 D 12 (a)(a)(b)(b)

13 Results of the Model Calculations. I. Total Cross Section Comparison with the Experimental Data

14 ABC peak Each of two mechanisms proposed gives a resonance enhancement in the respective invariant-mass spectrum: ABC enhancement is a consequence of σ-meson production; The peak in M dπ spectrum reflects the isovector dibaryon D 12 production. Results of the Model Calculations. II. Invariant-mass spectra at E=2.38 GeV Comparison with the Experimental Data

15 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 Experimental Data

16 Results of the Model Calculations. IV. Energy Dependence of M ππ Spectrum Comparison with the Experimental Data When approaching the ΔΔ threshold (E=2.46 GeV), the M ππ spectrum gets closer to pp→dπ + π 0 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 σ tot ; not fitted 2/5(pp→dπ + π 0 )

17 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 [I. Caprini, G. Colangelo, H. Leutwyler, PRL 96, (2006)] [M.N. Platonova, V.I. Kukulin, PRC 87, (2013)]

18 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 M π, M σ and Γ σ. [D. Blaschke et al., arXiv: ]

19 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. ρBTEh*ρBTEh* E q kin chiral condensate – order parameter of a chiral phase transition Γ(σ → ππ) m π ≈ const! quark kinetic energy baryonic density and/or temperature or hadron excitation energy Chiral Symmetry Restoration

20 The D 03 resonance: 1) dense quark matter ( r(D 03 ) ≈ 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 s 4 p 2 above a fully symmetric s 6 ). Thus, the CSR phenomenon is likely to occur in the D 03 state and also in other dibaryons. If so, the σ meson produced from the D 03 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

21 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- M ππ 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 Thank You For Your Attention!