Is there a narrow $N(1685)$?

TL;DR

This study reanalyzes recent experimental data on eta photoproduction and finds that a full partial wave analysis can explain the results without invoking a narrow $N(1685)$ resonance, challenging previous claims.

Contribution

The paper demonstrates that the data can be explained without a narrow resonance, questioning prior interpretations of the $N(1685)$ as a narrow state.

Findings

Full partial wave analysis fits the data well without a narrow resonance.

Introducing a narrow $N(1685)$ resonance worsens the fit quality.

No compelling evidence for the existence of a narrow $N(1685)$ resonance.

Abstract

The helicity-dependent observable $E$ for the reaction $\gamma d\to \eta n (p)$ with a spectator proton was recently measured by the A2 Collaboration at MAMI in Mainz. The data were interpreted as further evidence for a narrow resonance with spin and parity $J^P=1/2^+$ ($P_{11}$ wave). However, a full partial wave analysis without any narrow resonance leads to an excellent description of the data, imposing a narrow resonance with the properties suggested by the A2 Collaboration leads to a significant deterioration of the fit quality: there is no need for a narrow resonance.

Tables

Table 1. Table 1: Helicity amplitudes determined from a fit without a narrow N ​ ( 1685 ) 𝑁 1685 N(1685) resonance. The T-matrix couplings are the quantities which are listed in the RPP; K-matrix couplings are given in addition. The new results are compared to those obtained in Anisovich:2015tla which are listed in small numbers. The comparison shows the impact of the new data from Witthauer:2016mpi and Mueller:2017spl .

		$N\left(1535\right)1/2^{-}$	$N\left(1650\right)1/2^{-}$				$N\left(1535\right)1/2^{-}$	$N\left(1650\right)1/2^{-}$
$𝒑$	T-matrix	$0.093\pm 0.009$	$0.032\pm 0.006$	GeV-1/2	$𝒏$	T-matrix	-$0.088\pm 0.004$	$0.016\pm 0.004$	GeV-1/2
	Anisovich:2015tla	$0.114\pm 0.008$	$0.032\pm 0.007$	GeV-1/2		Anisovich:2015tla	-$0.095\pm 0.006$	$0.019\pm 0.006$	GeV-1/2
	Phase	8$\pm$4∘	7$\pm$7∘			Phase	5$\pm$4∘	-28$\pm$10∘
	Anisovich:2015tla	10$\pm$5∘	-2$\pm$11∘			Anisovich:2015tla	8$\pm$5∘	0$\pm$15∘
	K-matrix	$0.112\pm 0.008$	$0.075\pm 0.006$			K-matrix	-$0.160\pm 0.030$	-$0.052\pm 0.005$
	Anisovich:2015tla	$0.096\pm 0.007$	$0.075\pm 0.007$			Anisovich:2015tla	-$0.120\pm 0.006$	-$0.052\pm 0.006$

Full text

A narrow structure was observed at a mass of about 1685 MeV in the $\gamma d\to\eta n(p)$ excitation function Kuznetsov:2006kt ; Jaegle:2008ux ; Kuznetsov:2010as ; Jaegle:2011sw ; Werthmuller:2013rba ; Werthmuller:2014thb ; Kuznetsov:2015nla . The structure was interpreted Polyakov:2003dx ; N_1680 as the nonstrange member of the antidecuplet of pentaquarks with spin-parity $J^{P}=1/2^{+}$ predicted by Diakonov, Petrov, and Polyakov Diakonov:1997mm . In 2012, the observations reported in Kuznetsov:2006kt ; Kuznetsov:2010as ; Jaegle:2011sw were introduced into the Review of Particle Properties (RPP) under the heading of a new one-star nucleon resonance $N(1685)$ Beringer:1900zz but was removed from the listings in the most recent issue of RPP Olive:2016xmw . The interpretation of the structure as narrow resonance was supported by further studies Arndt:2003ga ; Choi:2006 ; Fix:2007 ; Shrestha:2012 , the results reported in Anisovich:2008wd were ambiguous.

However, also coupled-channel and interference effects of known nucleon resonances have been discussed in the literature to explain the narrow structure. The Gießen group interpreted the narrow dip in the $\gamma d\to\eta n(p)$ excitation function as $N(1650)1/2^{-}$ and $N(1710)1/2^{+}$ coupled-channel effect Shklyar:2006xw , Shyam and Scholten assign the dip to interference effects between the $N(1650)1/2^{-}$, $N(1710)1/2^{+}$, and $N(1720)3/2^{+}$ resonances Shyam:2008fr ; alternatively, the dip could be produced to effects from strangeness threshold openings Doering:2009qr .

The narrow dip can, however, also be explained naturally by interference effects in the $J^{P}=1/2^{-}$ wave Anisovich:2008wd ; Zhong:2011ti ; Anisovich:2013jya ; Anisovich:2015tla . In Anisovich:2015tla , the precise data reported by the A2 Collaboration at MAMI Werthmuller:2013rba ; Werthmuller:2014thb were used to study the structure. It was found that it can be explained quantitatively by interference of the two nucleon resonances $N(1535)1/2^{-}$ and $N(1650)1/2^{-}$ within the $J^{P}=1/2^{-}$ partial wave. Fits which included a narrow $J^{P}=1/2^{+}$ resonance returned a zero production strength. If the properties of the narrow $J^{P}=1/2^{+}$ resonance as reported in Werthmuller:2013rba ; Werthmuller:2014thb were imposed, the fit deteriorated significantly.

Recently, the A2 Collaboration at MAMI reported a measurement of the helicity-dependent double polarization variable $E$ of the $\gamma d\to\eta n(p)$ reaction Witthauer:2016mpi where $E=(\sigma_{1/2}-\sigma_{3/2})/(\sigma_{1/2}+\sigma_{3/2})$, with $\sigma_{h}$ being the cross section for $\gamma d\to\eta n(p)$ with neutron and photon spin aligned (helicity $h=3/2$) and or opposite ($h=1/2$). The data show clearly that the structure originates from the $h=1/2$ contribution. The authors fitted the angular distributions (five data points per energy interval) with third-order Legendre polynomial functions and found a narrow dip at 1650 MeV in the first order Legendre coefficient. They concluded: The extracted Legendre coefficients of the angular distributions for $\sigma_{1/2}$ are in good agreement with recent reaction model predictions assuming a narrow resonance in the $P_{11}$ wave as the origin of this structure. In this paper we will show that their conclusions are incompatible with the data.

As a first step, we repeated the fit with Legendre polynomials. Figure 1 shows the first-order Legendre coefficients A${}_{1}^{\sigma_{1/2}}$, A${}_{1}^{\sigma_{3/2}}$, and A${}_{1}^{\sigma_{\rm tot}}$ as functions of the $n\eta$ invariant mass for fits to the angular distributions of $\sigma_{1/2}$, $\sigma_{3/2}$, and $\sigma_{\rm tot}=(\sigma_{1/2}+\sigma_{3/2})/2$. The coefficients A${}_{0}^{\sigma_{1/2}}$, A${}_{0}^{\sigma_{3/2}}$, and A${}_{0}^{\sigma_{\rm tot}}$ are similar to the corresponding total cross sections, the coefficients A2 and A3 for the cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$ are shown in Witthauer:2016mpi . In the coefficient A${}_{1}^{\sigma_{1/2}}$ there is indeed a narrow dip at about 1650 MeV. Since the $J^{P}=1/2^{-}$ partial wave dominates the reaction, significant contributions to A${}_{1}^{\sigma_{1/2}}$ have to come from the interference between the $J^{P}=1/2^{-}$ partial wave and $P$-wave contributions. Indeed, a comparison of A${}_{1}^{\sigma_{1/2}}$ with fit results shows that a model assuming no $N(1685)$ (Fig. 1, solid curve) does not reproduce the narrow dip while a model which includes a narrow $N(1685)$ (Fig. 1, dotted curve) gives qualitative agreement between data and prediction. These observations are the basis for the conjecture in Witthauer:2016mpi that a narrow resonance has been observed.

There are, however, a few arguments which disagree with this conjecture.

The dip in A${}_{1}^{\sigma_{1/2}}$ is statistically significant. Relative to the solid line (representing the fit with no $N(1685)$), the dip in A${}_{1}^{\sigma_{1/2}}$ has a mean deviation $-0.24\pm 0.04$ and contributes $\chi^{2}=15.9$ for two data points.

However, there is a peak in A${}_{1}^{\sigma_{3/2}}$ as well, at the same mass and of similar size and shape as the dip in A${}_{1}^{\sigma_{1/2}}$. The peak deviates from the solid line by $+0.25\pm 0.04$, contributes $\chi^{2}=12.7$, and is thus of similar importance as the dip. The coefficient A${}_{1}^{\sigma_{\rm tot}}$ follows precisely the fit with no $N(1685)$, the data are compatible with the fit, with $\chi^{2}=2.1$ for the two data points. If the dip in A${}_{1}^{\sigma_{1/2}}$ had a physical significance, it should be seen in A${}_{1}^{\sigma_{\rm tot}}$ with a strength as given by the dotted line. But it is not. There is hence the suspicion that the dip might be a statistical fluctuation: a small change in the observable $E$ may lead to a disappearance of the dip and the peak.

To test this hypothesis, we performed overall fits. In these fits most particle properties are frozen to the values derived from fits to pion and photo-induced reactions off protons. For $\gamma n$ reactions we use the data listed in Anisovich:2015tla and, in addition, the new MAMI data Witthauer:2016mpi . The latter data are shown in Fig. 2 and Fig. 3, the solid line is our fit without introduction of a narrow resonance. For the differential cross sections from Werthmuller:2013rba ; Werthmuller:2014thb and Witthauer:2016mpi , the fit returns a $\chi^{2}_{\rm MAMI}=1205$ for 1150 data points. Obviously, there is no need to introduce $N(1685)$. When $N(1685)$ was enforced in the fit with properties as given in Werthmuller:2013rba , i.e. with $M=1670$ MeV, width $\Gamma=30$ MeV, and $\sqrt{Br(\eta n)}A_{n}^{1/2}=\tilde{a}$ [GeV${}^{-\frac{1}{2}}$ 10*-3*] = $12.3$ [GeV${}^{-\frac{1}{2}}$ 10*-3*], the fit returned $\chi^{2}_{\rm MAMI}=1834$ for the 1150 data points from Werthmuller:2013rba ; Werthmuller:2014thb ; Witthauer:2016mpi . The $\chi^{2}$’s for the new data from Witthauer:2016mpi are shown in Fig. 2 for each angular bin of $\sigma_{1/2}$ for $\gamma d\to\eta n(p)$, the sum is $\chi^{2}=187.9$ for the fit without narrow resonance and 265.8 when it is imposed.

If the production strength is fitted freely, it reduced to $1.2$ [GeV${}^{-\frac{1}{2}}$ 10*-3*] and the total $\chi^{2}$ improved by 12 units to 1193. This production strength corresponds to a contribution which is about 100 times smaller than the contribution claimed in Werthmuller:2013rba ; Werthmuller:2014thb . Fig. 4 shows how the $\chi^{2}$ increases with the strength of an imposed narrow $N(1670)$.

The new data on $E$ for the reaction $\gamma d\to\eta p(n)$ – with a spectator neutron – in Witthauer:2016mpi differed significantly from first BnGa fits which were performed before the data on double-polarization observables on $\gamma p\to\eta p$ on protons became available Mueller:2017spl . To explore this discrepancy, we included the new MAMI data for $\eta$ production off protons (bound in deuterons) Witthauer:2016mpi in the fits. Figures 2 and 3 show that the new data can be included in the fit without any problems, after a slight tuning of the parameters. In Table 1, we show the helicity amplitudes obtained in the new fit in comparison to the fit presented in Anisovich:2015tla . The changes in the photocouplings of $N(1535)1/2^{-}$ and $N(1650)1/2^{-}$ for protons are likely due to the inclusion of the new data on $\gamma p\to\eta p$ Mueller:2017spl .

Summarizing, we have studied the new data on the helicity dependence of the reaction $\gamma d\to\eta n(p)$ with a spectator proton measured by the A2 Collaboration at MAMI in Mainz Witthauer:2016mpi . We cannot confirm the conclusions of the authors that the dip in the first-order Legendre coefficient in an expansion of the angular distributions of $\sigma_{1/2}$ is due to a narrow $J^{P}=1/2^{+}$ resonance. First, the dip is accompanied by a peak in the first-order Legendre coefficient of $\sigma_{3/2}$ of the same shape suggesting that the dip is due to a statistical fluctuation in the measurement of $E$. Second, a partial wave analysis without a narrow $J^{P}=1/2^{+}$ resonance is excellent, the inclusion of it with the reported properties leads to a significantly worse description of the data.

Comments of Bernd Krusche and Volker Metag to an early version of this comment are kindly recognized. The work was supported by the Deutsche Forschungsgemeinschaft (SFB/TR110), the U.S. Department of Energy (DE-AC05-06OR23177), and the Russian Science Foundation (RSF 16-12-10267).