Chiral Symmetry Restoration in σ-meson production in hadronic processes

Some puzzles about the nature and properties of the lightest scalar meson, σ or f 0 (500), are analyzed in the paper. We studied the σ-meson production both in N + N , N + d , etc., collisions and also in J /ψ, ψ(2 S ), ψ(3 S ), Υ(2 S ), etc., two-pion decays. The fundamental distinctions between the basic σ-meson parameters found in various hadronic processes can be explained most naturally by the chiral symmetry restoration in intermediate excited hadronic resonances. In the present paper we discuss some important aspects of chiral symmetry restoration in hadronic processes with interrelation to the basic features of QCD.

The riddle of σ-meson • Initially the σ particle, the lightest scalar-isoscalar meson, was predicted (long ago) to exist as a chiral partner of the Nambu-Goldstone π meson, corresponding to the dynamical breaking of chiral symmetry (conserving in the massless limit of QCD), with mass m σ ≈ 2m q (m q is the constituent quark mass).
• This σ meson gives quark constituent masses and thus it plays the role of the Higgs particle in QCD.
• From the other hand, the σ meson was predicted to play a key role in nuclear force at intermediate distances r NN ≤ 1 fm.
• Just the above light scalar meson exchange between two nucleons should lead inevitably to a strong NN attraction at r NN ≤ 1fm, if such scalar meson exists! However, from the ππ phase-shift analysis derived from CERN-Münich experiment of 1974 one observes rather smooth behavior of  0 0 phase in ππ scattering up to E ππ = 1100 MeV which seems hardly compatible with a well defined scalar resonance.
After subtraction of a rapid contribution of the scalar resonance f 0 (980) (180°) the δ 0 0 does not exceed 90°, being insufficient for existence of the ππ resonance around m = 2m q = 500 -600 MeV.
So, most analyses far made on it have yielded conclusions against the existence of σ! (Figure from S. Ishida hep-ph/9712229) 6 As a result, the light σ particle disappeared from the list of PDG since 1976 edition for more than 20 years! And the direct t-channel σ exchange also disappeared from the current theories of nuclear forces.
However, in many old and recent experiments one still observes a very large event concentration in I=0 s-wave ππ channel which cannot be explained as a simple "background" and seems to strongly suggest the existence of σ.  • So, all the different data for m σ and Γ σ are in a general agreement with each other, and also with the ππ PSA data.
• However, the scalar meson with the huge width Γ σ~ 400 -550 MeV is so short-lived that it is absolutely unable to carry a strong intermediate-range attraction between two nucleons postulated in traditional OBE-like models of nuclear force, because its free path should be only λ σ~ 0.2 fm!
-path length for a highly unstable σ-meson • To avoid this difficulty some authors (Riska, Brown, Dürso) "invented" a meson-exchange mechanism with two-Delta two-pion exchange: •

But this is only beginning of the long story…
The dominant contribution to a unified meson cloud of the 6q bag comes from σ meson due to its very strong attraction to 6q core.
Dressed six-quark bag

Nuclear force model based on dibaryon mechanism
• The dibaryon mechanism looks to be ideally suited to describe the shortrange NN force. It is because the mechanism assumes generation of the intermediate "long-lived" quark-meson states and such a resonance-like state will enhance somehow the short-range NN interaction.
• The particular short-range mechanism proposed by us in 1998 [V.I. Kukulin, in Proc. XXXIII PIYaF Winter School, S.-Petersburg, 1998, p.207]: or in graphic form: • The above mechanism replaces the conventional t-channel -exchange between two nucleons (which is meaningless at r NN < 1 fm) by the schannel exchange of the -dressed dibaryon.
• Such a mechanism, in accordance to general rules for the Feynman graphs, corresponds to a separable potential: corresponds to a transition vertex NN  D; g(k) is proportional to the overlap of NN wavefunction and six-quark wavefunction with symmetry |s 4 p 2 [42] L=0,2; ST>, and the energydependent coupling constant (E) corresponds to the intermediate dressed dibaryon propagation: • In case of two channels 3 S 1 -3 D 1 coupled by a short-range tensor force (which is originated from one-gluon exchange) one gets the two-channel separable potential (for non-relativistic case): , turns out to be a nodal function where the stationary node position at r n = r c coincides with the hard core radius r c = 0.5 fm accepted in conventional NN potential models, when we choose the six-quark bag radius b = 0.55 fm in a way to reproduce the low-energy spectrum of nucleon excitations. r c • It should be stressed that such a dibaryon mechanism with σ loops can be effective only if the mass of intermediate dibaryon dressed with the σ-meson cloud is rather low (M D~ 2.3 -2.5 GeV), otherwise the coupling constant λ NN→D (E) will be small and the probability of dibaryon generation will be insufficient to provide intermediate-range NN attraction! • However, if one takes the bare mass of the 6q bag (~2.7 GeV) + bare σ mass (~500 MeV), the total mass of the above σ-dressed dibaryon exceeds 3 GeV, and thus a dibaryon mechanism seems to be ineffective.
• To our fortunate, the situation is not so bad due to an effect of Chiral Symmetry Restoration (χSR) in highly excited hadrons proposed by Glozman and others quite recently.
• The physical origin of χSR effect is rather simple: when the quark kinetic energy inside hadron is rising, the quark condensate is diminishing (it gets "uncoupled" from valence quarks) and thus the quark mass goes down to the bare (current) one. So, the chiral symmetry of QCD which is broken at low energy (or zero temperature) gets restored.
• Due to (partial) χSR effect the masses of six-quark bag and σ mesons surrounding the bag get renormalized strongly, i.e., M 6q → 2.2 GeV, m σ → 300 MeV. So, the dressed dibaryon formation can occur with a sufficient probability to yield the effective intermediate-range • The χSR effect leads to appearance of degenerated parity doublets in hadronic spectra, i.e., the excited states with opposite parities but with the same spins are degenerated, or approximately degenerated (partial χSR).
• The first (approximate) parity doublet in nucleon spectrum is the Roper N* 1/2 + (1440) and N* 1/2 -(1535) states. The puzzle of the Roper resonance state (abnormally low mass of the second positive-parity state) is explained by the χSR effect.
• The approximate degeneration between the positive and negative parity levels with the same spin in nucleon spectrum can be considered as an indicator for the χSR effect.
See, e.g.: • The issue needs more detailed investigation.

χSR in excited hadrons
• In fact, the novel WASA@COSY experiments on pn → d + (ππ) 0 reaction are an exclusive version of the old inclusive experiments performed at BNL more than 50 years ago by Abashian, Booth and Crowe who found the famous ABC puzzle in the invariant mass spectrum of two outgoing pions.
• In the most theoretical works done for the passed 50 years the puzzle has been explained by the nearby ΔΔ threshold. However, the new exclusive experimental data occurred to be incompatible with such a model.
• But first of all the experimentalists from WASA@COSY Collaboration have found a very clear signal of the dibaryon resonance production.
• Since this resonance is located only 70 MeV below the ΔΔ threshold, it can be treated in a model of ΔΔ near-threshold bound state. • So, the experimentalists suggested a new model for the ABC puzzle based on the idea of the ΔΔ bound state. Unfortunately, their model includes a non-realistic very soft form factor for ΔΔ bound state and thus looks to be not quite consistent.  • Such a reduction for the σ-meson parameters may indicate the partial χSR effect in the 3 + 0 dibaryon state.

2.37
• The riddle of the σ meson is interrelated very closely with the χSR phenomenon in QCD. • The χSR effects have been studied by many authors both in dense (or hot) nuclear matter and in a single hadron when it gets strongly excited. • It should be stressed that the 3 + 0 dibaryon (which has been discovered in pn collisions at T p~ 1 GeV) with the mass M D 03 ≈ 2.37 GeV is in fact a strongly excited hadron (with the excitation energy E* ≈ 500 MeV) and the χSR phenomenon is predicted for such states rather reliably. • According to our model for the ABC puzzle, just this χSR phenomenon is seen in the near-threshold two-pion enhancement observed in ABC-type experiments. • We emphasize simultaneously that the low-lying dibaryons which drive the short-range nuclear force in our approach also correspond to χSR due to their inner excitation. • Thus, the σ mesons which dress the dibaryons must be lighter and narrower as compared to the bare σ mesons in ππ scattering in free space.
As summary, we can suggest that the nature of short-range nuclear force is based on Chiral Symmetry Restoration.

χSR in short-range nuclear force induced by intermediate dibaryons
So, our prediction for the χSR phenomenon in dibaryon states, and thus as a driving QCD mechanism for short-range nuclear force, can help establish a fundamental QCD origin for nuclear physics at all. "It is only by the collective analysis of all of these that we can hope to solve the riddle of the σ. It is a puzzle worth solving, since the nature and properties of the σ lie at the heart of the QCD vacuum." -M.R. Pennington, hep-ph/9905241 A. Andronic, P. Braun-Munzinger, J. Stachel Phys. Lett. B673, 142 (2009); nucl-th/0812.1186 "Thermal hadron production in relativistic nuclear collisions: the hadron mass spectrum, the horn, and the QCD phase transition" "In summary, we have demonstrated that by inclusion of the σ meson and many higher mass resonances into the resonance spectrum employed in the statistical model calculations an improved description is obtained of hadron production in central nucleus-nucleus collisions at ultra-relativistic energies." "It is interesting to note that central questions in hadron spectroscopy such as the existence (and nature) of the σ meson apparently play an important role in quark-gluon plasma physics. Our results strongly imply that hadronic observables near and above the horn structure at a beam energy of 30 AGeV provide a link to the QCD phase transition." 33 The (unexpected) role of σ meson in heavy-ion collisions at ultra-relativistic energies