Energy and mass dependencies for the characteristics of p_T regions observed at LHC energies
SSciPost Physics Submission
Energy and mass dependencies for the characteristics of p T regions observed at LHC energies. Mais SuleymanovBaku State UniversityZ. Khalilov 23, Baku Azerbijan* [email protected] 2, 2021
Abstract
The p T distributions of the K - and φ - mesons produced in the pp collisions at √ s = 2 . T eV have been analyzed by fitting them using the exponential function.It was observed that the distributions contain several p T regions similar to thecases with the charged particles, π - and η - mesons produced in the same events.These regions could be characterized using three variables: the length of theregion L cK and free fitting parameters a cK and b cK . It was observed that the valuesof the parameters as a function of energy grouped around certain lines and thereare jump-like changes. These observations together with the effect of existing theseveral p T regions can say on discrete energy dependencies for the L cK , a cK and b cK .The lengths of the regions increase with the mass of the particles. This increasegets stronger with energy. The mass dependencies of the parameters a cK and b cK show a regime change at a mass (cid:39) M eV /c . According to the phenomenologyof string theory, these results could be explained by two processes occurringsimultaneously: string hadronization and string breaking. In the experimentwe can only measure the spectrum of the hadronized particles, since we cannotaccess the spectrum of the strings themselves. The string breaking effect couldbe a signal of string formations and the reason behind the observation of several p T regions and the jump-like changes for the characteristics of the regions. In the paper [1] authors argue that p T distribution data from the LHC on invariant differentialyield of the charged particles produced in pp collisions at √ s = 0 . T eV, . T eV, T eV andin
P b − P b collisions at √ s NN = 2 . T eV with six centrality bins contained several p T regionswith special properties. Similarly, the results presented in the paper [2] show the inclusive p T spectra of the π - and η - mesons produced in the pp collisions at LHC energies were composedof several p T regions . The regions could be characterized by the length L cK (see footnote The result was obtained by fitting the distributions, taking into account the errors in both axes (it was usedthe ROOT soft, version 5.34/02, 21st September 2012) how they are presented on the sites of hepdata. The p T distributions were fitted by the exponential function ( y = a cK e b cK p T , a cK and b cK are free fitting parameters,upperindexes c (see Table I) show the type of event to which the region applies and lower ones K ( K = I for thefirst region, K = II for the second one etc.) indicate the number of the region) in the intervals of p T between: a r X i v : . [ h e p - ph ] J a n ciPost Physics Submission
1) and two free fitting parameters a cK and b cK (upper indexes c show the type of events towhich the region applies (see Table 1) and lower ones K indicate the number of the region, seefootnote 1). It was observed that the values of the L cK increase with p T . The regions can beclassified into two groups depending on the values of the L cK , a cK and b cK . The values of the L cK and b cK for the first group don’t depend on the collision energy and the type of the particles,even though the values of a cK increase linearly with energy, whereas the characteristics inthe second group of regions show strong s -dependencies. It was found [2] that the ratio ofthe lengths (in case of the II regions) for the η -mesons ( < L η > ) to one for the π - mesons( < L π > ) produced in the pp collisions at 8 TeV is approximately equal to the ratio of theirmasses ( m η and m π respectively): < L η > : < L π > (cid:39) m η : m π . Assuming that the valuesof the L cK are directly proportional to the string tension, the result could be considered as asmoking gun for parton/string fragmentation dynamics. We propose this explanation since instring theory the masses of elementary particles and their energies are defined by the intensityof string vibration and strangeness of the string stretch, which are depend by the tension ofstrings. The increase in the lengths for the η -mesons’ regions is accompanied by an increaseof the values for the parameter b cK . Considering that Q (cid:39) / ( b cK ) they calculated the valuesof the α S for the p T regions and got that the values of α S decreased with p T [1]- [2]. Thesestudies have concluded that the η -mesons were produced at smaller values of α S comparedwith Table 1: energy(TeV) → particles ↓ chargedparticles 3 1 4 5 π -meson 31 11 41 51 η -meson 32 12 42 52 K -meson - 13 - - φ -meson - 14 - - that for π -mesons. The results show that for the first group of regions the lengths of theregions are 3-5 times greater than the lengths of neighboring lower p T regions. For the secondgroup of regions the lengths of the regions are 1-2 times greater than the lengths of neighboringlower p T region. In the framework of the string fragmentation and hadronization dynamicsthis could mean that the particles in the group I are produced from the previous generationsof strings decaying into ∼ ∼ p T distributions of the particles produced in the pp collisions at LHC energies using the technique applied in the Revs. [1]- [2]. We have analyzedthe data presented in the paper [3] on p T distributions of K - and φ - mesons produced inthe pp collisions at √ s = 2 .
76 TeV with the goal of acquiring additional information about p minT ÷ p maxT , here the p minT and p maxT are the minimum and the maximum values of p T , obtained as a resultof variation of p T values to get the best fitting results. The values of p T for the boundaries of the regionsfor fitting J cK are marked for I and II regions as J cI − II , for II and III ones as J cII − III and for
III and IV regions as J cIII − IV . The values of the J cK were used to calculate the lengths of the regions L cK as L cI = J cI ; L cII = J cII − III − J cI − II and L CIII = J cIII − V I − J cII − III . ciPost Physics Submission the energy and mass dependencies of the characteristics of the p T regions: L cK , a cK and b cK (for the K - and φ - mesons produced in pp collisions at 2.76 TeV the index c =13 and 14,see Table 1). Fig. 1 shows the invariant cross sections for the charged particles, π - , η -, K - and φ -mesons (index c =1, 11, 12, 13 and 14 respectively, see Table 1) production in pp collisionsat 2.76 TeV [3]- [5]. Actually, this is same figure as the figure 4 in the paper [2] with theaddition of the new data on p T -distributions of the K – and φ -meson and recalling the datausing the multiplier 10 n (the values of n are different for the different cases ( c ) in the figure).Apparently, there no any essential differences between the distributions. However, the resultsof fitting these distributions indicate some existing differences. The Table 2 shows the bestfitting results for these distributions .One can see from the data in theFigure 1: The invariant cross sections for the charged particles, π - , η -, K - and φ - mesons(index c =1;11;12;13;14 respectively, see Table 1) production in pp collisions at 2.76 TeV [1]- [3].table that p T distributions of invariant differential yield of the K - and φ - mesons producedin the pp collisions at √ s =2.76 TeV contained as well as the charged particles, the π - and η -mesons produced in the same events several p T regions with different values of L cK , a cK and b cK . Taking into account the results coming from the papers [1]- [2] on the p T distributionsof the charged particles, the π - and η - mesons and the new data coming from the Table 2for the K - and φ - mesons we have analyzed the energy and mass dependencies of the p T In the Table 2 the values of the parameter a cK (for the case of c =1) were multiplied to the cross sectionof inelastic charged particle production ( σ inel ) in the collisions, the values of the σ inel = 60 mb had been takenfrom Fig. 1 in the paper [6]. ciPost Physics Submission regions’ parameters to reach the aim of paper: to get an additional information on the energyand mass dependencies of the characteristics of the p T regions.Table 2: The best fit results c ↓ K → I II III c = 1 p minT p maxT J cK L cK χ /ndf;Prob. a cK (pb GeV c ) b cK (GeV/c) − (0.53 ± ÷ (3.0 ± J I,II =(3.6 ± (3.6 ± ± ± (4.2 ± ÷ (18.0 ± J II,III = (21.6 ± (18.0 ± ± ± (25.2 ± ÷ (99.3 ± J I II,IV =(100.0 ± (78.4 ± ± ± c =11 m π =0.135GeV/ c p minT p maxT J cK L cK χ /ndf;Prob. a cK ( pbGeV c ) b cK (GeV/c) − (0.5 ± ÷ (3.2 ± J I,II =(3.5 ± (3.5 ± ± ± (3.7 ± ÷ (14.9 ± J II,III =(15.9 ± (12.5 ± ± ± (16.9 ± ÷ (37.3 ± J III,IV =(-) (-)1.126/4;0.8901(3.2 ± ± c = 12 m η =0.548GeV/ c p minT p maxT J cK L cK χ /ndf;Prob. a cK ( pbGeV c ) b cK (GeV/c) − (0.7 ± ÷ (3.4 ± J I,II =(4.1 ± (4.1 ± ± ± (4.8 ± ÷ (13.7 ± J II,III =(15.8 ± (11.7 ± ± ± (17.8 ± ÷ () J III,IV =- ---- c =13 m K =0.498GeV/ c p minT p maxT J cK L cK χ /ndf;Prob. a cK ( pbGeV c ) b cK (GeV/c) − (0.0 ± ÷ (4.75 ± J I,II =(5.1 ± small(5.1 ± ± ± ± ÷ (18.0 ± J II − III =(21.6 ± (18.0 ± ± ± (5.5 ± ÷ (12.5.3 ± J III,IV = - -1.282/3;0.7334(1.4 ± ± c =14 m φ =1.020GeV/ c p minT p maxT J cK L cK χ /ndf;Prob. a cK ( pbGeV c ) b cK (GeV/c) − (0.5 ± ÷ (5.5 ± J I,II =(6.0 ± (6.0 ± ± ± (6.5 ± ÷ (18.5 ± J II − III =- -1.045/4; 0.9029(1.3 ± ± (17.8 ± ÷ () J III,IV =- ---- The Fig. 2 shows the energy dependences of the values of L cK ( I p T regions’ length) forthe charged particles, π -, η -, K - and φ -mesons produced in the pp collisions. The linesin the figure have been drawn manually. One can see that all points relevant to values ofthe L cI lie on 5 lines at L cI (cid:39) √ s = 8 TeV whereas the valuesof the L I decrease from the values of 3.7 GeV/c and occur on line at the level 2.25 GeV/c.For the values of L cI in case of π -mesons the s -dependence starts to observe at √ s =7 TeV.The corresponding points for the values of L cI at 7 and 8 TeV move from the line at level3.7 GeV/c to one at levels 2.55 GeV/c and 2.25 GeV/c again jump-like. The values of L cI for the η -mesons are on the line at level 3.7 GeV/c for the √ s = 2.76 TeV. With increasingthe energy in the interval of √ s = 7-8 TeV the values of the L cI for the eta mesons increasejump-like and occur on the line at the level 5.0 GeV/c and 6.4 GeV/c. The values of the L I ciPost Physics Submission Figure 2: The energy dependences of the values of L cK ( I p T regions’ length) for the chargedparticles, π -, η -, K - and φ -mesons produced in the pp collisions at the LHC energiesfor K -mesons and L I for φ -mesons are on the line at level 5.0 GeV/c and 6.4 GeV/c too.One can conclude that with energy the values of L cI , in the interval of: √ s ≤ π -, η -mesons; as soon as the energy reaches thevalues of √ s =7 TeV the values of L cI for all charged particles and π -mesons decrease thoughfor the η - mesons the values of lengths increase jump-like. If we take into account that themass of the η -, K - and φ - mesons much more than the average mass of all charged particles(produced in pp collisions) and π -mesons, so it can then be concluded that the p T regions’lengths change jump-like in the interval of energy √ s ≥ II p T regions’ lengths for the charged particles, π - and η -mesons produced in the pp collisions are shown in the Fig. 3. One can see that all definedvalues for the lengths are approximately on 3 lines at level L cII (cid:39) L cII for all charged particles do not depend on energy in the intervalof √ s ≤ √ s = 8 TeV. Whereas, the values of lengthfor the charged particles move from line at L cI (cid:39) L cII (cid:39) π -mesons we had 3 points for the values of lengths, for √ s = 2.76 TeVthe values of L II are on the line at L cII (cid:39) √ s = 7 TeV the values of L II are on the line L cII (cid:39) √ s = 8 TeV the values of L II do on the line L cII (cid:39) √ s = 8 TeV ( L II ) is on theline L cII (cid:39) L II > L II which means that the lengths of the IIp T regions for the eta mesons are greater than for the neutral pions. Again it can be notedthat there is jump-like energy dependence of the lengths for II p T regions - discrete energydependence. 5 ciPost Physics Submission Figure 3: The energy dependencies of the values of L cII ( II p T regions’ length) for the chargedparticles, φ - and η -mesons produced in the pp collisions at the LHC energies.The Fig. 4 shows the energy dependences of the values of the lengths for the III and
IV p T regions for the charged particles and π -mesons produced in the pp collisions. Thelines in the figure have been drawn manually. These show that the all values of the L cIII − IV roughly lie down on 3 lines at L cIII (cid:39) L III (cid:39)
II p T regions (see previous figure) and the linesat L IV (cid:39) I p T regions (see Fig. 2). The last again couldbe considered as a signal on discrete changes with energy for the lengths of the p T regions.So it can be concluded that with energy the lengths of the regions change jump-like,whereas the lengths for the light mesons decrease and these are increased for the heavy mesons.The last result is seen more cleanly from the Fig. 5, which shows the mass dependence forthe values of L cK (in cases 2 or more points in the distributions). The lines have been drawnmanually. One can see that with mass (in the I p T region at √ s = 2.76 TeV) the values ofthe lengths increase slowly and in the II p T regions at √ s =2.76 TeV (we have had only 2points) the values of the lengths show an independence on mass. At √ s = 7 TeV the valuesof L cK increase sharper than at 2.76 TeV , gets more strong at energy 8 TeV and the relationholds: < L η > : < L π > (cid:39) m η : m π (which was observed in the paper [2]). The dependenciesof the lengths of p T regions on the mass of particles and the strengthening of this dependencewith increasing energy of colliding protons and the result on < L η > : < L π > (cid:39) m η : m π together with jump-like energy dependencies can be arguments in favor of string theory.The energy dependencies for the parameters a cI ( I p T regions) are shown in the Fig. 6.It can be seen from the figure that the values of a cI for charged particles and π - mesonsincrease with energy. We tried to fit these distributions by the function: y = gs n ( where g The parameter a cK has unit pb GeV − c ciPost Physics Submission Figure 4: The energy dependences of the values of L cK of the III − IV p T regions’ lengths forthe charged particles, π - and η -mesons produced in the pp collisions at the LHC energies.and n are free fitting parameters) . The results of the fitting are shown in Fig. 6 (and inTable 3). It turned out that the distributions for charged particles fitted well by functionsof: y = 2 . s . ± . , and the data for π -mesons are in satisfactory agreement with thefunction : y = 4 . s . ± . only at energies of 0.9–7.0 TeV. At the energy 8.0 TeV, anincrease in a cK is observed and the corresponding point moves and how would it “jumps” onthe line y = 2 . s . ± . . We see again like in case of lengths the jump-like changing forthe parameter a cK in the I p T region. For the values of a cI in the case of η -mesons from region I , we had 3 points (at energies 2.76, 7 and 8 TeV) only. The result of fitting these data by afunction: y = 4 . s . ± . (only for two points corresponding to energies 2.76 and 7.0 TeV)is shown in the figure by a dashed line ( in the Table 3). As the energy increases to 8 TeV,the values of a I decrease and do not lie on the line: y = 4 . s . ± . . The point occurson the line describing by the function y = 2 . s . ± . (which describes well the energydependence of the parameter a cK for the neutral pions from II p T regions , see Fig. 7). It isinteresting that the single points for the values of a cK for K - and φ - mesons (at 2.76 TeV)are on the line: y = 4 . s . ± . too.Thus one can say that the values of the parameters a cK as a function of energy are groupedaround 4 lines with a power-law dependence on energy and show jump-like behavior at highenergy as a signature to discrete changing. The data on a cK for charged particles from the II region of p T (Fig. 7) were well fitted by a function: y = 8 . s (0 . ± . in the energy range0.9–7.0 TeV(the fitting results are shown in the Fig. 7), but the data for energies of 8 TeVstrongly deviate from this dependence, this point is close to the line: y = 2 . s (4 . ± . . We could not get satisfactory results for fitting (due to the small number of fit points). Therefore, we fixedthe values of g and found the values of n , then we fixed the found values of n and refined the values of g .Thus, we chose the values g and n . ciPost Physics Submission Figure 5: The mass dependences for the regions’ lengths.For neutral pins from this region, a satisfactory fit was obtained using a function: y =4 . s (5 . ± . . Here one can see a very strong dependence of a cK on energy. In the caseof η -mesons from the II p T region, we have only one point for the value a cK at an energy of8 TeV (it is approximately on the solid line at the level of 6.5 10 ). For the values of a cK of K - and φ - mesons from the second p T region, we also had one point at energy of 2.76 TeVand we can write that a II (cid:39) a II (cid:39) a II (we recall that here the a II , a II , a II are the values ofthe free fitting parameter a cK at an energy of 2.76 TeV for neutral pions, K - and φ - mesas,respectively, from the second p T region).For the 3 rd p T regions (see Fig.7) there have not had even 3 defined points for the valuesof a cK , and only in the case of charged particles the values of the a cK were determined at twoenergies: 2.76 and 7 TeV. It can be seen that the values of a cK decrease with energy (thedistribution was fitted by the function: y = 2 . s − (4 . ± . . Let us recall that the lengthsof the regions in this case did not change.For the case of π -mesons from the III p T region wehave had one point only (at energy 8 TeV, which is around the level a cK (cid:39) . ). There isa single point for the IV p T regions’ pions (it is around the values of a cK (cid:39) . ,see Fig.7).The energy dependences for the parameters b cK are shown in the Fig. 8 for the I p T regions’ data. To fit the distributions, we have used the function y = gs n (the results ofthe fitting are in the Table 4). One can see (from the Fig.8 and Table 4) that for chargedparticles from the I p T region, the values of b cK are almost independent of s and lie on the line y = (3 . ± . s ( − (0 . ± . s ∼ =0.9-8 TeV and for the π -mesons from this region, the values of b cK depend on s as y = (2 . ± . s (0 . ± . which is very close to one for thecharged particles. The data on b cK for the η -mesons from the I p T region shows the behaviorwhich could describe by function y = (4 . ± . s − (0 . ± . at s ∼ = 2.76-8 TeV. In this regionsfor K - and ϕ -mesons we have had only one point which are at the intersection of two linesdefined by functions : y = (3 . ± . s − (0 . ± . and y = (2 . ± . s (0 . ± . .8 ciPost Physics Submission Figure 6: The energy dependences for the parameters a cI ( I p T regions).The Fig . 9 shows the energy dependencies of the b cK for the particles from the II, III and
IV p T regions. One can see that for the charged particles, the values of b cK dependweakly (see Table 4 ) on s and lie on the line of y = (0 . ± . s − (0 . ± . at s ∼ = 0.9-7TeV, an energy dependence is observed at transition to the area of energy 8 TeV, whereasthe values of the b cK increase jump-like and is on the line y (cid:39) (0 . ± . s (0 . ± . . Thisline was found for the values of b cK in case of neutral pions at the energies 2.76-8 TeV. Thevalues of b cK for III region charged particles show non dependence on energy and lie on the y = (0 . ± . s (0 . ± . at the energies 2.76-7 TeV. In the cases of : III and IV regions forneutral pions; II region for eta mesons ; II regions for K - and φ -mesons we have had onlyone point.The above results for the behaviors of parameters b cK indicate that in the interval of s > b cK . In thepaper [1]- [2] it has been discussed that the observed p T regions at LHC could relate to thestring dynamics of fragmentation hadrons and hadronization of partons. For the neutral pionsthe values of b cK increase with s but for the eta mesons ones decrease with energy. As it hasbeen discussed in the paper [1] the parameter b cK might connect with the distance betweenpartons in the parton strings that is why the result can mean that eta mesons due to strangequarks containing produced in the shorter distance then the distance of the neutral pionsproduction.Fig. 10 shows the energy dependencies, of the lengths L cK multiplied by the values of thefree fitting parameter b cK in the same regions ( L cK ∗ b cK ) for the charged particles, π - , η -, K - and φ - mesons produced in pp collisions at LHC energies . It can be seen that withenergy, the values of L cK ∗ b cK for most of cases remain unchanged at the level of L cK ∗ b cK ∼ = 11. The data for the charged particles were taken from the paper [1] and the ones for the π - and η − mesonswere done from the paper [2] ciPost Physics Submission Table 3:I II III y y = 2 . s (0 . ± . y = 8 . s (0 . ± . y = 2 . s − (4 . ± . ch s χ /ndf ; P rob. y y = 4 . s (0 . ± . y = 2 . s (4 . ± . - π s - χ /ndf ; Prob. 1.991/2; 0.3695 0.6158/2 ; 0.735 - y y = 4 . s (1 . ± . - - η s - - χ /ndf ; P rob. y y = (3 . ± . s (0 . ± . y = (0 . ± . s − (0 . ± . y = (0 . ± . s (0 . ± . ch s χ /ndf;Prob. 6.828/3 ; 0.07758 1.011/1;0.3147 - y y = (2 . ± . s (0 . ± . y = (0 . ± . s − (0 . ± . - π s - χ /ndf;Prob. 5.662/2; 0.05895 0.7199/1; 0.3962 - y y = (4 . ± . s − (0 . ± . - - η s - - χ /ndf;Prob. 9.634/1; 0.00192 - -10 ciPost Physics Submission Figure 7: The data on a cK for the particles from the II − IV regions of p T .The deviations from this value begin to appear at energy of 7 TeV for charged particles andneutral pions from II p T region. For these events the values of L cK ∗ b cK ∼ = 8 or 6 . At energy 8TeV, deviations get stronger and have been observed for almost all cases (except for one casewith c= 52 - for the eta mesons at 8 TeV). Now the corresponding points are on the lines at8, 6 and 4. Again one can say that with energy the values of the L cK ∗ b cK change jump-likeas a signal on discrete change the values of L cK ∗ b cK .Fig. 11-12 show the mass dependence of the values of a cK and b cK for the cases when thereare at least 2 defined points for the values of a cK and b cK . One can see that with mass in the I p T region at √ s = 2.76 TeV the values of the parameters a cK and b cK first decrease in theinterval of mass m <
500 MeV/c and then are almost independent of mass in the interval ofm >
500 MeV/c . But for the II p T regions at √ s=2.76 the values of the parameters a cK and b cK don’t depend on mass. At √ s =7 TeV the values the parameters a cK and b cK decrease. Ata further increase the energy at 8 TeV the values of the a cK and b cK decrease sharply. So onecan note that unlike parameter L cK the mass dependencies of the parameters a cK and b cK showregime change at mass m ∼ = 500 MeV/c .Before the conclusion, we wrote up the list of the main results:1. The p T distribution data on the invariant differential yield of the K - and φ − mesonsproduced in the pp collisions at √ s =2.76 TeV contained several p T regions whichcould be characterized by the lengths of the regions and the values of the free fittingparameters a cK and b cK .2. All of the points relevant to values of the lengths for the I p T regions as a function ofenergy lie down on five lines at L cI ∼ = 2 . , . , . , .
0, 6.4 GeV/c; the II p T regions’points are approximately on three lines at levels L cII ∼ = 14.8, 4.5, 2.5 GeV/c; the III andIV p T regions’ points are roughly lie on three lines at L cIII − IV (cid:39) ciPost Physics Submission Figure 8: The energy dependences for the parameters b cK .The energy dependence shows jump-like changes and indicating discrete changes withenergy.3. The lengths of the regions increase with their masses. The mass dependence getsstronger with energy (at 8 TeV the following relation holds: < L η > : < L π > (cid:39) m η : m π which was obtained in the paper in [2]).4. The values a cI and a cII as a function of energy are grouped around several lines witha power-law dependence on energy and show jump-like behavior at high energies as asignature of discrete changes.5. The resulting behavior of the parameter b cK tells us that in the interval of s > b cK increase with s, but for the eta mesons b cK decreases with energy. As the energy increases the valuesof L cK ∗ b cK for most of the cases remain unchanged at the level of L cK ∗ b cK (cid:39) , , , a cK and b cK show regime change at 500 MeV/c . The p T distribution data on invariant differential yield of the K - and φ − mesons produced inthe pp collisions at √ s =2.76 TeV contain several p T regions, which have been observed forthe charged particles, neutral pions and eta mesons. The regions could be characterized bytheir lengths L cK and the free fitting parameters a cK and b cK . The values of L cK , a cK and b cK asa function of energy grouped around several lines and show jump-like changes behavior with12 ciPost Physics Submission Figure 9: The energy dependences for the parameters b cK ( II − IV p T regions).energy. These observations together with the effect of existing the several p T regions can sayon discrete energy dependencies for the L cK , a cK and b cK .The lengths of the regions increase with the mass of the particles and the rate of increasegets stronger with energy. The mass dependencies of the parameters a cK and b cK show regimechange at mass ∼ = 500 MeV/c .According to the phenomenology of string theory, the results could mean that partonstrings of the very first generation with maximum tensions T max formed immediately afterthe collision either hadronize or decay forming the next generation of strings with tensions T ’ < T max . The newly formed strings can, again, either hadronize or decay and create strings ofthe next generation with tensions T ” > T ’, etc., up to the minimum tensions T min after whichthe string decay halts. That is, two processes occur simultaneously: string hadronization andstring breaking. In the experiment we measure the spectrum of the hadronized hadrons,since we cannot have a spectrum of the strings themselves. The string breaking effect is thereason of observing several p T regions which has a discrete nature. The latter can explain theobserved results on jump-like change of the characteristics of the regions and grouping thevalues of the characteristics around certain lines of energy.Finally, it is important to note that in the experiment, we can see only the signatureof the last generations of strings, which are in the area of our p T measurements. It is verydifficult to have signature for the first generation of strings, since for this it is necessary tohave measurements of the p T in the interval up to several TeV / c.13 ciPost Physics Submission Figure 10: The energy dependencies, of the lengths L cK multiplied by the values of the freefitting parameter b cK . References [1] Mais Suleymanov. Int.J.Mod.Phys. E27 (2018) no.01, 1850008 (2018-01-29);DOI: 10.1142/S0218301318500088[2] Mais Suleymanov. Int.J.Mod.Phys. E28 (2019) no.10, 1950084 ; DOI:10.1142/S0218301319500848[3] The ALICE Collaboration. Phys. Rev. C 95, 064606(2017); DOI: 10.1103/Phys-RevC.95.064606[4] The CMS Collaboration. J. Eur. Phys. J. C 72 (2012) 1945[5] The ALICE Collaboration. Eur. Phys. J. C 77 (2017) 339; Phys. Lett. B 717 (2012)162.;Eur. Phys. J. C 78 (2018) 263.[6] The Totem Collaboration., Europhys. Lett. 101 (2013) 21004, doi:10.1209/0295-5075/101/21004. 14 ciPost Physics Submission
Figure 11: The mass dependence of the values of a cK .Figure 12: The mass dependence of the values of b cKcK