Transverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS
TTransverse momentum dependent multiplicities ofhadrons produced in DIS at COMPASS
Andrea Moretti on behalf of the COMPASS Collaboration
University and INFN, TriesteE-mail: [email protected]
The COMPASS Collaboration measured the transverse momentum dependent multiplicities ofcharged hadrons produced in Deep Inelastic Scattering (DIS) off unpolarized protons. Comple-menting previous COMPASS measurements obtained with an isoscalar target, the data have beencollected in 2016 and 2017 with 160 GeV/ c muon beams and a liquid hydrogen target. The multi-plicities are studied as a function of the square of the hadron transverse momentum with respect tothe virtual photon direction P hT in bins of the Bjorken variable x , of the photon virtuality Q andof the fraction z of the photon energy carried by the hadron. Preliminary results of this analysis,performed on a fraction of the available data sample, are shown here for the first time. XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS20198-12 April, 2019Torino, Italy c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - e x ] J u l ransverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS
1. Introduction
The intrinsic motion of the parton in the nucleon is a fundamental ingredient in a completedescription of the nucleon structure, which has to consider not only its projection along the nu-cleon momentum but also its transverse component in both momentum and coordinate space. Themomentum distributions of the partons in the transverse plane is described by the Transverse-Momentum-Dependent Parton Distribution Functions (TMD-PDFs). Analogously, Transverse-Momentum-Dependent Fragmentation Functions (TMD-FFs) are necessary for a complete treat-ment of the hadron production. In this respects, the Semi-Inclusive Deep Inelastic Scattering(SIDIS) is a powerful tool to investigate both TMD-PDFs and TMD-FFs. In SIDIS events, a leptonscatters off a nucleon and at least one hadron is detected in the final state. Integrating over the az-imuthal angle of the final state hadron and taking as nucleon an unpolarized proton, the differentialcross section at twist-two reads [1, 2]: d σ h dxdQ dzdP hT = π α ( xs ) + ( − y ) y F UU ( x , Q , z , P hT ) (1.1)where x is the Bjorken variable, Q the photon virtuality, z the fraction of the virtual photon energycarried by the hadron, P hT its transverse momentum with respect to the virtual photon, y the fractionof the lepton energy carried by the photon and s the energy in the center of mass squared, being Q = xys . The SIDIS structure function F UU can be written as: F UU ( x , Q , z , P hT ) = ∑ q e q (cid:90) d k T d p ⊥ δ ( ) ( P hT − z k T − p ⊥ ) f q ( x , Q , k T ) D h q ( x , Q , p ⊥ ) (1.2) = ∑ q e q f q ( x , Q , k T ) ⊗ D h q ( x , Q , p ⊥ ) (1.3)where the convolution integral is performed over the unobservable transverse momentum of thequark k T and over the transverse momentum acquired in the fragmentation process p ⊥ , related by P hT = z k T + p ⊥ ; f q ( x , Q , k T ) is the unpolarized TMD-PDF and D h q ( x , Q , p ⊥ ) the unpolarizedTMD-FF. The hadron multiplicities M h are defined as the ratio of the SIDIS cross section over theDIS cross section: d M h ( x , Q , z , P hT ) dzdP hT = (cid:18) d σ h dxdQ dzdP hT (cid:19) (cid:44) (cid:18) d σ DIS dxdQ (cid:19) = ∑ q e q f q ( x , Q , k T ) ⊗ D h q ( x , Q , p ⊥ ) ∑ q e q f q ( x , Q ) , (1.4)where f q ( x , Q ) is the unpolarized transverse momentum independent PDF. The multiplicities givethus access to the transverse momenta which, by the way, can not be disentangled with such mea-surement in a model independent way. In the ratio of the two cross sections many common terms(like the luminosity and the efficiencies in the muon detection, trigger and DAQ) cancel out and ineach x , Q , z and P hT bin the multiplicities can be measured as: d M h ( x , Q , z , P hT ) dzdP hT = N h ( x , Q , z , P hT ) N DIS ( x , Q ) ∆ z ∆ P hT a h ( x , Q , z , P hT ) , (1.5)1 ransverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS being N h the number of charged hadrons and N DIS the number of DIS events, ∆ z and ∆ P hT the binwidths and a h the hadron acceptance.The expression for the charged hadrons multiplicities deserves further corrections, due to theradiative effects, to the electron contamination and to the diffractively produced vector mesons [3].Such corrections are at the moment estimated but not applied, in view of more detailed studies tocome. Here we present preliminary results obtained in a kinematic region where such correctionsare estimated to be small. The results are obtained from about 10% of the data collected at COM-PASS during the 2016 run with a 160 GeV/ c muon beam (both µ + and µ − beams with balancedstatistics) and a 2.5 m long liquid hydrogen target.
2. Extraction of hadron multiplicities
The selection of DIS events has been performed asking for Q > c ) , 0 . < y < . W > c and 0 . < x < .
4. Hadrons have been selectedby requiring the material integrated over the path of the reconstructed trajectories not to exceed 10radiation lengths and with z and P hT in the ranges: 0 . < z < . P hT > . c . Plots ofkinematic distributions of x , Q , z and P hT are given in Fig. 1. The kinematic ranges shown in fullcolor in Fig. 1 correspond to the aforementioned kinematic cuts. Figure 1:
Top row: the kinematic distributions of x and Q of the selected DIS events. Bottom row: the z and P hT distributions of the selected charged hadrons. The shaded regions are removed with proper cuts. The hadron acceptance term a h has been estimated with a Monte Carlo simulation based onthe LEPTO generator [4] and defined as the ratio of reconstructed and generated hadrons, providedthe corresponding DIS event was reconstructed: 2 ransverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS a h ( x , Q , z , P hT ) = N hrec ( x , Q , z , P hT ) N hgen ( x , Q , z , P hT ) | DIS rec . (2.1)The acceptance shows a flat trend in P hT in the ( x , Q ) range 0 . < x < .
008 and 16 < Q / ( GeV / c ) <
81 and for all hadrons with z > .
3. Due to the 2016/2017 reduced geometricalacceptance of the spectrometer, this is not the case for hadrons with low y and simultaneously0 . < z < .
3, which are then not considered in this work. Further selections on the DIS and hadronsamples (like on the position of the vertex in the target) are expected to increase the acceptance infuture analyses and are currently under study.It is at high z , on the other hand, that the fraction of hadrons originating from the decay ofvector mesons diffractively produced shows its maximum. This is mostly due to the decay of ρ meson into a π + π − pair, while a limited contamination at intermediate z is induced by K + K − pairs produced in the decay of a φ meson. The contamination has been estimated combining thepredictions from two HEPGEN Monte Carlo samples [5] (one for ρ and one for φ mesons) and aLEPTO sample. Since the contamination increases with z , these preliminary hadron multiplicitiesare extracted up to z = .
6, i.e. in a range where it is estimated to be always smaller than 5%.
The multiplicities of positive and negative hadrons in the four-dimensional grid of kinematicbins are shown in Figs. 2 and 3. For each 3D bin in x , Q and z the multiplicities are shown asa function of P hT ; different z bins are superimposed in the same pads to better show the evolutionwith z . Uncertainties are statistical only; the systematic uncertainty is estimated to be smaller than10% of the multiplicity value. Current results are not corrected for radiative effects. Figure 2:
Unidentified positively-charged hadron multiplicities as a function of P hT in selected bins of x , Q and z . Not corrected for radiative effects. The hadron multiplicities have been fitted with two different functions, namely with a "doubleexponential" function f , and with the Tsallis function f :3 ransverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS Figure 3:
Unidentified negatively-charged hadron multiplicities as a function of P hT in selected bins of x , Q and z . Not corrected for radiative effects. Figure 4:
Fit of the hadron multiplicities for 0 . < z < . f forpositive (red) and negative hadrons (black). Figure 5:
Fit of the hadron multiplicities for 0 . < z < . f for positive (red)and negative hadrons (black). f = N α exp (cid:18) − P hT α (cid:19) + N (cid:48) α (cid:48) exp (cid:18) − P hT α (cid:48) (cid:19) , (2.2) f = N (cid:18) − ( − q ) P hT T (cid:19) − q . (2.3)Both functions aim at describing the two different kinds of power-law behaviour observed forsmall and larger P hT . At variance with f , f encodes the behaviour in the two regions in a singlefunctional form. In the corresponding bin, the values of the fitted parameters are in agreement withthe published ones [6]. The fits of the multiplicities in the third z bin (0 . < z < .
6) are shown inFigs. 4 and 5 for both functions. 4 ransverse momentum dependent multiplicities of hadrons produced in DIS at COMPASS
3. Conclusions and perspectives
Transverse momentum dependent hadron multiplicities are fundamental tools towards a thor-ough understanding of the nucleon structure: as such, they have aroused a growing interest inrecent years both on the theoretical and on the experimental side. The COMPASS Collaborationcontributed to this topic with a measurement of the multiplicities on an isoscalar target and it isstill actively working on the subject. We presented here for the first time COMPASS preliminaryresults on the multiplicities of charged hadrons produced with muon beams on an unpolarized pro-ton target. The multiplicities have been extracted as a function of the squared hadron transversemomentum P hT in three dimensional bins of x , Q and z . The current analysis has been performedon part of the data collected in 2016, in a selected kinematic range where acceptance is high andalmost flat in P hT and where possible contaminations have been estimated to be small. This analy-sis will be extended to a wider kinematic range and to the full 2016 and 2017 data set. The hadronazimuthal asymmetries, already measured by COMPASS on an iscoscalar target [7] and still cur-rently studied [8, 9], will be measured from the same proton data in the same x , Q and z bins. Allthese new results, together with other results by COMPASS, HERMES and JLab, will allow for acomplete analysis and possibly lead to an extraction of the still unknown Boer-Mulders TMD. References [1] A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P. J. Mulders and M. Schlegel,
Semi-inclusive deepinelastic scattering at small transverse momentum , JHEP (2007) 093 [ hep-ph/0611265 ].[2] M. Anselmino, M. Boglione, J. O. Gonzalez H., S. Melis and A. Prokudin, Unpolarised transversemomentum dependent distribution and fragmentation functions from sidis multiplicities , JHEP (2014) 5.[3] A. Kerbizi on behalf of the COMPASS Collaboration,
Interpretation of the unpolarized azimuthalasymmetries in SIDIS , in , 2018, .[4] G. Ingelman, A. Edin and J. Rathsman,
LEPTO 6.5: A Monte Carlo generator for deep inelastic lepton- nucleon scattering , Comput. Phys. Commun. (1997) 108 [ hep-ph/9605286 ].[5] A. Sandacz and P. Sznajder,
HEPGEN - generator for hard exclusive leptoproduction , .[6] M. Aghasyan et al. (COMPASS Collaboration), Transverse-momentum-dependent Multiplicities ofCharged Hadrons in Muon-Deuteron Deep Inelastic Scattering , Phys. Rev.
D97 (2018) 032006[ ].[7] C. Adolph et al. (COMPASS Collaboration),
Measurement of azimuthal hadron asymmetries insemi-inclusive deep inelastic scattering off unpolarised nucleons , Nucl. Phys.
B886 (2014) 1046[ ].[8] A. Moretti on behalf of the COMPASS Collaboration,
Measurement of azimuthal asymmetries in SIDISon unpolarized protons , in , 2019, .[9] J. Matousek on behalf of the COMPASS Collaboration,
Measurement of the azimuthal modulations ofhadrons in unpolarised SIDIS , these Proceedings ..