Comment on ``Evidence for Narrow Baryon Resonances in Inelastic pp Scattering''

1 Pages·0.06 MB·English

by  A. I. L'vov

Comment on “Evidence for Narrow Baryon Resonances in Inelastic pp Scattering”
In a recent Letter [1], Tatischeff et al. have claimed have measured the cross section for neutron knockout in
∗ ′
evidence for 3 neutral baryon resonances N between inelasticγdscattering,γ(d,γ n)p,forquasi-freekinemat-
the nucleon and the ∆(1232). Two of these have masses icsatenergiesaroundE =110MeV(theenergybinwas
γ
M =1004MeVand1044MeVbelowm +m andthus about40MeV).Althoughtheauthorsdidnotextractthe
N π
their widths (Γ=4 to 15 MeV) are radiative. The third differential cross section for γn scattering, they found
resonance (M = 1094 MeV) also might have a radiative agreement between the double differential cross section
decay. AlltheresonanceshavetocontributetoCompton d2σ/dΩγ′dΩn andthetheoreticalcalculationbyLevchuk
scattering on the nucleon and result in peaks at energies et al.[9],obtainedwiththe samekinematicalconditions.
E = 68, 112, and 169 MeV, respectively, which were Since the observed cross section is dominated by the
γ
never observed on protons [2–5] or neutrons [6,7] loosely γnsubprocess,rescalingargumentscanbeusedtoobtain
boundinthedeuteron. Sinceconstraintsofthis typeare experimentalestimatesforthedifferentialcrosssectionof
8
very sensitive and were not analyzed in the Letter, we γn scattering. This leads to the following result:
9
19 gseiveeReesft.im[8]a.tes below. For other theoretical constraints dσγn = 2.5±0.7 nb/sr, 90◦◦
ThedifferentialcrosssectionofγN scatteringnearthe dΩlab 3.2±0.7 nb/sr, 135
n (cid:26)
a resonance peak must be equally visible at any scattering at E = 110 MeV. Accordingly, we find X < 1.5·10−7
γ
J angle. For j = 1/2 it is just isotropic. For j = 3/2, the ∗
and hence Γ<6 eV for the n (1044) state.
7 angular distribution typically follows 18(3cos2θ+7) if a From data on elastic γd scattering at 69 MeV [7] one
2 dipole (E1 or M1) transition dominates, and is rather
can find the following bound for the total widths of the
1 flTahtewdiitffher≤en2t5ia%l cdreovsisatsieocntsiofnroamvearangaevderoavgeermanagglneistuadned. p∗(1004) and n∗(1004) states: Γp+Γn <∼1.5 eV.
Thus, the states of M = 1004 and 1044 MeV with
v
over a center-of-mass energy interval ∆W reads
7 the properties given in Ref. [1] are completely excluded
5 7.6, M =1004 MeV by Compton scattering data. The same is valid for the
0 hdσγNi= πX =aX × 3.0, M =1044 MeV 1094MeVstateunlessitsbranchingratioisanomalously
1 dΩcm 4Eγ2cm (1.5, M =1094 MeV suppressedincomparisonwithatypicalvalueofBrγ ∼α.
0
It is worth mentioning that a previous search [10] for
8 where a = 107 nb/sr, X = (j + 1)(Γ/∆W)Br2, and isospin 3/2 resonances in this mass region gave a null
9 2 γ
/ the radiative branching Brγ = 1 for the first two states. result.
h (Here we assume ∆W ≫Γ, which we show to be a very ThisworkwassupportedinpartbyaU.S.Department
t
- good approximation.) of Energy Grant No. DE-FG02-97ER41038.
l
c The data of Ref. [3] on γp scattering near Eγ = 68
u MeV have a scale of 10−15 nb/sr, with variations of at A.I. L’vov
n most3nb/srinenergybins of∆W ≃5MeV. Therefore, P.N. Lebedev Physical Institute,
v: a p∗ resonance near 1004 MeV must have X < 4·10−8 Leninsky Prospect 53, Moscow 117924,Russia
i andthetotalwidthΓ<0.2eVsevenordersofmagnitude
X less than Tatischeff et al. have reported. R.L. Workman
r Department of Physics,
If we assume j = 1/2, the interaction leading to the
a
∗ Virginia Tech, Blacksburg, VA 24061
transition γN ↔ N is dipole M1 (or E1 depending on
the parity of the resonance), Heff = −eH~ ·~σD. Here D PACS numbers: 14.20.Gk, 13.60.Fz, 11.55.Fv
is a transition magnetic (or electric) dipole moment and
e2/4π=α=1/137. The radiative width of the N∗ then
readsΓ =4αE3 D2. WithΓ <0.2eV,thetransition
dipole mγoment oγfcmN∗(1004) is Dγ <1.0·10−3 fm, that is [1] B. Tatischeff et al.,Phys. Rev.Lett. 79, 601 (1997).
[2] P. Baranov et al.,Phys. Lett.B 52, 122 (1974).
at least three orders of magnitude smaller than the size
[3] F.J. Federspiel et al.,Phys.Rev. Lett.67, 1511 (1991).
of the nucleon. The wave function of such a resonance
[4] B.E. MacGibbon et al.,Phys Rev.C 52, 2097 (1995).
would have a very small overlap with the nucleon wave
∗ [5] E.L. Hallin et al., Phys.Rev.C 48, 1497 (1993).
function, and it would be very difficult to produce N
[6] K.W. Rose et al.,Nucl.Phys. A514, 621 (1990).
with ordinary beams.
[7] M.A. Lucas, PhD thesis, Univ. of Illinois at Urbana
In the same way, data of Ref. [4] give an upper limit
Champaign (1994).
∗
Γ < 1.6 eV for the p (1044) resonance, and data of Ref. [8] L. Masperi and G. Violini, Mod. Phys. Lett. A 5, 101
2 ∗
[5] give BrγΓ<7 eV for the p (1094). (1990); Ya.I. Azimov, Phys.Lett. 32B, 499 (1970).
Information pertaining to neutral states can be ob- [9] M.I. Levchuket al.,Few Body Syst.16, 101 (1994).
tained, in principle, via the reaction γd → γnp in the [10] S. Ram et al.,Phys. Rev.D 49, 3120 (1994).
kinematics of quasi-free γn scattering. Rose et al. [6]
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