- Email: [email protected]
Precision QCD at HERA
Available online at www.sciencedirect.com
Nuclear Physics B (Proc. Suppl.) 234 (2013) 207–212 www.elsevier.com/locate/npbps
Precision QCD at HERA J¨org Behra,∗ a DESY
Hamburg, Notkestr. 85, 22607 Hamburg, Germany.
Abstract HERA was a high-energy electron/positron proton collider with a centre of mass energy of up to 320 GeV operated until summer 2007. The hadronic final state in the regime of deep-inelastic scattering as well as of photoproduction has been thoroughly investigated over a wide range of phase space with the two multi-purpose detectors H1 and ZEUS. The large available HERA data samples of about 0.5 fb−1 per experiment allowed stringent tests of quantum chromodynamics using a variety of different observables connected to the production of jets and heavy quarks. From the jet production measurements the strong coupling constant α s has been extracted with high precision. Some of the most recent results of the H1 and ZEUS collaborations are presented in this contribution. Keywords: jet production, heavy quark production, deep inelastic scattering, HERA 1. Introduction In electron-proton (ep) collisions at HERA the electron interacts with a parton from the proton via the exchange of a gauge boson. The virtuality of the exchanged boson, Q2 , is used to differentiate two kinematic regimes. The region with Q2 > 1 GeV2 is called deep-inelastic scattering (DIS), while in photoproduction (γp) the boson is quasi real and Q2 ≈ 0 GeV2 holds. In γp in lowest-order the direct process, where the photon takes part directly in the interaction, can be distinguished from resolved events in which the photon can be interpreted as a source of partons. The measurements of jet or heavy flavour production in ep collisions can be used to probe thoroughly various aspects of the theory of the strong force – quantum chromodynamics (QCD). In this contribution some of the most recent results of the H1 and ZEUS collaborations are presented. 2. Jet production At HERA jets are typically reconstructed utilising the kT cluster algorithm [1] which is infrared and collinear safe. In perturbative QCD (pQCD) the jet cross section, σjet , can be calculated using a series expansion in powers of the strong coupling, α s (μR ), where μR is the ∗ On
behalf of the H1 and ZEUS collaborations. Email address: [email protected] (J¨org Behr)
0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.12.015
renormalisation scale. The coefficients are determined by a convolution of the proton1 parton distribution functions (PDFs), and the lepton-parton cross section. While the latter describes the short-distance structure, the former is employed to parametrise the long-distance structure of the interaction. Both quantities depend on the factorisation scale, μF , and on x, which is in lowest order identical to the momentum fraction carried by the struck parton. The measurement of σjet allows pQCD to be tested or PDFs and α s to be extracted. 2.1. Multi-jets in DIS at high Q2 The theoretical uncertainties in pQCD due to missing higher orders in the calculations typically shrink with increasing values of μR , since at large μR the value of α s gets small due to the asymptotic freedom of QCD. That makes the high-Q2 region a perfect place to perform comprehensive investigations of pQCD. Hence, in a recent analysis [2] the H1 collaboration has measured inclusive jet, dijet, and trijet production in the boson-quark collinear frame in neutral current (NC) DIS and has confronted the theory predictions with high-precision data. The ratio between the measured inclusive dijet cross sections and the theory predictions at next-to-leading order (NLO) QCD as functions of Q2 and the average transverse momentum of the two leading jets, PT , is 1 In case of resolved γp also the photon PDFs have to be incorporated.
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Figure 1: Ratio between data and theoretical predictions for the production of
inclusive dijets in the region 150 < Q2 < 15000 GeV2 , 7 < PT < 50 GeV, and M j j > 16 GeV, where is the invariant dijet mass.
shown in figure 1, together with the relative experimental and theoretical uncertainties. The largest experimental uncertainties are due to the hadronic energy scale uncertainty of ±1%, which induces changes of the dijet cross sections of about ±2 − 5%, and due to the dependence of the acceptance correction on the exploited Monte Carlo (MC) model. The latter source of uncertainty amounts to an uncertainty of about 2 − 4% on jet cross section level. The data are very well described by the theoretical calculations. At lower values of Q2 and PT the theoretical uncertainties are mostly larger than the data uncertainties. The spread between the three prediction that use different PDF sets is significant which indicates that the jet data will provide valuable constrains when implemented in PDF extractions. In order to reduce experimental and theoretical uncertainties, the multi-jet cross sections have been normalised to the inclusive NC DIS cross section [3]. Furthermore, to improve the procedure of correcting for detector effects, a regularised unfolding procedure of the four measurements2 at once has been exploited taking into account point-to-point correlations as well as correlations between the individual data samples. The unfolded measurements are compared to NLO QCD predictions as indicated in figure 2. The theoretical calculations provide a very good description of the data in the whole investigated phase space. Due to the reduced uncertainties, the measurement is perfectly suited for a precision extraction of α s , because the jet data are sensitive to α s already in lowest order. The extraction was performed using a χ2 minimisation procedure, which makes use of the full covariance matrix obtained in the unfolding procedure. 2 The analysis has considered the inclusive NC DIS, inclusive jet, dijet, and trijet sample.
Figure 2: Normalised inclusive jet, dijet, and trijet cross sections as functions of Q2 and PT .
The systematic uncertainties are implemented as nuisance parameters in the fit. The combined α s (MZ ) fit to the normalised jet cross sections restricted to bins with k = σσNLO > 1.3, which is the ratio of the NLO and LO leading-order jet cross sections, yields [4] α s (MZ ) = 0.1163 ± 0.0011 exp. ± 0.0042 (theo.) with a total uncertainty of ≈ 3.7%. The value of α s (MZ ) is in good agreement with the world average [5] from 2012 of α s (MZ ) = 0.1184 ± 0.0007. 2.2. Inclusive jets in photoproduction At HERA the kT jet algorithm [1] has been extensively tested in various measurements. However, recently the anti-kT [7] and SIScone [8] algorithms have been developed. Both algorithms are infrared and collinear safe and they produce more circular-shaped jets than the kT algorithm, which make them potentially more suitable for jet calibrations at the LHC. Therefore, these new algorithms have been studied by ZEUS in γp [6] which is an environment closer to that encountered in protonproton collisions due to the resolved photon events. The inclusive jet cross sections for jets with transverse enjet ergies, ET , greater than 17 GeV in the pseudorapidity region −1 < ηjet < 2.5 have been measured using these three jet algorithms. Figure 3 shows the measurements compared to theoretical predictions at NLO QCD. The uncertainties of the data are typically governed by the jet energy scale uncertainty of ±1% which causes variations of the jet cross sections of the order of 5−10%. In general the uncorrelated uncertainties are mostly smaller than 4%. On the other hand, the theoretical uncertainties are larger
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Figure 4 shows a compilation of the extracted values of α s (MZ ) presented in this report and a comparison to the world average value [5] from 2012 as well as to some previous extractions at HERA [9–11] and LEP [12]. Within the total uncertainties all the extracted values of α s (MZ ) are in good agreement with each other. The achieved precision at HERA is competitive to that obtained at LEP. 2.3. Forward jets
dσ/dΔφ (pb/rad)
and mainly due to the choice of μR in the calculations. All three jet algorithms show a similar performance in terms of uncertainties and the degree of agreement between the data and the theory. The presented jet data in γp have been used to extract α s (MZ ) by parametrising the dependence of σjet on α s (MZ ) using a quadratic function. The extraction jet was restricted to the region 21 < ET < 71 GeV in order to suppress contributions from non-perturbative effects and to omit a region where the proton PDF uncertainties are relatively large. The obtained values of α s (MZ ) for the three jet algorithms are consistent with each other exhibiting similar total uncertainties of ≈ 3.9%.
forward jet
100 ●
H1 data Energy scale uncert. CDM CCFM DGLAP
80
60
40
20 2.0 ≤ Y < 3.4 < x > = 0.0024
R
Figure 3: Inclusive jet cross section in γp as a function of the jet transverse jet energy, ET .
The measurement of jet production is also a perfect tool for detailed studies of parton dynamics. For the simulation of the initial-state parton cascade (PC) several prescriptions are available, such as the DGLAP evolution equations [13] in which the emitted partons are strongly ordered in their transverse momenta, kT , the BFKL approach [14] in which an unordered emission of partons occurs, and the CCFM evolution equations [15]. The latter combines the first two methods by introducing an angular ordering of the emissions. In order to study the details of the PC, H1 has performed an analysis [16] of jet production close to the proton direction in the region 5 < Q2 < 85 GeV2 , because at low x a transition region between the applicability of the DGLAP and the BFLK approach is predicted.
3.4 ≤ Y < 4.25 < x > = 0.0012
4.25 ≤ Y < 5.75 < x > = 0.00048
1.25 1
αs(MZ)
0.125 0.12 0.115 0.11
R=
Phys.Rev.D86(2012)010001
world average (PDG 2012)
ALEPH 3-jet rate, NNLO
Phys.Rev.Lett.104(2010)072002
ZEUS: Jets (SIScone) in γ p (2012)
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DESY-12-045
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ZEUS: Jets (anti-k ) in γ p (2012)
DESY-12-045
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ZEUS: Jets (k ) in γ p (2012)
DESY-12-045
ZEUS-prel-10-002
ZEUS: Jets at high Q2 (2010)
H1: Multi-jets at high Q2 (2012)
H1prelim-12-031
DESY-09-032
DESY-09-162
H1: Multi-jets at high Q2 (2009)
H1: Jets at low Q2 (2009)
0.75
Figure 4: Extracted α s (MZ ) values at HERA and LEP compared to the world average from 2012.
1
2
3
1
2
3
1
norm. MC norm. data
2
3
Δφ(rad)
Figure 5: Differential cross sections for forward jet production as a function of
the azimuthal difference, Δφ, between the forward jet and the electron in regions of the electron-jet rapidity distance, Y.
Figure 5 shows the measured jet cross section as a function of the azimuthal difference, Δφ, between the forward jet and the electron compared to predictions of three MC models exploiting different implementations for the simulation of the PC. The solid line corresponds to a MC prediction in which the “colour dipole model”
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(CDM) [17] is exploited. The CDM gives similar predictions as the BFKL approach. At lowest order the electron and the jet are back-toback in the laboratory frame and, therefore, Δφ is close to π. However, due to hadronisation effects and higherorder processes a partial decorrelation is observed. This decorrelation increases with increasing electron-jet rapidity distance, Y. This quantity is related to the available phase space for additional parton emissions and is thus sensitive to the evolution scheme. All three MC models provide a good description of the shape of the data, whereas the BFKL-like approach also describes the normalisation, especially at large Y. 3. Heavy quark production The investigation of heavy quark production at HERA is an established tool for comprehensive studies of pQCD predictions, because multiple hard scales such as the transverse momentum, the mass of the heavy quark, mQ , and Q2 appear in those processes. Since heavy quarks are predominantly produced in the boson-gluon fusion (BGF) process, the measurements probe directly the gluon PDF and are therefore useful inputs to PDF fits. Furthermore, the measurement of heavy quark production is sensitive to mQ . The treatment e.g. of the charm mass in PDF fits turned out to be important for theory predictions of W boson production at the LHC [18]. Nowadays, several prescriptions for the heavy quark mass treatment in pQCD are available. In the “Fixed Flavour Number Scheme” (FFNS) the final-state massive heavy quarks are generated dynamically in the BGF process. This scheme is applicable at small scales μ2R ≈ m2c,b , where mc,b corresponds to the charm or beauty mass, respectively. The “Zero Mass Variable Flavour Number Scheme” (ZM-VFNS) treats the heavy quarks as massless making the scheme valid for large scales, μ2R m2c,b , while the number of active flavours depends on μF . In contrast, however, the “General Mass Variable Flavour Number Scheme” (GM-VFNS) aims to interpolate between the two schemes mentioned above.
π±s meson has a small momentum – indicated with the subscript “s” – in the center-of-mass system of the D∗± due to the small difference between the mass of the D∗± and the mass of the D0 -π±s system.
pT (D∗ ) > 1.8 GeV
Figure 6: Cross sections for D∗ meson production in γp using the decay chain D∗± → D0 π±s → K ∓ π± π±s .
In figure 6 the cross sections for D∗ meson production in γp [19] is shown as a function of the pseudorapidity, η (D∗ ), of the D∗ meson. In general the data are reasonably well described by NLO QCD predictions within their large uncertainties. However, the analysis shows that the predictive power of the theories is limited compared to the achieved experimental precision.
p∗T (D∗ ) > 2 GeV
3.1. D∗ production in γp and DIS The production of charm quarks can be measured by reconstructing the decay chain of mesons that contain heavy quarks. The cross section for the charmed D∗ meson have been determined by the H1 and ZEUS collaborations in γp [19] and DIS [20, 21] in the so-called “golden decay channel” given by D∗± → D0 π±s → K ∓ π± π±s , where the
Figure 7: Cross sections for D∗ meson production in DIS.
A similar measurement performed in DIS [20] is presented in figure 7, which shows the cross section for the production of D∗ mesons as a function of the inelastic-
J. Behr / Nuclear Physics B (Proc. Suppl.) 234 (2013) 207–212
ity, y. The data are compared to predictions exploiting both massive and massless schemes. Since the theoretical predictions in the massless scheme are only reliable for a sufficiently large transverse momentum, p∗T (D∗ ), of the D∗ meson in the photon-proton center-of-mass frame, a cut of 2 GeV is applied. The calculations with the massive scheme provide a reasonably good description of the data whereas the prediction with the massless approach exhibits a significantly different shape.
211
termine the decay length significance which allows to separate the heavy-flavour from the light-flavour contributions. In this approach charm quarks can be separated from beauty quarks on a statistical basis by making use of the invariant mass of the decay products in selected jets associated to the secondary vertices. This approach has been applied to the DIS [23] and to the γp data [24].
3.2. Charm and beauty production in γp and DIS
10
H1 Cross section: ep→ eccX→ ejjμX H1 Data 06/07 PYTHIA CASCADE HERWIG MC@NLO
jj
dσ/dΔφ [pb/deg]
In contrast to the measurement of charm production, beauty production can not be measured at HERA by reconstructing individual hadronic decay channels due to the limited statistics of the available data samples. Therefore, more inclusive approaches have been developed which make use of the large masses, of the longevity of the heavy-flavoured hadrons, and of the fact that these hadrons can decay semi-leptonically. In a recent measurement [22], the H1 collaboration has determined the cross section for charm production in γp by selecting dijet events and by tagging the decay muons. In order to discriminate signal from background, the relative transverse momentum, prel T , of the muon with respect to the jet has been used in conjunction with the impact parameter of its track.
1
Figure 9: The differential cross section for beauty production in γp as a function of Q2 .
In DIS the cross section for charm production [23] has been determined as a function of Q2 as indicated in figure 9. The data are reasonably well described by the FFNS NLO QCD calculations and have been used to extract the charm structure function, F2cc .
10-1 0
50
100
150 jj
Δφ [deg] Figure 8: The cross section as a function of the azimuthal difference, Δφ j j , between the two jets.
Figure 8 shows an example cross section as a function of the azimuthal difference, Δφ j j , between the two jets produced in the decay process. The correlation variable Δφ j j is sensitive to contributions from higher-order processes. The data are reasonably well described by the theory. The production of heavy quarks has been studied in ZEUS by employing the long lifetime of the quarks and by selecting events with jets. Due the long lifetime, displaced secondary vertices can be reconstructed to de-
Figure 10: The differential cross section for beauty production in γp as a function of the jet transverse momentum.
In figure 10 the result for beauty production in γp [24] is shown. The cross section has been measured in
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bins of the transverse momentum, pT , of the associated jet. A good agreement between the data and the FFNS NLO QCD calculations can be observed over the full jet pT range investigated. 3.3. Beauty production close to threshold
dσ / d [pb/GeV]
In γp investigations of beauty quarks with very low average transverse momentum, pT , are of special interest, because the hard scale of the process is provided solely by the mass of the beauty quark. To access the very low-pT region, the semi-leptonic decays of the beauty quarks can be used. Therefore, a data sample with dedicated online and offline electron identification algorithms has been recorded and analysed by the H1 collaboration [25] in order to study the threshold region. These dedicated algorithms allowed to lower the applied cuts on the transverse momentum of the electrons to about 1 GeV. The signal has been discriminated statistically from the light-flavour, open charm, and J/ψ background using the invariant mass and the azimuthal angular correlation of the two electrons as well as their charge product.
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H1 Beauty Cross Section
4. Conclusions In this overview a selection of recent results for jet and heavy quark production at HERA has been presented. In general pQCD calculations describe the HERA data over a wide range of phase space reasonably well. However, the theoretical uncertainties are often substantially larger than the experimental ones. The jet data have been used for a competitive extractions of α s . Acknowledgements I would like to thank the organisers of the QCD 2012 conference for the opportunity to contribute. Additionally, I thank also the members of the H1 and ZEUS collaborations who have performed the measurements presented in this article. References [1] [2] [3] [4]
[5]
ep → e bb X [6] [7] [8] [9] [10] [11] [12] [13]
|η(b)|, |η(b)| < 2 0.05 < y < 0.65
104
Q2 < 1 GeV2
H1 Data NLO QCD (FMNR)
103
μ2 = 1/4 (m2 +2) b 0 0.5 μ < μ < 2 μ
102
0
0
4.5 GeV < mb < 5.0 GeV PDF = CTEQ6M
10
data/NLO QCD
1
[14] 2 1 0 0
[15] 5
10
15
20
25
30
< PT(b) > [GeV]
[16] [17]
Figure 11: Cross section for beauty production as a function of the average transverse momentum, pT , of the beauty quarks.
The result from this analysis is presented in figure 11, where the measured cross section as a function of pT is compared to the predictions of FFNS NLO QCD calculations. The data are described reasonably well by the theory within the uncertainties. In this analysis the cross sections were measured down to the lowest values of pT ever achieved in ep collisions.
[18] [19] [20] [21] [22] [23] [24] [25]
S. Catani et al., Nucl. Phys. B 406 (1993) 187. H1 Collab., preliminary result, H1prelim-11-032 (2011). H1 Collab., preliminary result, H1prelim-12-031 (2012). Daniel Britzger, “Measurement of Normalised Multi-jet Cross Sections using Regularised Unfolding and Extraction of α s (MZ ) in DIS at High Q2 ”, talk given at the DIS 2012 conference (2012). J. Beringer et al. [Particle Data Group Collaboration], Phys. Rev. D 86 (2012) 010001. ZEUS Collab., Nucl. Phys. B 864 (2012) 1. M. Cacciari, G.P. Salam and G. Soyez, JHEP 0804 (2008) 063. G.P. Salam and G. Soyez, JHEP 0705 (2007) 086. H1 Collab., Eur.Phys.J. C 67 (2010) 1. H1 Collab., Eur.Phys.J. C 65 (2010) 363. ZEUS Collab., preliminary result, ZEUS-prel-10-002 (2010). G. Dissertori et al., Phys. Rev. Lett. 104 (2010) 072002. V. Gribov and L. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438 and 675; L. Lipatov, Sov. J. Nucl. Phys 20 (1975) 94; G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; Y. Dokshitzer, Sov. Phys. JETP 46 (1977) 641. E. Kuraeva et al., Sov. Phys. JETP 44 (1976) 443; E. Kuraev et al., Sov. Phys. JETP 45 (1977) 199; Y. Balitsky and L. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 822. M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani et al., Phys. Lett. B 234 (1990) 339; S. Catani et al., Nucl. Phys. B 336 (1990) 18. H1 Collab., Eur. Phys. J. C 72 (2012) 1910. L. L¨onnblad, ARIADNE 4.10, Comput. Phys. Commun. 71 (1992) 15. H1 and ZEUS Collab., preliminary result, H1-prelim-10-143, ZEUS-prel-10-019 (2010). H1 Collab., Eur. Phys. J. C 72 (2012) 1995. H1 Collab., Eur. Phys. J. C 71 (2011) 1769. ZEUS Collab., preliminary result, ZEUS-prel-11-012 (2011). H1 Collab., DESY-12-059 (2012). ZEUS Collab., preliminary result, ZEUS-prel-12-002 (2012). ZEUS Collab., Eur. Phys. Journal C 71 (2011) 1659. H1 Collab., DESY-12-072 (2012).
Nuclear Physics B (Proc. Suppl.) 234 (2013) 207–212 www.elsevier.com/locate/npbps
Precision QCD at HERA J¨org Behra,∗ a DESY
Hamburg, Notkestr. 85, 22607 Hamburg, Germany.
Abstract HERA was a high-energy electron/positron proton collider with a centre of mass energy of up to 320 GeV operated until summer 2007. The hadronic final state in the regime of deep-inelastic scattering as well as of photoproduction has been thoroughly investigated over a wide range of phase space with the two multi-purpose detectors H1 and ZEUS. The large available HERA data samples of about 0.5 fb−1 per experiment allowed stringent tests of quantum chromodynamics using a variety of different observables connected to the production of jets and heavy quarks. From the jet production measurements the strong coupling constant α s has been extracted with high precision. Some of the most recent results of the H1 and ZEUS collaborations are presented in this contribution. Keywords: jet production, heavy quark production, deep inelastic scattering, HERA 1. Introduction In electron-proton (ep) collisions at HERA the electron interacts with a parton from the proton via the exchange of a gauge boson. The virtuality of the exchanged boson, Q2 , is used to differentiate two kinematic regimes. The region with Q2 > 1 GeV2 is called deep-inelastic scattering (DIS), while in photoproduction (γp) the boson is quasi real and Q2 ≈ 0 GeV2 holds. In γp in lowest-order the direct process, where the photon takes part directly in the interaction, can be distinguished from resolved events in which the photon can be interpreted as a source of partons. The measurements of jet or heavy flavour production in ep collisions can be used to probe thoroughly various aspects of the theory of the strong force – quantum chromodynamics (QCD). In this contribution some of the most recent results of the H1 and ZEUS collaborations are presented. 2. Jet production At HERA jets are typically reconstructed utilising the kT cluster algorithm [1] which is infrared and collinear safe. In perturbative QCD (pQCD) the jet cross section, σjet , can be calculated using a series expansion in powers of the strong coupling, α s (μR ), where μR is the ∗ On
behalf of the H1 and ZEUS collaborations. Email address: [email protected] (J¨org Behr)
0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.12.015
renormalisation scale. The coefficients are determined by a convolution of the proton1 parton distribution functions (PDFs), and the lepton-parton cross section. While the latter describes the short-distance structure, the former is employed to parametrise the long-distance structure of the interaction. Both quantities depend on the factorisation scale, μF , and on x, which is in lowest order identical to the momentum fraction carried by the struck parton. The measurement of σjet allows pQCD to be tested or PDFs and α s to be extracted. 2.1. Multi-jets in DIS at high Q2 The theoretical uncertainties in pQCD due to missing higher orders in the calculations typically shrink with increasing values of μR , since at large μR the value of α s gets small due to the asymptotic freedom of QCD. That makes the high-Q2 region a perfect place to perform comprehensive investigations of pQCD. Hence, in a recent analysis [2] the H1 collaboration has measured inclusive jet, dijet, and trijet production in the boson-quark collinear frame in neutral current (NC) DIS and has confronted the theory predictions with high-precision data. The ratio between the measured inclusive dijet cross sections and the theory predictions at next-to-leading order (NLO) QCD as functions of Q2 and the average transverse momentum of the two leading jets, PT , is 1 In case of resolved γp also the photon PDFs have to be incorporated.
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J. Behr / Nuclear Physics B (Proc. Suppl.) 234 (2013) 207–212
Figure 1: Ratio between data and theoretical predictions for the production of
inclusive dijets in the region 150 < Q2 < 15000 GeV2 , 7 < PT < 50 GeV, and M j j > 16 GeV, where is the invariant dijet mass.
shown in figure 1, together with the relative experimental and theoretical uncertainties. The largest experimental uncertainties are due to the hadronic energy scale uncertainty of ±1%, which induces changes of the dijet cross sections of about ±2 − 5%, and due to the dependence of the acceptance correction on the exploited Monte Carlo (MC) model. The latter source of uncertainty amounts to an uncertainty of about 2 − 4% on jet cross section level. The data are very well described by the theoretical calculations. At lower values of Q2 and PT the theoretical uncertainties are mostly larger than the data uncertainties. The spread between the three prediction that use different PDF sets is significant which indicates that the jet data will provide valuable constrains when implemented in PDF extractions. In order to reduce experimental and theoretical uncertainties, the multi-jet cross sections have been normalised to the inclusive NC DIS cross section [3]. Furthermore, to improve the procedure of correcting for detector effects, a regularised unfolding procedure of the four measurements2 at once has been exploited taking into account point-to-point correlations as well as correlations between the individual data samples. The unfolded measurements are compared to NLO QCD predictions as indicated in figure 2. The theoretical calculations provide a very good description of the data in the whole investigated phase space. Due to the reduced uncertainties, the measurement is perfectly suited for a precision extraction of α s , because the jet data are sensitive to α s already in lowest order. The extraction was performed using a χ2 minimisation procedure, which makes use of the full covariance matrix obtained in the unfolding procedure. 2 The analysis has considered the inclusive NC DIS, inclusive jet, dijet, and trijet sample.
Figure 2: Normalised inclusive jet, dijet, and trijet cross sections as functions of Q2 and PT .
The systematic uncertainties are implemented as nuisance parameters in the fit. The combined α s (MZ ) fit to the normalised jet cross sections restricted to bins with k = σσNLO > 1.3, which is the ratio of the NLO and LO leading-order jet cross sections, yields [4] α s (MZ ) = 0.1163 ± 0.0011 exp. ± 0.0042 (theo.) with a total uncertainty of ≈ 3.7%. The value of α s (MZ ) is in good agreement with the world average [5] from 2012 of α s (MZ ) = 0.1184 ± 0.0007. 2.2. Inclusive jets in photoproduction At HERA the kT jet algorithm [1] has been extensively tested in various measurements. However, recently the anti-kT [7] and SIScone [8] algorithms have been developed. Both algorithms are infrared and collinear safe and they produce more circular-shaped jets than the kT algorithm, which make them potentially more suitable for jet calibrations at the LHC. Therefore, these new algorithms have been studied by ZEUS in γp [6] which is an environment closer to that encountered in protonproton collisions due to the resolved photon events. The inclusive jet cross sections for jets with transverse enjet ergies, ET , greater than 17 GeV in the pseudorapidity region −1 < ηjet < 2.5 have been measured using these three jet algorithms. Figure 3 shows the measurements compared to theoretical predictions at NLO QCD. The uncertainties of the data are typically governed by the jet energy scale uncertainty of ±1% which causes variations of the jet cross sections of the order of 5−10%. In general the uncorrelated uncertainties are mostly smaller than 4%. On the other hand, the theoretical uncertainties are larger
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Figure 4 shows a compilation of the extracted values of α s (MZ ) presented in this report and a comparison to the world average value [5] from 2012 as well as to some previous extractions at HERA [9–11] and LEP [12]. Within the total uncertainties all the extracted values of α s (MZ ) are in good agreement with each other. The achieved precision at HERA is competitive to that obtained at LEP. 2.3. Forward jets
dσ/dΔφ (pb/rad)
and mainly due to the choice of μR in the calculations. All three jet algorithms show a similar performance in terms of uncertainties and the degree of agreement between the data and the theory. The presented jet data in γp have been used to extract α s (MZ ) by parametrising the dependence of σjet on α s (MZ ) using a quadratic function. The extraction jet was restricted to the region 21 < ET < 71 GeV in order to suppress contributions from non-perturbative effects and to omit a region where the proton PDF uncertainties are relatively large. The obtained values of α s (MZ ) for the three jet algorithms are consistent with each other exhibiting similar total uncertainties of ≈ 3.9%.
forward jet
100 ●
H1 data Energy scale uncert. CDM CCFM DGLAP
80
60
40
20 2.0 ≤ Y < 3.4 < x > = 0.0024
R
Figure 3: Inclusive jet cross section in γp as a function of the jet transverse jet energy, ET .
The measurement of jet production is also a perfect tool for detailed studies of parton dynamics. For the simulation of the initial-state parton cascade (PC) several prescriptions are available, such as the DGLAP evolution equations [13] in which the emitted partons are strongly ordered in their transverse momenta, kT , the BFKL approach [14] in which an unordered emission of partons occurs, and the CCFM evolution equations [15]. The latter combines the first two methods by introducing an angular ordering of the emissions. In order to study the details of the PC, H1 has performed an analysis [16] of jet production close to the proton direction in the region 5 < Q2 < 85 GeV2 , because at low x a transition region between the applicability of the DGLAP and the BFLK approach is predicted.
3.4 ≤ Y < 4.25 < x > = 0.0012
4.25 ≤ Y < 5.75 < x > = 0.00048
1.25 1
αs(MZ)
0.125 0.12 0.115 0.11
R=
Phys.Rev.D86(2012)010001
world average (PDG 2012)
ALEPH 3-jet rate, NNLO
Phys.Rev.Lett.104(2010)072002
ZEUS: Jets (SIScone) in γ p (2012)
0
DESY-12-045
T
ZEUS: Jets (anti-k ) in γ p (2012)
DESY-12-045
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Figure 4: Extracted α s (MZ ) values at HERA and LEP compared to the world average from 2012.
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Figure 5: Differential cross sections for forward jet production as a function of
the azimuthal difference, Δφ, between the forward jet and the electron in regions of the electron-jet rapidity distance, Y.
Figure 5 shows the measured jet cross section as a function of the azimuthal difference, Δφ, between the forward jet and the electron compared to predictions of three MC models exploiting different implementations for the simulation of the PC. The solid line corresponds to a MC prediction in which the “colour dipole model”
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(CDM) [17] is exploited. The CDM gives similar predictions as the BFKL approach. At lowest order the electron and the jet are back-toback in the laboratory frame and, therefore, Δφ is close to π. However, due to hadronisation effects and higherorder processes a partial decorrelation is observed. This decorrelation increases with increasing electron-jet rapidity distance, Y. This quantity is related to the available phase space for additional parton emissions and is thus sensitive to the evolution scheme. All three MC models provide a good description of the shape of the data, whereas the BFKL-like approach also describes the normalisation, especially at large Y. 3. Heavy quark production The investigation of heavy quark production at HERA is an established tool for comprehensive studies of pQCD predictions, because multiple hard scales such as the transverse momentum, the mass of the heavy quark, mQ , and Q2 appear in those processes. Since heavy quarks are predominantly produced in the boson-gluon fusion (BGF) process, the measurements probe directly the gluon PDF and are therefore useful inputs to PDF fits. Furthermore, the measurement of heavy quark production is sensitive to mQ . The treatment e.g. of the charm mass in PDF fits turned out to be important for theory predictions of W boson production at the LHC [18]. Nowadays, several prescriptions for the heavy quark mass treatment in pQCD are available. In the “Fixed Flavour Number Scheme” (FFNS) the final-state massive heavy quarks are generated dynamically in the BGF process. This scheme is applicable at small scales μ2R ≈ m2c,b , where mc,b corresponds to the charm or beauty mass, respectively. The “Zero Mass Variable Flavour Number Scheme” (ZM-VFNS) treats the heavy quarks as massless making the scheme valid for large scales, μ2R m2c,b , while the number of active flavours depends on μF . In contrast, however, the “General Mass Variable Flavour Number Scheme” (GM-VFNS) aims to interpolate between the two schemes mentioned above.
π±s meson has a small momentum – indicated with the subscript “s” – in the center-of-mass system of the D∗± due to the small difference between the mass of the D∗± and the mass of the D0 -π±s system.
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Figure 6: Cross sections for D∗ meson production in γp using the decay chain D∗± → D0 π±s → K ∓ π± π±s .
In figure 6 the cross sections for D∗ meson production in γp [19] is shown as a function of the pseudorapidity, η (D∗ ), of the D∗ meson. In general the data are reasonably well described by NLO QCD predictions within their large uncertainties. However, the analysis shows that the predictive power of the theories is limited compared to the achieved experimental precision.
p∗T (D∗ ) > 2 GeV
3.1. D∗ production in γp and DIS The production of charm quarks can be measured by reconstructing the decay chain of mesons that contain heavy quarks. The cross section for the charmed D∗ meson have been determined by the H1 and ZEUS collaborations in γp [19] and DIS [20, 21] in the so-called “golden decay channel” given by D∗± → D0 π±s → K ∓ π± π±s , where the
Figure 7: Cross sections for D∗ meson production in DIS.
A similar measurement performed in DIS [20] is presented in figure 7, which shows the cross section for the production of D∗ mesons as a function of the inelastic-
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ity, y. The data are compared to predictions exploiting both massive and massless schemes. Since the theoretical predictions in the massless scheme are only reliable for a sufficiently large transverse momentum, p∗T (D∗ ), of the D∗ meson in the photon-proton center-of-mass frame, a cut of 2 GeV is applied. The calculations with the massive scheme provide a reasonably good description of the data whereas the prediction with the massless approach exhibits a significantly different shape.
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termine the decay length significance which allows to separate the heavy-flavour from the light-flavour contributions. In this approach charm quarks can be separated from beauty quarks on a statistical basis by making use of the invariant mass of the decay products in selected jets associated to the secondary vertices. This approach has been applied to the DIS [23] and to the γp data [24].
3.2. Charm and beauty production in γp and DIS
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H1 Cross section: ep→ eccX→ ejjμX H1 Data 06/07 PYTHIA CASCADE HERWIG MC@NLO
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In contrast to the measurement of charm production, beauty production can not be measured at HERA by reconstructing individual hadronic decay channels due to the limited statistics of the available data samples. Therefore, more inclusive approaches have been developed which make use of the large masses, of the longevity of the heavy-flavoured hadrons, and of the fact that these hadrons can decay semi-leptonically. In a recent measurement [22], the H1 collaboration has determined the cross section for charm production in γp by selecting dijet events and by tagging the decay muons. In order to discriminate signal from background, the relative transverse momentum, prel T , of the muon with respect to the jet has been used in conjunction with the impact parameter of its track.
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Figure 9: The differential cross section for beauty production in γp as a function of Q2 .
In DIS the cross section for charm production [23] has been determined as a function of Q2 as indicated in figure 9. The data are reasonably well described by the FFNS NLO QCD calculations and have been used to extract the charm structure function, F2cc .
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Δφ [deg] Figure 8: The cross section as a function of the azimuthal difference, Δφ j j , between the two jets.
Figure 8 shows an example cross section as a function of the azimuthal difference, Δφ j j , between the two jets produced in the decay process. The correlation variable Δφ j j is sensitive to contributions from higher-order processes. The data are reasonably well described by the theory. The production of heavy quarks has been studied in ZEUS by employing the long lifetime of the quarks and by selecting events with jets. Due the long lifetime, displaced secondary vertices can be reconstructed to de-
Figure 10: The differential cross section for beauty production in γp as a function of the jet transverse momentum.
In figure 10 the result for beauty production in γp [24] is shown. The cross section has been measured in
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bins of the transverse momentum, pT , of the associated jet. A good agreement between the data and the FFNS NLO QCD calculations can be observed over the full jet pT range investigated. 3.3. Beauty production close to threshold
dσ / d
In γp investigations of beauty quarks with very low average transverse momentum, pT , are of special interest, because the hard scale of the process is provided solely by the mass of the beauty quark. To access the very low-pT region, the semi-leptonic decays of the beauty quarks can be used. Therefore, a data sample with dedicated online and offline electron identification algorithms has been recorded and analysed by the H1 collaboration [25] in order to study the threshold region. These dedicated algorithms allowed to lower the applied cuts on the transverse momentum of the electrons to about 1 GeV. The signal has been discriminated statistically from the light-flavour, open charm, and J/ψ background using the invariant mass and the azimuthal angular correlation of the two electrons as well as their charge product.
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H1 Beauty Cross Section
4. Conclusions In this overview a selection of recent results for jet and heavy quark production at HERA has been presented. In general pQCD calculations describe the HERA data over a wide range of phase space reasonably well. However, the theoretical uncertainties are often substantially larger than the experimental ones. The jet data have been used for a competitive extractions of α s . Acknowledgements I would like to thank the organisers of the QCD 2012 conference for the opportunity to contribute. Additionally, I thank also the members of the H1 and ZEUS collaborations who have performed the measurements presented in this article. References [1] [2] [3] [4]
[5]
ep → e bb X [6] [7] [8] [9] [10] [11] [12] [13]
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Figure 11: Cross section for beauty production as a function of the average transverse momentum, pT , of the beauty quarks.
The result from this analysis is presented in figure 11, where the measured cross section as a function of pT is compared to the predictions of FFNS NLO QCD calculations. The data are described reasonably well by the theory within the uncertainties. In this analysis the cross sections were measured down to the lowest values of pT ever achieved in ep collisions.
[18] [19] [20] [21] [22] [23] [24] [25]
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