The feasibility of measuring the pion and kaon structure functions has been
investigated. A high luminosity electron-proton collider would make these
measurements feasible. Also, it appears feasible to measure these structure
functions in a nuclear medium. Simulations using the RAPGAP Monte Carlo of a
possible pion structure function measurement are presented.Comment: To appear in the proceedings of the Second Workshop on Physics with
  an Electron Polarized Light-Ion Collider, 14-16 Sept 2000, Cambridge, Ma 6
  pages, 5 figures, late

Holt, Roy J.

Reimer, Paul E.

English

arXiv

Roy J. Holt

Crossref

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Structure of the Goldstone Bosons
Roy J. Holt and Paul E. Reimer
Argonne National Laboratory
Argonne, Illinois 60439
Abstract. The feasibility of measuring the pion and kaon structure functions has
been investigated. A high luminosity electron-proton collider would make these mea-
surements feasible. Also, it appears feasible to measure these structure functions in
a nuclear medium. Simulations using the RAPGAP Monte Carlo of a possible pion
structure function measurement are presented.
Understanding hadron structure from the underlying quark and gluon degrees of
freedom and understanding modifications of hadrons in nuclear matter are two of
the most important goals of nuclear physics. The light mesons have a central role
in nucleon and nuclear structure. The masses of the lightest hadrons, the mesons,
are believed to arise from explicit chiral symmetry breaking. In particular, the light
mesons are the Goldstone bosons of quantum chromodynamics [1]. The pion, being
the lightest meson, is particularly interesting not only because of its importance
in chiral perturbation theory, but also because of its importance in explaining the
quark sea in the nucleon and the nuclear force in nuclei.
THE PION STRUCTURE FUNCTION
At present, the pion is believed to contain a valence quark and antiquark as
well as a partonic sea. Several theoretical calculations are aimed at explaining
the pion structure function in the valence region. These include Dyson-Schwinger
[2] and Nambu Jona-Lasinio models [3,4]. Lower order moments of the structure
function were determined in lattice gauge calculations [5]. Typical agreement with
the pion structure function is shown in Fig. 1. Here, a curve from the Dyson-
Schwinger model is compared with the data from a pionic Drell-Yan experiment [6]
in the valence region. The general features of the valence structure of the pion are
qualitatively understood. However, there is no good understanding of the pion sea.
Recently, measurements of the pion structure function [7] at very low x, in the
region of the pion sea have been performed. The results of this work show two
interesting findings: (1) the sea in the pion has the same shape in x as the sea in
the proton, and (2) the pion sea has approximately one-third of the magnitude as
0.00 0.20 0.40 0.60 0.80 1.00
x
0.00
0.10
0.20
0.30
0.40
0.50
xu
v(
x)
E615 πN Drell−Yan 4GeV
x uv(x;q=4GeV)
FIGURE 1. Existing data for the pion structure function from Drell-Yan scattering [6]. The
solid curve represents a calculation of Hecht et al. [2].
the sea in the proton. This latter result is especially surprising since one expects
that the pion sea to be two-thirds the value of the proton sea. These findings are
even more surprising from the viewpoint of a chiral quark model [8]. This model
predicts that the pion sea carries a larger momentum fraction than the proton
sea. It appears that a comparison of the sea in the pion and the proton is a clue
to understanding the nonperturbative structure of constituent quarks. Thus, it
is essential to measure the pion structure function, especially the sea component,
throughout the x region from 0.02, the highest value of the HERA data, up to
0.3, the lower value of the Drell-Yan data. This will map out the sea region where
models should have a high degree of validity. Also, since there appears to be
a discrepancy between the data and the theoretical calculation at very high x,
another measurement using a different technique at high x would be important.
KAON STRUCTURE FUNCTION
The valence structure of the kaon is comprised of a light u or d quark/antiquark
and a strange quark/antiquark. If our understanding of the meson structure is
correct, then the large difference between the strange quark and u or d quark
masses gives rise to a very interesting effect for the kaon structure function. In
this case, the strange quark, because of its large mass, carries more of the kaon’s
momentum than the u quark, say. Then, the uv quark distribution in the kaon
should be shifted lower in x than that in the pion.
A Nambu Jona-Lasinio calculation [3,4] exhibits this behavior as shown in Fig. 2.
Here, the ratio of the valence u quark in the kaon to that in the pion is shown as
the curve in the figure. Drell-Yan measurements [9] of the ratio of K− to π− shows
a consistency with unity over most of the x region, with a suggestion that the ratio
(x
) 
/ 
u
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0 1.00.80.60.40.2
x Bj
u
K
π
(x
)
FIGURE 2. Existing data for K−/π− ratio from Drell-Yan scattering [9]. The solid curve
represents a calculation of Suzuki [12,3].
is dropping at high x. However, the data are not of sufficient quality to verify
our understanding of this process. Thus, it is essential to measure the structure
function at high x as well as in the sea region.
MESON STRUCTURE IN THE NUCLEAR MEDIUM
The role of pions, and particularly, pion excess in the nuclear medium have been
long-standing issues in nuclear physics. The pion excess has not been observed in
either Drell-Yan experiments [10] at FNAL or in A(e,e’π) reactions [11] at Jefferson
Lab. The main question is whether the pion or kaon structure function in a nuclear
medium is modified from the free structure function. Calculations within the frame-
work of a Nambu Jona-Lasinio model [12] indicate that the medium modification
for the pion structure function should be small. However, if one invokes Brown-
Rho scaling [13], then the effect is large. These calculations are shown in Fig. 3.
Here the NJL calculation is the solid curve, while the dashed curve represents the
Brown-Rho scaling.
MEASUREMENT OF THE MESON STRUCTURE
FUNCTIONS
The scattering process illustrated in Fig. 4 was simulated using the RAPGAP
Monte Carlo program [14]. RAPGAP models processes in which there is a large
rapidity gap between a fast outgoing nucleon and the remainder of the inelastic
scattering fragments. These processes include DIS from an exchanged pion [15–17]
x
xq
(x
) v
al
0.2 0.4 0.6 0.8 1.0
0.5
0.4
0.3
0.2
0.1
0.0
Brown-Rho
Scaling
Free
Pion
FIGURE 3. The solid curve represents the NJL calculation in a nuclear medium, while the
dashed curve gives the effect of Brown-Rho scaling in nuclear matter [12].
or pomeron.. A comparison of results from RAPGAP with HERA data show rea-
sonable agreement for fast outgoing neutrons [7].
For a 5 GeV electron beam on a 25 GeV proton beam, RAPGAP calculates 22 nb
cross section for the eq → e′q′ process. The expected accuracy of the experiments
was calculated using events in which a “spectator” neutron was identified. In
general, the neutron is scattered less than 50 mrad from the nominal proton beam
axis. Events were cut on −q2 > 1 GeV2. The expected errors are shown in Fig. 5.
A luminosity of 1032 cm−2s−1 was assumed for a run lasting 106 s.
The K+ structure function can be measured by considering deep inelastic scat-
tering from the kaon cloud surrounding a proton. The basic Feynman diagram
would be the same as in Fig. 4 with the pion replaced by a kaon and the neutron
replaced by a Λ. The probability for scattering from the K+ cloud surrounding the
proton should be comparable to that for the π+ since the KNΛ coupling constant
is comparable to that of the πNN vertex. In fact, one would only expect about a
factor of two reduction in the vertex function for the kaon compared to the pion.
The difficulty with this process is in the detection of the Λ. The Λ decays
predominantly (64%) to a proton and a π−. Thus, a special forward proton spec-
trometer as well as a forward pion spectrometer would be necessary. This should
p n
πγ
FIGURE 4. Deep inelastic scattering from the pion cloud surrounding a proton.
0.85
0.9
0.95
1
1.05
1.1
1.15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
xπ
FIGURE 5. Simulated errors for DIS events using a 5 GeV electron beam on a 25 GeV proton
beam with a luminosity of 1032cm−2s−1 and 106s of running.
be feasible since the ZEUS and H1 experiments at HERA have already successfully
employed forward proton spectrometers. When designing the ring magnets, one
should take into account the possibility of detecting both positively and negatively
charged forward going hadrons. Simulations for this part of the experiment would
be necessary to optimize the detection efficiency.
A collider should also render these studies feasible for nuclei up to 4He. For
the pion case, the idea would be to detect all of the forward going nucleons from
the deep inelastic scattering from the pion. In the case of a deuterium target, for
example, one would detect both forward going neutrons or forward going protons,
depending on whether the DIS occurred from the π+ or the π−, respectively.
SUMMARY
In summary, a measurement of the pion and kaon structure functions over a large
xπ/K region was shown to be feasible with an electron proton collider, where the
electron energy is 5 GeV, the proton energy is 25 GeV, and the luminosity is 1032
cm−2s−1. A collider will also open up other very interesting possibilities such as a
measurement of the meson structure function in the nuclear medium.
ACKNOWLEDGMENTS
We wish to thank C. Roberts, G. Levman, M. Derrick and T.-S. H. Lee for very
useful discussions. In addition, we thank H. Jung and D. H. Potterveld for valuable
assistance with RAPGAP. This work was supported by the U. S. Department of
Energy, Nuclear Physics Division, under contract No. W-31-109-ENG-38.
REFERENCES
1. Maris, P., Roberts, C.D., Tandy, P.C., Phys. Lett. B420, 287 (1998).
2. Hecht, M. B., Roberts, C. D., Schmidt, S. M., preprint (2000), nucl-th/0008049.
3. Shigetani, T., Suzuki, K., Toki, H. Phys. Lett. B308, 383 (1993).
4. Davidson, R. M., Arriola, E. Ruiz Phys. Lett B348, 163 (1995).
5. Best, C. et al. Phys. Rev. D56, 2743 (1997).
6. Conway, J. S. et al. Phys. Rev. D39, 39 (1989).
7. Adloff, C. et al. (H1 Collaboration) Eur. Phys. J. C 6, 587 (1999).
8. Suzuki, K., Weise, W. Nucl. Phys. A634, 141 (1998).
9. Badier, J., et al. Phys. Lett. B93, 354 (1980).
10. Alde, D. M. et al. Phys. Rev. Lett. 64, 2479 (1990).
11. Jackson, H. E. (NucPi Collaboration) Sixteenth Int’l Conf. on Few Body Systems
Taipei, preprint (2000).
12. Suzuki, K. Phys. Lett. B368, 1 (1996).
13. Brown, G. E., Rho, M. Phys. Rev. Lett. 66, 2720 (1991).
14. Jung, H., Comp. Phys. Commun. 86, 147 (1995).
15. D’Alesio, U. and Pirner, H. J. Eur. Phys. J. A 7, 109 (2000).
16. Holtmann, H. et al. Nucl. Phys. A569, 631 (1996).
17. Kopeliovich, H. et al. Z. Phys. 6, 587 (1999).


Structure of the Goldstone bosons

Holt, R. J.

Reimer, P. E.

UNT (University of North Texas) Digital Library

Structure of the Goldstone BosonsRoy J. Holt and Paul E. ReimerArgonne National LaboratoyArgonne, Illinois 60439Abstract. The feasibility of measuring the pion and kaon structure functions hasbeen investigated. A high luminosity electron-proton collider would make these mea-surements feasible. Also, it appears feasible to measure these structure functions ina nuclear medium. Simulations using the RAP GAP Monte Carlo of a possible pionstructure function measurement are presented.Understanding hadron structure from the underlying quark and gluon degrees offreedom and understanding modifications of hadrons in nuclear matter are two ofthe most important goals of nuclear physics. The light mesons have a central rolein nucleon and nuclear structure. The masses of the lightest hadrons, the mesons,are believed to arise from explicit chiral symmetry breaking. In particular, the lightmesons are the Goldstone bosons of quantum chromodynamics [1]. The pion, beingthe lightest meson, is particularly interesting not only because of its importancein chiral perturbation theory, but also because of its importance in explaining thequark sea in the nucleon and the nuclear force in nuclei.THE PION STRUCTURE FUNCTIONAt present, the pion is believed to contain a valence quark and antiquark aswell as a partonic sea. Several theoretical calculations are aimed at explainingthe pion structure function in the valence region. These include Dyson-Schwinger[2] and Nambu Jona-Lasinio models [3,4]. Lower order moments of the structurefunction were determined in lattice gauge calculations [5]. Typical agreement withthe pion structure function is shown in Fig. 1. Here, a curve from the Dyson-Schwinger model is compared with the data from a pionic Drell-Yan experiment [6]in the valence region. The general features of the valence structure of the pion arequalitatively understood. However, there is no good understanding of the pion sea.Recently, measurements of the pion structure function [7] at very low z, in theregion of the pion sea have been performed. The results of this work show twointeresting findings: (1) the sea in the pion has the same shape in z as the sea inthe proton, and (2) the pion sea has approximately one-third of the magnitude asDISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orjmplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.~iKxm%E. .Novo82M8(M3TI,0.50 / ! 1 1 1 1} I0.400.30~3’x 0.200.100.00● E615 KNDrell-Yan 4GeV-0.00 0.20 0.40 0.60 0.80 1.00xFIGURE 1. Existing data for the pion structure function from Drell-Yan scattering [6]. Thesolid curve represents a calculation of Hecht et al. [2].the sea in the proton. This latter result is especially surprising since one expectsthat the pion sea to be two-thirds the value of the proton sea. These findings areeven more surprising from the viewpoint of a chiral quark model [8]. This modelpredicts that the pion sea carries a larger momentum fraction than the protonsea. It appears that a comparison of the sea in the pion and the proton is a clueto understanding the nonperturbative structure of constituent quarks. Thus, itis essential to measure the pion structure function, especially the sea component,throughout the z region from 0.02, the highest value of the HERA data, up to0.3, the lower value of the Drell-Yan data. This will map out the sea region wheremodels should have a high degree of validity. Also, since there appears to bea discrepancy between the data and the theoretical calculation at very high z,another measurement using a different technique at high z would be important.KAON STRUCTURE FUNCTIONThe valence structure of the kaon is comprised of a light u or d quark/antiquarkand a strange quark/antiquark. If our understanding of the meson structure iscorrect, then the large difference between the strange quark and u or d quarkmasses gives rise to a very interesting effect for the kaon structure function. Inthis case, the strange quark, because of its large mass, carries more of the kaon’smomentum than the u quark, say. Then, the Uv quark distribution in the kaonshould be shifted lower in z than that in the pion.A Nambu Jona-Lasinio calculation [3,4] exhibits this behavior as shown in Fig. 2.Here, the ratio of the valence u quark in the kaon to that in the pion is shown asthe curve in the figure. Drell-Yan measurements [9] of the ratio of K- to m- showsa consistency with unity over most of the x region, with a suggestion that the ratio: 04Y‘ 0.4‘“’%).2 0.4 0.6 0,8 1.(IxBjFIGURE 2. Existing data for K-/r- ratio from Drell-Yan scattering [9]. The solid curverepresents a calculation of Suzuki [12,3].is dropping at high x. However, the data are not of sufficient quality to verifyour understanding of this process. Thus, it is essential to measure the structurefunction at high x as well as in the sea region.MESON STRUCTURE IN THE NUCLEAR MEDIUMThe role of pions, and particularly, pion excess in the nuclear medium have beenlong-standing issues in nuclear physics. The pion excess has not been observed ineither Drell-Yan experiments [10] at FNAL or in A(e,e’n) reactions [11]at JeffersonLab. The main question is whether the pion or kaon structure function in a nuclearmedium is modified from the free structure function. Calculations within the frame-work of a Nambu Jona-Lasinio model [121indicate that the medium modificationfor the pion structure function should be small. However, if one invokes Brown-Rho scaling [13], then the effect is large. These calculations are shown in Fig. 3.Here the NJL calculation is the solid curve, while the dashed curve represents theBrown-Rho scaling.MEASUREMENT OF THE MESON STRUCTUREFUNCTIONSThe scattering process illustrated in Fig. 4 was simulated using the RAPGAPMonte Carlo program [14]. RAP GAP models processes in which there is a largerapidity gap between a fast outgoing nucleon and the remainder of the inelasticscattering fragments. These processes include DIS from an exchanged pion [15–17]0.5- r I 1 IBrown-Rho0.4- /’Scaling,-------.“ ....“ ‘..’> ,2 ●~0.2 .0.10.00.2 0.4 0.6 0.8 1.0xFIGUIIE 3. The solid curve represents the NJL calculation in a nuclear medium, while thedashed curve gives the effect of Brown-Rho scaling in nuclear matter [12].or pomeron.. A comparison of results from RAPGAP with HERA data show rea-sonable agreement for fast outgoing neutrons [7].For a 5 GeV electron beam on a 25 GeV proton beam, RAPGAP calculates 22 nbcross section for the eq + e’q’ process. The expected accuracy of the experimentswas calculated using events in which a “spectator” neutron was identified. Ingeneral, the neutron is scattered less than 50 mrad from the nominal proton beamaxis. Events were cut on –q2 >1 GeV2. The expected errors are shown in Fig. 5.A luminosity of 1032cm-2s-l was assumed for a run lasting 106 s.The K+ structure function can be measured by considering deep inelastic scat-tering from the kaon cloud surrounding a proton. The basic Feynman diagramwould be the same as in Fig. 4 with the pion replaced by a kaon and the neutronreplaced by a A. The probability for scattering from the K+ cloud surrounding theproton should be comparable to that for the r+ since the KNA coupling constantis comparable to that of the TNN vertex. In fact, one would only expect about afactor of two reduction in the vertex function for the kaon compared to the pion.The difficulty with this process is in the detection of the A. The A decayspredominantly (64%) to a proton and a m–. Thus, a special forward proton spec-trometer as well as a forward pion spectrometer would be necessary. This shouldFIGURE 4. Deep inelastic scattering from the pion cloud surrounding a proton.,1.151.1 T1.051 10.950.9 10.85 1!1! 11[1 Ill I I III i Ill II {1 III! 111! !1!1 IIIL0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1xxFIGURE 5. Simulated errors for DIS events using a 5 GeV electron beam on a 25 GeV protonbeam with a luminosity of 1032cm–2s-l and 106s of running.be feasible since the ZEUS and HI experiments at HERA have already successfullyemployed forward proton spectrometers. When designing the ring magnets, oneshould take into account the possibility of detecting both positively and negativelycharged forward going hadrons. Simulations for this part of the experiment wouldbe necessary to optimize the detection efficiency.A collider should also render these studies feasible for nuclei up to 4He. Forthe pion case, the idea would be to detect all of the forward going nucleons fromthe deep inelastic scattering from the pion. In the case of a deuterium target, forexample, one would detect both forward going neutrons or forward going protons,depending on whether the DIS occurred from the ~+ or the n-, respectively.SUMMARYIn summary, a measurement of the pion and kaon structure functions over a largexT/K region was shown to be feasible with an electron proton collider, where theelectron energy is 5 GeV, the proton energy is 25 GeV, and the luminosity is 1032cm–2s-l. A collider will also open up other very interesting possibilities such as ameasurement of the meson structure function in the nuclear medium.ACKNOWLEDGMENTSWe wish to thank C. Roberts, G. Levman, M. Derrick and T.-S. H. Lee for veryuseful discussions. In addition, we thank H. Jung and D. H. Potterveld for valuableassistance with RAP GAP. This work was supported by the U. S. Department ofEnergy, Nuclear Physics Division, under contract No. W-31-109-ENG-38.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.REFERENCESMaris, P., Roberts, C.D., Tandy, P. C., Phys. Lett. 13420, 287 (1998).Hecht, M. B., Roberts, C. D., Schmidt, S. M., preprint (2000), nucl-th/0008049.Shigetani, T., Suzuki, K., Toki, H. l%ys. Lett. B308, 383 (1993).Davidson, R. M., Arriola, E. Ruiz Phys. Lett B348, 163 (1995).13est, C. et al. Phys. Rev. D56, 2743 (1997).Conway, J. S. et aL Phys. Rev. D39, 39 (1989).Adloff, C. et al. (HI Collaboration) Eur. Phys. J. C 6, 587 (1999).Suzuki, K., Weise, W. NUCLPhys. A634, 141 (1998).Badier, J., et aL Phys. Lett. B93, 354 (1980).Aide, D. M. et al Phys. Rev. Lett. 64, 2479 (1990).Jackson, H. E. (NucPi Collaboration) Sizteenth Int’/ Conf on Few Body SystemsTaipei, preprint (2000).Suzuki, K. Phys. Lei!t. B368, 1 (1996).Brown, G. E., Rho, M. Phys. Rev. Lett. 66,2720 (1991).Jung, H., Comp. Phys. C07WLUTL. 86, 147 (1995).D’Alesio, U. and Pirner, H. J. Eur. Phys. J. A 7, 109 (2000).Holtmann, H. et al. Nucl. Phys. A569, 631 (1996).Kopeliovich, H. et d. Z. Phys. 6, 587 (1999).

Structure of the Goldstone bosons.