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CMS ridge effect at LHC as a manifestation of bremsstralung of gluons off quarks accelerated in a strong color field
B. A. Arbuzov, E.E. Boos and V.I. Savrin SINP MSU, Moscow, Russia The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with 1 G eV < p T < 3 G eV . In the talk (based mostly on our work [1]) we propose a simple qualitative mechanism which corresponds to gluon bremsstralung of quarks moving with acceleration defined by the string tension. The smallness of azimuth angle difference along with large at large multiplicities in this inter val of p T are natural in the mechanism. The mechanism predicts also bremsstralung photons with mean values of p T 2.9G eV 2.5/mu ( M eV ) and 0.72 G eV 5/md ( M eV ). 1. B.A. Arbuzov, E.E. Boos and V.I. Savrin, Eur. Phys. J. C 71: 1730 (2011); arXiv:1104.1283[hep-ph]
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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The well-known classical expression for dipole electromagnetic radiation of electric charge e moving with acceleration being parallel to velocity of the motion [17] 2 w2 dE = ; dt 3 (1)

For strongly interacting quarks we change (1) for the following relation s dE = dt 9 A2 m
2

;

(2)

where acceleration w = A2 /m with A and m being
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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the string tension and a light quark mass. m u = 2 .5 M e V ; m d = 5 M e V ; A = 4 2 0 M e V ; (3)

where light quark masses are chosen to be in the middle of inter val of their possible values: 1.7 M eV < mu < 3.3 M eV ; 4.1 M eV < md < 5.8 M eV [18].
2

E s = t 9

A2 m

;

(4)

E t = 1 .
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

(5)
3


E =

s A2 . 9m

(6)
s

Then we use the standard one loop expression for at scale E s ( E) = 12

( 33 - 2 N f ) l n

E 2 C Q

2 D

;

(7)

E u 1 1 .2 G e V ;

E d 5 .6 G e V .

(8)

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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First of all let us consider an explanation of large differences in pseudo-rapidity along with small differences in azimuth angle . Here we are to take into account both quarks constituting the extended object (a cigar). Namely let "the cigar" be produced with some overall momentum k while its position remains being (almost) parallel to the line of p p collision. Such situation is presented in Fig.1.

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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k q2 Е B Е i q1 Е wf f Е 1ЕЕ 2 E ' r f r E' p p Fig.1 The string moving with momentum k from the point of collision of two protons, 1 , 2 are angles in Eq. (9) and q1 , q2 are momenta of the quarks.

Then velocities of quarks are not parallel to the direction of acceleration, but constitute some angles 1 , 2 with this direction in laborator y reference frame. When a velocity and an acceleration are not parallel v w = v w cos and there are two accelerated quarks we have the following angular distribution [17]

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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s dE = dt 24

A2 m

2

Ч
d ; (9)

(1 , , , v1 ) + (2 , , , v2 ) X + v2 Y (, , , v) = Z5 X = sin2 - 2v sin sin cos

Y = cos2 sin2 + sin2 sin2 cos2 Z = 1 - v(cos cos + sin sin cos ); where t is a time with account of a retardation [17],
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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1 , 2 are respectively angles for the first and the second quark. From Fig.2, Fig.3 we see that may be quite significant while is small. One should note that the peaks in Fig.2 and Fig.3 become narrower with increasing of speed and with increasing of . Emphasize that the effect of a peak around = 0 is connected with transverse movement of "the cigar" (Fig. 1). The more is transverse momentum k, i.e. angles i , the narrower becomes the distribution in .

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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s d E() = dt 24


A2 m

2

d () 2; cosh
cos =
sinh cosh

() =

-

12 (i , vi , , ) A m
2 2

d ;

(10)

s d E() = dt 24


() d ; (11)

() =
0

12 (i , vi , , ) sin d ;

12 (i , vi , , ) = (1 , , , v1 ) + (2 , , , v2 ).

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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N ()

1.0

0.8

0.6

0.4

0.2

4

2

2

4



Fig. 2. Behavior of N (), v = 0.999, 1 = 0.1, 2 = - 0.1, -5 < < 5.
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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N ()

2.5

2.0

1.5

1.0

0.5

3

2

1

1

2

3



Fig. 3. Behavior of N (), v = 0.999, 1 = 0.1, 2 = - 0.1, - < < .
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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Now let us consider properties of gluon radiation of a single quark. s dE = dt 24 s 24 A2 m
2

A2 m


2

sin2 d = )5 (1 - v cos (12)

0 ( ) d ;

0 ( ) = (0, , , v) ; where v is a velocity of a quark, is a polar angle and d = sin d d. Using angular distribution of the radiation (12) we estimate the mean pT of the radiated gluon
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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I1 < p >= ; 1 - v2 I2
g T

E

I2 =

0 ( ) d ; (13)
2

I1 =

0 ( ) A(v, ) sin d ;

2

cos (1 - v ) - v sin ; A(v, ) = 1 + 2 cos2 1-v where 0 ( ) is defined in (12). Calculating integrals in (13) with the aid of the following relation valid for ч v 1 a nd > 2
0

sin d = (1 - v cos ) (1 - v2 )

ч -1

2

ч-



ч 2



1 2

(2 - ч )
1- ч 2

;

- ч /2

()

+
13

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks


we obtain for quark u and d respectively with v 1 9 Eu g < pT (u) > = 9 .9 G e V ; 32 9 Ed g < pT (d) > = 4 .9 5 G e V . (14) 32 Then we estimate the multiplicity for gluon energy in an accompanying reference frame (8) by the following expression valid in the region of few G eV for charged multiplicity [19] < Nch > = a + b ln s ; a = - 0 .4 3 + 0 .0 9 ; b = 2 .7 5 + 0 .0 6 . (15)
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B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks


Neutral particles factor 3 . Mean multiplicity: 2 u: s = 4 .1 5 G e V ; < N > = 5 .2 ; s = 3 .3 7 G e V ; < N > = 4 .3 . d: Estimate for transverse momenta of hadrons g pT = pT / N u : 1 .3 G e V < p T < 3 .0 G e V ; d : 0 .8 G e V < p T < 2 .0 G e V .

(16)

(17)

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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Average angular spread for gluons

< p > Ng ? < > ; < E g > Ng
? Small multiplicity increases the effect disappears. Ng 2

? ; < > x1 x2 s
g T

g T

(18)

(19)

where x1 , x2 are values of x for quark in the first proton and the anti-quark in the second one. Number of radiated gluons Ng depends on angle
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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and velocity v. Using again formulas from [17] we have the following estimate x1 x2 s . (20) Ng = 2 sin 2 E 1 + (1- v2 ) For example with = 0.1 and v = 0.999, average E = ( Eu + Ed )/2 = 8.4 G eV , s = 7 TeV [2] and with average of the product < x1 x2 > 0.01 (see, e.g. [20] and references therein) we have Ng 17. Now in our interpretation one bremsstralung gluon gives average number of charged hadrons Nch 3.2. Bearing in mind, that our quasi-classical estimate
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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corresponds to non-coherent production of gluons, with Ng 17 we estimate total number of charged q particles produced by a quark Nch = 54 that gives just multiplicity 100 for two radiating quarks. Now with Ng = 17, s = 7 TeV , average g < pT >= 7.4 G eV and < x1 x2 >= 0.01 we have from (19) ? < > 0 .0 9 ; This angular spread actually gives widening of distributions in and . Widening of the ridge with s decreasing.
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

(21)

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? s = 0.9 TeV < > = 0.8 vanishing of the effect. Thus, one can conclude the simple mechanism of gluon bremsstralung off quarks moving in a strong colour field describes qualitatively the CMS ridge effect. Of course, a real situation could be much more involved. In particular, other colour configurations, as was pointed out in various studies (see, for example, [13]), may play a significant role. Our consideration based on simple quasi-classical estimations shows that constituting string configurations may lead to basic features of the
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks



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ridge effect, namely, correlations in particular kinematic region at ver y high multiplicities. Obviously, in order to show more accurate properties of proposed mechanism one should elaborate in more detail corresponding model and develop corresponding event generator to perform more realistic simulations.

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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The accelerated quarks radiate photons as well. Mean pT : 2e 3 e 3 2 .5 : p T 2 .9 G e V Ч ; m u ( M eV ) 5 : p T 0 .7 2 G e V Ч . m d ( M eV ) (22)

information on masses of light quarks mu , md . Recent data from ATLAS [21] (1107.0581 [hep-ex]): Single photon ET distributions show unexpected fluctuation at ET 5 G eV mu 1.45 M eV .

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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entries/GeV

600 500 400 300 200 100 0 -5 0 5 10 15 20
iso

ATLAS Data 2010, s=7 TeV, Ldt = 37 pb



-1

(leading photon)

25

ET,1 [GeV]

Fig. 4. Data driven signal isolation distribution for leading photon obtained usingthe photon candidates (solid circles) or extrapolated from electrons (continuous line)(extracted from [21] Fig. 2a).
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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entries/GeV

400 350 300 250 200 150 100 50 0 -50 -5 0 5 10 15 20
iso

ATLAS Data 2010, s=7 TeV, Ldt = 37 pb



-1

(sub-leading photon)

25

ET,2 [GeV]

Fig. 5. Data driven signal isolation distribution for leading photon obtained usingthe photon candidates (solid circles) or extrapolated from electrons (continuous line)(extracted from [21] Fig. 2b).
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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RG evolution mu ( E) = 1+ m u ( E0 )
4/7 7 s ( E0 ) 4

;

E0 = 2 G eV . (23)

ln

E E

2 2 0

mu ( E0 ) = 2.5 M eV (3), E = 300 G eV , s ( E0 ) = 0.3 mu ( E) = 1.425 M eV 5.1 G eV spikes. Recent results of CMS for two photons [22] (1109.3310 [hep-ex]) also may ser ve as indications on behalf of the present mechanism - excess for small of the two photons. Just "CMS ridge effect" for photons.

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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References
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[11] A. Kovner and M. Lublinsky, Phys. Rev. D 83, 034017 (2011); arXiv:1012.3398 [hep-ph]. [12] K. Werner, Iu. Karpenko, T. Pierog, Phys. Rev. Lett. 106, 122004 (2011); arXiv:1011.0375[hep-ph]. [13] M Yu. Azarkin, I. M. Dremin, A. V. Leonidov, arXiv:1102.3258[hep-ph]. [14] R. C. Hwa and C. B. Yang, Phys. Rev. C 83, 024911 (2011); arXiv:1011.0965 [hep-ph]. [15] S. M. Troshin and N. E. Tyurin, arXiv:1103.0626 [hep-ph]. [16] X. Artru, Phys. Rep. 97, 147 (1983). [17] L. D. Landau and E. M. Lifshitz, Field Theor y (FIZMATLIT, Moscow, 2001). [18] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010). [19] Dubna-Bucharest-Eotves U.-et al collaboration, Yad.Fiz. 16, 989 (1972). [20] P. M. Nadolski et al., Phys.Rev. D 78, 013004 (2008). [21] ATLAS collaboration, arXiv:1107.0581 [hep-ex].
B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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[22] L.Millischer (CMS collaboration), arXiv:1109.3310 [hep-ex].

B.A. Arbuzov, E.E. Boos, V.I. Savrin: CMS ridge effect and gluon bremsstralung off quarks

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