1. Physics of cumulative particles
Speaker: Dr. Grigori Feofilov (St Petersburg State University (RU))
NA61 meeting in Krakow, 24 Febr.2017, Vydio 1

2. Layout Introduction Theoretical approaches
What is new proposed for NA61?
Study of cumulative number and energy dependence of p_t spectra of various particles in pA collsions at the SPS
Study of correlations between cumulative particles and strangeness and/or charm forward production
Summary and plans 2

3. Cumulative effect Flucton
The 1st experimental observations [1,2]:
Collisions p+d (Ep=660 MeV), fixed target :
Observation of backward protons
Collisions p+A (Ep=675 MeV), Li, Be, C, and O
fixed target:
Observation of high yields of deutrons
The 1st explanation: the hypothesis of nuclear fluctons
(D.I.Blokhintsev, [3])
The production of high-energy fragments
from the collision of fast nucleons with nuclei
can be treated as the result of the collision
of the nucleon with fluctuations of nuclear matter.
SIZE OF FLUCTUATION ~ NUCLEON SIZE
References
G. A. Leksin et al., ZhETF 32, 445 (1957).
L.S. Azhgirej et al., ZhETF 33, 1185 (1957).
D. I. Blokhintsev, ZhETF 33, 1295 (1957).
the A(e,e′) inclusive electron scattering
Идея первых экспериментов по наблюдению коллективных эффектов при взаимодействии релятивистских ядер была впервые высказана в ра- боте [1]. Она состояла в том, что при взаимодействии релятивистских ядер возможно наблюдение вторичных частиц с энергией, превышаю-щей энергию на нуклон в налетающем ядре, т.е. во взаимодействии может участвовать группа нуклонов. Экспериментально этот эффект был обнаружен в Дубне в 1973 г. группой профессора В.С.Ставинского и получил название ядерного кумулятивного эффекта [2]. Впоследствии кумулятивный эффект был детально исследован как в ОИЯИ, так и в других научных центрах, в частности в ИТЭФ* (Москва) группой про- фессора Г.А.Лексина. (А.М.Балдин, А.И.Малахов, А.Н.Сисакян НЕКОТОРЫЕ ПРОБЛЕМЫ РЕЛЯТИВИСТСКОЙ ЯДЕРНОЙ ФИЗИКИ И МНОЖЕСТВЕННОГО РОЖДЕНИЯ ЧАСТИЦ
Препринт, Дубна 2001, направлено в ЭЧАЯ
Flucton . 3 3

4. First beams of relativistic nuclei at Nuclotron in Dubna (1971)
Cumulative particles production from fragmentation of fast projectile nucleus.
The first study - fragmentation of relativistic deuterons, D, into pions.
Baldin A.M. et al., Yad.Fiz.18 (1973) 79 (p0=5 GeV/c)
D + Target =>  + X
p0>>mN : p0 < k < 2p cumulative pions
Target

5. Kinematics of cumulative production in pA
for fixed target
The frame in which
the fragmenting nucleus
is at rest.
Cumulative particles:
Typical momenta ~ m
Angles in backward hemisphere ~ .
Ideal to measure in fixed-target experiments =>
The avalanche of experiments, see e.g. review in V. K. Bondarev, Phys. Part. Nucl. 28, 5 (1997) L.L. Frankfurt, M.I. Strikmann, Phys. Rep. 76, 215 (1981); ibid 160, 235 (1988). 5

6. Theoretical approaches (Mechanisms of cumulative particle production)
Fireball
M.I. Gorenstein, G.M. Zinovjev. In: Phys. Lett. B 67 (1977), p. 100.
M.I. Gorenstein G.M. Zinovjev V.P.Shelest. In: Yad. Fiz. 26 (1977), p. 788.
M.I. Gorenstein G.M. Zinovjev Yu.M. Sinyukov . In: Pis’ma ZhETF 28 (1978), p. 371.
G. Bogatskaya, C. B. Chiu, M. I. Gorenstein, and G. M. Zinovjev, Phys. Rev. C 22, 209 (1980).
M.I. Anchishkin G.M. Zinovjev D.V. Gorenstein. In: Phys. Lett. B 108 (1982), p. 47.
Resonance
A. Motornenko, M.I. Gorenstein. J. Phys. G: Nucl. Part. Phys , 2017;
arXiv: [hep-ph] (2016).
Rescattering
V.B. Kopeliovich. In: JETP Lett. 23 (1976), p. 313.
V.B. Kopeliovich. In: Phys. Rep. 139 (1982), p. 51.
M.A. Braun, V. V. Vechernin. In: Sov.J.Nucl.Phys 25 (1977), p. 676.
  M.A. Braun, V. V. Vechernin In: Sov. J. Nucl. Phys. 43 (1986), p
  M.A. Braun, V. V. Vechernin. In: Sov. J. Nucl. Phys. 40 (1984), p
M.A. Braun, V. V. Vechernin. In: J.Phys. G 19 (1993), p. 517; ibid 531.
Flucton
D. I. Blokhintsev, ZhETF 33, 1295 (1957).
V. Efremov. In: Phys.Part.Nuclei 13 (1982), p. 613.
R. Blankenbecler I.A. Shcmidt. In: Phys. Rev. D 16 (1988), p
….continued on the next page -> 6

7. Theoretical approaches (Mechanisms of cumulative particle production)
Few nucleon short-range correlations in a nucleus L.L. Frankfurt, M.I. Strikmann, Phys. Rep. 76, 215 (1981); ibid 160, 235 (1988) But the nucleons in a nucleus when the distances between them are smaller than their radius should be considered in accordance with QCD [Schmidt I.A., Blankenbecler R. Phys.Rev. D15 (1977) 3321] as multi-quarks bags, i.e. fluctons. So one has to go from the study of nucleon short-range correlations to the quark short-range correlations in flucton: Flucton and formation of cumulative particles from flucton M.A. Braun, V. V. Vechernin. In: Nucl. Phys. B 427 (1994), p M.A. Braun, V. V. Vechernin. . In: Phys. Atom. Nucl. 60 (1997), p M.A. Braun, V. V. Vechernin. In: Theor. and Math. Phys 139 (2004), p M.A. Braun, V. V. Vechernin. In: Nucl. Phys. B (Proc. Suppl.) 92 (2001), p M.A. Braun, V. V. Vechernin. In: Phys. Atom. Nucl. 63 (2000), p V.V. Vechernin. In: AIP Conference Proceedings. Vol 7

8. Flucton
Droplet of dense cold nuclear matter : 2N fluctuation – 6 quark state (Blokhintsev D.I., 1957)
Theoretical description near threshold: k -> 2p0 , x = k/p0 -> 2
1 < x < the cumulative region ( 1 < x < f - for the fN flucton )
Quark counting rules: ~ 2n-3
n – the number of constituents, n = 6
–the deviation from the threshold, = 2 – x ,  << 1
[1] Blokhintsev D.I., JETP 33 (1957) 1295
[2]Brodsky S.J., Chertok B.T. Phys.Rev. D14 (1976) 3003; Phys.Rev.Lett. 37 (1976) 269
[3]Schmidt I.A., Blankenbecler R. Phys.Rev. D15 (1977) 3321 8

9. Hypotheses to be tested for cumulative particles production mechanisms
A: Result of interactions of projectile with nuclear media (Rescattering? Resonances?Formation of “a fireball”?)… or
B: Intrinsic presence of rare configurations (few nucleon short-range correlations or fluctons) in the wave function of nucleus (“Drops of cold QGP”)? 9

10. The principal physical difference between the hypotheses A and B (!)
The DIS experiments [1] demonstrate in the A(e,e′) inclusive electron scattering the intrinsic presence of fast “cumulative” quark in the normal cold nuclear matter, what can be explaind only in the framework of the hypothesis B [see e.g. M.A. Braun, V.V. Vechernin. Nucl. Phys. B 427 (1994), p.614.].
The ratios of inclusive GeV
e+4He, e+12C and e+56Fe to e+3He scattering cross sections have been measured at 1 < xB < 3 in [1].
This is the first measurement of 3-nucleon SRC probabilities in nuclei.
[1] K.S. Egiyan, et al., The CLAS Collaboration,
Phys.Rev.Lett.96:082501, 2006, [arXiv: nucl-ex/ ] 10

11. What is proposed for NA61
Study of cumulative number and energy dependence of p_t spectra of various particles (pions and protons) produced in pA collsions at the SPS
Study of correlations between cumulative particles and strangeness and/or charm forward production 11

12. Study of pT distribution of cumulative particles (pions and protons) as a function of the cumulative number
It is shown in [1] that the cumulative protons are formed predominantly via a coherent coalescence of three fast cluster quarks, whereas the production of cumulative pions is dominated by one fast cluster quark hadronization,
…see further:
[1] V.V. Vechernin. In: AIP Conference Proceedings. Vol 12

13. (illustration for 6 quark flucton)
Coherent Quark Coalescence and Production of Cumulative Protons and Pions
(illustration for 6 quark flucton)
the cumulative pion production
kT – dependence:
M.A. Braun, V.V. Vechernin, Phys.Atom.Nucl. 63, 1831 (2000)
the cumulative proton production
coherent quark coalescence mechanism:
M.A. Braun, V.V. Vechernin,
Nucl.Phys. B92, 156 (2001); Theor.Math.Phys 139, 766 (2004)
p1=p2=p3=1 13

14. Transverse momentum dependence of spectra of cumulative particles produced in pA 10GeV/c collisions
The observed transverse momentum dependence of spectra of cumulative particles produced from droplets of dense nuclear matter is different for protons and pions
Experiment is well reproduced by 1 param— the constituent quark mass, taken to be equal 300 MeV. , see [1]
The observed transverse momentum dependence should not depened on the collision energy –> the energy independence could be tested at the NA61(SHINE)
[1] V.V. Vechernin. In: AIP Conference Proceedings. Vol [2] Experiment: see S.V. Boyarinov et al., Sov.J.Nucl.Phys. 46, 871 (1987) ; S.V. Boyarinov et al., Physics of Atomic Nuclei 57, 1379 (1994); S.V. Boyarinov et al., Sov.J.Nucl.Phys. 55, 917 (1992). 14

15. Study of correlations between cumulative particles and strangeness or charm forward production
-- the cumulative pion production in backward hemisphere
ssbar or ccbar formation in forward hemisphere
The analysis of the diagrams shows that all donor quarks related to the cumulative quark have large virtuality and must interact with the projectail, so one can expect an enhanced yield of strange and charm particles in the process of their hadronization See M. A. Braun, V. V. Vechernin, Nucl. Phys. B 427, 614 (1994); Physics of Atomic Nuclei 60, 432 (1997); Theor. and Math. Phys. 139, 766 (2004). 15

16. Summary and Plans Summary Plans 23.2.17 16
The details of mechanism of cumulative particle production is still not completely understood in spite of rather large wealth of experimental data
Two major directions of studies are proposed in pA collisions in NA61 at the SPS for 2020 program : cumulative number and collision energy dependence of pT spectra of cumulative pions and protons in pA collisions at SPS and correlations between the cumulative particle and strangeness or charm yield
Plans
Model simulations for kinematics of possible correlations between the cumulative particle (in backward) and strangeness or charm yield (in the NA61+new VD acceptance)
–in this spring
Writing a proposal….
-- before this summer? 16