Selected Recent HERMES results on Parton Distribution and Fragmentation Functions K. Rith (on behalf of the HERMES collaboration) a u Universit¨t Erlangen-N¨rnberg, Physikalisches Institut, Erwin-Rommel-Str. 1, D-91058 Erlangen, Germany In this contribution three aspects are addressed: a novel determination of the unpolarised strange quark (plus anti-quark) distribution; the measurement of single-spin azimuthal asym- metries for pions and kaons in semi-inclusive deep-inelastic scattering from a transversely polarised hydrogen target, that are related to the quark transversity distribution in conjunc- tion with the spin-dependent Collins fragmentation function and to the Sivers distribution function; and the measurement of azimuthal hadron asymmetries in unpolarised deep-inelastic scattering related to the so-called Cahn eﬀect and the Boer-Mulders distribution function. 1 Introduction HERMES is one of the three experiments at the HERA electron-proton collider that took data until mid 2007, when the accelerator complex was shut down. It used the high-current longitu- dinally polarised electron/positron beam of HERA with an energy of E = 27.6 GeV together with polarised and unpolarised gas targets internal to the storage ring. Scattered electrons and particles produced in the deep-inelastic lepton-nucleon interactions were detected and identiﬁed by an open-geometry forward spectrometer 1 with large momentum and solid-angle acceptance. The primary scientiﬁc goal of HERMES was the detailed investigation of the spin-structure of the nucleon. From the precise measurement of the polarised deuteron structure function g1 the d contribution of quark spins, ΔΣ, to the spin of the nucleon was determined in NLO-QCD and in the M S-scheme to be 2 : ΔΣ = 0.330 ± 0.025(stat) ± 0.030(sys). Precise informations about ¯ the ﬂavor-separated quark (anti-quark) helicity distribution functions have been obtained from double-spin asymmetries for various identiﬁed hadrons in semi-inclusive polarized deep-inelastic scattering 3 . But the physics reach of this experiment is well beyond this speciﬁc aspect of hadron physics and the experiment can be considered as a facility to explore many details of hadron structure, hadron production and hadronic interactions with electromagnetic probes at centre- of-mass energies of around 7 GeV. In this contribution HERMES measurements are presented that provide novel information on various parton distribution and fragmentation functions. 2 The strange quark distribution function s The experimental information about the distribution function (DF) s(x) (¯(x)) of strange quarks (antiquarks) as a function of the dimensionless Bjorken scaling variable x is surprisingly scarce. Most of the experimental constraints are based on measurements of oppositely charged muon pairs in deep-inelastic neutrino and antineutrino scattering. In absence of signiﬁcant experi- 0.15 xS(x) DIS Fit dN /dN 0.1 0.4 CTEQ6L K – – x(u(x)+d(x)) 0.05 0.2 0 2 10 0 <Q > GeV 1 0.02 0.1 0.6 2 0.02 0.1 0.6 X x Figure 1: HERMES results for the multiplicity of charged kaons in semi-inclusive DIS from a deuterium target (left panel) and of the derived strange parton distribution xS(x) at Q2 = 2.5 GeV2 (right panel), as a function of 0 Bjorken x. mental constraints, current global QCD ﬁts of particle distribution functions (PDFs) assume s(x) (¯(x)) to be related to the DFs of light antiquarks by s(x) = s(x) = r[¯(x) + d(x)]/2 s ¯ u ¯ with r ≈ 0.3 − 0.5 at some low factorisation scale. HERMES has recently performed the ﬁrst ¯ extraction of S(x) = s(x) + s(x) from the multiplicity of charged kaons in semi-inclusive deep- inelastic scattering (SIDIS) from a deuteron target 4 . Because strange quarks carry no isospin, the strange seas in the proton and the deuteron can be assumed to be identical. In the deuteron, an isoscalar target, the fragmentation process in deep-inelastic scattering (DIS) can be described by fragmentation functions (FFs) that have no isospin dependence. Aside from isospin symme- try between proton and neutron, the only symmetry assumed is charge-conjugation invariance in fragmentation. In Leading Order the charged kaon multiplicities are then given by: K K dN K (x) Q(x) D1,Q (z)dz + S(x) D1,S (z)dz = . (1) dN DIS (x) 5Q(x) + 2S(x) ¯ Here Q(x) ≡ u(x) + u(x) + d(x) + d(x), D1,Q (z) ≡ 4D1,u (z) + D1,d (z) and D1,S (z) ≡ 2D1,s (z), ¯ K K K K K and z ≡ EK /ν with ν and EK the energies of the virtual photon and the detected kaon in the target rest frame. The measured kaon multiplicity corrected to 4π is shown in the left panel of Fig. 1 as a function of x. The data are not reproduced (see dotted curve) by ﬁtting the points using the CTEQ6L 5 strange quark DFs and with D1,Q (z)dz and D1,S (z)dz as free K K 0.8 K parameters. Instead 0.2 D1,Q (z)dz = 0.398 ± 0.010 was determined from the data at x > 0.15, where S(x) is compatible with zero. This value was then used together with values of Q(x) from CTEQ6L and the value D1,S (z)dz = 1.27 ± 0.13 from de Florian et al. 6 to obtain in K an iterative procedure the distribution xS(x) presented in the right panel of Fig. 1. Hereby the multiplicities were evolved to a common Q2 = 2.5 GeV2 . The solid curve is a ﬁt to the data. 0 The shape is incompatible with xS(x) from CTEQ6L as well as the assumption of an average of an isoscalar nonstrange sea. 3 Transverse-momentum dependent distribution and fragmentation functions A complete description of the partonic structure of the nucleon in leading twist requires three DFs that survive integration over intrinsic transverse momenta. These are the unpolarized quark DF q x, Q2 , the quark helicity DF Δq x, Q2 , and the chiral-odd transversity DF δq x, Q2 7 . In addition there are ﬁve other transverse-momentum dependent DFs that do not survive the integration 8 . Experimentally these are essentially unexplored. Examples are the time-reversal ⊥ odd Sivers DF 9 , f1T (x)), that describes the distribution of unpolarised quarks in a transversely polarised nucleon and can be related to orbital angular momenta of quarks 10 , and the Boer- Mulders DF 11 , h⊥ (x), for transversely polarised quarks in an unpolarised nucleon. 1 III III 2 〈sin(φ+φS)〉UT 2 〈sin(φ-φS)〉UT + K+ h h 0.2 K+ HERMES PRELIMINARY 2002-2005 HERMES PRELIMINARY 2002-2005 π lepton beam asymmetry, Collins amplitudes 0.25 π + lepton beam asymmetry, Sivers amplitudes 0.15 8.1% scale uncertainty 8.1% scale uncertainty 0.2 0.1 0.15 0.05 0.1 0 0.05 -0.05 0 -0.1 2 〈sin(φ+φS)〉UT 2 〈sin(φ-φS)〉UT K- - h h 0.15 - K π 0.15 π- 0.1 0.1 0.05 0.05 0 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.15 0.1 0.2 0.3 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 x z Ph⊥ [GeV] x z Ph⊥ [GeV] Figure 2: HERMES results for the ”Collins moments” (left panel) and the ”Sivers moments” (right panel) for charged pions and kaons obtained with a transversely polarised hydrogen target. 3.1 Transversity, Collins and Sivers Eﬀect Measurements with transversely polarised targets allow to access transverse-momentum depen- ⊥ dent DFs and FFs, like transversity, the Collins FF H1,q 12,13 , which is also odd under naive time reversal, and the Sivers DF. In SIDIS they manifest themselves in single-spin asymmetries in the distribution of hadrons in the azimuthal angles φ (φs ) around the virtual photon direction between the lepton scattering plane and the hadron production plane (transverse component of the target spin vector). The Collins (Sivers) mechanism will cause a sin(φ + φS ) (sin(φ − φS )) ⊥ ⊥ moment proportional to a convolution of δq (x) and H1,q (z) (f1T,q (x) and D1,q (z)). Preliminary HERMES results 14 for the Collins and Sivers moments for charged pions and kaons, obtained from data taken with a transversely polarised hydrogen target, are shown in Fig. 2. The measured Collins asymmetries (left panel) are small but diﬀerent from zero providing ⊥ evidence for the existence of both δq (x) and H1,q (z). The large π − moment indicates that the unfavored Collins FF has similar magnitude as the favored one, but opposite sign. The π + and K + Sivers asymmetries (right panel) are signiﬁcantly positive, providing the ﬁrst evidence for a T-odd PDF appearing in leptoproduction. Consequently one has to conclude from this result that orbital angular momenta of quarks inside the nucleon are non-zero. At present it is, however, not jet possible to quantitatively relate the magnitude of this asymmetry to the fraction of nucleon spin which can be attributed to orbital angular momenta of quarks. The positive kaon amplitudes appear to be larger than the pion amplitudes, which might point to a large Sivers function for sea-quarks. These date were an important input for an extraction of transversity, Collins FF and Sivers DF from world data 15,16 . 3.2 Cahn and Boer-Mulders eﬀect If the semi-inclusive unpolarised DIS cross section is unintegrated over the hadron momentum component transverse to the virtual photon direction, Ph⊥ , an azimuthal dependence around the virtual photon direction exists, which has a cosφ and a cos2φ component. Two mechanisms are expected to give important contributions to this azimuthal dependence: the Cahn eﬀect, a pure kinematic eﬀect, generated by the non-zero intrinsic transverse motion of quarks 17 and the Boer-Mulders eﬀect, which originates from a coupling between quark transverse momentum and quark transverse spin. To extract the cosφ and cos2φ modulations from the unpolarised HERMES hydrogen (H) and deuterium (D) data taking into account radiative and detector smearing a multi-dimensional unfolding procedure was used, in which the event sample is binned simultaneously in the relevant kinematic variables x, z, Ph⊥ and y = ν/E. The preliminary cosφ moments from the H and D 0.2 + h UU h HERMES Preliminary 2〈 cos(φ )〉 Hydrogen 0.1 Deuterium 0 -0.1 -0.2 -0.3 10-1 1 0.4 0.6 0.8 .2 0.4 0.6 0.8 1 0.2 0.4 0.6 x y z Ph [GeV] 0.2 - h UU h HERMES Preliminary 2〈 cos(φ )〉 Hydrogen 0.1 Deuterium 0 -0.1 -0.2 -0.3 10-1 1 0.4 0.6 0.8 .2 0.4 0.6 0.8 1 0.2 0.4 0.6 x y z Ph [GeV] Figure 3: cosφ moments for positive (upper panel) and negative (lower panel) hadrons, extracted from hydrogen (circles) and deuterium (squares) data, shown as projections versus the kinematic variables x, y, z and Ph⊥ . data are shown in Fig. 3 as projections versus the four variables. Corresponding data exist for the cos2φ moments. Both H and D data show similar behaviour. cosφ moments receive ⊥ contributions from both the product h⊥ H1 and the product f1 D1 . They are found to be sizable 1 and negative for positive hadrons, the signal for negative hadrons is signiﬁcantly lower. The ⊥ cos2φ moments are proportional to h⊥ H1 . They are found to be slightly negative for positive 1 hadrons and slightly positive for negative hadrons in agreement with models which predict opposite Boer-Mulders contributions for diﬀerently charged hadrons. Acknowledgments u This work has been supported by the German Bundesministerium f¨r Bildung und Forschung (Contract Nr. 06 ER 143). References 1. K. Ackerstaﬀ et al.(HERMES), Nucl. Instrum. Methods A 417, 230 (1998). 2. A. Airapetian et al.(HERMES), Phys. Rev. D 75, 012007 (2007). 3. A. Airapetian et al.(HERMES), Phys. Rev. D 71, 012003 (2005). 4. A. Airapetian et al.(HERMES), Phys. Rev. Lett. 666, 466 (2008). 5. J. Pumplin et al., J. High Energy Phys. 7, 12 (2002). 6. D. de Florian et al., Phys. Rev. D 75, 114010 (2007). 7. V. Barone and P.G. Ratcliﬀe, Transverse Spin Physics, World Scientiﬁc, 2003. 8. P. J. Mulders and R. D. Tangerman, Nucl. Phys. B 461, 197 (1996); Erratum Nucl. Phys. B 484, 538 (1997). 9. D. W. Sivers, Phys. Rev. D 41, 83 (1990); Phys. Rev. D 43, 261 (1991). 10. M. Burkardt, Phys. Rev. D 66, 114005 (2002); Phys. Rev. D 69, 074032 (2004). 11. D. Boer and P.J. Mulders, Phys. Rev. D 57, 5780 (1998). 12. J. Collins, Nucl. Phys. B 396, 161 (1993). 13. J. Collins et al., Nucl. Phys. B 420, 565 (1994). 14. M. Diefenthaler (for the HERMES collaboration), Proceedings of the 15th International Workshop on Deep-Inelastic Scattering (DIS2007), 16-20 April 2007,(2007). 15. M. Anselmino et al., arXiv:0809.3743 [hep-ph]. 16. M. Anselmino et al., Eur. Phys. J. A 39, 89 (2009). 17. R.N. Cahn, Phys. Lett. B 78, 269 (1978); Phys. Rev. D 40, 3107 (1989).