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Small x physics and hard QCD processes at LHC
Nikolay P. Zotov
(SINP, Lomonosov Moscow State University)


N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

OUTLINE

1. Introduction 2. Unintegrated parton distributions (overview) 3. The kT -factorization approach in hadroproduction (overview) 4. Ingredients of the kT -factorization approach in resp ect to our numerical calculations 5. Numerical results with kT -factorization at LHC 6. Conclusions

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1. Introduction
The so-called small x regime of QCD is the kinematic region, where the characteristic hard scale of the process µ µ2 p
2 T 2 MT = M 2 + p2 , M MQ T D

is large as compared to the QC c.m.s. energy S of the process: Q
CD

but µ is much less than the total S.

µ

In this sense, HERA was the first small x machine, and LHC is more of a small x collider. Typical x values prob ed at the LHC in the central rapidity region are almost two orders of magnitude smaller than x values prob ed at HERA at the same scale. Hence, small x corrections start b eing relevant even for a final state with a characteristic electroweak scale M 100 GeV.
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It means the pQCD expansion any observable quantity in s contains large coefficients (lnn (S/M 2 )) (lnn (1/x)) (b esides the usual R.G. ones (lnn (µ2 /2 C D ))). Q The resummation of these terms (s (ln(1/x))n ( 1 at x 0) results in the so called unintegrated gluon distribution F (x, k2 ). The (u.g.d.) T ob ey certain evoluation equations: · BFKL: · CCF M :
E.A. Kuraev, L.N. Lipatov, V.S. Fadin, Sov. Phys. JETP 44 (1976) 443, 45 (1977) 199; Y.Y. Balitskii, L.N. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 822. M. Ciafaloni, Nucl. Phys. B296 (1988) 49; S. Catani, F. Fiorani, G. Marchesini, Nucl. Phys. B336 (1990) 18; G. Marchesini, Nucl. Phys. B445 (1995) 49.

In last case the u.g.d. dep end additionaly on the probing scale µ: A(x, k2 , µ2 ). T

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The BFKL evolution equation predict more rapid growth of gluon disity ( x- , where 1 + is the intercept of so-called hard BFKL Pomeron). However it is clear that this growth cannot continue for ever, b ecause it would violate the unitarity constraint:
L.V. Grib ov, E.M. Levin, M.G. Ryskin, Phys. Rep. 100 (1983) 1.

Consequently, the parton evolution dynamics must change at some p oint, and new phenomenon must come into play. Indeed as the gluon density increases, non-linear parton interactions are exp ected to b ecome more and more imp ortant, resulting eventually in the slowdown of the parton density growth (known as "saturation effect"):
L.V. Grib ov, E.M. Levin, M.G. Ryskin (1983); A.H. Mueller, J. Qiu, NP B268 (1986) 427; L.McLerran, R. Venugopalan, PR D49 (1994) 2233, PR D49 (1994) 3352, D50 (1994) 2225, D53 (1996) 458, D59 (1999) 094002... K. Golec-Biernat, M. Wusthoff, PR D59 (1999) 014017, D60 (1999) 114023.

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The underlying physics can b e describ ed by the non-linear BalitskyKovchgov (BK) equation:
I.I. Balitsky, NP B463 (1996) 99; Y.V. Kovchegov, PR D60 (1999) 034008.

These nonlinear interactions lead to an equilibrium-like system of partons with some definite value of the average transverse momentum kT and the corresp onding saturation scale Qs (x). This equilibrium-like system is the so called Color Glass Condesate (CGC):
M. Gyulassy, L. McLerran, nucl-th/0405013; A.V. Leonidov, UFN 175 (2005) 345. decreasing of x: Q2 (x, A) s E. Iancu, arXiv:0901.0986 [hep-ph], J.P. Blaizot, arXiv:1101.0260 [hep-ph]

Since the saturation scale increases with x- A with 0.3, 1/3:

one may exp ect that the saturation effect will b e more clear at LHC energies.

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2. Unintegrated parton distributions (uPDF or TMD)
The basic dynamical quantity in the small x physics is transversemomentum-dep endent (TMD) (kT -dep endent) or unintegrated parton distribution (uPDF) A(x, k2 , µ2 ). T To calculate the cross sections of any physical process the uPDF A(x, k2 , µ2 ) has to b e convoluted with the relevant partonic cross secT tion : ^ dz dk2 (x/z , k2 , µ2 )A(x, k2 , µ2 ). = T^ T T z For the uPDF there is no unique definition, and as a cosequence it is for the phenomenology of these quantities very imp ortant to identify uPDF which are used in description of h.e. processes. For a general introduction to small x physics and the small x evolution equations, as well as tools for calculation in terms of MC programs, we refer to the reviews:
B. Andersson et al. (Small-x Collab oration), Eur. Phys. J. C25 (2002) 77; J. Andersen et al. (Small-x Collab oration), Eur. Phys. J. C35 (2004) 67; C48 (2006) 53.

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During roughly the last decade, there has b een steady progress toward a b etter understanding of the kT -factorization (high energy factorization) and the uPDF (for example):
F. Dominguez et al., Phys. Rev. D83 (2011) 105005; S.M. Aybat, T.C. Rogers, Phys. Rev. D83 (2011) 114042; I.O. Cherednikov, arXiv:1102.0892; I.O. Cherednikov, N.G. Stefanis, arXiv:1108.0811.

Workshop on Transvere Momentum Distributions (TMD 2010), which was held in Trento (Italy), was dedicated to the recent developments in small x physics, based on the kT -factorization and the uPDF: http://www.pv.infn.it/ bacchett/TMDprogram.htm. Recently the definition for the TMDs determined by the requirement of factorization, maximal universality and internal consistency have b een done by J.C. Collins:
J.C. Collins, Foundations of Perturbative QCD (Cambridge University Press, Cambridge, 2011); J.C. Collins, arXiv:1107.4123 [hep-ph].

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The results obtained in previous works are reduced to the following: kT (TMD)-factorization is valid in · Back-to-back hadron or jet production in e+ e- -annihilation, · Drell-Yan process (PA + PB ( , W/Z ) + X ), · Semi-inclusive DIS (e + P e + h + X ). In hadroproduction of back-to-back jets or hadrons (h1 + h2 H1 + H2 + X ) TMD-factorization is problematic. For expample, partonic picture gives the following qT -dep endent hadronic tensor for DY cross section (Collins, 2011): W d2 k1T d2 k2T Ff
/P1 µ

= f |Hf (Q; µ)|

µ

(1)

(x1 , k1T ; µ; 1 )F

f /P2

(x2 , k2T ; µ; 2 ) (k1T + k2T - qT ) + Y (Q, qT ).

The hard part Hf (Q; µ) is calculable to arbitrary order in s , µ - the renormalization scale. The term Y (Q, qT ) describ es the matching to large qT where the approximations of TMD-factorization break down.
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The scales 1 , 2 are related to the regulation of light-cone divergences and 1 .2 = Q4 . The soft factors connected with soft gluons are contained in the definitions of the TMDs, which cannot b e predicted from the theory and must b e fitted to data.

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3. The kT -factorization approach in hadroproduction
The kT -factorization approach in hadroproduction is based on the work by Catani, Ciafaloni and Hautman (CCH). The factorization formula for pp-collision in physical gauge (n.A = µ µ 0, nµ = aP1 + bP2 ) is 1 = 4M
2

d k1

2

T

d x1 x1

d k2

2

T

d x2 F (x1 , k1T )gg (/(x1 x2 ), k1T , k2T )F (x2 , k2T ), (2) ^ x2

where = 4M 2 /s,M is the invariant mass of heavy quark, and F 's are the unintegrated gluon distributions, definded by the BFKL equation: F (x, k; Q2) = 0 1 (1 - x) (k2 - Q2 ) + 0 (3)

+

s

d2 q q2

dz [F (x/z , k + q; Q2 ) - (k - q )F (x/z , k; Q2 )], 0 0 z

were s = s Nc / . It means that the rapidity divergencies are cut off since there are an implicit cuts in the BFKL formalism.
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Effectively one introduces a cuts 1 , 2 , and then sets 1 = x1 , 2 = x2 in (2). The declaration that F is defined via the BFKL equation (3) means that the BFKL unintegrated gluon distribution reduces to the dip ole gluon distribution:
V. Barone, M. Genovese, N.N. Nikolaev, E. Predazzi, B.G. Zakharov, Phys. Lett. B326 (1994) 161 A. Bialas, H. Navelet, R. Peschanski, Nucl. Phys. B593 (2001) 438.

The connections b etween different uPDF recently were analyzed in
E. Avsar, arXiv:1108.1181 [hep-ph].

The procedure for resumming inclusive hard cross-sections at the leading non-trivial order through kT -factorization was used for an increasing numb er of processes: photoproduction ones, DIS ones, DY and vector b oson production, direct photon production, gluonic Higgs production b oth in the p oint-like limit, and for finite top mass mt . Please look (for example)
S. Marzani, arXiv:1006.2314 [hep-ph].

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The hadroproduction of heavy quarks was considered in
R.D. Ball, R.K. Ellis, JHEP 0105 (2001) 053

,

and recently in
R.D. Ball, Nucl. Phys. B796 (2008) 137.

In last pap er it was shown that when the coupling runs the dramatic enhancements seen at fixed coupling, due to infrared singularities in the partonic cross-sections, are substantially reduced, to the extent that they are largely accounted for by the usual NLO and NNLO p erturbative corrections. It was found that resummation modifies the B -production c.s. at the LHC by at most 15%, but that the enhancement of gluonic W production may b e as large 50% at large rapidities.

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4. Ingredients of our kT -factorization numerical calculations
We have used the kT -factorization approach to discrib e exp. data on: · heavy quark photo- and electroproduction at HERA · J / production in photo- and electroproduction at HERA with CSM and COM · D , D + j et, D + 2j et photoproduction and D production in DIS
c c · charm contribution to the s.f. F2 (x, Q2 ), FL , FL · B -meson and b¯ production at Tevatron b

· charm, b eauty, D and J / production in two-photon collisions at LEP2 · Higgs production at Tevatron and LHC · prompt photon production at HERA and Tevatron · W/Z production at Tevatron
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The main motivations of our study · to demonstrate the p ossibilities of the kT -factorization approach · search the "universal" unintegrated gluon distribution · search the effects of BFKL and CCFM dynamics · p ossible saturation effects · to use this the BFKL- and CCFM-based unintegrated gluon distribution to predict cross sections for different processes at LHC. Here I want to present the results of b-quark and J / production at LHC in comparison with first exp. data obtained by ATLAS, CMS and LHCb Collab orations:
H. Jung, M. Kr¨mer, A.V. Lipatov, N. Z., DESY 11-086, arXiv:1105.6276 [hep-ph]; a S.P. Baranov, A.V. Lipatov, N.Z., DESY 11-143, arXiv:1108.2856.

The description of prompt photon production and DY pairs was done by
M.A. Malyshev, talk at this Workshop.

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According to the kT -factorization approach to calculate the cross sections of any physical process the unintegrated gluon distribution A(x, k2 , µ2 ) has to b e convoluted with the relevant partonic cross secT tion : ^ dz dk2 (x/z , k2 , µ2 )A(x, k2 , µ2 ). = T^ T T z · The partonic cross section has to b e taken off mass shell (kT ^ dep endent). · It also assumes a modification of their p olarization density matrix. It has to b e taken in so called BFKL form: µ
µ kT kT = 2. kT

· Concerning the uPDF in a proton, we used two different sets. First of them is the KMR one. The KMR approach represent an approximate treatment of the parton evolution mainly based on the
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DGLAP equation and incorp otating the BFKL effects at the last step of the parton ladder only, in the form of the prop erly defined Sudakov formfactors Tq (k2 , µ2 ) and Tg (k2 , µ2 ), including logarithmic loop correcT T tions.
M. Kimb er, A. Martin, M. Ryskin, Phys. Rev. D63 (2001) 114027.

1

â

x

s (k2 ) T â Aq (x, , µ ) = T ,µ ) 2 x x2 xx2 , k ( - z ) + Pqg (z ) g ,k dz Pq q (z ) q z zT z zT k2 T
2 2 q (kT 2

(4) ,

1

â

dz
x q

s (k2 ) T Ag (x, , µ ) = T ,µ ) â 2 x x2 xx2 , kT + Pgg (z ) g , kT ( - z ) . Pg q (z ) q z z z z k2 T
2 2 g (kT 2

(5)

-functions imply the angular-ordering constraint = µ/(µ + kT ) sp ecifically to the last evalution step (to regulate the soft gluon singularities). For other evolution steps the strong ordering in transverse
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momentum within DGLAP eq. automatically ensures angular orderin g. Ta (k2 , µ2 ) - the probability of evolving from k2 to µ2 without parton T T 2 2 2 2 emission. Ta (kT , µ ) = 1 at kT > µ . Such definition of the Aa (x, k2 , µ2 ) is correct for k2 > µ2 only, where T T 0 µ0 1 GeV is the minimum scale for which DGLAP evolution of the collinear parton densities is valid. We use the last version of KMRW uPDF obtained from DGLAP eqs.: In this case (a(x, µ2 ) = xG or a(x, µ ) = xq ): The normalization condition 2
µ G. Watt, A.D. Martin, M.G. Ryskin, Eur. Phys. C31 (2003) 73. 2

a(x, µ2 ) =
0

Aa (x, k2 , µ2 )dk2 , T T = a(x, µ2 )Ta (µ2 , µ2 ), 0 0

is satisfied, if Aa (x, k2 , µ2 )| T
2 kT <µ2 0

where Ta (µ2 , µ2 ) are the quark and gluon Sudakov form factors. 0 The UPD Aa (x, k2 , µ2 ) is defined in all k2 region. T T
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The other uPDF was obtained using the CCFM ev. eq. The CCFM ev. eq. have b een solved numerically using a Monte-Carlo method:
H. Jung, heph/9908497; H. Jung, G. Salam, EPJ C19 (2001) 359; H. Jung, S.P. Baranov, M. Deak at al., EPJ C70 (2010) 1237.

According to the CCFM ev. eq., the emission of gluons during the initial cascade is only allowed in an angular-ordered region of phase space. The maximum allowed angle related to the hard quark b ox ^ sets the scale µ: µ2 = s + Q2 (= µ2 ). T f The unintegrated gluon distribution are determined by a convolution of the non-p erturbative starting distribution A0 (x) and CCFM ¯ evolution denoted by A(x, k2 , µ2 ): T xA(x, k2 , µ2 ) = T where
2 xA0 (x) = N xp0 (1 - x)p1 exp(-k2 /k0 ). T

x¯x dz A0 (z ) A( , k2 , µ2 ), zzT

The parameters were determined in the fit to F2 data.
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Heavy quark production in pp-interaction
¯ The hard partonic subprocess g g QQ amplitude is describ ed by three Feynman's diagrams,

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which corresp ond to m.e. p 1 - q1 + M ^ ^ ( -i g ) ( p 1 - q1 ) 2 - M 2 p 1 - q2 + M ^ ^ ( -i g µ ) µ M2 = u(p1 )(-ig ) (q2 )i ¯ ( p 1 - q2 ) 2 - M 2 g 2 µ ( q 1 ) ( q 2 µ M3 = u(p1 )C (-q1 , -q2 , q1 + q2 ) ¯ ( q1 + q2 ) 2 M1 = u(p1 )(-ig µ )µ (q1 )i ¯ where C
µ

( q2 ) v ( p 2 ) , ( q1 ) v ( p 2 ) , ) v (p2 ),

( q1 , q2 , q3 ) = i ( (q2 - q1 ) g

µ

+ (q3 - q2 )µ g +(q1 - q3 ) g µ ).

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¯ The Sudakov decomp osition for the process pp QQX has form: p1 = 1 P1 + 1 P2 + p1T , p2 = 2 P1 + 2 P2 + p2T , q 1 = x 1 P 1 + q 1T , q 2 = x 2 P 2 + q 2T ,
2 2 2 2 p 2 = p 2 = M 2 , q 1 = q 1T , q 2 = q 2T . 1 2 In the center of mass frame of colliding particles 2 2 P1 = (E , 0, 0, E ), P2 = (E , 0, 0, -E ), E = s/2, P1 = P2 = 0, (P1 P2 ) = s/2.

Sudakov variables: 1 1 q +q M2T M1T = exp(y1 ), 2 = exp(y2 ), s s M1T M2T = exp(-y1 ), 2 = exp(-y2 ), s s
2T

1T

=p

1T

+ p2T , x1 = 1 + 2 , x2 = 1 + 2 .
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¯ The cross section of the process pp QQX is 1 ¯ X) = ¯ ¯ (pp QQ ¯ A(x1 , k2T , µ2 )A(x2 , k2T , µ2 )|M(g g QQ)|2 â 1 2 2 16 (x1 x2 s) . d 1 d 2 âdp2T dk2T dk2T dy1 dy2 2 1 1 2 2 In the numerical calculations we have used three different sets, namely CCFM A0 (B0) and KMR ones. The difference b etween A0 and B0 sets is connected with the different values of soft cut and width of the intrinsic kT distribution. A reasonable description of the F2 data can b e achieved by b oth these sets. For the input, we have used the standard MSTW'2008 (LO) (in LZ calculations) and MRST 99 (in CASCADE) sets. The unintegrated gluon distributions dep end on the renormalization and factorization scales µR and µF . We set µ2 = m2 + (p2T + p2T )/2, R Q 1 2 2 2 µF = s + QT , where QT is the transverse momentum of the initial off^ shell gluon pair, mc = 1.4 ± 0.1 GeV, mb = 4.75 ± 0.25 GeV. We use the LO formula for the coupling s (µ2 ) with nf = 4 active quark flavors at R 2 QCD = 200 MeV, such that s (MZ ) = 0.1232.
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5. Numerical results
Recently we have demonstrated reasonable agreement b etween the kT -factorization predictions and the Tevatron data on the b-quarks, b¯ b di-jets, B + - and D-mesons:
H. Jung, M. Kr¨mer, A.V. Lipatov, N.Z., JHEP 1101 (2011) 085. a

Based on these results, here we give here analysis of the CMS data in the framework of the kT -factorization approach. We produce the relevant numerical calculations in two ways: · We will p erforme analytical parton-level calculations (which are lab eled as LZ). · The measured cross sections of heavy quark production will be compared also with the predictions of full hadron level Monte Carlo event generator CASCADE:
H. Jung, Comp. Phys. Comm. 143 (2002) 100; H. Jung, S. Baranov, M. Deak at al. Eur. Phys. J. C70 (2010) 1237.

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We b egin the discussion by presenting our results for the muons originating from the semileptonic decays of the b quarks. The CMS collaboration has measured the transverse momentum and pseudorapidity distributions of muons from b-decays. The measurements have b een p erformed in the kinematic ange pµ > 6 GeV and | µ | < 2.1 at the r T total center-of-mass energy s = 7 TeV. To produce muons from b-quarks, we first convert b-quarks into B mesons using the Peterson fragmentation function with default value b = 0.006 and then simulate their semileptonic decay according to the standard electroweak theory taking into account the decays b µ as well as the cascade decay b c µ.

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LZ

Sochi, Russia, Sep. 27, 2011
Cascade
CMS 800 CCFM set A0 CCFM set B0 KMR 600

800

600

d/d (pp b+X µ+X') [nb]

d/dµ [nb]

1000

1000

400

400

µ

200

200

0

-2

-1

0

1

2

0

-2

-1

0

1

µ

2



µ

The pseudo-rapidity distributions of muons arising from the semileptonic decays of beauty quarks. The first column shows the LZ numerical results while the second one depicts the CASCADE predictions. The solid, dashed and dashdotted, dotted histograms correspond to the results obtained with the CCFM A0, B0 and KMR unintegrated gluon densities. The experimental data are from C MS .

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LZ

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Cascade
10
3

d/dp (pp b+X µ +X') [nb/GeV]

d/dpµ [nb/GeV] T

103

CMS CCFM set A0 CCFM set B0

10

2

102

KMR

101

10

µ

T

100 10 15 20

1 10 15 20 25

pµ T

25

30

p [GeV]
T

µ

30

[GeV]

The transverse decays of beaut the second one is the same as

momentum y quarks. T depicts the on previous

distributions of muons arising from the semileptonic he first column shows the LZ numerical results while CASCADE predictions. Notation of al l histograms slide. The experimental data are from CMS.

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LZ

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LZ

600

d/dpµ [nb/GeV] T

d/dµ [nb]

800

103

102

400 101 200 100 0 -2 -1 0 1 2
µ

10

15

20



pµ T

25

30

[GeV]

The dependence of our predictions on the fragmentation scheme. The solid, dashed and dash-dotted histograms correspond to the results obtained using the Peterson fragmentation function with b = 0.006, b = 0.003 and the nonperturbative fragmentation functions respectively. We use CCFM (A0) gluon density for il lustration. The experimental data are from CMS.

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LZ

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d/d [µb]

100

80

60

40

20

0

2

3

4

5

6

Hb

The pseudorapidity distributions of b-flavored hadrons at LHC. The histograms - LZ results with the CCFM AO, BO and KMR u.g.d. The exp. data are from LHCb col laboration.

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LZ |y| < 0.5
105 104 103 10
2

Sochi, Russia, Sep. 27, 2011
LZ 0.5 < |y| < 1

d/dy dpT [µb/GeV]

d/dy dpT [µb/GeV]

106

106 105 104 103 102 101 100 10-1

101 100 10-1 102

10-2

102

b-jet pT [GeV] d/dy dpT [µb/GeV] d/dy dpT [µb/GeV]
106 10
5

b-jet pT [GeV]
106 105 104 103 102 101 100 10-1

LZ 1 < |y| < 1.5

LZ 1.5 < |y| < 2

104 103 10
2

101 100 10-1 102

10-2

102

b-jet pT [GeV]

b-jet pT [GeV]

The double differential cross sections d /dy dpT of inclusive b-jet production.
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105

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LZ d/d [pb] pT > 84 GeV
104

LZ pT > 120 GeV

d/d [pb]

104

103

103

102

102

0

1

2

3

101

0

1

2

3

d/dR [pb] pT > 84 GeV
104

d/dR [pb]
104

105

LZ

LZ pT > 120 GeV

103

103 102 10
2

101

0

1

2

3

4

101

0

1

2

3

4

R

R

Importance of non-zero kT of incoming gluons. Ditted histograms - the results obtained without the virtualities gluons and with k2 < µ2 in m.e.. The CMS T R data.

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Quarkonium production in pp-interaction
The production of prompt J / () mesons in pp collisions can proceed via either direct gluon-gluon fusion or the production of P -wave states c (b ) and S -wave state followed by their radiative decays c (b ) J / () + . In the CS model the direct mechanism corresp onds to the partonic subprocess g + g J / () + g . The production of P -wave mesons is given by g + g c (b ), and there is no emittion of any additional gluons. The feed-down contribution from S -wave state is describ ed by g + g + g . The cross sections charmonium states dep end on the renormalization ^ and factorization scales µR and µF . We set µ2 = m2 +p2 and µ2 = s+Q2 , R T F T 2 where QT is the tr. momentum of initial off-shell gluon pair. Following to PDG, we set mJ/ = 3.097 GeV, mc1 = 3.511 GeV, mc2 = 3.556 GeV, m = 3.686 GeV and use the LO formula for the coupling constant 2 s (µ2 ) with nf = 4 quark flavours at QC D = 200 Mev, such that (MZ ) = 0.1232.
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The charmonium wave functions are taken to b e equal to |RJ/ (0)|2 = 0.0876 GeV3 , |R (0)|2 = 0.075 GeV5 , |R (0)|2 = 0.0391 GeV3 and the following branching fractions are used B (c1 J / + ) = 0.356, B (c2 J / + ) = 0.202, B ( J / + X ) = 0.561 and B (J / µ+ µ- ) = 0.0593. Since the branching fraction for c0 J / + decay is more than an order of magnitide smaller than for c1 and c2 , we neglect its contribution to J / production. As J / + X decay m.e. are unknown, these events were generated according to the phase space.

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N.P. Zotov, QFTHEP 2011
101

Sochi, Russia, Sep. 27, 2011

B d/dy dpT [nb/GeV]

CMS

B d/dy dpT [nb/GeV]

|y| < 1.2

102

CMS

1.2 < |y| < 1.6

100

101

100

10-1 10-1 10 20 30 10 20 30

pT [GeV] B d/dy dpT [nb/GeV]
CMS

pT [GeV]

1.6 < |y| < 2.4 102

101

100

10-1 0 10 20 30

pT [GeV]

Double differential cross section d /dy dpT of prompt J / production at LHC. Solid, dashed and dashed-dotted curves correspond to the results obtained using the CCFM A0, B0 and KMR u.p.d.. Dotted curves represent the contribution from sole direct production mechanism calculated with the CCFM A0 u.g.d..
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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

Differential cross section J / mesons at LHC in CASCADE. The experimental data are from CMS

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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

B d/dy dpT [nb/GeV]

101 100 10-1 10-2 10-3 10-4

ATLAS

B d/dy dpT [nb/GeV]

ATLAS

|y| < 0.75

101 100 10-1 10-2 10-3 10-4

0.75 < |y| < 1.5

10

40

10

40

pT [GeV] B d/dy dpT [nb/GeV]
ATLAS

pT [GeV] B d/dy dpT [nb/GeV]
ATLAS

103 102 101 100 10-1 10-2 10-3

1.5 < |y| < 2

101

2 < |y| < 2.4

100

10-1

10-2 1 10 10

pT [GeV]

pT [GeV]

Double differential cross section d /dy dpT of the J / production at LHC compared to the ATLAS data.
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N.P. Zotov, QFTHEP 2011
104 104

Sochi, Russia, Sep. 27, 2011

d/dy dpT [nb/GeV]

LHCb

d/dy dpT [nb/GeV]

LHCb

2.5 < y < 3 103

3 < y < 3.5 103

102

102

101

101

100

0

2

4

6

8

10

12

14

100

0

2

4

6

8

10

12

14

pT [GeV] d/dy dpT [nb/GeV]
LHCb

pT [GeV] d/dy dpT [nb/GeV]
104
LHCb

104

3.5 < y < 4 103

4 < y < 4.5 103

102

102

101

101

100 0 2 4 6 8 10 12 100 0 2 4 6 8 10

pT [GeV]

pT [GeV]

Double differential cross section d /dy dpT of the J / production at LHC compared to the LHCb data.
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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

Conclusions
· There is steady progress toward a b etter understanding of the kT factorization (high energy factorization) and the uPDF (TMD). · We have describ ed the first exp. data of b-quark and J / production at LHC in the kT -factorization approach. · We have obtained reasonable agreement of our calculations and the first exp erimental data taken by the CMS and ATLAS Collab orations. · The dep endence of our predictions on the u.g.d. app ears at small transverse momenta and at large rapidities in Hb and J / production covered by the LHCb exp eriment. · Our study has demonstrated also that in the framework of the kT -factorization approach is no room for a CO contributions for the charmonium production at the LHC.
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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

· The future exp erimental analyses of quarkonium p olarization at LHC turend out to b e very imp ortant and informative for discriminating the different theoretical models.

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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

Back up
Considering the p olarization prop erties of J / () mesons originating from radiative decays of P -wave states we rely up on the dominance of electric dip ole E 1 transitions. The corresp onding invariant amplitides can b e written as iA(c1 J / + ) = g1 µ kµ Polarization of the decay products
V (h=0) ( iA(c2 J / + ) = g2 pµ c2 ) J ( / ) (c1 ) (J / ) ( ) ( )

,
( ) µ

kµ - k

.

= B (1 V ) (1/2) + B (2 V ) (2/3) = B (1 V )

1 (|h|=1) 2 (h=0)

+ (1/2)

2 (|h|=1)



V (|h|=1)

1 (h=0)

+ (1/2)

1 (|h|=1) 2 (|h|=1)

+ B (2 V ) (1/3)

2 (h=0)

+ (1/2)

+

2 (|h|=2)

.

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N.P. Zotov, QFTHEP 2011

Sochi, Russia, Sep. 27, 2011

(1S ) Spin alignement at the TEVATRON

Dash-dotted lines ­ JB gluons; dashed ­ dGRV gluons; Thin lines ­ direct only; thick lines ­ with b decays added. Theor. predictions are from S.P. Baranov, N.Z. Pis'ma v ZhETF, 88 (2008) 825; D.Acosta et al.(CDF), Phys. Rev. Lett. 88 (2002) 161802; â V.M.Abazov et al.(DO), Phys. Rev. Lett.101 (2008) 182004. 41