HEAVY QUARK PRODUCTION AT HERA IN K T FACTORIZATION SUPPLEMENTED WITH CCFM EVOLUTION

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1 HEAVY QUARK PRODUCTION AT HERA IN K T FACTORIZATION SUPPLEMENTED WITH CCFM EVOLUTION H. JUNG Physics Deparmen, Lund Universiy, Box 8, S-22 Lund, Sweden Hannes.Jung@desy.de The applicaion of k - facorizaion, supplemened wih he CCFM small-x evoluion equaion, o heavy quark producion is discussed. Differenial cross secions of b b producion and also inelasic J/ψ producion as measured a HERA are compared o he hadron level CCFM Mone Carlo generaor Cascade, using he uninegraed gluon densiy obained wihin he CCFM evoluion approach from a fi o HERA F 2 daa. Inroducion The calculaion of inclusive quaniies, like he srucure funcion F 2 (x, Q 2 ) a HERA, performed in NLO QCD is in perfec agreemen wih he measuremens. Bu in exclusive quaniies like je or heavy quark producion large so-called K-facors (normalizaion facors),2 are needed o bring he NLO calculaions close o he daa. A large energies (small x), he evoluion of paron densiies proceeds over a large region in rapidiy y log(/x) and effecs of finie ransverse momena of he parons may become increasingly imporan. Cross secions canhenbek - facorized 3 ino an off-shell (k dependen) paronic cross secion ˆσ( x z,k )andak - uninegraed paron densiy funcion F(z,k ): dz σ = z d2 k x ˆσ( z,k )F(z,k ) () The uninegraed gluon densiy F(z,k ) is described by he BFKL evoluion equaion in he region of asympoically large energies (small x). An appropriae descripion valid for boh small and large x is given by he CCFM evoluion equaion 4,5,6,7, resuling in an uninegraed gluon densiy A(x, k, q), which is a funcion also of he addiional evoluion scale q. Caani 8,9 argues ha by explicily carrying ou he k inegraion in eq.() one can obain a form fully consisen wih collinear facorizaion: he coefficien funcions and also he DGLAP spliing funcions are no longer evaluaed in fixed order perurbaion heory bu supplemened wih he all-order resum- 345: submied o World Scienific on Ocober 29, 2

2 maion of he α s log /x conribuion a small x. This all-loop resummaion showsupinaso-callednon-sudakov form facor ns for CCFM. In his paper he k facorizaion approach is discussed wih respec o resolved phoon srucure and nex-o-leading correcions in he collinear approach. Then calculaions for b b and inelasic J/ψ producion a HERA are presened, using he uninegraed gluon densiy obained previously from a CCFM fi o he HERA srucure funcion F 2 (x, Q 2 ) 2 k -facorizaion versus higher order processes in collinear facorizaion LO NLO resolved phoon k facorizaion k = k = k = =/ k =/ k off shell ME Figure. Diagrammaic represenaion of LO, NLO and resolved phoon processes in he collinear approach compared o he k -facorizaion approach. The diagrams for LO, NLO and resolved phoon processes in he collinear approach are shown schemaically in Fig.. In collinear facorizaion, he incoming paron is on-mass-shell and has vanishing ransverse momenum k, whereas in k -facorizaion he parons enering he hard scaering marix elemen are free o be off-mass-shell. The advanage of he k -facorizaion approach becomes visible, when addiional hard gluon radiaion o a 2 2 process like γg Q Q is considered. If he ransverse momenum p g of he addiional gluon is of he order of ha of he quarks, hen in he collinear approach he full O(α 2 s ) marix elemen for 2 3 has o be calculaed. In k -facorizaion such processes are naurally included, even if only he LO α s off-shell marix elemen is used, since he k of he incoming gluon is no resriced from above, and herefore can acquire a virualiy similar o he ones in a complee fixed order calculaion. In Fig. he basic ideas are shown schemaically. No only does k -facorizaion include (a leas pars of) NLO diagrams, i also includes diagrams of he resolved phoon ype, wih he naural ransiion from real o virual phoons. 345: submied o World Scienific on Ocober 29, 2 2

3 The O(α s ) marix elemen in k -facorizaion includes he O(α s ) marix elemen of collinear facorizaion bu in addiion also higher order conribuions because he incoming gluon is off-shell and he uninegraed gluon densiy resums pars of he virual correcions (Fig. 2). p g(k ) g g(k ) BFKL CCFM Figure 2. Schemaic diagrams for k - facorizaion: lef is shown he oneloop correcion o he Born diagram for phoo-producion righ is shown he allloop improved correcion wih he facorized srucure funcion F(x, k 2 ) dn/dx g b - je - muon (ZEUS) no consrained from CCFM fi o F x g Figure 3. The fracional energy x g of he gluon of he process γg b b saisfying he kinemaic selecion of ZEUS 2. The uninegraed gluon densiy xa(x, k 2, q),3,4, was obained in he framework of k facorizaion using he CCFM evoluion equaion o fi he srucure funcion F 2 (x, Q 2 ). This gluon densiy xa(x, k 2, q) isusedin he hadron level Mone Carlo generaor Cascade 5 for any comparison wih measuremens. 3 Heavy quark producion a HERA The predicion of Cascade for he oal b b cross secion was compared o he exrapolaed measuremens of he H 6 and ZEUS 7 experimens a HERA. Since Cascade generaes full hadron-level evens, a direc comparison wih measuremens can be done, before exrapolaing he measuremen over he full phase space o he oal b b cross secion. I has been shown 3, ha he visible b b cross secion as measured by he ZEUS experimen 7 is in perfec agreemen wih he predicions from Cascade. However, large uncerainies come from he exrapolaion of he measured cross secion o he oal b b cross secion. If he exrapolaion is performed wih Cascade (or any oher program of he Lund family), approximae agreemen wih he NLO predicion is also achieved in he case of he ZEUS measuremen 7. The predicion of Cascade has also been compared 3 o he measuremen of H 6, where i was also shown ha he experimenal resuls from H and 345: submied o World Scienific on Ocober 29, 2 3

4 ZEUS are differen by a facor 2. I has been checked, ha he difference beween he experimens is no due o differen kinemaics. ZEUS ZEUS Figure 4. Differenial boom cross secion 2 as a funcion of he muon pseudo-rapidiy (ransverse momenum) for even wih wo jes and a muon, compared o Cascade and Pyhia (wih and w/o heavy quark exciaion). In Fig. 4 he differenial cross secion of µ s coming from b-quark decays as measured by ZEUS 2 is compared wih he predicion of Cascade. Again good agreemen is observed, excep in he region of large η µ. However his region is dominaed by large x g >.3 (see Fig. 3), where he applicaion of k -facorizaion is quesionable and also where he uninegraed gluon densiy is no a all consrained by he fi o F 2. dσ/dp 2 (nb/gev 2 ) H prel(96-97) CASCADE EPJPSI (a) dσ/dz (nb) H prel(96-97) CASCADE EPJPSI (b) p 2 (GeV 2 ) z Figure 5. The cross secion of γp J/ψ + X as a funcion of he ransverse momenum (a) and of of he fracional momenum z (b) ofhej/ψ as measured by H 8 compared o he predicions of Cascade and Epjpsi. The cross secion for γp J/ψ+X as a funcion of he ransverse momen- 345: submied o World Scienific on Ocober 29, 2 4

5 um of he J/ψ shows a significan deviaion from he leading order color single model predicion (as implemened in Epjpsi 9 ) in collinear facorizaion. In Fig. 5, he preliminary H measuremen 8 is compared o he predicion of Epjpsi 9. In collinear facorizaion, he harder ransverse momenum specrum is inerpreed as a signal for significan nex-o-leading order correcions. Also shown in Fig. 5a is he predicion of Cascade using he same CCFM uninegraed gluon densiy as before ogeher wih he k -facorized marix elemen 2 for γg J/ψg. The inelasic J/ψ phooproducion cross secion (z <.9) as a funcion of p T is nicely described by Cascade. Especially he large ransverse momenum par is explained as addiional hard iniial sae QCD radiaion. The same is also observed in full NLO calculaions, and i shows again he advanage of he k -facorizaion in simulaing a large par of he NLO correcion of he collinear approach, due o he non zero virualiy of he incoming gluon. The disribuion in he fracional momenum z of he J/ψ is also reasonably well described (Fig. 5b). 4 Conclusion The applicaion of he k -facorizaion approach o heavy quark producion a HERA has been discussed. I is shown, ha he visible b b producion cross secion as measured a ZEUS is nicely reproduced by Cascade, using he CCFM evolved uninegraed gluon densiy obained from a fi o F 2 (x, Q 2 ). I was poined ou, ha he exrapolaion from he measured o he oal b b cross secion conains large model dependencies. The differenial cross secions for inelasic J/ψ phooproducion can be reasonably well described wih Cascade, boh in erms of shape and normalizaion. The large ransverse momenum ail is a direc signal for addiional hard iniial sae QCD radiaion. I is he advanage of he k -facorizaion approach ha imporan pars of NLO and even NNLO conribuions are consisenly included due o he off-shell gluons, which ener ino he hard scaering process. Acknowledgmens I wan o hank he organizers M. Kienzle and M. Wadhwa for his very nice workshop. I am also graeful o S. Frixione for he inviaion o his workshop and his ineres in k -facorizaion. Many hanks also go o S. Baranov and N. Zoov for ineresing discussions and our fruiful collaboraion. I am also graeful o L. Gladilin, B. Naroska and J. Whimore for careful reading of he manuscrip. All hanks for he grea imes wih Anje. 345: submied o World Scienific on Ocober 29, 2 5

6 References. CDF Collaboraion; F. Abe e al., Phys. Rev. D55(997) D Collaboraion; B. Abbo e al., Phys. Le. B 487 (2) S. Caani, M. Ciafaloni, F. Haumann, Nucl. Phys. B 366 (99) M. Ciafaloni, Nucl. Phys. B 296 (988) S. Caani, F. Fiorani, G. Marchesini, Phys. Le. B 234 (99) S. Caani, F. Fiorani, G. Marchesini, Nucl. Phys. B 336 (99) G. Marchesini, Nucl. Phys. B 445 (995) S. Caani, k -facorisaion and perurbaive invarians a small x, inproceedings of he Inernaional Workshop on Deep Inelasic Scaering, DIS 96 (Rome, Ialy, 5-9 April, 996), hep-ph/ S. Caani, Aspecs of QCD, from he Tevaron o LHC, in Proceedings of he Inernaional Workshop Physics a TeV Colliders (Les Houches, France, 8-8 June, 999), hep-ph/ H. Jung, G. Salam, Eur. Phys. J. C9(2) 35, hep-ph/243.. S. Baranov, N. Zoov, Phys. Le. B 49 (2). 2. ZEUS Collaboraion; M. Derrick e al., Beauy phooproducion in he muon semi-leponic decay mode a HERA, in Conribued paper 496 o IECHEP 2, Budapes, Hungary (2). 3. H. Jung, Uninegraed paron densiies applied o heavy quark producion in he CCFM approach, in Proceedings of he Rinberg workshop on New rends in HERA physics, Ringberg Casle, Tegernsee, Germany. (2), hep-ph/ H. Jung, submied o Phys. Rev. D (2), DESY--36, hepph/ H. Jung, The CCFM Mone Carlo generaor Cascade for lepon - proon and proon - proon collisions, Lund Universiy, acceped by Comp. Phys. Comm., 2, hep-ph/92, DESY -4, hp:// 6. H Collaboraion; C. Adloff e al., Phys. Le. B 467 (999) 56, and erraum ibid. 7. ZEUS Collaboraion; J. Breiweg e al., Eur. Phys. J. C8(2) H Collaboraion; C. Adloff e al., Inelasic phooproducion of J/ψ and ψ(2s) ah,inconribued paper 57aj o IECHEP 999, Tampere, Finnland (999). 9. H. Jung, EPJPSI: A Mone Carlo generaor for J/ψ mesons in high energy γ p, e p and p p collisions, version 3.3, Lund Universiy, 995, hp://www-h.desy.de/~jung/epjpsi.hml. 2. V. Saleev, N. Zoov, Mod. Phys. Le. A9(994) : submied o World Scienific on Ocober 29, 2 6