Measurement of semi-inclusive ${\ensuremath{\pi}}^{+}$ electroproduction off the proton

Measurement of semi-inclusive $π^{+}$ electroproduction off the proton

M. Osipenko et al. (CLAS Collaboration)

Phys. Rev. D 80, 032004 – Published 21 August 2009

Abstract

Semi-inclusive $π^{+}$ electroproduction on protons has been measured with the CLAS detector at Jefferson Lab. The measurement was performed on a liquid-hydrogen target using a 5.75 GeV electron beam. The complete five-fold differential cross sections were measured over a wide kinematic range including the complete range of azimuthal angles between hadronic and leptonic planes, $ϕ$ , enabling us to separate the $ϕ$ -dependent terms. Our measurements of the $ϕ$ -independent term of the cross section at low Bjorken $x$ were found to be in fairly good agreement with pQCD calculations. Indeed, the conventional current fragmentation calculation can account for almost all of the observed cross section, even at small $π^{+}$ momentum. The measured center-of-momentum spectra are in qualitative agreement with high-energy data, which suggests a surprising numerical similarity between the spectator diquark fragmentation in the present reaction and the antiquark fragmentation measured in $e^{+} e^{-}$ collisions. We have observed that the two $ϕ$ -dependent terms of the cross section are small. Within our precision the $\cos 2 ϕ$ term is compatible with zero, except for the low- $z$ region, and the measured $\cos ϕ$ term is much smaller in magnitude than the sum of the Cahn and Berger effects.

23 More

Received 6 September 2008

DOI:https://doi.org/10.1103/PhysRevD.80.032004

Authors & Affiliations

Click to Expand

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 80, Iss. 3 — 1 August 2009

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic representation of current (a) and target (b) fragmentation processes in the virtual photon-proton center-of-momentum frame neglecting transverse momenta of particles. Blobs represent nonperturbative functions: the parton density function $f_{i} (x)$ , parton fragmentation function $D_{i}^{h} (z)$ and fracture function $M_{i}^{h} (x, z)$ as given in Eq. (29). $X_{1}$ and $X_{2}$ indicate two components of the undetected final state hadronic system $X$ .
Reuse & Permissions
Figure 2
Definition of the azimuthal angle between the leptonic and hadronic planes $ϕ$ and hadron momentum components $p_{T}$ and $p_{‖}$ .
Reuse & Permissions
Figure 3
Kinematical regions covered by the present experiment in different independent variables. Numbers on the plots give base-10 logarithm of the number of events.
Reuse & Permissions
Figure 4
Contour plot of particle momentum $p$ from tracking versus particle energy deposited in the calorimeter $E C_{tot}$ normalized by $| p |$ . Events on the left correspond to pions and those on the right to electrons. Only fiducial cuts were applied. The Cherenkov detector, providing the basic electron identification, allows to identify clearly the electrons up to $| p | \approx 2.7 GeV / c$ . The dashed line shows the cut applied to the data to remove remaining pion contamination at $| p | > 2.7 GeV / c$ .
Reuse & Permissions
Figure 5
Measured squared mass of positive hadrons (left) and squared missing mass for the $e^{-} h^{+}$ -system in the region of the $π^{+} n$ exclusive peak (right). The shaded area indicates hadrons identified as pions. The exclusive $π^{+} n$ was removed from the analysis by a cut $M_{X}^{2} > 1.08 (GeV / c^{2})^{2}$ .
Reuse & Permissions
Figure 6
Comparison of $e^{-} π^{+}$ coincidence data (full triangles) and MC raw yields (open circles) as a function of one of the kinematic variables. The other variables were kept fixed at $Q^{2} = 2.4 (GeV / c)^{2}$ , $x = 0.30$ , $z = 0.37$ , $p_{T}^{2} = 0.22 (GeV / c)^{2}$ . The MC simulation yield was normalized to the integrated luminosity of the experiment. Error bars are statistical only and they are smaller than the symbol size.
Reuse & Permissions
Figure 7
Inclusive structure function $F_{2}$ at $Q^{2} = 2 (GeV / c)^{2}$ extracted from the present experiment (full triangles) in comparison with previous world data (open circles) from Ref. [77] and references therein. The curve is a parametrization from Ref. [77]. The error bars are statistical only and an overall systematic uncertainty for the present experiment of the order or 5% is estimated.
Reuse & Permissions
Figure 8
Ratio of $e^{-} p$ coincidence events from the data and GSIM Monte Carlo simulations. The simulation event generator was based on proton form-factors from Ref. [55]. The coincidences were selected by the following set of cuts: $| W^{2} - M^{2} | < 0.2 (GeV / c^{2})^{2}$ , $| M_{X}^{2} | < 0.01 (GeV / c^{2})^{2}$ and $| | ϕ_{h} - ϕ_{e} | - π | < 4$ degrees. The error bars are statistical only and an overall systematic uncertainty of the order or 10% is estimated. Error bars are smaller than the symbol size.
Reuse & Permissions
Figure 9
Extracted Fourier components of the raw data (full triangles) and the Monte Carlo (open circles) yields. Error bars are statistical only and they are smaller than the symbol size.
Reuse & Permissions
Figure 10
Stability of the $V_{2}$ cross section term as a function of the number of moments $N$ taken into account in the extraction procedure. Error bars are statistical only.
Reuse & Permissions
Figure 11
The $ϕ$ -dependence of the data taken at $Q^{2} = 2 (GeV / c)^{2}$ , $x = 0.24$ , $z = 0.18$ and $p_{T}^{2} = 0.5 (GeV / c)^{2}$ (full triangles) together with the results of the azimuthal moment (solid lines) and fitting (dashed line) methods. Error bars are statistical only.
Reuse & Permissions
Figure 12
The $p_{T}^{2}$ -dependence of the $⟨ \cos ϕ ⟩$ taken at $Q^{2} = 2 (GeV / c)^{2}$ , $x = 0.30$ and $z = 0.21$ obtained from two different detector acceptance regions (triangles and squares). Full markers correspond to the data before the acceptance correction and the empty markers show acceptance-corrected $⟨ \cos ϕ ⟩$ . The two data sets are shifted equally along the $x$ -axis in opposite directions from their central values for visibility. Error bars are statistical only.
Reuse & Permissions
Figure 13
Same as Fig. 12 except for $⟨ \cos 2 ϕ ⟩$ .
Reuse & Permissions
Figure 14
The $p_{T}^{2}$ -dependence of the $ϕ$ -independent term $H_{2} + ϵ H_{1}$ at $x = 0.24$ and $z = 0.30$ . The lines represent exponential fits to the data for $Q^{2} = 1.74 (GeV / c)^{2}$ (full circles and solid line), $Q^{2} = 2 (GeV / c)^{2}$ (full squares and dashed line), and $Q^{2} = 2.37 (GeV / c)^{2}$ (triangles and dotted line). The errors bars are statistical only.
Reuse & Permissions
Figure 15
The $z$ -dependence of $⟨ p_{T}^{2} ⟩$ at $Q^{2} = 2.37 (GeV / c)^{2}$ and $x = 0.27$ . The points are the data from the present analysis. The curves show the maximum allowed $p_{T}^{2} = (p_{T}^{2})^{\max }$ (dashed), the parametrization of high-energy data from Eq. (8) (solid), and the low- $z$ modification from Eq. (23). The error bars are statistical only and they are smaller than the symbol size.
Reuse & Permissions
Figure 16
The $x$ -dependence of $⟨ p_{T}^{2} ⟩$ at $Q^{2} = 2.37 (GeV / c)^{2}$ and $z = 0.34$ . The points are from the present analysis. The curves show $p_{T}^{2} = (p_{T}^{2})^{\max }$ (dashed) and a constant fit to the data (solid). The error bars are statistical only.
Reuse & Permissions
Figure 17
The $z$ -dependence of $H_{2}$ at $Q^{2} = 2.37 (GeV / c)^{2}$ . The data are shown by full triangles. The error bars give statistical and systematic uncertainties combined in quadrature. The solid line shows LO pQCD calculations using the prescription from Ref. [61], CTEQ 5 parton distribution functions [23], and the Kretzer fragmentation functions [26]. NLO calculations performed within the same framework (using CTEQ 5M PDFs) are shown by the shaded area, for which the width indicates systematic uncertainties due to factorization and renormalization scale variations [62].
Reuse & Permissions
Figure 18
Same as Fig. 17 except with $H_{2}$ plotted as a function of $x$ rather than $z$ .
Reuse & Permissions
Figure 19
Same as Fig. 17 except with $H_{2}$ plotted as a function of $Q^{2}$ rather than $z$ at $x = 0.33$ .
Reuse & Permissions
Figure 20
Same as Fig. 17 except with $H_{2}$ plotted as a function of $Q^{2}$ rather than $z$ at $z = 0.5$ .
Reuse & Permissions
Figure 21
Same as Fig. 17 except with $H_{2} / F_{2}$ , where $F_{2}$ is the inclusive structure function obtained in the same experiment. And NLO calculations are shown by the dashed line, without systematic uncertainties due to factorization and renormalization scales.
Reuse & Permissions
Figure 22
Schematic representation of the leading-particle target fragmentation mechanism. The hatched blob represents the structure function of a particle or a set of particles exchanged. In case of $π^{+}$ production the first particle in the blob is the neutron.
Reuse & Permissions
Figure 23
The $t$ -dependence of the $ϕ$ -independent term $H_{2} + ϵ H_{1}$ at $Q^{2} = 2 (GeV / c)^{2}$ , $x = 0.24$ and $z = 0.18$ . The data are shown as solid squares. The curves represent the exponential fit to the data (dashes) and the expected behavior of leading-particle target fragmentation (solid), assuming it to be 1% of the $t$ -channel exchange term. The error bars are statistical only and they are smaller than symbol size.
Reuse & Permissions
Figure 24
The $x_{F}$ -dependence of the $ϕ$ -independent term $H_{2} + ϵ H_{1}$ at $Q^{2} = 2 (GeV / c)^{2}$ and $x = 0.26$ . The data are compared to LO pQCD calculations combined with a Gaussian $p_{T}$ -dependence from Eq. (7) for $p_{T}^{2} = 0.005 (GeV / c)^{2}$ (full circles and solid curve), $p_{T}^{2} = 0.13 (GeV / c)^{2}$ (full triangles and dashed curve), $p_{T}^{2} = 0.34 (GeV / c)^{2}$ (open squares and dotted curve), and $p_{T}^{2} = 0.74 (GeV / c)^{2}$ (open diamonds and dot-dashed curve). The coverage in $x_{F}$ is limited for the data by detector acceptance. The error bars are statistical only.
Reuse & Permissions
Figure 25
Same data as in Fig. 24. The curves are the same as in Fig. 24 except for the fragmentation functions, which are evaluated at $z_{G}$ rather than $z$ .
Reuse & Permissions
Figure 26
The $p_{T}^{2}$ -dependence of $H_{3} / (H_{2} + ϵ H_{1})$ (open squares—moments, full triangles—fits) for different $z$ averaged over $x$ and $Q^{2}$ . The thick curves show theoretical predictions of the Cahn effect [31, 32] (dashed), predictions of the Berger effect [41] using a convex pion wave function (dotted) and their sum (solid). The two data sets (from moments and fits extractions) are shifted equally along the $x$ -axis in opposite directions from their central values for visibility. The hatched area show the systematic uncertainties.
Reuse & Permissions
Figure 27
Same as Fig. 26 except for $H_{4} / (H_{2} + ϵ H_{1})$ arising from the $⟨ \cos 2 ϕ ⟩$ moment (open triangles—moments, full squares—fits).
Reuse & Permissions
Figure 28
Same as Fig. 26 except with $H_{3} / (H_{2} + ϵ H_{1})$ plotted as a function of $z$ rather than $p_{T}^{2}$ .
Reuse & Permissions
Figure 29
Same as Fig. 27 except with $H_{4} / (H_{2} + ϵ H_{1})$ plotted as a function of $z$ rather than $p_{T}^{2}$ .
Reuse & Permissions
Figure 30
The $Q^{2}$ -dependence of $H_{3} / H_{2}$ (full triangles) and $H_{4} / H_{2}$ (full squares) extracted using $R = 0.12$ from the present data in comparison with measurements from Ref. [72] (open circles— $H_{3} / H_{2}$ , diamonds— $H_{4} / H_{2}$ ) at $x = 0.24$ . Both data sets are integrated over $z > 0.2$ and $p_{T} > 0.2 GeV / c$ ( $⟨ z ⟩ = 0.27$ , $⟨ p_{T}^{2} ⟩ = 0.22 (GeV / c)^{2}$ ). The curves show predictions of the Cahn effect [31, 32] for $H_{4} / H_{2}$ (dotted) and $H_{3} / H_{2}$ (solid), corrected for the phase space shrinkage using Eqs. (32) and (31), respectively. The statistical and systematic uncertainties are combined in quadrature.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology

Measurement of semi-inclusive $π^{+}$ electroproduction off the proton

M. Osipenko et al. (CLAS Collaboration)

Phys. Rev. D 80, 032004 – Published 21 August 2009

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review D

covering particles, fields, gravitation, and cosmology

Measurement of semi-inclusive π+ electroproduction off the proton

M. Osipenko et al. (CLAS Collaboration)

Phys. Rev. D 80, 032004 – Published 21 August 2009

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Measurement of semi-inclusive $π^{+}$ electroproduction off the proton