NASA Technical Reports Server (NTRS) 19940006144: Squeezed colour states in gluon jet

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by  NASA Technical Reports Server (NTRS)

N94-10599
SQUEEZED COLOUR STATES IN GLUON JET
S.YLKi]In, V.I.KuwJhinov
l_,_e i/Phy_ca
Sh6rl_a a_.70, Mi_k UO0_I, Bel4n,,.,
S.A.FiraSo
Belaewian $_a_e U_dv_
Sha_a.a av.,_, Mi_k UO080, BeLavua
Abstract
The pomibi]/ty offonutios of,qusmai st-tin d slum fkkk is quntam ckzomodynmics
dle to ioalisesr sospertarbltive _Mmte_'_ol dusiaj jet evolatien is the p_-im of e+e -
uai]Silatioa isto h_, wldr.b are auaIcqiou to the quutam foton 0quintal statm is
quutum ,dactsmlyaamicsisdemoutrsted sad the aquinaS8 p_am_tors am calculate.
1 Evolution equation for gluon field
The SJuon _ d the quantum chromodynmnks Hsmiltonlu hu the form [1]
e, = _ +a',.,=, f{,_(R_..+_.J.)- eau.,.z,.Zo+
O)
te_.u.,.I, _& + ½g'(o.._,_¢)'+_0*(½c._,x&),}e,
.hr, _. = -_A°- _7..,J. = _ x &,&-,_r poten_ ofSlno_f_d, C._-,tructu_
comasats of the SU(3), a,b, c,- 1,... ,8 are colour indkm; i,j, k, J-ind_.ea of 3-vectorl.
The reid of SJuous sppenrs in the form of SJuon jet or cascade, which iJ produced by the
quark with larse trsademd momentum. Due to the cubic sad quadratic nonlinesritim in (l)
bremstrshluns 8luous divide end at the end of perturbutive cucsde we have a jet of sluous with
spp_ equ,d enersm sad mounnta [2].
At the end of cucmcle multiplicity distribution of sluou b close to nesative binomial distribu-
tion [3, 43which can be comidemd ml a i_ of Pc_mon (coherent) dJltributious.
The importsace of nouperturbstive hsdrcobation mtqp b _ with confinement, sub-
ponon multiplicity distributions at thin etqge [5, 6], connection with intermittency [7_, pairing
of psrtom durin8 colour lomins, nonlinenxitiee of (1) hiat on the pom/bdlitim of eclueeaed IOuon
states.
Let us trim for simplicity that all sluous in jet have equal enersiee sad moment.L Choose such
the system of coordmat_ that haJ axe ascoinciding with the direction of sluon momentum. Then
in the momentum representation the operator of Sluon m]fmteraction tslms the form
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,,h_A_(A",_),,r_etm (_uctm) o_._-, d _w,- ,,_tbh-a_o_ud _-_
Evolution equation for gluon operator with indices a and k
_A_ = IAL (4)
then takes the form
i_A_ --fIA_ + faA'_ + f (5)
The function/'1, h, f do not contain explicitly A| and A_',/s z _ [9].
2 Squeesing of the gluon field in jet
ThentheKa'utionof
Let us solve the equation (5) for small time A_ << l/K, E = _/_ -I/2l=.
(5), is written in the matriz form
{ AZ(O_ -I ,,r(,))+.(I-)
a.,A_(,)/=, (-_ //:1/A_(,) 1 (6)
A_'(_)) --ap /'+/2
(7)
.,(o)' I, I:) ]
Let us tsJm st some moment to ffi 0 the conditions: f -- O,_f= = O,snd that )'_ and f2 vm7 slowly.
Then the solution tskm the form
Al(t) = AZ(O-) _Z(0)/_ - _(0)/_. (s)
This expremion coincides with the expression fm ideal m.ueesed state [8]
A| = A_chv + eamA_ (9)
chr = 1-- if:¢, shr = f=, e_ = -i (10)
where r and 0 are _ueesin s parmmtem. Thus the mlbqueesing b pomibie for the 8luon field with
fixed colour and Lorents component.
In quantum optics such ,farm are named m pure quantum dated and operatom z_ = (A -
A÷)12 ud z_ = (a = A - A+)/2 can have a_rqe flu_u_on_ m_n' then 1/4.
3 Evolution of gluon multiplicity distribution in jet
Take vector ofJtste ]_, _,... ,_ > wbere n,- the number of sluons witb ddnite indices i _nd
a. The operstor of full _luon number _ acts on the vector M
_1_,.'_,...,n. >= (,_+,_ +... +n.)l,_,n_,...,_. > (11)
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It is clear that ,my part of H,a acts on the vector am
INe_ >= A_+_Ay+bA_cAIdIr_x,no,... ,r_, >= Ir_l,no,... ,_+x,_+2,... ,r_-x,nv-x, .., ,_ > (]2)
It does not cbanse the number of particle
]_lJv_ >= (nl+,_ +... + n.)lN_ > (13)
and then
[_,B] =0. (14)
Thus the total number of Sluon is jet under made conditions (_ -- co'st, _ - const) does not
cbanse with the time and it is not difficult to see that sluon multiplicity distribution does not
change with the time.
It can be also shown that the value squeesin s she for every mode is limited [9]. Foton multi-
plicity of squeesinS states distributiom bare been used earlier for pbenomenolosical description
of mome properties of hadron nmltiplicity distribution [10, 11].
Here we obtain for model sluon jet that the squeesed states of colour Sluon field can appear
due selfinteraction and nonperturbative mechanism of Sluon selfintersction and can be particularly
important at nonperturbative stqe of jet evolution.
Due to nonperturbativenem, peirin s of SlUOnand subpoimon multiplicity distributions squees-
in8 states can be responsible partly for hsdronisation of colour psmons (confinment) and inter-
mittency (fractal dimension) pbenomenom in multiparticle procemu.
References
[]] W.M,uN_uoH, .Pas,_,Phy,.P,_pS.aC,14a0978)
[2] Yu.A.Dolr.hitser st al., Ph_.Rep. 5SC, 269 (1980)
[3] A.(]li__ Nncl.Phys., B15T, 269 (1979)
[4] E.D.M_a, B.Weber, Z.Phy_., C$1, 143 (1980)
[5] V.I.Kuv_hinov, E.S.Kolmulina, Acts Phlm.PoL, B15, 633 (1982)
[6] V.I.Kuvshinov et al., Sovist.Jour.NucLPhys 81,199 (1980)
[7] D.V.Klenitsky, V.I.Kuvzdxinov, Rapid Communicotion on _eo_*/c_ 104yl/ca. Preprint IP,
Minsk 636(3), 23 (1991)
[8] S.YLKilin, Quutum Optic,, 1990
[9] S.YLKilin, V.I.Ku_hinov, S.A.Fir_o, Proceed. of Sere. "Non]ine_ phenomena in complez
q,stem" Polat_, 1992.
[10] B.A.Bamb_, M.V.Satyanar_ana,, Phy_.Rev., D88 2202 (1988)
[11] A.Vourdm, R.M.Weiuer, Phlm.Rev., D85 _09 (1988)
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