FR9703192
C.E. SACLAY DE rnrni DES MIDCUES DSM
DAPNIA/SPP 96-19 October 1996
QCD DIPOLE PREDICTION FOR DIS AND DIFFRACTIVE STRUCTURE FUNCTIONS
Ch. Royon
28th International Conference on High Energy Physics 25-31 July 1996, Warsaw, Poland QCD DIPOLE PREDICTION FOR DIS AND DIFFRACTIVE STRUCTURE FUNCTIONS
Ch.ROYON DAPNIA-SPP, Centre d'Etudes de Saclay, F-91 191 Gif-sur-Yvette Cedex, France
The Fj, FQ, R = FL/FT proton structure functions are derived in the QCD dipole picture of BFKL dynamics. We get a three parameter fit describing the 1994 Hi proton structure function F2 data in the low x, moderate Q2 range. Without any additional parameter, the gluon density and the longitudinal structure functions are predicted.The diffractive dissociation processes are also discussed, and a new prediction for the proton diffractive structure function is obtained. a "Invited talk given at the 28th International Conference on High Energy Physics (ICHEP 96), 25-31 July 1996, Warsaw, Poland
The purpose of this contribution is to show where ff/Q2 is the (7 g(k) -4 q q) Born cross sec- that the QCD dipole picture l which contains the tion for an off-shell gluon of transverse momentum BFKL dynamics provides a pertinent model for k. F(z, (kr)2) is the unintegrated gluon distribu- describing the proton structure function at HERA tion of an onium state of size r and contains the in the low 1 and moderate Q2 range, as well as physics of the BFKL pomeron. the diffractive structure function. The recently Using once more the kr factorisation in ex- published HI data might provide an opportunity tracting a gluon from a dipole of transverse radius to distinguish between the different QCD evolu- r and assuming renormalisation group properties tion equations (DGLAP and BFKL equations 2) of F, one can show that5: for small x physics. This is why it is very impor- ton 2 tant to test the BFKL dynamics using the dipole F'" (*,Q ;Q§)= (2) model and k? factorisation 3. We can then get j predictions for F>, FG, and R = FL/FT proton structure functions, and for the proton diffractive where u can be interpreted as the Mellin trans- structure functions which represents a new predic- formed probability of finding an onium of trans- 2 tion of the dipole model. verse mass M in the proton, and Q\ is a typically non perturbative proton scale. We can use this generic result to get some 1 BFKL dynamics in the QCD dipole frame- predictions for FT, Ft, and FG (respectively the work transverse, longitudinal, and gluon structure func- tions) corresponding to /ij, hi, and ha'- To obtain the structure function Fo, we use the kj 3 factorisation theorem which is valid at high energy ((r(i-»)r(i+7)) 1 (small x). In a first step, we calculate the deep 3*7 r(2-2-y)r(2+2i) 1^ inelastic cross section aon"im of a photon of virtu- ality Q2 on an onium state (heavy qq state). This 7(1-7) (3) onium state can be described by dipole configu- 1 rations '. The photon-onium cross-section reads 2 0) o-onium _ f d rdz
F2~FT + Ft. (4) 3 Hard diffraction in the QCD dipole model:
4aA ln2 where aP - 1 = ^ . C, aP and Qo will The success of the dipole model applied to the be taken as free parameters for the fit of the HI proton structure function suggests to extend the data, it will then be possible to compare with the investigations to other inclusive processes, in par- values of ap predicted by theory. We get finally R, ticular to diffractive dissociation. We can distin- and FG/FI, which are independent of the overall guish two different components: normalisation C: - the "elastic" term which represents the elastic scattering of the onium on the target proton ~? (5) - the "triple-pomeron" term which represents the sum of all dipole-dipole interactions (it is domi- r(i -ici nant at large masses of the excited system). Let us describe in more details each of the two (6) components. The "triple-pomeron" term domi- nates at low /?, where 0 is the ratio between Bjorken- where yc is the saddle point value. x and rp, the proton momentum fraction carried by the "pomeron" 6. This component, integrated over /, the momentum transfer, is factorisable in 2 Fo fit and prediction for FG and R a part depending only on xp (flux factor) and on a part depending only on 0 and Q- ("pomeron" In order to test the accuracy of the F> parametri- 6 sation obtained in formula (4), a fit using the re- structure function) . cently published data from the HI experiment4 has been performed 5. We have only used the (7) 2 2 -3 points with Q < 150GW to remain in the do- l 2ap 2 = Sxp ~ (&NC7C(3) In — (8) main of validity of the QCD dipole model. The x V XP is 101 for 130 points, and the values of the param- eters are aP = 1.282, Qo = O.QZGeV, C = 0.077. The effective exponent (the slope oilnFp in Inxp) The result of the fit is shown in figure la. The is found to be dependent on xp and much smaller corresponding effective coupling constant to the than the BFKL exponent due to the ln(xp) in the obtained value of ap is a = 0.11, close to a(Mz) flux factor. F is equivalent to the proton structure used in the HI QCD fit. The value of QQ corre- function at small 0. sponds to a tranverse size of 0.3 fm which is the The elastic component behaves quite differ- expected non perturbative scale. ently 7. First it dominates at 0 ~ 1. It is also Relation (5) provides a paramater-free predic- factorisable like the inelastic component, but with tion for the gluon density (not shown in the fig- a different flux factor, which means that the sum of ure) which is in good agreement with the results the two components will not be factorisable. The obtained by the HI QCD fits based on a NLO 0 dependence is quite flat at large 0, and this is DGLAP evolution equation5. We also give a pre- due to the fact that there is an interplay between diction for the value of R, which is given in figure the longitudinal and transverse components. The lb. The only parameters which enters this pre- sum remains almost independent of/?, whereas the diction is Qo, determined by the Fi fit. The cor- R = FL/FT ratio is strongly 0 dependent. Once responding curve (full line) is compared with the more, a R measurement now in diffractive pro- one loop approximation of the h functions (dashed cesses will be an interesting way to distinguish the curve) of formula (3). The comparison of the two different models, as the dipole model predicts dif- curves exhibits the (In I/a;) terms resummation ef- ferent 0 and O2 behaviours from the others9. fects on the coefficient functions hy and hi. The The sum of the two components shown in fig- measurement of R might be an opportunity to dis- ure 2 describes quite well the HI data. There is tinguish between the BFKL and DGLAP mech- no further fit of the data as we chose to take the anisms, R being expected to be higher with the different parameters (Qa,ap, and the normalisa- DGLAP mechanism. We thus think that a mea- tion factor) from the Fj fit. The most striking surement of R. in this region would be useful. point is that we describe quite well the factorisa- tion breaking due to the resummation of the two components at low and large /?8. The full line is the sum of the two components, the dashed line the inelastic one (which dominates at low /?), and the dotted line the elastic one (which dominates at high (3). Acknowledgments
The results described in the present contribution 2.3 c^ \ 3(W come from a fruitful collaboration with A.Bialas, H.Navelet, R.Peschanski and S.Wallon. References V V I5OV 1. A.H.Mueller and B.Patel, Nucl. Phys. B425 (1994) 471., A.H.Mueller, Nucl. \ Phys. B437 (1995) 107., N.N.Nikolaev and fv B.G.Zakharov, Zeit. fiir. Phys. C49 (1991) \ 23CM' \ 49GM* 607., A.H.Mueller, Nucl. Phys. B415 (1994) 373.
2. G. Altarelli and G. Parisi, Nucl. Phys. L \ «oo*" \ 120 0.05 0.1 0=0.04 (3=0.04 0 = 0.04 (3=0.04 0=0.04 0=0.04 0=0.04 J 2 2 Q =2.5 Q2=3.5 Q =5 Q:=8.5 Q =12 Q2 = 20 Q3=35 0.05 0.1 13=0.1 (3 = 0.1 (3=0.1 (3=0.1 0=0.1 (3 = 0.1 Li. Q"=2.5 O:=3.5 Q3=8.5 0;=12 Q2=20 02=35 QJ=65 0.05 0.1 (3 = 0.2 0 = 0.2 (3 = 0. 0=0.2 0 = 0.2 0 = 0.2 02 = 2.5 Q2=X5 Q; = 8.5 O2=12 O2 = 20 0.05 0.1 0=0.4 0 = 0.4 0 = 0.4 0 = 0.4 0 = 0.4 3 : Q2 = 2.5 Q =8.5 0 =12 0.05 0.1 0=0.65 0 = 0.65 0=0.65 0 = 0.65 0=0.65 0=0.65 = 0.65 Q2 = 2.5 02=3.5 Q2=8.5 Q"=12 0.05 0.1 0=0.9 0 = 0.9 0 = 0.9 0 = 0.9 0=0.9 0: = 2.5 0;=8.5 Q: = 20 0.05 nJiliJ ilimJ J «7777iJ i ntJtuii J JIIIIJIJ I liiiJnJ i IIIUJ J I imjiliiiul ytuml i L tmi imJ l 1 ILIILIJ llliuiiluj l l nuj lliiuj lllllllnjj llllllJ I 111U J io"Jio-2 io"* io° in"2 xp xp xp xp xp xp xp xp Figure 2: Prediction on F2D (cf text)