Measurements of Double-Spin Asymmetries in SIDIS of Longitudinally Polarized Leptons off Transversely Polarized Protons
aa r X i v : . [ h e p - e x ] J u l Measurements of Double-Spin Asymmetries inSIDIS of Longitudinally Polarized Leptons offTransversely Polarized Protons
L.L. Pappalardo ∗ and M. Diefenthaler † ∗ INFN – University of Ferrara - Dipartimento di Fisica, Via Saragat 1, 44100 Ferrara, Italy † University of Illinois, Department of Physics, 1110 West Green Street, Urbana, USA (on behalf of the HERMES Collaboration)Abstract.
A Fourier analysis of double-spin azimuthal asymmetries measured at HERMES insemi-inclusive deep-inelastic scattering of longitudinally polarized leptons off tranversely polarizedprotons is presented for pions and charged kaons. The extracted amplitudes can be interpretedas convolutions of transverse momentum-dependent distribution and fragmentation functions andprovide sensitivity to e.g. the poorly known worm-gear quark distribution g ⊥ T . Keywords:
Deep inelastic scattering, transverse momentum dependent distribution functions
PACS:
ACCESSING TMDS IN SEMI-INCLUSIVE DIS
In recent years, semi-inclusive deep-inelastic-scattering (SIDIS) processes are being ex-plored by several experiments to investigate the nucleon structure through the measure-ments of new observables, not accesible in inclusive DIS. The detection of a final-statehadron in coincidence with the scatterd lepton has the advantage of providing uniqueinformation on the quark flavors involved in the scattering process ("flavor tagging")through the identification of the final state hadrons (e.g. p , K , etc), and allows to accessnew dimensions, such as the transverse-spin and transverse-momentum degrees of free-dom of the nucleon. For instance, the recent first extraction of the chiral-odd transversitydistribution h q ( x ) [1], the least known of the three fundamental leading-twist collinearparton distribution functions (PDFs), required the measurement of specific azimuthalasymmetries (the "Collins asymmetries") in SIDIS of unpolarized leptons off trans-versely polarized protons [2, 3, 4] and deuterons [5, 6]. Here x denotes the fractionof the longitudinal momentum of the parent (fast-moving) nucleon carried by the activequark.When the transverse momentum p T of the quarks is not integrated out, a variety ofnew PDFs arise, describing correlations between the quark or the nucleon spin withthe quark transverse momentum, often referred to as spin-orbit correlations . Thesepoorly known PDFs, typically denoted as transverse-momentum-dependent PDFs (orsimply TMDs), encode information on the 3-dimensional structure of nucleons and areincreasingly gaining theoretical and experimental interest. At leading-twist, eight TMDs,each with a specific probabilistic interpretation in terms of quark number densities, enterthe SIDIS cross section in conjunction with a fragmentation function (FF) (see e.g. [7]).hen the polarization of the final hadrons is not regarded, this can be either the chiral-odd Collins function H ⊥ ( z , K T ) , describing left-right asymmetries in the fragmentationof transversely polarized quarks, or the relatively well known spin-independent chiral-even D ( z , K T ) FF. Here z and K T denote the fraction of the energy of the exchangedvirtual photon carried by the produced hadron and the transverse momentum of thefragmenting quark with respect to the outgoing hadron direction, respectively.Among the leading-twist TMDs, the ’worm-gear’ h ⊥ L ( x , p T ) and g ⊥ T ( x , p T ) are thosethat have received the least attention so far. They are, nevertheless, very intriguing ob-jects: g ⊥ T ( x , p T ) ( h ⊥ L ( x , p T ) ) describes the probability of finding a longitudinally (trans-versely) polarized quark inside a transversely (longitudinally) polarized nucleon. Inter-estingly, they are the only two leading-twist TMDs whose corresponding GeneralizedParton Distributions vanish in light-come quark models [8], and are found to be one theopposite of the other ( g ⊥ T ( x , p T ) = − h ⊥ L ( x , p T ) ) in various quark models [9, 10, 11, 12].Despite their similarities, these two TMDs have a different behaviour under chiral trans-formations: h ⊥ L ( x , p T ) is chiral-odd and can be probed in SIDIS in combination with theCollins FF, while g ⊥ T ( x , p T ) is chiral-even and can thus be accessed in SIDIS combinedwith the unpolarized FF. Another important difference, especially from the experimentalpoint of view, is that h ⊥ L ( x , p T ) can be accessed in longitudinal target A UL single-spinasymmetries (SSAs), whereas in the case of g ⊥ T ( x , p T ) the longitudinal polarization ofthe active quark leads to A LT double-spin asymmetries (DSAs), requiring both a longi-tudinally polarized beam and a transversely polarized target [7].At leading-twist, the term of the SIDIS cross section that accounts for this DSAexhibits a cos ( f − f S ) modulation in the azimuthal angles f and f S , respectively ofthe detected hadron and of the target transverse polarization with respect to the leptonscattering plane and about the virtual-photon direction. In SIDIS experiments the worm-gear g ⊥ T ( x , p T ) can be accessed at leading-twist through the measurement of the DSA:2 h cos ( f − f S ) i hL ⊥ = R d f d f S cos ( f − f S ) s LT R d f d f S s UU = C (cid:2) − P h ⊥ · p T | P h ⊥ | M g ⊥ , q T ( x , p T ) D q → h ( z , K T ) (cid:3) C (cid:2) f q ( x , p T ) D q → h ( z , K T ) (cid:3) , (1)where s LT denotes the cross-section difference for opposite target polarization states, P h ⊥ is the transverse momentum of the produced hadron, f q ( x , p T ) is the unpolarizeddistribution function and C denotes a convolution integral over the intrinsic transversemomenta. Other Fourier components of s LT are the sub-leading twist contributionscos ( f S ) and cos ( f − f S ) , where the worm-gear g ⊥ T ( x , p T ) appears in convolution withthe higher-twist ˜ D ⊥ ( z , K T ) FF besides several other contributions of PDFs and FFs.In this work, preliminary results for the Fourier components of the DSAs, measuredat the HERMES experiment with a longitudinally polarized beam and transverselypolarized protons, are discussed for identified pions and charged kaons.
DATA ANALYSIS AND RESULTS
The data analysed was recorded during the 2003–2005 running period of the HERMESexperiment using a longitudinally polarized 27 . − p , K , p )in the 2 −
15 GeV momentum range. Events were selected subject to the kinematicrequirements W >
10 GeV , 0 . < y < .
95 and Q > , where W is the invariantmass of the photon-nucleon system, y is the fractional beam energy transfered to thetarget and − Q is the squared four-momentum of the virtual photon. Coincident hadronswere accepted in the range 0 . < z < . h cos ( f − f S ) i hL ⊥ , 2 h cos ( f S ) i hL ⊥ and 2 h cos ( f − f S ) i hL ⊥ were ex-tracted, together with six previously measured A UT SSAs [3, 15, 16], in a maximumlikelihood fit (unbinned in f and f S ) of the selected SIDIS events, based on the proba-bility density function: F ( f , f S ) = + P T h h sin ( f + f S ) i hU ⊥ sin ( f + f S ) + ... i ++ P T P B h h cos ( f − f S ) i hL ⊥ cos ( f − f S ) + h cos ( f S ) i hL ⊥ cos ( f S ) + h cos ( f − f S ) i hL ⊥ cos ( f − f S ) i , (2)where P T ( P B ) denotes the target (beam) polarization and "..." stands for the contributionof the five A UT SSAs 2 h sin ( f − f S ) i hU ⊥ , 2 h sin ( f − f S ) i hU ⊥ , 2 h sin ( f S ) i hU ⊥ , 2 h sin ( f − f S ) i hU ⊥ , 2 h sin ( f + f S ) i hU ⊥ .The systematic uncertainty, including contributions from acceptance effects, instru-mental smearing, QED radiation and hadron misidentification, was evaluated as de-scribed in [3]. An additional 8 .
0% scale uncertainty, arising from the uncertainty onthe beam and target polarization measurements, has to be considered.The preliminary results for the 2 h cos ( f − f S ) i hL ⊥ asymmetry amplitudes are reportedin Fig. 1 for pions and charged kaons as a function of x , z or P h ⊥ . The results show apositive amplitude for p − and a hint of a positive signal also for p + and K + , whereasamplitudes consistent with zero are observed for p and K − . The positive amplitudefor p − reported here is similar to that recently measured at Jefferson Lab (E06010experiment in Hall-A) but on a transversely polarized He (i.e. neutron) target [17].The amplitudes for the sub-leading twist DSAs 2 h cos ( f S ) i hL ⊥ and 2 h cos ( f − f S ) i hL ⊥ ,not shown, are both consistent with zero for all measured mesons. REFERENCES
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