Coherent dibaryons

TL;DR

This paper discusses experimental evidence and theoretical models for coherent dibaryons, which are excitations in compressed nucleon systems potentially representing coherent states of quark oscillators, with implications for baryon matter phase transitions.

Contribution

It introduces new models for the creation of coherent dibaryons and interprets experimental data as possible confirmation of these states.

Findings

Evidence from EVA collaboration supports quark oscillator excitations.

Models of coherent dibaryon creation are formulated.

Hints of phase transitions in baryon matter are discussed.

Abstract

There are encouraging evidences for registration of excitations of quark oscillator levels in compressed 2-nucleon systems, which were hidden in two independently published experimental works for many years. Data obtained by EVA collaboration can be considered as the third possible confirmation of this conjecture. Moreover, they drop hints about existence of coherent dibaryons which may be interpreted as usual or generalized coherent states of the oscillator. These data may also be an explicit example of a physical process described by Landau and Peierls in their reasoning concerning the energy-time uncertainty relation. Two models of the coherent dibaryon creation are formulated. Phase transitions of baryon matter in few-nucleon systems are discussed.

Equations

$${\mathbf{p}}^{cm}={\mathbf{p}}_f+{\mathbf{p}}_n,{\mathbf{p}}^{rel}={\mathbf{p}}_f-{\mathbf{p}}_n.$$

$${\mathbf{p}}_f={\mathbf{p}}_1+{\mathbf{p}}_2-{\mathbf{p}}_0.$$

$$⟨{\mathrm{p}}_z^{cm}⟩\approx 0,{\sigma }_z^{cm}\approx 0.1,⟨{\mathrm{p}}_z^{rel}⟩\approx 0.3,{\sigma }_z^{rel}\approx \mathrm{0.1.}$$

$$⟨{\mathrm{p}}_x^{cm}⟩\approx 0,{\sigma }_x^{cm}\approx 0.6,⟨{\mathrm{p}}_x^{rel}⟩\approx 0.6,{\sigma }_x^{rel}\approx \mathrm{0.2.}$$

$${\mathbf{p}}^{cm}={\mathbf{p}}_f+{\mathbf{p}}_n,{\mathbf{p}}^{rel}={\mathbf{p}}_f-{\mathbf{p}}_n+2\Delta {\mathbf{p}}_f,$$

$${\mathbf{p}}^{cm}=({\mathbf{p}}_f+{\mathbf{\Delta }}_f)+({\mathbf{p}}_n+{\mathbf{\Delta }}_n),$$

$$\Delta v_x=\hslash /(\Delta p_x\Delta t).$$

$$|({\mathbf{p}}_f-{\mathbf{p}}_n{)}_x|<|({\mathbf{p}}_f-{\mathbf{p}}_n{)}_z|$$

$$\alpha =({\alpha }_1,{\alpha }_2),a=(a_1,a_2),[n]=(n_1,n_2),[n]!=n_1!n_2!,$$

$$(a^{†}{)}^{[n]}=(a_1^{†}{)}^{n_1}(a_2^{†}{)}^{n_2},|[n]⟩=(a^{†}{)}^{[n]}|0⟩/\sqrt{[n]!}.$$

$$|\alpha ⟩=D(\alpha )|0⟩,D(\alpha )=\exp (\alpha a^{†}-{\alpha }^{\ast }a).$$

$$|\alpha ⟩=\exp \left(\alpha a^{†}\right)|0⟩=\exp \left(-{\left|\alpha \right|}^2/2\right)\sum _{[n]}\frac{{\alpha }^{[n]}}{\sqrt{[n]!}}|[n]⟩.$$

$$|[n]⟩\equiv a_1^{†n_1}{a}_2^{†n_2}|0⟩\otimes |0⟩/\sqrt{n_1!n_2!}.$$

$$a_{+}=(a_1+i{a}_2)/\sqrt{2},a_{-}=(a_1-i{a}_2)/\sqrt{2},$$

$$L_3=x_1{p}_2-p_1{x}_2=\hslash (a_{-}^{†}{a}_{-}-a_{+}^{†}{a}_{+})=\hslash (n_{-}-n_{+})$$

$$H=\hslash \omega (n_1+n_2+1)=\hslash \omega (n_{+}+n_{-}+1).$$

$$w_n=\exp (-{\left|\alpha \right|}^2)\sum _{n_i+n_j=n}\frac{{\left|{\alpha }_i\right|}^{2n_i}{\left|{\alpha }_j\right|}^{2n_j}}{n_i!n_j!},n=0,1,...$$

$$K=a_i{a}_j,K^{†}=a_i^{†}{a}_j^{†},K_0=\frac{1}{2}\left(a_i^{†}{a}_i+a_j^{†}{a}_j+1\right),$$

$$\left[K_0,K\right]=-K,\left[K_0,K^{†}\right]=K^{†},\left[K,K^{†}\right]=2K_0.$$

$$|\xi ⟩=D(\xi ){|0⟩}_k=$$

$${\left(1-{\left|\zeta \right|}^2\right)}^k\exp \left(\zeta K^{†}\right){|0⟩}_k={\left(1-{\left|\zeta \right|}^2\right)}^k\sum _{m=0}^{\infty }{\left[\frac{\Gamma (m+2k)}{m!\Gamma (2k)}\right]}^{1/2}{\zeta }^m|k,k+m⟩,$$

$$D(\xi )=\exp (\xi K^{†}-{\xi }^{\ast }K),$$

$$\zeta =\tanh \left(\left|\xi \right|\right)\exp (i\psi ),\beta =2\ln \cosh \left(\left|\xi \right|\right)=-\ln \left(1-{\left|\zeta \right|}^2\right),\gamma =-{\zeta }^{\ast }.$$

$$H|k,k+m⟩\equiv 2\hslash \omega K_0|k,k+m⟩=2\hslash \omega (k+m)|k,k+m⟩,m=0,1,...$$

$$w_m={\left(1-{\left|\zeta \right|}^2\right)}^{2k}\frac{\Gamma (m+2k)}{m!\Gamma (2k)}{\left|\zeta \right|}^{2m}.$$

$$w_m={\left(1-{\left|\zeta \right|}^2\right)}^2(m+1){\left|\zeta \right|}^{2m},$$

$$a^{†}\to a^{\prime †}=D^{†}(\alpha )a^{†}D(\alpha )=a^{†}+{\alpha }^{\ast },a\to a^{\prime }=D^{†}(\alpha )aD(\alpha )=a+\alpha .$$

$$H=\hslash \omega (a^{†}a+1)\to H^{\prime }=\hslash \omega ({a^{\prime }}^{†}{a}^{\prime }+1)=\hslash \omega (a^{†}a+1)+\hslash \omega \left[{\left|\alpha \right|}^2+(a^{†}\alpha +a{\alpha }^{\ast })\right].$$

$$\begin{array}[]{l}{a_{i}}\to{a_{i}}^{\prime}={a_{i}}\cosh\xi+a_{j}^{\dagger}\sinh\xi,\qquad a_{i}^{\dagger}\to{({a_{i}}^{\prime})^{\dagger}}=a_{i}^{\dagger}\cosh\xi+{a_{j}}\sinh\xi,\\ \hskip 2.84544pt{a_{j}}\to{a_{j}}^{\prime}={a_{j}}\cosh\xi+a_{i}^{\dagger}\sinh\xi,\qquad a_{j}^{\dagger}\to{({a_{j}}^{\prime})^{\dagger}}=a_{j}^{\dagger}\cosh\xi+{a_{i}}\sinh\xi.\end{array}$$

$$H=\hslash \omega (a^{†}a+1)\to H^{\prime }=\hslash \omega \left[2\cosh (2\xi )K_0+\sinh (2\xi )\left(K^{†}+K\right)\right].$$

Full text

1 Introduction

It was suggested in [1, 2] to use a cumulative particle (CP) as a trigger for a detection of the multibaryon (MB) production. Our estimations showed that appearance of CP is a signature of “deep cooling” of a multiquark system, which brings it close to its ground state and allows it to have a narrow width thereby giving a chance to separate MB from a secondary particle background. Another method of deep cooling was described implicitly in [3]. In this case, events of n-p interactions with sufficient numbers of secondary pions were selected and dibaryons were supposed to be observed as peaks on the plot of yield versus effective masses of outgoing p-p pairs. These data may be described by a simple formula $M_{2B}\approx M_{pp}+10n$ MeV, where $n$ is a positive integer. Although not each such $n$ was matched with a dibaryon in [3], it was natural to assume that they exist too but were not seen against the background.

The possibility of deep cooling by CP was checked using data of paper [4] in which a hint on existence of an “excited state of deutron” was noticed already in 1979. Our analysis showed [5, 6] that subtle contours of the dibaryon which was observed by WASA-at-COSY Collaboration [7] are seen indeed in a right place suggested in [4]. Hereafter these data are referred to as the Stavinskii group experiment (SGE) and data from [3] as the Troyan experiment (TE) data.

The main surprise waited for us in the range of two other peaks observed in SGE, which were never analyzed before but identified a priori with elastic d-d and d-N scattering. Calculations revealed this is definitely not so, and the peaks correspond very surprisingly to transitions between different dibaryons from TE [5, 6]. It will be shown below that an explanation of this unexpected result is connected with elucidation of a transverse momentum anomaly found out in data of EVA group [8] in paper [2]. All the facts in the aggregate will allow to assume a chance of experimental observation of phase transitions in two-nucleon systems.

2 Clarification from EVA experiment

We shall consider the total and relative momenta of intranuclear proton (IP) and neutron (IN) affiliated to a short range correlation (SRC), which are defined via momenta of IP and IN as follows:

[TABLE]

In the model of quasifree knockout (MQK), $\mathbf{p}_{f}$ may be expressed via momenta of the incoming proton and the secondary registered ones in the following way [8]:

[TABLE]

It is also assumed in MQK that IN leaves the target nucleus C12 without essential changes of the momentum $\mathbf{p}_{n}$ it had before the interaction.

It was shown in [8] that experimental data for longitudinal (along $\mathbf{p}_{0}$) components of $\mathbf{p}^{cm}$ and $\mathbf{p}^{rel}$ are in a good agreement with MQK and SRC. Our analysis of the data confirmed this conclusion and gave the following estimations for the values under consideration (hereafter all momenta are in GeV/c):

[TABLE]

Some additional work allowed us to obtain also similar estimations for the vertical, in the laboratory system, components of momenta and they turned out to be very different (see [2] for more details):

[TABLE]

Mathematical modeling in the frame of the intranuclear cascade model [9] did not reveal any visible influence of intranuclear scattering (see [2]) and then interaction between IP and IN was studied. It may be shown that in this case the formulas which were used in [8] for calculation of $\mathbf{p}^{cm}$ and $\mathbf{p}^{rel}$ by means of the external momenta $\mathbf{p}_{0}$, $\mathbf{p}_{1}$ and $\mathbf{p}_{2}$ give

[TABLE]

where $\Delta\mathbf{p}_{f}$ is a momentum transfer from IN to IP. Thus, the difference between $\left\langle{\mathrm{p}_{z}^{rel}}\right\rangle$ and $\left\langle{\mathrm{p}_{x}^{rel}}\right\rangle$ may be, in principle, explained by the IP-IN interaction which became involved.

A reason for the difference between $\sigma_{z}^{cm}$ and $\sigma_{x}^{cm}$ is not so trivial. Whereas $\sigma_{z}^{cm}$ is well explained by the intranuclear Fermi motion [2], large value of $\sigma_{x}^{cm}$ is provided by an unobvious quantum effect firstly noted by L.D. Landau and R. Peierls [10, 11]. The fact is that an attempt to measure $p_{x}^{cm}$ in the EVA experiment exactly coincides with the well-known Landau-Peierls gedanken experiment which demonstrates an inevitable influence of a momentum measurement procedure on a final value of momentum if the process lasts a limited time111A possible reason for finiteness of the interaction time is the localization of projectile’s wave function in a restricted domain of space. $\Delta t$. The corresponding momentum perturbation of SRC may be written in an explicit form as,

[TABLE]

where for a change of velocity of SRC, $\Delta\mathbf{v}=(\mathbf{\Delta}_{f}+\mathbf{\Delta}_{n})/(m_{f}+m_{n})$, we have $\Delta{v_{z}}=0$, since $z$-component of the total momentum is not measured, and

[TABLE]

The last expression contains $\Delta{p_{x}}$ which is a precision of measurement of $p_{x}^{cm}$. It may be estimated as $\sigma_{x}^{rel}=\left\langle{\left|{{\Delta_{fx}}-{\Delta_{nx}}}\right|}\right\rangle$. After substitution $\left\langle\Delta{v_{x}}\right\rangle=\sigma_{x}^{cm}/(m_{f}+m_{n})$ in (4), we find $\Delta t\sim 10^{-23}$ s and $\Delta E\sim\hbar/\Delta t=66$ MeV.

Now we can understand the reason for observation of excited deuteron levels in the Stavinskii group experiment. Indeed, due to Landau-Peierls uncertainty relation, masses of target and incident deuterons in the initial state were not fixed exactly and some of the excited dibaryon levels might show themselves in the peaks observed. Overwhelming contribution of projectile’s excited states as compared with target’s ones, which was established in [5, 6], may be a manifestation of the relativistic effect of time dilation that allows highly excited states to exist much longer in the incident deuteron (see section 5).

Kinematics of EVA experiment was designed to select events with

[TABLE]

due to a preferable choice of those of them in which IP was rapidly moving forward in the same direction as the incident proton (cross-section dependence on $\sqrt{s}$ described by the quark counting rules [12], [13] was used). Taking into account the last inequality and (1), (2), (3), we obtain $2\left\langle{\left|{\Delta{p_{fx}}}\right|}\right\rangle>0.3$. At the same time, validity of MQK for z-direction, which was established by EVA collaboration [8], gives $\left\langle{\left|{\Delta{p_{fz}}}\right|}\right\rangle\approx 0$. Significance and possible consequences of these two relations are discussed in next section.

3 Coherent dibaryons

The most important observation concerning the results of EVA is $2\left\langle{\left|{\Delta{p_{fx}}}\right|}\right\rangle>0.3$ in combination with the quasifree knockout in the longitudinal direction. This definitely implies impossibility to consider IP-IN interaction as elastic scattering initiated by previous elastic projectile-IP interaction. Indeed, in a case like that IP would obtain a recoil momentum directed in the transversal plane and thus should necessarily transfer to IN some longitudinal momentum. But experimentally we see something strictly opposite: the whole of momentum transfer is confined to the transversal plane. Therefore IP-IN interaction should propagate through a very unusual intermediate state which has such a property. This conclusion is in a qualitative agreement with the observation following from TE and SGE about dimensionality of the 6-q excited oscillator222Indeed, energy of the ground state of the oscillator should be equal to $\hbar\omega/2+\hbar\omega/2$ according to TE and SGE. Thus it might consist of one degree of freedom oscillating in 2-D space or of two independent 1-D oscillators. The ground state was observed as dibaryon with mass 1.886 GeV/c2 in [3] and may also be extracted from [4] as a particle X in processes: X+d $\to$ Y+d, d+X $\to$ d+d, d+X $\to$ X+d, X+X $\to$ X+d, X+X $\to$ Y+d (see [5, 6]).. We shall consider intermediate states appearing in EVA experiment as 2-D coherent excitations of quantum oscillator because they can maintain relative distance and momentum of colliding particles with maximal accuracy permitted by the uncertainty relation, $\Delta{p_{i}}(t)\Delta{x_{i}}(t)\sim\hbar$, and transfer them safely in 2-D kinematics to outgoing particles, thereby keeping their emission in the transversal plane. Thus glueing two nucleons into a single 6-quark system together with strong excitation of its inner oscillators seems to be the most plausible explanation of the EVA experiment puzzle.

Before discussing Glauber’s coherent state for 2-D oscillator, it is convenient to define some vector notations [14]:

[TABLE]

[TABLE]

The Glauber coherent state of 2-D oscillator may be written as a unitary transformation of the ground one,

[TABLE]

This expression can be transformed to

[TABLE]

Actually, (6) corresponds to two independent 1-D oscillators swinging along $x_{1}$- and $x_{2}$-directions, and

[TABLE]

It is also possible to define operators describing excitations with negative and positive helicities,

[TABLE]

accordingly. Corresponding basis vectors $\;\;\left|{[n]}\right\rangle=a_{+}^{{\dagger}{n_{+}}}a_{-}^{{\dagger}{n_{-}}}\left|0\right\rangle\otimes\left|0\right\rangle/\sqrt{{n_{+}}!{n_{-}}!}$ are eigenvectors of operators

[TABLE]

and

[TABLE]

Thus, it is possible to define Glauber’s coherent states with nonzero projections of orbital momentum along $x_{3}$-axis of two different quarks belonging to the same 6-q system.

Probabilities of registration of dibaryon lying on $n$-th oscillator level are

[TABLE]

Hereafter $i=1$ or $+$ and $j=2$ or $-$, correspondingly.

It is useful also to have explicit expressions for generalized coherent states [14] which may be observed experimentally as coherent dibaryons too. They should be considered as excitations above different ground states of oscillator, which are possible now and determined by different representations of $su(1,1)$ algebra. In this case, quants of excitations are created and annihilated in pairs and that is described by three generators of $SU(1,1)$ group:

[TABLE]

where

[TABLE]

These coherent states are also defined as a unitary transformation of one of the ground states,

[TABLE]

[TABLE]

[TABLE]

index $k=1,3/2,2,5/2,...$ determines a ground oscillator state,

[TABLE]

Energies of oscillator states are eigenvalues of the Hamiltonian,

[TABLE]

and the probabilities of the dibaryon observation are

[TABLE]

Taking into account [3, 4], we should choose $k=1$. Then

[TABLE]

where $\left|\zeta\right|<1$, see (10).

4 Coherent dibaryons and phase transitions

There is a natural correlation between coherent states and phase transitions, which becomes apparent if we shall study metamorphoses of the oscillator Hamiltonian under unitary transformations $D(\alpha)$ and $D(\xi)$ defined above by (5) and (9). Good explanatory comments concerning calculations in this section can be found in [15].

Transformation of creation and annihilation operators corresponding to (5) is the following (in vector notations):

[TABLE]

This alteration leads to a change of the oscillator Hamiltonian,

[TABLE]

Thus we see that the Hamiltonian gains two additional terms $\hbar\omega{{\left|\alpha\right|}^{2}}$ and $\hbar\omega({a^{\dagger}}\alpha+a{\alpha^{*}}).$ The first of them may be interpreted as energy spent on creation of a complex field $\alpha$ (quantum condensate), the second one describes an interaction between oscillator excitations and this new field. In the general case, energy of the system varies due to the transformation (5) which therefore may be interpreted as describing a phase transition of the first order.

Unitary transformation ${a^{\dagger}}\to{a^{\prime{\dagger}}}={D^{\dagger}}(\xi){a^{\dagger}}D(\xi)$ and $a\to a^{\prime}={D^{\dagger}}(\xi)aD(\xi)$ with $D(\xi)$ described by (9) gives the Bogoliubov transformation for Bose operators [16],

[TABLE]

Then the oscillator Hamiltonian takes the form:

[TABLE]

In the limit $\xi\to 0$, we have $H^{\prime}=2\hbar\omega{K_{0}},$ in line with (11). Subject to this extreme condition, we can identify ground state ${\left|0\right\rangle_{k=1}}$ of $su(1,1)$ oscillator with state $\left|0\right\rangle\otimes\left|1\right\rangle$ of the usual 2-D oscillator, since it satisfies the necessary characteristic properties of ${\left|0\right\rangle_{k=1}}$:

[TABLE]

So far as oscillator excitations are produced now by pairs, the spectrum doubles (phase transition of the second order). In the general case, when $\xi\neq 0$, relations (12) describe a first-order phase transition. It ends with nontrivial renormalization of spectrum and creation of a quantum condensate $\varphi=\sinh(2\xi)$ which interacts with pairs of oscillator excitations. This phase transition occurs after the minimal excitation of one of the oscillators, $\left|0\right\rangle\to{\left|0\right\rangle_{k=1}}$. Experiments [3, 4] allow existence of these processes with small values of $\varphi$.

There is a difference between phase transitions in macro- and microsystems. An amplitude $\alpha$ of coherent state $\left|\alpha\right\rangle$ may be interpreted as a macroscopic field only in the limit of large average number of excitations. Otherwise it seems that a possibility of observing superpositions of coherent states with different amplitudes may exist333One special case of superposition of $N$ Glauber’s coherent states was considered in [17].. Then for Glauber’s coherent states, we should take instead of (6):

[TABLE]

where ${C_{i}}({\mu_{i}})$ and ${C_{j}}({\mu_{j}})$ describe the superposition supposed, and $\alpha=\chi{\mu_{i}}$, $\chi=i$ or $-1$, $\mu$ is a real number. It is obvious,

[TABLE]

where ${\tilde{f}}_{i}$ is Fourier or Laplace transform of ${C_{i}}({\mu_{i}})\exp(-\mu_{i}^{2}/2).$ The generalized coherent states can be modified similarly using (8).

5 Discussion and conclusion

In this paper we have inverted the conventional logic of utilization of canonical transformations in theory of phase transitions. Usually they are applied for diagonalization of a model Hamiltonian and estimation of its spectrum. Here we assumed that the oscillator spectrum and coherent states were indeed disclosed in [3, 4, 8] for search of non-diagonalized Hamiltonian which might generate the states hypothetically detected.

Although none of the discussed experimental papers [3, 4, 8] contains sufficient grounds for the definite conclusion about existence of oscillator excitations in 6-quark systems, interconnections between them appear striking. For example, let us estimate numbers of levels observed in [4] using the measurement time determined in [8]. We can hope for nearly the same value of the measurement time, though the measurement of momentum of p-n pair is performed444For a quantum measurement of the required type to be carried out it is sufficient that an information about stopping power of secondary particles to be stored in an environment. A person may neither participate in making measuring apparatus nor in observing results. According to R. Feynman, it is quite enough that “nature knows” [18]. by scattering accelerated deuteron in [4] rather than proton in [8]. Then the Landau-Peierls uncertainty relation tells us that we can observe 6-7 oscillator levels in target deuteron and, due to the relativistic effect of time dilation, 32 levels in incident one. In [5, 6], there were found 31 consecutive levels of the second type in agreement with this estimation and only 2 of the first type. It seems that the residual 4-5 of them were lost because of the SRC-d scattering dominance over SRC-SRC one at least at the experimental conditions in [4], where the recoil deuterons were registered.

An alternative explanation of the number of the levels observed in [4] is identification of $10^{-23}$ s with a time of the excitation energy transfer through SRC with subsequent repeating the previous estimations. It is worth noting in this connection that data obtaining during JLab Hall A experiment [19] can convince us even more easily than the EVA data in existence of this energy transfer. Indeed, it is possible to check that without this assumption a situation shown in Fig. 1 of [19] corresponds to violation of the energy conservation law at a level of 294 MeV.

Relying on the facts discussed above, it is reasonable to assume that phase transitions of baryon matter can be observed at light nuclei interactions as well as at heavy ions collisions usually considered. As far as this important assumption is based on the results of only 3 experimental papers [3, 4, 8], they should be verified once again with an accuracy maximum possible to enhance reliability of the assertion. In any case, the surest method to recognize what nature really knows is to ask nature itself about that.

The assumption that the Landau-Peierls phenomenon has something to do with an explanation of the EVA experiment [8] is the most unexpected one in this paper. It has nevertheless a chance of success, though nothing like that was observed by the JLab Hall A Collaboration [19], where a more convincing method of finding $\mathbf{p}^{cm}$ was used. The fact is that beams with very different wave packets of projectiles were employed in [8] and [20]. According to [21] and [22], $(\Delta p/p)_{EVA}=5$ $10^{-2}$ and $(\Delta E/E)_{HallA}=10^{-4}$, accordingly. This means that localization in space $\Delta x\sim\hbar/\Delta p$ of wave packets of projectiles was different in these experiments and thus the time of Landau-Peierls measurements might be different. Using well-known properties of the Fourier transformation, it is easy to check that the localization of projectile electrons in JLab experiments was large than 214 fm. Concerning the BNL beam for EVA we can only say that it might be more than two order less, though a more exact estimation require solving a difficult quantum state tomography problem.

In one of a recent review [20], representatives of the EVA and JLab Hall A Collaborations arranged to take for granted that the total momentum of the intranuclear pair observed by EVA conforms to that observed by JLab. Our analysis revealed that this assumption leads to a distinct worse agreement between simulated events and data of the EVA experiment, see [2]. However, it is more important that even in that case we still should agree with the conclusion about exactly the same values of momentum transfer through SRC pair in the transverse plane (see [2] for more details). Existence of this momentum transfer (coupled with quasi-free knock-out in the longitudinal direction observed in [8]) is the main experimental evidence for the conclusion about the possibility of the coherent dibaryon excitation inside n-p SRC.

The review [20] together with a recent publication [23] suggests an important development of the previous version of the SRC model due to L. Frankfurt and M. Strikman [24]. This change requires comparison with a consideration in the present paper and deserves inserting the renovation into a general context of already existing physics. The main assertion in the new version of SRC model is a recognition of the fact that “nucleons are modified substantially when they fluctuate into SRC pairs” [23]. Authors of [20] rename the previous version of the SRC correlations into 2N-SRC ones, or two-nucleon clusters, and reserve the name SRC correlations for the new hypothetical objects. The renaming like that is hardly reasonable and may lead to a confusion. Logically, it would be better to save the old name for the Frankfurt-Strikman SRC and to give a new denomination to the new objects. Since the suggested fluctuations of the nuclear density are supposed to have modified quark momentum distribution which is the characteristic property of the fluctons [25, 26, 27, 28, 29, 30], that makes sense to designate them as the flucton phase of the SRC pairs.

It is also important to note that the new ground state fluctuations in nuclear matter were reported to be found in neutron-proton SRC pairs only, see [23]. According to the present paper, the coherent 6-q states which might be observed in the EVA experiment were excited in n-p SRC pairs too, after their interactions with the projectile protons. This gives a hint that the coherent dibaryons are excited states of the ground state fluctuations suggested by the CLAS Collaboration. Besides, quarks oscillator levels, existence of which are the necessary condition for existence of the coherent dibaryon, were presumably observed by Baldin et al. [4] also in n-p systems after hard scattering the projectile off it. The same levels as in [4] were also observed after “deep cooling” of highly excited n-p systems by secondary pions in [3]. That all leads us to one more possible explanation of the difference between the results of the EVA and JLab Hall A collaborations experiments different from the Landau-Peierls mechanism suggested above. Indeed, it is rational to assume that the flucton phase which is allowed only in neutron-proton SRC is characterized by a more intense interaction with the residual nucleus than the usual SRC and therefore by a wider momentum distribution in the transverse plane. Now such an explanation can be considered as alternative to the Landau-Peierls mechanism.

In conclusion, investigation of SRC persists to be an actual branch of physics containing many unsolved puzzles. Recent developments show that it also opens the door into the area of phase transitions in hadronic matter. Interrelations found in the present paper inspire exploration of the n-p systems first of all to obtain information about the 6-q system in its ground and excited states.

Acknowledgment

I thank my co-authors J. Pribiš and V. Filinova which assisted me with numerical calculations in an early stage of the study. Valuable remarks of S.S. Shimanskiy are gratefully acknowledged. I dedicate this paper to M.Z. Yuriev for many valuable discussions.