arXiv:1607.00790v1 [hep-ex] 4 Jul 2016 aawl rvd h ai o nesadn h structure the understanding for basis com the been measur provide recently on will have Collaborations data scattering ZEUS and wid inelastic a deep the covering inclusive from and data All precision high range. pro the to HERA of from performed structure Data the measurements LHC. of the understanding as our such ot of used to backbone be application will direct has or stru also are the but nucleons understand level, to basic the most trying of its in extractions at important precise is and d This a proton yielding the constant. force, of strong structure the the of dynamics of the probing of way a ∗ ia obndde nlsi cteigcossections cross scattering inelastic deep combined Final rs etospeiul ulse yteH n EScollaboration current ZEUS charged and and H1 neutral the for by HERA published previously sections cross 6 e n neeto emeeg f2. e.Tedt corresp data squared, fb 1 The four-momentum-transfer about GeV. negative 27.5 of in 820, of luminosity 920, nitude energy of integrated beam energies an beam to an proton at and taken GeV 460 were data The sation. esrmnso epieatclpo–ulo scattering –nucleon inelastic deep of Measurements o highlights Brief d possible. parton constant presented. of coupling are determination results strong cros precise the jet-production and and of simultaneous butions nex inclusion a at the f made distribution and Additionally, sections parton order of HERAPDF2.0. set next-to-leading new called order, a wer providing leading sections order, at cross next-to-leading combined analyses The a QCD evaluated combination. to were the uncertainties for account systematic into the of correlations The rsne tEctdQD21 Workshop. 2016 QCD Excited at Presented eateto hsc n srnm,Uiest olg London College University Astronomy, and Physics of Department h obnto speetdo l nlsv epieatcscattering inelastic deep inclusive all of presented is combination The o eafo h 1adZU Collaborations) ZEUS and H1 the of behalf (on ate Wing Matthew .Introduction 1. tHERA at (1) ep − cteigfrzr empolari- beam zero for scattering ∗ 1 n pnsxodr fmag- of orders six span and Q 2 n Bjorken and , e rjcswhere projects her ie 1.These [1]. bined togcoupling strong tr fmatter of cture ihnumerous with aeln been long have tie picture etailed fteproton the of unctions, kinematic e dtaken nd 7 and 575 input e mnsof ements ie the vides istri- the f t-to- at s ond x s . 2 HERA˙Wing printed on October 17, 2018 for many years to come. The data provide many beautiful demonstrations of fundamental physical phenomena such as scaling violations of the cross section and electroweak unification. The high precision also allows their sole use in a QCD fit to determine the parton distribution functions in the proton (called HERAPDF2.0).

2. Data combination The data, taken over the 15-year lifetime of the HERA accelerator, corre- spond to a total luminosity of about 1 fb−1 of deep inelastic electron–proton and –proton scattering. All data used were taken with an electron beam energy of 27.5 GeV. Roughly equal amounts of data for electron– proton and positron–proton scattering were recorded. The bulk of the data were taken with a proton beam energy of 920 GeV, but samples with proton beam energies of 820, 575 and 460 GeV were also collected. The data were combined separately for the e+p and e−p data and the different centre-of- mass energies. Overall, 41 separate data sets were used in the combination, 2 2 −7 spanning the ranges 0.045

3. Physics highlights The data in Fig. 1 also demonstrate beautifully the effect of scaling violations in deep inelastic scattering. At xBj ∼ 0.1, the cross section is flat 2 2 with Q , whereas the cross section falls with increasing Q at high xBj and 2 rises rapidly with increasing Q at low xBj. This rapid rise is indicative of HERA˙Wing printed on October 17, 2018 3

H1 and ZEUS 1.8 HERA NC e+p 0.5 fb–1

+ r, NC

σ 1.6 √s = 318 GeV x = 0.002 Bj ZEUS HERA II x = 0.0002 1.4 Bj ZEUS HERA I H1 HERA II 1.2 H1 HERA I

1 xBj = 0.008

0.8

0.6 xBj = 0.032

xBj = 0.008 x = 0.08 0.4 Bj xBj = 0.08

0.2

xBj = 0.25

0 2 3 4 5 1 10 10 10 10 10 Q2/GeV2

+ 2 Fig.1. Neutral current reduced cross section, σr, NC, versus Q for H1 and ZEUS data sets (open points) and after the HERA combination (solid points). A selection of data for fixed xBj is shown. an ever-increasing gluon density being probed, shown here for a subset of the data sample. The differential cross sections at high Q2 are shown in Fig. 2 for neutral and charged current events for both e+p and e−p interactions. At Q2 ∼ 200 GeV2, the neutral current cross section is significantly higher than the charged current cross section due to the dominance of photon exchange. At Q2 > 10 000 GeV2, the cross sections become similar, due to the exchange of massive vector bosons, indicative of the unification of the electromagnetic and weak forces. The difference in the neutral current cross sections for e+p and e−p data is due to γ−Z interference effects; this allowed an extraction of the xF3 structure function which is related to the density of valence quarks (not shown). The helicity structure of the W ± exchange and the different quarks being probed also leads to the observed difference in e+p and e−p data in charged current interactions. The data demonstrating these fundamental physical properties are well 4 HERA˙Wing printed on October 17, 2018

H1 and ZEUS ) 2 10 HERA NC e-p 0.4 fb-1 HERA NC e+p 0.5 fb-1 HERAPDF2.0 NC e-p (pb/GeV 2 HERAPDF2.0 NC e+p -1

/dQ 10 σ d

10-3 y < 0.9 s = 318 GeV

HERA CC e-p 0.4 fb-1 -5 10 HERA CC e+p 0.5 fb-1 HERAPDF2.0 CC e-p HERAPDF2.0 CC e+p 10-7 103 104 Q2 / GeV2

Fig.2. Neutral current (open points) and charged current (solid points) differential cross sections versus Q2 compared to predictions (solid curves).

described by the Standard Model, encompassed on the QCD fit, HERA- PDF2.0, described in the next section.

4. QCD analysis, HERAPDF2.0 The HERA data was then used as the sole input to a QCD analysis using the DGLAP equations at leading (LO), next-to-leading (NLO) and next-to- next-to-leading order (NNLO). The data were restricted to 3.5 < Q2 < 50 000 GeV2, with the minimum Q2 value varied and the effects studied as shown in Fig. 3. As can be seen in the figure, the overall χ2/d.o.f. for the full Q2 range is about 1.2 (at both NLO and NNLO), but becomes lower until about 10 GeV2 where is levels out at a value of about 1.14. The same trend with Q2, but just with different absolute values was present in the HERA I data (1992–2000) [2]. This trend towards lower Q2 indicates that something more is needed beyond DGLAP evolution and a full and HERA˙Wing printed on October 17, 2018 5 consistent description of these data will lead to a deeper understanding of QCD. However, it should be noted that predictions for LHC processes do 2 2 2 not differ between the fits with Qmin of 3.5 GeV or 10 GeV .

H1 and ZEUS

1.3 RTOPT LO /d.o.f.

2 RTOPT NLO

χ RTOPT NNLO

1.2

1.1

1

RTOPT NLO HERA I

0.9

5 10 15 20 25 2 2 Qmin /GeV Fig. 3. χ2/d.o.f. of QCD fit to HERA data for differing minimum values of Q2. Results are shown at different orders for the calculation and also for the fit to HERA I data only. The RTOPT [3] label signifies the scheme used to treat heavy quarks.

A comparison of HERAPDF2.0 is shown with predictions from other groups [4, 5, 6] in Fig. 4. Overall the expectations from different groups are compatible. Jet and charm data were also included in an NLO QCD fit allowing an extraction of the strong coupling constant. The QCD fit described the data well and yielded a value of the strong coupling constant consistent with the world average and with an experimental precision of better than 1%. The theoretical uncertainty due to varying the renormalisation and factorisation scales was significantly larger, about 3%, and could hopefully be improved with a NNLO jet calculation and so allowing a NNLO fit of the data. 6 HERA˙Wing printed on October 17, 2018

H1 and ZEUS 2 v µ2 = 10 GeV v 0.6 1 f

xu HERAPDF2.0 NNLO xd MMHT2014 NNLO 0.5 0.8 CT10 NNLO NNPDF3.0 NNLO 0.4 0.6 0.3 0.4 0.2

0.2 0.1

0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 x 1 10 10 10 10 x 1 5 xg 16 xS

14 4 12

10 3

8 2 6

4 1 2

0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 x 1 10 10 10 10 x 1 Fig.4. Comparison of HERAPDF2.0 at NNLO with QCD fits from other groups, showing the u and d valence, gluon and sea parton density functions.

Acknowledgements Support from DESY and the Alexander von Humboldt Stiftung are gratefully acknowledged.

REFERENCES

[1] H1 and ZEUS Coll., H. Abramowicz et al., Eur. Phys. J. C 75 (2015) 580. [2] H1 and ZEUS Coll., H. Abramowicz et al., JHEP 1001 (2010) 109. [3] R.S. Thorne and R.G. Roberts, Phys. Rev. D 57 (1998) 6871; R.S. Thorne, Phys. Rev. D 73 (2006) 054019; R.S. Thorne, Phys. Rev. D 86 (2012) 074017. [4] L. Harland-Lang, A.D. Martin, P. Motylinski and R. Thorne, Eur. Phys. J. C 75 (2015) 204. [5] M. Guzzi et al., Phys. Rev. D 82 (2010) 074024. [6] NNPDF Coll., R.D. Ball et al., JHEP 1004 (2015) 040. H1 and ZEUS i HERA NC e– p 0.4 fb–1 7 + –1 x 2 10 HERA NC e p 0.5 fb √s = 318 GeV xBj = 0.00005, i=21

r, NC 6 x = 0.00008, i=20 10 Bj x = 0.00013, i=19 Fixed Target σ Bj x = 0.00020, i=18 – Bj HERAPDF2.0 e p NNLO x = 0.00032, i=17 5 Bj + 10 xBj = 0.0005, i=16 HERAPDF2.0 e p NNLO

xBj = 0.0008, i=15 xBj = 0.0013, i=14 4 10 xBj = 0.0020, i=13 xBj = 0.0032, i=12

xBj = 0.005, i=11 3 10 xBj = 0.008, i=10

xBj = 0.013, i=9

xBj = 0.02, i=8 10 2 xBj = 0.032, i=7

xBj = 0.05, i=6 xBj = 0.08, i=5 10 xBj = 0.13, i=4

xBj = 0.18, i=3

1 xBj = 0.25, i=2

-1 xBj = 0.40, i=1 10

-2 10 xBj = 0.65, i=0

-3 10 2 3 4 5 1 10 10 10 10 10 Q2/ GeV2