The strong coupling constant α s is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic ep scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of α s ( m Z ) at the Z-boson mass m Z are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be α s ( m Z ) = 0.1157 ( 20 ) exp ( 29 ) th . Complementary, α s ( m Z ) is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value α s ( m Z ) = 0.1142 ( 28 ) tot obtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations.

1 Physikalisches Institut der RWTH Aachen Germany

2 Physikalisches Institut Universität Göttingen Göttingen Germany

Aix Marseille Université CNRS IN2P3 CPPM UMR 7346 13288 Marseille France

CERN Geneva Switzerland

Departamento de Fisica Aplicada CINVESTAV Mérida Yucatán Mexico

Department of Physics and Astronomy Purdue University 525 Northwestern Ave West Lafayette IN 47907 USA

Department of Physics and Astronomy University of Sussex Pevensey 2 Brighton UK

Department of Physics and Astronomy Vrije University De Boelelaan 1081 Amsterdam The Netherlands

Department of Physics Oxford University Oxford UK

Department of Physics University of Lancaster Lancaster UK

Department of Physics University of Liverpool Liverpool UK

Department of Physics University of Toronto Toronto ON M5S 1A7 Canada

DESY Hamburg Germany

DESY Zeuthen Germany

Dipartimento di Fisica Università di Roma Tre and INFN Roma 3 Rome Italy

Fachbereich C Universität Wuppertal Wuppertal Germany

Faculty of Mathematics and Physics Charles University Prague Czech Republic

Faculty of Science University of Montenegro Podgorica Montenegro

Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering Bucharest Romania

Institut für Experimentalphysik Universität Hamburg Hamburg Germany

Institut für Physik TU Dortmund Dortmund Germany

Institut für Teilchenphysik ETH Zürich Zurich Switzerland

Institute for Information Transmission Problems RAS Moscow Russia

Institute for Nuclear Research and Nuclear Energy Sofia Bulgaria

Institute for Particle Physics Phenomenology Ogden Centre for Fundamental Physics Durham University South Road Durham UK

Institute for Theoretical and Experimental Physics Moscow Russia

Institute of Nuclear Physics Polish Academy of Sciences 31342 Kraków Poland

Institute of Physics Academy of Sciences of the Czech Republic Prague Czech Republic

Institute of Physics and Technology of the Mongolian Academy of Sciences Ulaanbaatar Mongolia

Inter University Institute for High Energies ULB VUB Brussels and Universiteit Antwerpen Antwerp Belgium

IPNL Université Claude Bernard Lyon 1 CNRS IN2P3 Villeurbanne France

Irfu SPP CE Saclay Gif sur Yvette France

Joint Institute for Nuclear Research Dubna Russia

Karlsruher Institut für Technologie Wolfgang Gaede Str 1 Karlsruhe Germany

LAL Université Paris Sud CNRS IN2P3 Orsay France

LAPP Université de Savoie CNRS IN2P3 Annecy le Vieux France

Lebedev Physical Institute Moscow Russia

LLR Ecole Polytechnique CNRS IN2P3 Palaiseau France

Max Planck Institut für Physik Munich Germany

Moscow Institute of Physics and Technology Dolgoprudny Moscow Region Russian Federation

National Institute for Subatomic Physics Science Park 105 Amsterdam The Netherlands

Paul Scherrer Institute Villigen Switzerland

Physik Institut der Universität Zürich Zurich Switzerland

Physikalisches Institut Universität Heidelberg Heidelberg Germany

School of Physics and Astronomy Queen Mary University of London London UK

School of Physics and Astronomy University of Birmingham Birmingham UK

Skobeltsyn Institute of Nuclear Physics Lomonosov Moscow State University Moscow Russia

STFC Rutherford Appleton Laboratory Didcot Oxfordshire UK

Ulaanbaatar University Ulaanbaatar Mongolia

Yerevan Physics Institute Yerevan Armenia

See more in PubMed

Dissertori G. Adv. Ser. Dir. High Energy Phys. 2016;26:113. doi: 10.1142/9789814733519_0006. DOI

Particle Data Group Collaboration, C. Patrignani et al., Chin. Phys. C 40, 100001 (2016)

K.H. Streng, T.F. Walsh, P.M. Zerwas, Z. Phys. C 2, 237 (1979)

R.K. Ellis, W.J. Stirling, B.R. Webber, QCD and Collider Physics. Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology. (Cambridge University Press, Cambridge, 1996)

D. Graudenz, The three jet cross-section at order alpha-s**2 in deep inelastic electron–proton scattering. Ph.D. thesis, Universität Hamburg, Hamburg, Germany, DESY-T-90-01 (1990)

Graudenz D. Phys. Lett. B. 1991;256:518. doi: 10.1016/0370-2693(91)91801-2. DOI

Kosower DA. Phys. Rev. D. 1998;57:5410. doi: 10.1103/PhysRevD.57.5410. DOI

Gehrmann-De Ridder A, Gehrmann T, Glover EWN. JHEP. 2005;0509:056. doi: 10.1088/1126-6708/2005/09/056. DOI

Daleo A, Gehrmann-De Ridder A, Gehrmann T, Luisoni G. JHEP. 2010;1001:118. doi: 10.1007/JHEP01(2010)118. DOI

Currie J, Glover EWN, Wells S. JHEP. 2013;1304:066. doi: 10.1007/JHEP04(2013)066. DOI

Currie J, Gehrmann T, Niehues J. Phys. Rev. Lett. 2016;117:042001. doi: 10.1103/PhysRevLett.117.042001. PubMed DOI

Currie J, Gehrmann T, Huss A, Niehues J. JHEP. 2017;1707:018. doi: 10.1007/JHEP07(2017)018. DOI

Currie J, Glover EWN, Pires J. Phys. Rev. Lett. 2017;118:072002. doi: 10.1103/PhysRevLett.118.072002. PubMed DOI

J. Currie, A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss, J. Pires, Phys. Rev. Lett. 119, 152001 (2017). arXiv:1705.10271 PubMed

H1 Collaboration, V. Andreev et al., Eur. Phys. J. C 77, 215 (2017). arXiv:1611.03421 PubMed PMC

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 13, 397 (2000). arXiv:hep-ex/9812024

H1 Collaboration, C. Adloff et al. Eur. Phys. J. C 19, 289 (2001). arXiv:hep-ex/0010054

H1 Collaboration, C. Adloff et al., Phys. Lett. B 542, 193 (2002). arXiv:hep-ex/0206029

H1 Collaboration, A. Aktas et al., Eur. Phys. J. C 33, 477 (2004). arXiv:hep-ex/0310019

H1 Collaboration, A. Aktas et al., Eur. Phys. J. C 37, 141 (2004). arXiv:hep-ex/0401010

H1 Collaboration, A. Aktas et al., Phys. Lett. B 653, 134 (2007). arXiv:0706.3722

H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 65, 363 (2010). arXiv:0904.3870

H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 67, 1 (2010). arXiv:0911.5678

H1 Collaboration, V. Andreev et al., Eur. Phys. J. C 75, 65 (2015). arXiv:1406.4709

ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B 479, 37 (2000). arXiv:hep-ex/0002010

ZEUS Collaboration, S. Chekanov et al., Eur. Phys. J. C 23, 13 (2002). arXiv:hep-ex/0109029

ZEUS Collaboration, S. Chekanov et al., Phys. Lett. B 547, 164 (2002). arXiv:hep-ex/0208037

ZEUS Collaboration, S. Chekanov et al., Eur. Phys. J. C 35, 487 (2004). arXiv:hep-ex/0404033

ZEUS Collaboration, S. Chekanov et al., Nucl. Phys. B 765, 1 (2007). arXiv:hep-ex/0608048

ZEUS Collaboration, S. Chekanov et al., Phys. Lett. B 649, 12 (2007). arXiv:hep-ex/0701039

ZEUS Collaboration, H. Abramowicz et al., Eur. Phys. J. C 70, 965 (2010). arXiv:1010.6167

ZEUS Collaboration, H. Abramowicz et al., Phys. Lett. B 691, 127 (2010). arXiv:1003.2923

H1 Collaboration, T. Ahmed et al., Phys. Lett. B 346, 415 (1995)

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 5, 625 (1998). arXiv:hep-ex/9806028

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 6, 575 (1999). arXiv:hep-ex/9807019

Biekötter T, Klasen M, Kramer G. Phys. Rev. D. 2015;92:074037. doi: 10.1103/PhysRevD.92.074037. DOI

ZEUS Collaboration, H. Abramowicz et al., Nucl. Phys. B 864, 1 (2012). arXiv:1205.6153

Klasen M, Kramer G, Michael M. Phys. Rev. D. 2014;89:074032. doi: 10.1103/PhysRevD.89.074032. DOI

OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 47, 295 (2006). arXiv:hep-ex/0601048

JADE Collaboration, J. Schieck, S. Bethke, O. Biebel, S. Kluth, P.A. Movilla Fernandez, C. Pahl, Eur. Phys. J. C 48, 3 (2006). arXiv:0707.0392 [Erratum: Eur. Phys. J. C 50, 769 (2007)]

Dissertori G, Gehrmann-De Ridder A, Gehrmann T, Glover EWN, Heinrich G, Stenzel H. JHEP. 2008;0802:040. doi: 10.1088/1126-6708/2008/02/040. DOI

Dissertori G, Gehrmann-De Ridder A, Gehrmann T, Glover EWN, Heinrich G, Stenzel H. Phys. Rev. Lett. 2010;104:072002. doi: 10.1103/PhysRevLett.104.072002. PubMed DOI

Dissertori G, Gehrmann-De Ridder A, Gehrmann T, Glover EWN, Heinrich G, Luisoni G, Stenzel H. JHEP. 2009;0908:036. doi: 10.1088/1126-6708/2009/08/036. DOI

JADE Collaboration, J. Schieck, S. Bethke, S. Kluth, C. Pahl, Z. Trocsanyi, Eur. Phys. J. C 73, 2332 (2013). arXiv:1205.3714

CDF Collaboration, T. Affolder et al., Phys. Rev. Lett. 88, 042001 (2002). arXiv:hep-ex/0108034 PubMed

D0 Collaboration, V.M. Abazov et al., Phys. Rev. D 80, 111107 (2009). arXiv:0911.2710

D0 Collaboration, V.M. Abazov et al., Phys. Lett. B 718, 56 (2012). arXiv:1207.4957

Malaescu B, Starovoitov P. Eur. Phys. J. C. 2012;72:2041. doi: 10.1140/epjc/s10052-012-2041-y. DOI

CMS Collaboration, S. Chatrchyan et al., Eur. Phys. J. C 73, 2604 (2013). arXiv:1304.7498

CMS Collaboration, V. Khachatryan et al., Eur. Phys. J. C 75, 288 (2015). arXiv:1410.6765 PubMed

CMS Collaboration, V. Khachatryan et al., Eur. Phys. J. C 75, 186 (2015). arXiv:1412.1633 PubMed

CMS Collaboration, V. Khachatryan et al., JHEP 1703, 156 (2017). arXiv:1609.05331

H1 Collaboration, A. Aktas et al., Eur. Phys. J. C 46, 343 (2006). arXiv:hep-ex/0512014

OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 71, 1733 (2011). arXiv:1101.1470

ZEUS Collaboration, S. Chekanov et al., Eur. Phys. J. C 42, 1 (2005). arXiv:hep-ph/0503274

H1 and ZEUS Collaboration, H. Abramowicz et al., Eur. Phys. J. C 75, 580 (2015). arXiv:1506.06042

Ball RD, Bertone V, Del Debbio L, Forte S, Guffanti A, Latorre JI, Lionetti S, Rojo J, Ubiali M. Phys. Lett. B. 2012;707:66. doi: 10.1016/j.physletb.2011.11.053. DOI

Harland-Lang LA, Martin AD, Motylinski P, Thorne RS. Eur. Phys. J. C. 2015;75:204. doi: 10.1140/epjc/s10052-015-3397-6. PubMed DOI PMC

CMS Collaboration, A.M. Sirunyan et al., Eur. Phys. J. C 77, 746 (2017). arXiv:1705.02628

Gehrmann-De Ridder A, Gehrmann T, Glover EWN, Huss A, Morgan TA. JHEP. 2016;1607:133. doi: 10.1007/JHEP07(2016)133. DOI

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 13, 609 (2000). arXiv:hep-ex/9908059

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 19, 269 (2001). arXiv:hep-ex/0012052

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 30, 1 (2003). arXiv:hep-ex/0304003

H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 71, 1579 (2011). arXiv:1012.4355

H1 Collaboration, F.D. Aaron et al., JHEP 1209, 061 (2012). arXiv:1206.7007

H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 72, 2163 (2012). arXiv:1205.2448 [Erratum: Eur. Phys. J. C 74, 2733 (2012)]

H1 Collaboration, I. Abt et al., Nucl. Instrum. Methods A 386, 310 (1997)

H1 Collaboration, I. Abt et al., Nucl. Instrum. Methods A 386, 348 (1997)

H1 SPACAL Group Collaboration, R.D. Appuhn et al., Nucl. Instrum. Methods A 386, 397 (1997)

H1 Calorimeter Group Collaboration, B. Andrieu et al., Nucl. Instrum. Methods A 336, 460 (1993)

Ellis SD, Soper DE. Phys. Rev. D. 1993;48:3160. doi: 10.1103/PhysRevD.48.3160. PubMed DOI

C. Duprel, T. Hadig, N. Kauer, M. Wobisch, Comparison of next-to-leading order calculations for jet cross-sections in deep inelastic scattering, in Monte Carlo Generators for HERA Physics. Proceedings, Workshop, Hamburg, Germany 1998–1999 (1999), p. 142. arXiv:hep-ph/9910448

Potter B. Comput. Phys. Commun. 2000;133:105–118. doi: 10.1016/S0010-4655(00)00158-2. DOI

J.C. Collins, D.E. Soper, G. Sterman, Factorization of Hard Processes in QCD, vol. 5 of Advanced Series on Directions in High Energy Physics, ch. 1 (World Scientific Pub Co Inc, Singapore, 1988), p. 1. arXiv:hep-ph/0409313

van Ritbergen T, Vermaseren JAM, Larin SA. Phys. Lett. B. 1997;400:379. doi: 10.1016/S0370-2693(97)00370-5. DOI

Czakon M. Nucl. Phys. B. 2005;710:485. doi: 10.1016/j.nuclphysb.2005.01.012. DOI

V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972) [Yad. Fiz. 15, 781 (1972)]

Altarelli G, Parisi G. Nucl. Phys. B. 1977;126:298. doi: 10.1016/0550-3213(77)90384-4. DOI

Y.L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977) [Zh. Eksp. Teor. Fiz. 73, 1216 (1977)]

Moch S, Vermaseren JAM, Vogt A. Nucl. Phys. B. 2004;688:101. doi: 10.1016/j.nuclphysb.2004.03.030. DOI

Vogt A, Moch S, Vermaseren JAM. Nucl. Phys. B. 2004;691:129. doi: 10.1016/j.nuclphysb.2004.04.024. DOI

The NNPDF Collaboration, R.D. Ball et al., Eur. Phys. J. C 77, 663 (2017). arXiv:1706.00428 PubMed PMC

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 13, 415 (2000). arXiv:hep-ex/9806029

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 6, 421 (1999). arXiv:hep-ex/9808013

ZEUS Collaboration, S. Chekanov et al., Eur. Phys. J. C 52, 813 (2007). arXiv:0708.1415

H1 Collaboration, A. Aktas et al., JHEP 0710, 042 (2007). arXiv:0708.3217

H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 72, 1970 (2012). arXiv:1111.0584

H1 Collaboration, V. Andreev et al., JHEP 1503, 092 (2015). arXiv:1412.0928

H1 Collaboration, V. Andreev et al., JHEP 1505, 056 (2015). arXiv:1502.01683

B. Pötter, Transition from photoproduction to deep inelastic scattering in jet production at HERA in NLO QCD, in Proceedings of the 6th International Workshop on Deep Inelastic Scattering and QCD (DIS 98): Brussels, Belgium, April 4–8, 1998 (1998), p. 574. arXiv:hep-ph/9804373

Pötter B. Comput. Phys. Commun. 1999;119:45. doi: 10.1016/S0010-4655(99)00190-3. DOI

D. Britzger, K. Rabbertz, F. Stober, M. Wobisch, New features in version 2 of the fastNLO project, in Proceedings, 20th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2012): Bonn, Germany, March 26–30, 2012. (2012), p. 217. arXiv:1208.3641

Buckley A, Ferrando J, Lloyd S, Nordström K, Page B, Rüfenacht M, Schönherr M, Watt G. Eur. Phys. J. C. 2015;75:132. doi: 10.1140/epjc/s10052-015-3318-8. DOI

V. Bertone, APFEL++: A new PDF evolution library in C++, in 25th International Workshop on Deep Inelastic Scattering and Related Topics (DIS 2017) Birmingham, UK, April 3–7, 2017 (2017). arXiv:1708.00911. https://inspirehep.net/record/1614327/files/arXiv:1708.00911.pdf

Bertone V, Carrazza S, Rojo J. Comput. Phys. Commun. 2014;185:1647. doi: 10.1016/j.cpc.2014.03.007. DOI

Botje M. Comput. Phys. Commun. 2011;182:490. doi: 10.1016/j.cpc.2010.10.020. DOI

M. Botje, Erratum for the time-like evolution in QCDNUM. Unpublished (2016). arXiv:1602.08383

Schmidt B, Steinhauser M. Comput. Phys. Commun. 2012;183:1845. doi: 10.1016/j.cpc.2012.03.023. DOI

Jegerlehner F. Nucl. Phys. Proc. Suppl. 2008;181–182:135. doi: 10.1016/j.nuclphysbps.2008.09.010. DOI

H. Spiesberger, EPRC: a program package for electroweak physics at HERA, in Future Physics with Light and Heavy Nuclei at HERMES. Contributions to the Proceedings of the ’95–’96 Workshop on Future Physics at HERA, Working Group on Light and Heavy Nuclei at HERA. Part 2 (1995)

D. Britzger et al., The ALPOS fit framework. Unpublished. http://www.desy.de/~britzger/alpos/

James F, Roos M. Comput. Phys. Commun. 1975;10:343. doi: 10.1016/0010-4655(75)90039-9. DOI

Antcheva I, et al. Comput. Phys. Commun. 2009;180:2499. doi: 10.1016/j.cpc.2009.08.005. DOI

S. Alekhin, J. Blümlein, S. Moch, R. Placakyte, Phys. Rev. D 96, 014011 (2017). arXiv:1701.05838

Dulat S, Hou T-J, Gao J, Guzzi M, Huston J, Nadolsky P, Pumplin J, Schmidt C, Stump D, Yuan CP. Phys. Rev. D. 2016;93:033006. doi: 10.1103/PhysRevD.93.033006. DOI

Lai H-L, Huston J, Li Z, Nadolsky P, Pumplin J, Stump D, Yuan CP. Phys. Rev. D. 2010;82:054021. doi: 10.1103/PhysRevD.82.054021. DOI

M. Botje et al., The PDF4LHC working group interim recommendations. Unpublished (2011). arXiv:1101.0538

S. Bethke, alpha s 2016, in Proceedings, 19th International Conference in Quantum Chromodynamics (QCD 16): Montpellier, France, July 4–9, 2016, vol. 282–284 (2017), p. 149

Gfitter Collaboration, M. Baak et al., Eur. Phys. J. C 74, 3046 (2014). arXiv:1407.3792

M. Klein, V. Radescu, Partons from the LHeC. CERN-LHeC-Note-2013-002 (2013). https://cds.cern.ch/record/1564929

Alekhin S, Blümlein J, Moch S. Phys. Rev. D. 2012;86:054009. doi: 10.1103/PhysRevD.86.054009. DOI

Blümlein J, Böttcher H, Guffanti A. Nucl. Phys. B. 2007;774:182. doi: 10.1016/j.nuclphysb.2007.03.035. DOI

Jimenez-Delgado P, Reya E. Phys. Rev. D. 2009;79:074023. doi: 10.1103/PhysRevD.79.074023. DOI

List of H1 publications https://www-h1.desy.de/publications/H1publication.short_list.html

H1 Collaboration, C. Adloff et al., Eur. Phys. J. C 21, 33–61 (2001). arXiv:hep-ex/0012053

Measurement of the t t ¯ production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at s = 13 Te

Determination of the strong coupling constant α s ( m Z ) in next-to-next-to-leading order QCD using H1 jet cross section measurements: H1 Collaboration