Low-x QCD studies with forward jets in proton-proton collisions at 14 TeV
aa r X i v : . [ h e p - e x ] M a y Low-x QCD studies with forward jets in p-p at 14 TeV
Salim Cerci , ∗ and David d’Enterria , † for the CMS collaboration Cukurova University, Adana, Turkey and CERN, CH-1211 Geneva 23, Switzerland
The Large Hadron Collider will provide hadronic collisions at energies in the multi-TeVrange, never explored before. The parton fractional momenta probed at such energies can beas low as x ≈ p T / √ s e − y ≈ − at large rapidities y , opening up attractive opportunitiesfor low- x QCD studies. The combination of the CMS HF (3 < | η | <
5) and CASTOR (5.1 < | η | < x gluon densities and non-linear QCD evolution. I. INTRODUCTION
The parton distribution functions (PDFs) in the proton have been studied in detail in deep-inelastic-scattering (DIS) ep collisions at HERA [1]. For decreasing parton momentum fraction x = p parton /p hadron , the gluon density is observed to grow rapidly as xg ( x, Q ) ∝ x − λ ( Q ) , with λ ≈ Q . As long as the densities are not too high, this growth isdescribed by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) [2] or by the Balitski-Fadin-Kuraev-Lipatov (BFKL) [3] evolution equations which govern, respectively, parton radiation in Q and x . Eventually, at high enough centre-of-mass energies (i.e. at very small x ) the gluon densitywill be so large that non-linear (gluon-gluon fusion) effects will become important, saturating thegrowth of the parton densities [4]. Studies of the high-energy (low- x ) limit of QCD have attractedmuch theoretical interest in the last 10–15 years, in the context of DIS and of nucleus-nucleuscollisions [5]. Experimentally, direct information on the parton structure and evolution can beobtained in hadron-hadron collisions from the perturbative production of e.g. jets or prompt γ ’s, which are directly coupled to the parton-parton scattering vertex. From leading-order (LO)kinematics, the rapidities and momentum fractions of the two colliding partons are related via x = ( p T / √ s ) · ( e − y + e − y ) and x = ( p T / √ s ) · ( e y + e y ) . (1)The minimum momentum fractions probed in a 2 → p T produced at pseudo-rapidity η are x min = x T e − η − x T e η , x min = x x T e η x − x T e − η , where x T = 2 p T / √ s , (2)i.e. x min decreases by a factor of ∼
10 every 2 units of rapidity. From Eq. (2), it follows that themeasurement of jets with transverse energy E T ≈
20 GeV in the CMS forward calorimeters (HF,3 < | η | < < | η | < x values as low as x ≈ − .Figure 1 shows the actual log( x , ) distribution for two-parton scattering in p-p collisions at 14 TeVproducing at least one jet above 20 GeV in the HF and CASTOR acceptances. We present heregenerator-level studies of two forward-jet measurements in CMS sensitive to small- x QCD [6]: ∗ Supported by Fermilab US-CMS HCAL, and Turkish Atomic Energy Board (TAEK) † Support from 6th EU Framework Programme MEIF-CT-2005-025073 acknowledged. . single inclusive jet cross section in HF at moderately high virtualities ( E T ≈
20 – 100 GeV),2. differential cross sections and azimuthal (de)correlation of “Mueller-Navelet” (MN) [7] dijetevents, characterized by jets with similar E T separated by a large rapidity interval (∆ η ≈ x (and high- x ) proton PDFs, whereas the secondone yields information on BFKL- [7, 8, 9, 10] and saturation- [11, 12] type dynamics. ) (x log-6 -5 -4 -3 -2 -1 0 ( G e V ) T E =14 TeVs, +jet GenJet: p+p->jet | < 5.0) h in HF (3.0 < | jetIterative cone, R = 0.5 ) (x log-6 -5 -4 -3 -2 -1 0 ( G e V ) T E =14 TeVs, +jet GenJet: p+p->jet | < 6.6) h in CASTOR (5.1< | jetIterative cone, R = 0.5 FIG. 1: log( x , ) distribution of two partons producing at least one jet above E T = 20 GeV within HF(3 < | η | <
5, left) and CASTOR (5 . < | η | < .
6, right) in p-p collisions at √ s = 14 TeV [6]. II. EXPERIMENTAL SETUP
The combination of HF, TOTEM, CASTOR and ZDC (Fig. 2) makes of CMS the largest ac-ceptance experiment ever built at a collider. Very forward jets can be identified using the HF [13]and CASTOR [14] calorimeters. The HF, located 11.2 m away on both sides of the interac-tion point (IP), is a steel plus quartz-fiber ˇCerenkov calorimeter segmented into 1200 towers of∆ η × ∆ φ ∼ × λ I interaction lengths and is sensitive to deposited electro-magnetic (EM) and hadronic (HAD) energy. CASTOR is an azimuthally symmetric EM/HADcalorimeter placed at 14.37 m from the IP, covering 5.1 < | η | < X (10.3 λ I ) radiation (interaction) lengths. III. FORWARD JETS RECONSTRUCTION IN HF
Jets in CMS are reconstructed at the generator- and calorimeter-level using 3 different jet algo-rithms [15]: iterative cone [16] with radius of R = 0 . η, φ ), SISCone [17] ( R = 0 . k T [18] ( E seed = 3 GeV and E thres = 20 GeV). The Monte Carlo samples used in this analysiswere part of the official CMS QCD-jets simulation using PYTHIA [19] in seven 1M-events ˆ p T binsacross the E T = 15–230 GeV range. Events are selected where at least one jet above 20 GeVfalls in the forward HF acceptance. The matching radius between generated and reconstructedjets, for reconstruction performance studies, is set at ∆R = 0.2. The E T resolutions for the three2 IG. 2: Layout of the detectors in the CMS forward region used for the low- x QCD studies [6]. different algorithms are very similar: ∼
18% at E T ∼
20 GeV decreasing to ∼
12% for E T & η , φ ) resolutions (not shown here) for jets in HF are also verygood: σ φ,η = 0.045 at E T = 20 GeV, improving to σ φ,η ∼ E T range) [16]. IV. SINGLE INCLUSIVE FORWARD JET MEASUREMENT
Figure 3 right shows the single jet spectrum expected in both HFs for 1 pb − integrated luminos-ity obtained at the parton-level from pythia for two different PDF sets (CTEQ5L and MRST03)compared to a NLO calculation (CTEQ6M, R = 0 .
5, scales µ = 0.5 E T –2 E T ) [20]. The single jetspectra obtained for different PDFs are similar at high E T , while differences as large as O (60%)appear below ∼
60 GeV. The measurement of low- E T forward jets in HF seems in principle feasible:the statistical errors are negligible and the HF energy resolution is very good (Fig. 3, left). Yet, inthe “interesting” low- E T range, the main experimental issue will be the control of the jet-energy scale whose uncertainty propagates into up to ±
40% differences in the final jet yield. Use of thismeasurement to constrain the proton PDFs in the low- x range will thus require careful studies ofthe HF jet calibration. V. MUELLER-NAVELET (MN) DIJETS MEASUREMENT
Inclusive dijet production at large pseudorapidity intervals in high-energy hadron-hadron colli-sions has been since long considered an excellent testing ground for BFKL [7, 8, 9, 10] and alsofor saturation [11, 12] QCD evolutions. Both colliding partons in the MN kinematics are large- x valence quarks ( x , ≈ E T ,i with a largerapidity interval between them: Y = log( x x s/ ( Q Q )) , (3)where Q i ≈ E T ,i are the corresponding parton virtualities. The presence of a large rapidity sep-aration ( Y = ∆ η ) between jets enhances the available phase-space in longitudinal momentum forextra BFKL-type radiation. In CMS, jet rapidity separations as large as ∆ η ≈
12 are accessible3 eV TGenJet
E20 40 60 80 100 120 140 160 180 200 220 f i t > T G e n Je t / E T C a l o Je t / < E f i t T G e n Je t / E T C a l o Je t E s |<5. h Jet Energy resolution (HF), 3.<| [CMS Preliminary]
Iterative cone (R=0.5)SISCone (R=0.5) (D=0.4) T Fast k (GeV) T E20 40 60 80 100 - G e V h d T / d E H F j e t s d N | < 5 h jet +X , 3 < | fi pp -1 L dt=1 pb (cid:242) , PYTHIA CTEQ5L (parton-level)PYTHIA MRST03 (parton-level)NLO (CTEQ6M ICone R=0.5)
FIG. 3: Left: Energy resolution for jets measured in HF as a function of E T [15]. Right: Single inclusive jetyields in HF expected in (1 fb − ) p-p collisions at 14 TeV obtained with pythia combining both HF and CASTOR opposite hemispheres. As a proof of principle, we have reana-lyzed the pythia jet samples discussed in the previous Section, and selected events which satisfythe following Mueller-Navelet-type selection cuts: • E T,i >
20 GeV • | E T, − E T, | < Q ≈ p E T, · E T, , to minimise DGLAP evolution) • < | η , | < • η · η < • || η | − | η || < . η bin computed as d σ/dηdQ = N jets / (∆ η ∆ Q R L dt), where N is the observednumber of jets in the bin and 1 pb − the assumed integrated luminosity. The left plot in Fig. 4shows the expected dijet yields passing the MN kinematics cuts as a function of Q for thepseudo-rapidity separation ∆ η ≈
8. The obtained MN dijet statistics appears large enough tocarry out detailed studies of the ∆ η dependence, that would e.g. provide evidence for a possibleMueller-Navelet “geometric scaling” behaviour [12]. An enhanced azimuthal decorrelation forincreasing rapidity separation between the Mueller-Navelet jets is the classical “smoking-gun” ofBFKL radiation [8, 9, 10]. The generator-level ∆ φ jet distributions are plotted in the right plotof Fig. 4 for ∆ η = 7.5, 8.5 and 9.5. The peak at ∆ φ = ( φ − φ ) − π = 0 indicates that the twojets are highly correlated with each other. As the ∆ η between the two jets increases, the peaksdiminish and the distributions get increasingly larger, signaling a loss in correlation. Since pythia is a leading-order generator without any BFKL (or saturation) effect, the observed azimuthaldecorrelation is just due to parton shower effects and initial- or final-state radiation. Such a resultprovides, thus, a baseline of the minimal decorrelation expected in non-BFKL scenarios. Detailedsimulation studies are ongoing to test the sensitivity of such forward jet measurements to signal(or not) the presence of “genuine” low- x decorrelations.4 GeV] T E0 20 40 60 80 100 ] - [ G e V h d T / d E M N d ij e t s d N | = [4.,4.5] h | = | h | = | h | , ICone, R=0.5 +jet pp->jet Muller-Navelet dijet cuts fD -3 -2 -1 0 1 2 3 fD / N d N / d |<5.) h HF dijets (3.<| <8 hD hD hD Mueller-Navelet cutsGenerator-level
FIG. 4: Dijet events passing the Mueller-Navelet cuts described in the text. Left: Expected yields (in1 pb − ) for a separation ∆ η ≈ φ distributions for jet separations ∆ η = 7.5, 8.5 and 9.5. References [1] M. Klein and R. Yoshida, arXiv:0805.3334 [hep-ex].[2] V.N. Gribov and L.N. Lipatov, Sov. Journ. Nucl. Phys. (1972) 438; G. Altarelli and G.Parisi, Nucl. Phys. B126 (1977) 298; Yu. L. Dokshitzer, Sov. Phys. JETP (1977) 641.[3] L.N. Lipatov, Sov. J. Nucl. Phys. (1976) 338; E.A. Kuraev, L.N. Lipatov and V.S. Fadin,Zh. Eksp. Teor. Fiz , (1977) 3; I.I. Balitsky, L.N. Lipatov, Sov. J. Nucl. Phys. (1978) 822.[4] L. Gribov, E. M. Levin and M. G. Ryskin, Phys. Rept. (1983) 1; A. H. Mueller and J. w.Qiu, Nucl. Phys. B (1986) 427[5] See e.g. F. Gelis, T. Lappi and R. Venugopalan, Int. J. Mod. Phys. E (2007) 2595[6] M. Albrow et al. [CMS and TOTEM Collaborations], CERN/LHCC 2006-039/G-124[7] A. H. Mueller and H. Navelet, Nucl. Phys. B (1987) 727.[8] V. Del Duca and C. R. Schmidt, Phys. Rev. D (1994) 4510[9] L.H. Orr, W.J. Stirling, Phys. Lett. B (1998) 371[10] A. Sabio Vera, F. Schwennsen, Nucl. Phys. B (2007) 170; Nucl. Phys. B (2006) 1[11] C. Marquet and C. Royon, Nucl. Phys. B (2006) 131; and arXiv:0704.3409 [hep-ph].[12] E. Iancu, M. S. Kugeratski and D. N. Triantafyllopoulos, arXiv:0802.0343 [hep-ph].[13] A. S. Ayan et al. , J. Phys. G (2004) N33.[14] X. Aslanoglou et al. , Eur. Phys. J. C (2007) 495[15] L. L.Apanasevich et al. , “Performance of Jet Algorithms in CMS”, CMS PAS JME-07-003.[16] CMS Physics TDR, Volume 1, CERN-LHCC-2006-001, 2 February 2006[17] G. P. Salam and G.Soyez, JHEP05 (2007) 086[18] M.Cacciari and G. P. Salam, Phys. Lett. B (2006) 57.[19] T. Sjostrand, S. Mrenna and P. Skands, JHEP (2006) 026.[20] B. Jager, M. Stratmann, W. Vogelsang, Phys. Rev. D70