Abstract
Inclusive e ± p single and double differential cross sections for neutral (NC) and charged current (CC) deep inelastic scattering processes are measured with the H1 ashley99@example.org. The data were taken at a centre-of-mass energy of √ s = 319 GeV with a total integrated luminosity of 327.8 pb −1 shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative four-momentum transfer squared, Q 2 , between 60 and 50 000 GeV 2 , and Bjorken x between 0.0008 and 0.65. The measurements are combined with earlier published unpolarised H1 data to improve statistical precision and used to determine the structure function xF γZ 3 . A measurement of the structure function F γZ 2 , sensitive to parity violating effects in NC, is presented for the first time. The polarisation dependence of the CC total cross section is also measured. The new measurements are well described by a next-to-leading order QCD fit based on all published H1 inclusive cross section data which are used to extract the parton distribution functions of the proton.
Introduction
The ep collider HERA used to be the largest electron microscope of the world. The inclusive neutral current (NC) and charged current (CC) deep inelastic scattering (DIS) cross section data measured by H1 and ZEUS at HERA I (1992-2000) [1] , where the unpolarised electron 1 beam of up to 27.5 GeV collided with the unpolarised proton beam of up to 920 GeV, have been the primary source for constraining of parton distribution functions (PDFs) of the proton. In HERA II (2003) (2004) (2005) (2006) (2007) , spin rotators were installed around the interaction points of H1 and ZEUS to provide longitudinally polarised electron beam there. Most of the data at HERA II were taken at the nominal proton beam energy E p of 920 G eV in four distinct data sets: e The corresponding integrated luminosity (mean polarisation P e ) values 2 are 46.5 pb −1 (+36.0%), 102.6 pb −1 (−25.8%), 99.5 pb −1 (+32.5%) and 79.3 pb −1 (−37.0%), respectively. The e − p data corresponds to an almost tenfold increase in luminosity over the HERA I data set.
The new results reported here and published in [2] concern the final NC and CC cross sections at high Q 2 measured using all HEAR-II data and a new QCD analysis of all H1 data to obtain a new set of PDFs, H1PDF 2012.
To appreciate the constraint on PDFs from the inclusive NC and CC cross sections, it is helpful to write down explicitly the expressions of the differential NC and CC cross sections in terms of different structure functions
where Y ± = 1 ± (1 − y) 2 and y characterises the inelasticity of the interaction and is related to Bjorken x, Q 2 and centre-of-mass energy √ s by y = Q 2 /(xs), α ≡ α(Q 2 = 0) is the fine structure constant, G F is the Fermi constant and M W is the propagator mass of the W boson. For the NC interaction, the generalised structure functionsF ± 2 and xF ± 3 can be further decomposed as 4) with M Z being the mass of the Z boson,
in the on-mass-shell scheme, v e and a e the vector and axial-vector couplings of the electron to the Z boson. In Eq.(1.3), F 2 corresponds to the dominant electromagnetic structure function of photon exchange, the other structure function terms are due to photon-Z interference and pure Z exchange. The generalised longitudinal structure functionF L may be similarly decomposed. 1 In this proceedings, "electron" refers generically to both electrons and positrons. Where distinction is required the terms e − and e + are used. 2 The luminosity values given here differ from [2] by -1.8% due to the revised measurement based on the QED Compton events [3] .
In the quark-parton model (QPM), the structure functions F 2 , F Fig. 1 (right) also in a reduced form (σ CC ) by removing the kinematic factor
2). The CC reduced cross sections for the L and R data sets are very different for all Q 2 as parity violation is maximal with W boson exchange. These cross sections agree well with the expectation from H1PDF 2012 fit. Both the statistical and systematic precision have substantially improved with respect to the corresponding measurements from HERA I with the unpolarised lepton beams.
3. NC polarisation asymmetry and structure functions F The Standard Model (SM) predicts a difference in the NC cross section for leptons with different helicity states arising from the chiral structure of the neutral electroweak exchange. With longitudinally polarised lepton beams in HERA II such electroweak effects can be tested through a polarisation asymmetry, A ± , defined as
where P ± L and P ± R are the longitudinal lepton beam polarisation in the e ± p R and L data sets. The measured asymmetry is shown in Fig. 2 dependence is expected and therefore the measurement is transformed to a common Q 2 value of 1 500 GeV 2 using the H1PDF 2012 fit and is averaged in each x bin. The result is shown in Fig. 2 (bottom-left) in comparison to the H1PDF 2012 fit. This is the first measurement of the structure function F γZ 2 . The structure function xF γZ 3 , probing the valence quarks of the proton, has been determined previously by H1 with limited statistical precision due in particular to the small integrated luminosity available in e − p interactions at HERA I [4, 5] . Combining the new HERA II data with that of HERA I, the structure function has been updated in Fig. 2 (bottom-right) with two new data points at low x and substantially improved precision for other data points.
(top). The magnitude of the asymmetry is observed to
4. Total CC cross section σ tot CC and NC and CC cross section dσ NC,CC /dQ 2
The total CC cross sections σ tot CC for e ± L,R p scattering have been measured in the kinematical region of Q 2 > 400 GeV 2 and y < 0.9. Together with the corresponding cross sections measured at HERA I with unpolarised e ± beams, the linear dependence of the cross sections on P e (Fig. 3(left) ) can be verified for both e − p and e + p interactions (in the latter case with more data than that previously published [6] ). The data are consistent with the absence of right handed weak charged currents.
[%] Dependence of the e ± p CC cross sections on the longitudinal lepton beam polarization P e . Right: Q 2 dependence of the NC and CC cross sections dσ /dQ 2 for the combined HERA I+II unpolarised e ± p data. In both figures, the inner and full error bars represent the statistical and total errors, respectively.
The single differential NC and CC cross sections dσ NC,CC /dQ 2 have been measured for y < 0.9 and in Q 2 varying over more than two orders of magnitude (the combined version with unpolarised HERA I e ± p data is shown in Fig. 3(right) ). The NC cross sections exceed the CC cross sections at 
H1PDF 2012
To assess the impact of the new H1 NC and CC cross sections at high Q 2 measured with the longitudinally polarised electron beams on the determination of PDFs, a new QCD analysis (H1PDF 2012) has been performed. In addition to the new HERA II data, the previously published unpolarised HERA I data at high Q 2 and at low Q 2 , as well as the H1 measurements at lower proton beam energies have been used. This analysis supersedes the previous H1PDF 2009 fit. The resulting PDFs are shown in Fig.4 (left) and the impact of HERA II data on the PDF precision is shown as an example for the down quark density xD in Fig.4 (right). 
Summary
The NC and CC cross sections at high Q 2 with the nominal E p and all polarised e ± data from HERA II have been measured. Both the statistical and systematic uncertainties of the measurements have been substantially reduced compared to previous HERA I H1 data. The NC lepton polarisation asymmetry A ± , sensitive to parity violation, has been determined separately for e + p and e − p scattering. The asymmetry is found to increase in magnitude with Q 2 in agreement with the expectation of the SM. The structure function F γZ 2 has been measured for the first time using the polarisation dependence of the e ± p NC cross sections. At high Q 2 the structure function xF γZ 3 has been determined using unpolarised NC cross sections obtained from the complete HERA I and HERA II data sets. The polarization dependence of the CC total cross section for Q 2 > 400 GeV 2 and y < 0.9 has been measured and compared to the unpolarised HERA I measurements. The data exhibit a linear scaling of the cross sections with P e which is positive for e + p and negative for e − p scattering. The data are consistent with the absence of right handed weak currents. The new QCD analysis shows a significant impact of the new data on the increased precision of the PDFs. These data are being combined with those from ZEUS and a new QCD fit HERAPDF2.0 is being performed. The combined data are expected to provide a better precision on PDFs in particular at medium and high x.

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