References - Bogoliubov Laboratory of Theoretical Physics - JINR

Re(T 01 /T 00 )
0.4
0.2
0
HERMES preliminary
ep(d)→e´ρ 0 p(d)
Proton
Deuteron
-t / [GeV 2 0.1 0.2 0.3
]
Q*Im(T 01 /T 00 ) [GeV]
0.5
0
HERMES preliminary
ep(d)→e´ρ 0 p(d)
Proton
Deuteron
-t / [GeV 2 0.1 0.2 0.3
]
Figure 3: The t ′ dependence of A3 =Re(T01/T00) andA4 =Im(T01/T00) for hydrogen and deuterium
targets. Inner (outer) error bars show the statistical (total) uncertainties, as in Fig. 2. The different
curves represent the fit parameterizations and their uncertainties, also as in Fig. 2.
parameters a and b while the dashed curves correspond to ± one standard deviation of the
total uncertainty. No t ′ dependence of A1 and A2 was observed in the region −t ′ < 0.4
GeV 2 . The result for A1 is in agreement with the prediction [10, 7] valid at high Q 2 ,
T11/T00 ∝ MV /Q, obtained within a perturbative QCD (pQCD) framework. The linear
increase of A2 with Q disagrees with the asymptotic behaviour of T11/T00 predicted in
pQCD. The phase difference δ11 between the amplitudes T11 and T00 increases with Q 2
(since tan δ11 = A2/A1 = bQ 2 /a) and its mean value is about 30 ◦ . This is in a sharp
disagreement with the prediction of Ref [9] based on the GPD approach in pQCD.
According to pQCD calculations [10, 7], the asymptotic behaviour of T01/T00 at high
Q 2 is √ −t ′ /Q. The best fit of the combined p + d data however, is to A3 = c √ −t ′ , giving
c =0.40 ± 0.02 GeV −1 with χ 2 /Ndf =0.72; fitting A4 to d √ −t ′ /Q yields d =0.20 ± 0.07
with χ 2 /Ndf =1.09. The result of the fit for A3 does not support the 1/Q dependence
predicted by the pQCD asymptotic behaviour while the behaviour of A4 is in accordance
with it. The phase difference δ01 between T01 and T00 is given by tan δ01 = d/(cQ) for
these parameterizations; it decreases with Q and is equal to (29 ◦ ± 9 ◦ )atQ 2 =0.8 GeV 2 .
A comparison of the curves calculated with the parameters c and d with values of A3 and
A4 in four −t ′ bins is presented in Fig. 3.
Finally, we note that the result of the fit of the combined p + d data to |U11/T00| =
g, yields g = 0.391 ± 0.013 with χ 2 /Ndf =0.44. This results contradicts the pQCD
asymptotic behaviour U11/T00 ∝ MV /Q. The absence of any t dependence means that
U11 cannot correspond solely to single-pion-exchange.
References
[1] K. Schilling, G. Wolf, Nucl. Phys. B61 (1973) 381.
[2] H. Fraas, Ann. Phys. 87 (1974) 417.
[3] M. Diehl, JHEP (2007) 0709:064.
[4] A. Airapetian et al., Eur. Phys. J. C62 (2009) 659.
[5] K. Ackerstaff et al., NIM A417 (1998) 230.
[6] N. Akopov et al., NIM A479 (2002) 511.
[7] E.V. Kuraev, N.N. Nikolaev, B.G. Zakharov, JETP Lett. 68 (1998) 696.
[8] C. Adloff et al., Phys. Lett. B483 (2000) 360.
[9] S.V. Goloskokov, P. Kroll, Eur. Phys. J. C59 (2009) 809.
[10] D.Yu. Ivanov, R. Kirshner, Phys. Rev. D58 (1998) 114026.
243