PoS(DIFF2006)016. Diffraction at the Tevetron: CDF Results

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1 Diffraction at the Tevetron: CDF Results The Rockefeller University, 30 York Avenue, New York, NY 03, USA The diffractive roram of the CDF Collaboration at the Fermilab Tevatron Collider is reviewed with emhasis on recent results from Run II at s =.96 TeV. Udated results on the x B j and Q deendence of the diffractive structure function obtained from dijet roduction, and on the sloe arameter of the t-distribution of diffractive events as a function of Q in the rane GeV < Q < 4 GeV, are resented and comared with theoretical exectations. Results on cross sections for exclusive dijet and dihoton roduction are also resented and used to calibrate theoretical estimates for exclusive His roduction at the Lare Hadron Collider. DIFFRACTION International Worksho on Diffraction in Hih-Enery Physics Setember Adamantas, Milos island, Greece Seaker. Presented on behalf of the CDF collaboration. c Coyriht owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. htt://os.sissa.it/

2 . Introduction The CDF collaboration has been involved in a systematic and comrehensive roram of studies of diffractive interactions since the start of oerations of the Fermilab Tevatron collider in 989. The ultimate oal of this roram is to rovide exerimental results which will be of hel in elucidatin the QCD character of hadronic diffraction []. Diffractive interactions are characterized by lare raidity as in the final state, resumed to occur via the exchane of a quark/luon combination carryin the quantum numbers of the vacuum. This exchane is traditionally referred to as Pomeron []. The rocess which is directly analoous to the classical diffraction of liht is elastic scatterin, but it is inelastic diffraction rocesses that rovide the most strinent tests for QCD insired models of diffraction. The total cross section is also of interest in testin theoretical models of diffraction, since it is related to the imainary art of the forward elastic scatterin amlitude throuh the otical theorem. In this aer, we resent results obtained at the Tevatron by CDF and comment on their hysics sinificance. The names / dates of the Tevatron runs and interated luminosities of data collected by CDF are listed below: Run Number Date Lum (b ) Run I IØ Ia Ib Ic Run II IIa IIb currently in roress In Run IØ, CDF measured elastic, sinle diffractive, and total cross sections at s =630 and 800 GeV. In Runs Ia, Ib and Ic, CDF studied both soft and hard diffractive rocesses, with the latter incororatin a hard artonic scatterin in addition to the characteristic lare raidity a of diffraction. Fiure shows schematically the diarams and final state event tooloies of the rocesses studied by CDF in Run I. In Run II, the CDF diffractive roram was enhanced by extendin the kinematic rane of the measurements of hard diffractive rocesses and by additional studies of exclusive roduction rocesses. All Run I results have been ublished. These results are briefly summarized. The Run II results are discussed in more detail. Recent results on the x-bjorken and Q deendence of the diffractive structure function and on the t-deendence of diffractive cross sections are reorted and characterized in terms of their hysics content. In addition, results on exclusive dijet and dihoton roduction are resented and their sinificance in calibratin redictions for exclusive His boson roduction at the LHC is discussed. Raidity as are reions of raidity devoid of articles; raidity, y = E+ L E, and seudoraidity, η = lntan θ L, are used interchaneably, as in the kinematic reion of interest the values of these two variables are aroximately equal.

3 Fiure : Schematic diarams and event tooloies in azimuthal anle φ versus seudoraidity η for (a) elastic and total cross sections, and (b) sinle diffraction (SD), double diffraction (DD), double Pomeron exchane (DPE), and double lus sinle diffraction cross sections (SDD=SD+DD). The hatched areas reresent reions in which there is article roduction.. Run IØ Results In Run IØ, CDF measured the elastic, soft sinle diffractive, and total cross sections at s =630 and 800 GeV. The measurement was erformed with the CDF I detector, which durin run IØ had trackin coverae out to η 7 and Roman Pot Sectrometers on both sides of the Interaction Point (IP). The normalization was obtained by the luminosity indeendent method, which is based on simultaneously measurin the total interaction rate, which deends on σ T, and the elastic scatterin differential rate at t = 0, which deends on σt (otical theorem): σ T L ( Nel + N inel ) & σt dn el + ρ dt t=0 σ T = 6π + ρ dn el N el + N inel dt t=0 Paradoxically, overestimatin the total rate, as for examle due to backround events, yields smaller elastic and total cross sections, while loss of inelastic events results in larer cross sections. Fiure (left) shows Ree based fits to total and elastic scatterin data usin the eikonal aroach to ensure unitarity [3]. Good fits are obtained, which are consistent with the CDF cross sections at the Tevatron even if the Tevatron cross sections are not used in the fit [3]. In contrast, the standard Ree fit to total sinle diffractive cross sections, shown in Fi. (riht), overestimates the Tevatron cross sections by a factor of. This discreancy reresents a breakdown of factorization, which is restored by the renormalization rocedure roosed in Ref. [4]. 3

4 Total Sinle Diffraction Cross Section (mb) 0 ξ < 0.05 Albrow et al. Armitae et al. UA4 CDF E7 Cool et al. "knee" at GeV 0 s (GeV) Renormalized flux 00 Standard flux Fiure : (left) Simultaneous fit to, π ±, and K ± total cross section and ρ-value data usin eikonalized (solid) and Born level (dashed) amlitudes [3] - the rise of the cross section with s is ulled by the rise of the π ± cross sections and would ass throuh the CDF oint at s = 800 GeV even if this oint were not used in the fit; (riht) total / sinle diffraction dissociation cross section data (sum of and dissociation) for ξ < 0.05 comared with Ree redictions based on standard and renormalized Pomeron flux [4]. 3. Run Ia,b,c Results The diffractive rocesses studied by CDF in Tevatron Runs Ia,b,c (99-996) are schematically shown in Fi. b. Both soft and hard rocesses were studied. A discussion of the results obtained and of their sinificance in deciherin the QCD nature of the diffractive exchane can be found in Ref. [5]. The most interestin discoveries from this diffractive roram were the breakdown of factorization and the restoration of factorization in events with multile raidity as. 000 Breakdown of factorization. At s =800 GeV, the SD/ND ratios (a fractions) for dijet, W, b-quark, and J/ψ roduction, as well the ratio of DD/ND dijet roduction, are all %. This reresents a suression of a factor of relative to redictions based on diffractive arton densities measured from DDIS at HERA, indicatin a breakdown of QCD factorization comarable to that observed in soft diffraction rocesses relative to Ree theory exectations. However, factorization aroximately holds amon the four different diffractive rocesses at fixed s, which indicates that the suression has to do with the formation of the raidity a, as redicted by the eneralized a renormalization model (see [5]). Restoration of factorization in multi-a diffraction. Another interestin asect of the data is that ratios of two-a to one-a cross sections for both soft and hard rocesses obey factorization. This rovides both a clue to understandin diffraction in terms of a comosite Pomeron and an exerimental tool for diffractive studies usin rocesses with multile raidity as (see [5]). 4

5 4. The Run II Diffractive Proram In Run II, CDF has been conductin the followin studies of diffraction: structure function in dijet roduction, t distributions, exclusive dijet, dihoton, and e + e roduction, structure function in W roduction, a between jets: deendence of the cross section on a size for fixed η jet. In this aer, we resent reliminary results on the first three toics. The diffractive W and a between jets analyses are in roress and results are exected in early Run II forward detectors ROMAN POTS A-48 DIPOLES ELECTROSTATIC SEPARATOR ESS TOROID MINIPLUG QUADS CDF z m 3.63 m 3.3 m 6.59 m 0 BSC-4 BSC-3 BSC- BSC- MP Fiure 3: The CDF detector in Run II: (left) location of forward detectors alon the direction; (riht) osition of the Cerenkov Luminosity Monitor (CLC) and MiniPlu calorimeters (MP) in the central detector. The Run II diffractive roram was made ossible by an uraded CDF detector [6], which includes the followin secial forward comonents (Fi. 3): Roman Pot Sectrometer (RPS) to detect leadin antirotons, MiniPlu (MP) forward calorimeters aroximately coverin the reion 3.5 < η < 5.5, Beam Shower Counters (BSC) ositioned around the beam ie at four (three) locations alon the () beam direction to ta raidity as within 5.5 < η < 7.5. The Roman Pot Sectrometer is the same one that was used in Run Ic. It consists of X-Y scintillation fiber detectors laced in three Roman Pot Stations located at an averae distance of 57 m downstream in the direction. The detectors have a osition resolution of ±0 µm, which makes ossible a 0.% measurement of the momentum. In Run Ic, the -beam was behind the roton beam, as viewed from the RPS side. An inverted olarity (with resect to Run I) of the electrostatic beam searators enabled movin the RPS detectors closer to the -beam and thereby ain accetance for small t down to ξ x F ( ) = 0.03 (for larer t, lower ξ values can be reached). 5

6 χ / ndf 3.6 / Prob Const 0.03 ± sloe.07 ± The MiniPlu calorimeters are laced within the holes of the muon toroids. They consist of layers of lead lates immersed in liquid scintillator. The scintillation liht is icked u by wavelenth shiftin fibers strun throuh holes in the lead lates and read out by multi-channel PMT s. The calorimeter tower" structure is defined by arranin fibers in rous to be read out by individual PMT ixels. There are 84 towers in each MiniPlu, and the sinals they rovide can be used to measure enery and osition for both electromanetic and hadron initiated showers [7]. The Beam Shower counters are rins of scintillation counters huin" the beam ie. The BSC- rins are semented into four quadrants, while in the other BSCs are semented into two halves. The BSC- are also used to rovide raidity a triers and for measurin beam losses. 4. Diffractive structure function from dijet roduction In Run II, CDF has obtained reliminary results for the x B j, Q, and t deendence of the diffractive structure function from dijet roduction at s = 960 GeV. The measured x B j rates confirm the factorization breakdown observed in Run I (see review in Ref. [8]). The Q and t deendence results are shown in Fi 4. ) / ND ξ Ratio ( SD / Q Q Q Q Q CAL 0.03< ξ <0.09 * * jet jet Q <E T >, <E T >=(E T +E T )/ overall syst. uncertainty: ± 0% (norm), ± 6% (sloe) 0 GeV 400 GeV,600 GeV 3,000 GeV 6,000 GeV Q,000 GeV -3 - x - Bj ) at t =0 (arbitrary units) b(q <ξ RPS <0.08 RPS inclusive norm. to unity and set at Q = GeV Q (GeV ) Fiure 4: (left) Ratio of diffractive to non-diffractive dijet event rates as a function of x B j (momentum fraction of arton in antiroton) for different values of E T = Q ; (riht) b t=0 sloe vs Q. Q deendence. In the rane GeV < Q < 4 GeV, where the inclusive E T distribution falls by a factor of 4, the ratio of the SD/ND distribution increases, but only by a factor of. This result indicates that the Q evolution in diffractive interactions is similar to that in ND interactions. t-deendence. The sloe arameter b(q ) t=0 of an exonential fit to t distributions near t = 0 shows no Q deendence in the rane GeV < Q < 4 GeV. These results suort the icture of a comosite Pomeron formed from color sinlet combinations of the underlyin arton densities of the nucleon (see [5]). 4.3 Exclusive Dijet Production Exclusive roduction in collisions is of interest not only for testin QCD insired models of diffraction, but also as a tool for discoverin new hysics. The rocess that has attracted the 6

7 most attention is exclusive His boson roduction. The search for His bosons is amon the to riorities in the research lans of the LHC exeriments. While the main effort is directed toward searches for inclusively roduced His bosons, an intense interest has develoed toward exclusive His roduction, / + / + H +. This His roduction channel resents several advantaes: it can rovide clean events in an environment of suressed QCD backround, in which the His mass can accurately be measured usin the missin mass technique by detectin and measurin the momentum of the outoin roton and (anti)roton. However, exclusive roduction is hamered by exected low roduction rates [9]. As rate calculations are model deendent and enerally involve non-erturbative suression factor(s), it is considered rudent to calibrate them aainst rocesses involvin the same suression factors(s), but have hiher roduction rates that can be measured at the Tevatron. One such rocesses is exclusive dijet roduction, which roceeds throuh the same mechanism as His roduction, as shown in Fi. 5. Jet Jet Fiure 5: Lowest order diarams for exclusive dijet (left) and His (riht) roduction in collisions. The search for exclusive dijets is based on measurin the dijet mass fraction, R j j, defined as the mass of the two leadin jets in an event, M j j, divided by the total mass reconstructed from the enery deosited in all calorimeter towers, M X. The sinal from exclusive diets is exected to aear at hih values of R j j, smeared by resolution and radiation effects. Events from inclusive DPE roduction, +a+ j j +X +a, are exected to contribute to the entire M j j reion. Any such events within the exclusive M j j rane contribute to backround and must be subtracted when evaluatin exclusive roduction rates. H The method used to extract the exclusive sinal from the inclusive R j j distribution is based on fittin the data with MC simulations []. Two methods have been used. In the first one, the POMWIG and ExHuME enerators are used for simulatin inclusive and exclusive events, resectively; in the second, inclusive (exclusive) distributions are simulated usin the POMWIG (DPEMC) roram. Exerimentally, the MC non-exclusive dijet backround shae is checked by a study of hih E T b-taed dijet events, as quark jet roduction throuh qq is suressed in LO QCD by the J z = 0 selection rule as m q /M jet 0. Fiure 6 shows measured R j j distributions lotted versus dijet mass fraction. On the left, the number of events within the secified kinematic reion is comared with fits based on POMWIG lus ExHuME distribution shaes, and on the riht with fits based on POMWIG DPEMC redictions. Both aroaches yield ood fits to the data. The suression factor exected for exclusive b-taed dijet events is checked with CDF data in Fi. 7. Within the quoted errors, this result validates the MC based method for extractin the exclusive sinal. 7

8 Events F excl = 5.0 ±. % (stat. only) DPE data (stat. only) POMWIG: CDF H ExHuME Best Fit to Data 3.6 < η a < 5.9 jet E T > GeV jet3 E T < 5 GeV R jj = M jj / M X Events F excl = 5.8 ±.3 % (stat. only) DPE data (stat. only) POMWIG: CDF H Exclusive DPE (DPEMC) Best Fit to Data 3.6 < η a < 5.9 jet E T > GeV jet3 E T < 5 GeV R jj = M jj / M X Fiure 6: Extraction of exclusive dijet roduction sinal usin Monte Carlo techniques to subtract the inclusive dijet backround: (left) dijet mass fraction in data (oints) and best fit (solid line) obtained from MC events enerated usin the POMWIG (dashed) and ExHuME (filled) MC enerators for inclusive and exclusive events, resectively; (riht) the same data fitted with POMWIG and exclusive DPEMC enerators. F F F MC incl = POMWIG + Backround (CDF H-fit) normalized to Data incl at R jj <0.4 : stat. error only F F bc/incl MC incl / F bc/incl (R jj <0.4) / Data incl F Systematic Uncertainty R = M jj /M jj X Fiure 7: (circles) Fraction of heavy flavor (b, c) to all dijet events in data, F, as a function of dijet mass fraction showin the exected suression at hih M j j ; (squares) fraction, F, of inclusive MC to data from Fi. 6 (left). The areement between the measured suression levels in F and F serves to validate the MC based technique for extractin the exclusive roduction rate from the data. (b) excl jj σ 3 - jet, min E T > E T jet, η < < η a < < ξ < 0.08 Data corrected to the hadron level stat. error Exclusive DPE (DPEMC) ExHuME stat. syst. error min Jet E T (GeV) b GeV/c excl dσ jj jj dm jet, η < < η a < < ξ < 0.08 ExHuME (Hadron Level) Default Derived from CDF Run II excl min Preliminary σ jj (E T ) Systematic Uncertainty M (GeV/c ) jj Fiure 8: (left) Measured exclusive dijet cross sections versus the minimum E T of the two leadin jets comared with ExHuME and DPEMC redictions; (riht) ExHuME hadron level differential exclusive dijet cross section vsersus dijet mass normalized to the CDF cross sections at left. The systematic errors shown are roaated from those in the data; the ExHuME redictions have comarable systematic uncertainties. 8

9 In Fi. 8 (left), interated cross sections above a minimum E jet, are comared with ExHuME T and DPEMC redictions. The data favor the ExHuME rediction. ExHuME hadron level differential cross sections dσ excl /dm j j normalized to the measured data oints of Fi. 8 (left) are shown in Fi. 8 (riht) with errors roaated from the uncertainties in the data. Within the errors, the ood areement with the default ExHuME rediction u to masses in the reion of the standard model His mass redicted from lobal fits to electroweak data lends credence to the calculation of Ref. [9]. for exclusive His boson roduction at the LHC. 4.4 Exclusive γγ roduction Exclusive γγ roduction in collisions roceeds throuh a lowest order diaram similar to that of Fi. 5 (riht), but with the luons that roduce the His relaced by γ s. Therefore, like exclusive dijet roduction, exclusive γγ roduction can also be used for calibratin models of His roduction at hadron colliders. A search for exclusive γγ roduction has been erformed on a samle of events collected by requirin a hih E T electromanetic shower in combination with a loose forward raidity a requirement. In the data analysis, the raidity a requirement was tihtened, and the search was narrowed down to events with two hih E T hoton showers satisfyin certain exclusivity requirements. In a data samle of 53 b total interated luminosity, three exclusive γγ candidate events with E γ > 5 GeV were found with no tracks ointin to the electromanetic clusters. As a check of T the robustness of the raidity a requirement, CDF measured the cross section for the urely QED rocess + + e + e +, whose cross section can be reliably calculated. Twelve exclusive e + e candidate events were found in the data with an estimated backround of , yieldin σ(γγ) = (stat) ± 0.03(syst) b and σ(e+ e ) = (stat) ± 0.3(syst) b, which arees with an exectation of.7 ± b. For γγ roduction, the backround estimate is not yet comlete; based on Ref. [9], the number of events exected in this data samle is Summary The diffractive roram of the CDF Collaboration at the Fermilab Tevatron Collider has been reviewed with emhasis on recent results from Tevatron Run II at s =.96 TeV. Run I results have been briefly resented and their hysics sinificance laced in ersective. Processes studied by CDF in Run I include elastic and total cross sections, soft diffractive cross sections with sinle and multile raidity as, and hard sinle diffractive roduction of dijet, W, b-quark, and J/ψ roduction, as well as central dijet roduction in events with two forward raidity as (double Pomeron exchane). The results obtained suort a icture of universality of diffractive raidity a formation across soft and hard diffractive rocesses, which favors a comosite over a article-like Pomeron made u from color sinlet quark and/or luon combinations with vacuum quantum numbers. Run II results on the x B j and Q deendence of the diffractive structure function obtained from dijet roduction have been resented, as well as on the sloe arameter of the t-distribution of diffractive events as a function of Q. In the rane GeV < Q < 4 GeV, where the inclusive E T distribution falls by a factor of 4, the ratio of SD/ND distributions varies by only a factor of, indicatin that the Q evolution in diffractive interactions is similar to that in ND 9

10 ones; and the sloe arameter b(q ) t=0 of an exonential fit to t distributions near t = 0 in the rane GeV < Q < 4 GeV shows no Q deendence. These results suort a icture of a comosite diffractive exchane (Pomeron) made u from the underlyin arton densities of the nucleon. Results on cross sections for exclusive dijet and dihoton roduction have also been resented and their sinificance for calibratin theoretical estimates for exclusive His roduction at the Lare Hadron Collider discussed. The exclusive dijet cross section was measured u to jet ET min of 35 GeV. When exressed as a function of dijet mass M j j, cross sections u to masses of M j j 40 GeV are obtained, which are in the reion of the standard model His mass exected from lobal fits to electroweak data. A measurement of exclusive γγ roduction, a rocess which can also be used for calibratin His roduction models, yielded three events corresondin to a cross section in the rane of that redicted in Ref. [9]. References [] K. Goulianos, Diffractive and total cross sections at Tevatron and LHC, in Hadron Collider Physics Symosium 006, May -6, Duke University, Durham, NC, USA. [] P. D. B. Collins, An Introduction to Ree Theory and Hih Enery Physics, Cambride University Press (977); V. Barone and E. Predazzi, Hih-Enery Particle Diffraction, Sriner Press (00); S. Donnachie, G. Dosch, O. Nachtmann, and P. Landshoff, Pomeron Physics and QCD, Cambride University Press (00). [3] R. J. M. Covolan, J. Montanha, and K. Goulianos, A New Determination of the Soft Pomeron Intercet, Phys. Lett. B 389, 76 (996). [4] K. Goulianos, Renormalization of Hadronic Diffraction and the Structure of the Pomeron, Phys. Lett. B 358, 379 (995); Erratum-ib. 363, 68 (995). [5] K. Goulianos, Hadronic Diffraction: Where do we Stand?, in La Thuile 004, Results and Persectives in Particle Physics, edited by M. Greco, Proc. of Les Rencontres de Physique de la Vallé d Aoste, La Thuile, Aosta Valley, Italy, February 9 - March 6, 004,. 5-74; e-print Archive: he-h/ [6] R. Blair et al. (CDF Collaboration), The CDF II Detector: Technical Desin Reort, FERMILAB-Pub-96/390-E. [7] K. Goulianos and S. Lami, Performance of a Prototye Position Sensitive Towerless Calorimeter, Nucl. Instrum. Meth. A 430, (999); K. Goulianos et al., The CDF MiniPlu calorimeters, Nucl. Instrum. Meth. A 496, (003). [8] M. Gallinaro (for the CDF collaboration), Diffractive and exclusive measurements at CDF, Presented at 4th International Worksho on Dee Inelastic Scatterin (DIS 006), Tsukuba, Jaan, 0-4 Ar 006; e-print Archive: he-ex/ [9] V. Khoze, A. Kaidalov, A. Martin, M. Ryskin, and W. Stirlin, Diffractive rocesses as a tool for searchin for new hysics, e-print Archive:he-h/ , and references therein. [] Monte Carlo rorams used in the CDF analysis: POMWIG (imlements diffraction into the HERWIG Monte Carlo Generator) B. Cox and J. Forshaw, Comut. Phys. Commun. 44, 4 (00); DPEMC (extends POMWIG to include inclusive and exclusive DPE) M. Boonekam and T. Kucs, Comut. Phys. Commun. 67, 7 (005); ExHuME (imlements the exclusive dijet roduction calculation of Ref. [9]), J. Monk and A. Pilkinton, e-print Archive: he-h/